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Time-independant stochastic quantization, DS equations, and infrared
critical exponents in QCD: We derive the equations of time-independent stochastic quantization, without
reference to an unphysical 5th time, from the principle of gauge equivalence.
It asserts that probability distributions $P$ that give the same expectation
values for gauge-invariant observables $<W > = \int dA W P$ are physically
indistiguishable. This method escapes the Gribov critique. We derive an exact
system of equations that closely resembles the Dyson-Schwinger equations of
Faddeev-Popov theory, which we then solve non-perturbatively for the critical
exponents that characterize the asymptotic form at $k \approx 0$ of the
tranverse and longitudinal parts of the gluon propagator in Landau gauge, $D^T
\sim (k^2)^{-1-\a_T}$ and $D^L \sim a (k^2)^{-1-\a_L}$, and obtain $\a_T = -
2\a_L \approx - 1.043$ (short range), and $\a_L \approx 0.521$, (long range).
Although the longitudinal part vanishes with the gauge parameter $a$ in the
Landau gauge limit, $a \to 0$, there are vertices of order $a^{-1}$, so the
longitudinal part of the gluon propagator contributes in internal lines,
replacing the ghost that occurs in Faddeev-Popov theory. We compare our results
with the corresponding results in Faddeev-Popov theory.
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Superstring Gravitational Wave Backgrounds with Spacetime Supersymmetry: We analyse the stringy gravitational wave background based on the current
algebra $E^{c}_{2}$. We determine its exact spectrum and construct the modular
invariant vacuum energy. The corresponding N=1 extension is also constructed.
The algebra is again mapped to free bosons and fermions and we show that this
background has N=4 (N=2) unbroken spacetime supersymmetry in the type II
(heterotic case).
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Cubic Twistorial String Field Theory: Witten has recently proposed a string theory in twistor space whose
D-instanton contributions are conjectured to compute N=4 super-Yang-Mills
scattering amplitudes. An alternative string theory in twistor space was then
proposed whose open string tree amplitudes reproduce the D-instanton
computations of maximal degree in Witten's model.
In this paper, a cubic open string field theory action is constructed for
this alternative string in twistor space, and is shown to be invariant under
parity transformations which exchange MHV and googly amplitudes. Since the
string field theory action is gauge-invariant and reproduces the correct cubic
super-Yang-Mills interactions, it provides strong support for the conjecture
that the string theory correctly computes N-point super-Yang-Mills tree
amplitudes.
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Probing Quantization Via Branes: We re-examine quantization via branes with the goal of understanding its
relation to geometric quantization. If a symplectic manifold $M$ can be
quantized in geometric quantization using a polarization ${\mathcal P}$, and in
brane quantization using a complexification $Y$, then the two quantizations
agree if ${\mathcal P}$ can be analytically continued to a holomorphic
polarization of $Y$. We also show, roughly, that the automorphism group of $M$
that is realized as a group of symmetries in brane quantization of $M$ is the
group of symplectomorphisms of $M$ that can be analytically continued to
holomorphic symplectomorphisms of $Y$. We describe from the point of view of
brane quantization several examples in which geometric quantization with
different polarizations gives equivalent results.
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Scalar fluctuations in dilatonic brane-worlds: We derive and solve the full set of scalar perturbation equations for a class
of five-dimensional brane--world solutions, with a dilaton scalar field coupled
to the bulk cosmological constant and to a 3-brane. The spectrum contains one
localized massless scalar mode, to be interpreted as an effective dilaton on
the brane, inducing long--range scalar interactions. Two massive scalar modes
yield corrections to Newton's law at short distances, which persist even in the
limit of vanishing dilaton (namely, in the standard Randall--Sundrum
configuration).
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Warped Compactifications and AdS/CFT: In this talk we discuss two classes of examples of warped products of AdS
spaces in the context of the AdS/CFT correspondence. The first class of
examples appears in the construction of dual Type I' string descriptions to
five dimensional supersymmetric fixed points with E_{N_f+1} global symmetry.
The background is obtained as the near horizon geometry of the D4-D8 brane
system in massive Type IIA supergravity. The second class of examples appears
when considering the N=2 superconformal theories defined on a 3+1 dimensional
hyperplane intersection of two sets of M5 branes. We use the dual string
formulations to deduce properties of these field theories.
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Cosmological brane systems in warped spacetime: In this paper, we discuss the time-dependent brane solutions in
higher-dimensional supergravity theories. We particularly focus on the
dynamical extensions of the intersecting brane solutions involving three
branes. We also show that in the near-horizon limits, where the time dependence
is negligible, these branes describe warped anti-de Sitter spacetimes as in the
corresponding static solutions. We finally examine the lower-dimensional
cosmological dynamics obtained after compactifications of the
higher-dimensional solutions and show the solutions we have found give the
four-dimensional universe with power-law expansion.
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Observations on Integral and Continuous U-duality Orbits in N=8
Supergravity: One would often like to know when two a priori distinct extremal black
p-brane solutions are in fact U-duality related. In the classical supergravity
limit the answer for a large class of theories has been known for some time.
However, in the full quantum theory the U-duality group is broken to a discrete
subgroup and the question of U-duality orbits in this case is a nuanced matter.
In the present work we address this issue in the context of N=8 supergravity in
four, five and six dimensions. The purpose of this note is to present and
clarify what is currently known about these discrete orbits while at the same
time filling in some of the details not yet appearing in the literature. To
this end we exploit the mathematical framework of integral Jordan algebras and
Freudenthal triple systems. The charge vector of the dyonic black string in D=6
is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified
by a set of two arithmetic U-duality invariants. Similarly, the black hole
(string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge
canonical form, again uniquely fixed by a set of three arithmetic U-duality
invariants. The situation in four dimensions is less clear: while black holes
preserving more than 1/8 of the supersymmetries may be fully classified by
known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield
increasingly subtle orbit structures, which remain to be properly understood.
However, for the very special subclass of projective black holes a complete
classification is known. All projective black holes are E_{7(7)}(Z) related to
a four or five charge canonical form determined uniquely by the set of known
arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the
charge vectors of black holes with a given leading-order entropy.
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Effective Topological Theory for Gravitational Anyon Scatterings at
Ultra-High Energies: The idea of the effective topological theory for high-energy scattering
proposed by H. and E. Verlinde is applied to the $(2+1)$ dimensional gravity
with Einstein action plus Chern-Simons terms. The calculational steps in the
topological description are compared with the eikonal approximation. It is
shown that the Lagrangian of the effective topological theory turns out to
vanish except for boundary terms.
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Unitary Quantum Field Theory on the Noncommutative Minkowski space: This is the written version of a talk I gave at the 35th Symposium Ahrenshoop
in Berlin, Germany, August 2002. It is an exposition of joint work with S.
Doplicher, K. Fredenhagen, and Gh. Piacitelli [1]. The violation of unitarity
found in quantum field theory on noncommutative spacetimes in the context of
the so-called modified Feynman rules is linked to the notion of time ordering
implicitely used in the assumption that perturbation theory may be done in
terms of Feynman propagators. Two alternative approaches which do not entail a
violation of unitarity are sketched. An outlook upon our more recent work is
given.
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Experimental test of Non-Commutative Quantum Gravity by VIP-2 Lead: Pauli Exclusion Principle (PEP) violations induced by space-time
non-commutativity, a class of universality for several models of Quantum
Gravity, are investigated by the VIP-2 Lead experiment at the Gran Sasso
underground National Laboratory of INFN. The VIP-2 Lead experimental bound on
the non-commutative space-time scale $\Lambda$ excludes $\theta$-Poincar\'e far
above the Planck scale for non vanishing ``electric-like" components of
$\theta_{\mu \nu}$, and up to $6.9 \cdot 10^{-2}$ Planck scales if they are
null. Therefore, this new bound represents the tightest one so far provided by
atomic transitions tests. This result strongly motivates high sensitivity
underground X-ray measurements as critical tests of Quantum Gravity and of the
very microscopic space-time structure.
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A Study of Anyon Statistics by Breit Hamiltonian Formalism: We study the anyon statistics of a $2 + 1$ dimensional Maxwell-Chern-Simons
(MCS) gauge theory by using a systemmetic metheod, the Breit Hamiltonian
formalism.
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An AdS/dS duality for a scalar particle: The motion of a scalar particle in (d+1)-dimensional AdS space may be
described in terms of the Cartesian coordinates that span the (d+2)-dimensional
space in which the AdS space is embedded. Upon quantization, the mass
hyperboloid defined in terms of the conjugate momenta turns into the wave
equation in AdS space. By interchanging the roles of coordinates and conjugate
momenta in the (d+2)-dimensional space we arrive at a dual description. For
massive modes, the dual description is equivalent to the conventional
formulation, as required by holography. For tachyonic modes, this interchange
of coordinates and momenta establishes a duality between Euclidean AdS and dS
spaces. We discuss its implications on Green functions for the various vacua.
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$E_8$ instantons on type-A ALE spaces and supersymmetric field theories: We consider the 6d superconformal field theory realized on M5-branes probing
the $E_8$ end-of-the-world brane on the deformed and resolved
$\mathbb{C}^2/\mathbb{Z}_k$ singularity. We give an explicit algorithm which
determines, for arbitrary holonomy at infinity, the 6d quiver gauge theory on
the tensor branch, the type-A class S description of the $T^2$
compactification, and the star-shaped quiver obtained as the mirror of the
$T^3$ compactification.
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Holographic Phase Transitions with Fundamental Matter: The holographic dual of a finite-temperature gauge theory with a small number
of flavours typically contains D-brane probes in a black hole background. At
low temperature the branes sit outside the black hole and the meson spectrum is
discrete and possesses a mass gap. As the temperature increases the branes
approach a critical solution. Eventually they fall into the horizon and a phase
transition occurs. In the new phase the meson spectrum is continuous and
gapless. At large N and large 't Hooft coupling, this phase transition is
always of first order, and in confining theories with heavy quarks it occurs at
a temperature higher than the deconfinement temperature for the glue.
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Relation between full traces of Green functions for initial and Darboux
transformed Dirac problems: We establish the relation between full traces of the Green functions for some
initial and the Darboux transformed one-dimensional two component Dirac
problems with the most general form of potential. The result is used to check
the completeness of set of wave functions obtained by the Darboux
transformation of the eigenfunctions set for the initial Dirac problem with
some typical boundary conditions.
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Holographic Entanglement Entropy in Insulator/Superconductor Transition: We investigate the behaviors of entanglement entropy in the holographical
insulator/superconductor phase transition. We calculate the holographic
entanglement entropy for two kinds of geometry configurations in a completely
back-reacted gravitational background describing the insulator/superconductor
phase transition. The non-monotonic behavior of the entanglement entropy is
found in this system. In the belt geometry case, there exist four phases
characterized by the chemical potential and belt width.
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Summing up perturbation series around superintegrable point: We work out explicit formulas for correlators in the Gaussian matrix model
perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this
paper, we concentrate on the example of a single Miwa variable. The ordinary
Gaussian model is superintegrable, i.e. the average of the Schur functions
$S_Q$ is an explicit function of the Young diagram $Q$. The question is what
happens to this property after perturbation. We show that the entire
perturbation series can be nicely summed up into a kind of Borel transform of a
universal exponential function, while the dependence on $R$ enters through a
polynomial factor in front of this exponential. Moreover, these polynomials can
be described explicitly through a single additional structure, which we call
``truncation'' of the Young diagram $Q$. It is unclear if one can call this an
extended superintegrability, but at least it is a tremendously simple
deformation of it. Moreover, the vanishing Gaussian correlators remain
vanishing and, hence, are not deformed at all.
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Inflationary Universe with Anisotropic Hair: We study an inflationary scenario with a vector field coupled with an
inflaton field and show that the inflationary universe is endowed with
anisotropy for a wide range of coupling functions. This anisotropic inflation
is a tracking solution where the energy density of the vector field follows
that of the inflaton field irrespective of initial conditions. We find a
universal relation between the anisotropy and a slow-roll parameter of
inflation. Our finding has observational implications and gives a counter
example to the cosmic no-hair conjecture.
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Gauging Yang-Mills Symmetries In 1+1-Dimensional Spacetime: We present a systematic and 'from the ground up' analysis of the 'minimal
coupling' type of gauging of Yang-Mills symmetries in (2,2)-supersymmetric
1+1-dimensional spacetime. Unlike in the familiar 3+1-dimensional N=1
supersymmetric case, we find several distinct types of minimal coupling
symmetry gauging, and so several distinct types of gauge (super)fields, some of
which entirely novel. Also, we find that certain (quartoid) constrained
superfields can couple to no gauge superfield at all, others (haploid ones) can
couple only very selectively, while still others (non-minimal, i.e., linear
ones) couple universally to all gauge superfields.
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Anomalies of 4d $Spin_G$ Theories: We consider 't Hooft anomalies of four-dimensional gauge theories whose
fermion matter content admits $Spin_G(4)$ generalized spin structure, with $G$
either gauged or a global symmetry. We discuss methods to directly compute
$w_2\cup w_3$ 't Hooft anomalies involving Steifel Whitney classes of gauge and
flavor symmetry bundles that such theories can have on non-spin manifolds, e.g.
$M_4=\mathbb{CP}^2$. Such anomalies have been discussed for $SU(2)$ gauge
theory with adjoint fermions, where they were shown to give an effect that was
originally found in the Donaldson-Witten topological twist of ${\cal N}=2$ SYM
theory. We directly compute these anomalies for a variety of theories,
including general $G$ gauge theories with adjoint fermions, $SU(2)$ gauge
theory with fermions in general representations, and $Spin(N)$ gauge theories
with fundamental matter. We discuss aspects of matching these and other 't
Hooft anomalies in the IR phase where global symmetries are spontaneously
broken, in particular for general $G_{\rm gauge}$ theory with $N_f$ adjoint
Weyl fermions. For example, in the case of $N_f=2$ we discuss anomaly matching
in the IR phase consisting of $h^\vee _{G_{\rm gauge}}$ copies of a
$\mathbb{CP}^1$ non-linear sigma model, including for the $w_2w_3$ anomalies
when formulated with $Spin_{SU(2)_{\rm global}}(4)$ structure.
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N=2 supersymmetric radiation damping problem on a noncommutative plane: It is well known that a direct Lagrangian description of radiation damping is
still missing. In this paper a specific approach of this problem was used,
which is the standard way to treat the radiation damping problem. A $N=2$
supersymmetric extension for the model describing the radiation damping on the
noncommutative plane with electric and magnetic interactions was obtained. The
entire supercharge algebra and the total Hamiltonian for the system were
analyzed. Finally, noncommutativity features were introduced and its
consequences were explored..
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Restricted Supergauge invariance, N=2 Coadjoint Orbit and N=2 Quantum
Supergravity: It is shown that the N=2 superconformal transformations are restricted N=1
supergauge transformations of a supergauge theory with Osp(2,2) as a gauge
group. Based on this result, a canonical derivation of the Osp(2,2) current
algebra in the superchiral gauge formulation of N=2 supergravity is presented.
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A simple holographic scenario for gapped quenches: We construct gravitational backgrounds dual to a family of field theories
parameterized by a relevant coupling. They combine a non-trivial scalar field
profile with a naked singularity. The naked singularity is necessary to
preserve Lorentz invariance along the boundary directions. The singularity is
however excised by introducing an infrared cutoff in the geometry. The
holographic dictionary associated to the infrared boundary is developed. We
implement quenches between two different values of the coupling. This requires
considering time dependent boundary conditions for the scalar field both at the
AdS boundary and the infrared wall.
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Multi-fixed point numerical conformal bootstrap: a case study with
structured global symmetry: In large part, the future utility of modern numerical conformal bootstrap
depends on its ability to accurately predict the existence of hitherto unknown
non-trivial conformal field theories (CFTs). Here we investigate the extent to
which this is possible in the case where the global symmetry group has a
product structure. We do this by testing for signatures of fixed points using a
mixed-correlator bootstrap calculation with a minimal set of input assumptions.
This 'semi-blind' approach contrasts with other approaches for probing more
complicated groups, which 'target' known theories with additional spectral
assumptions or use the saturation of the single-correlator bootstrap bound as a
starting point. As a case study, we select the space of CFTs with product-group
symmetry $O(15)\otimes{O}(3)$ in $d=3$ dimensions. On the assumption that there
is only one relevant scalar ($\ell=0$) singlet operator in the theory, we find
a single 'allowed' region in our chosen space of scaling dimensions. The
scaling dimensions corresponding to two known large-$N$ critical theories, the
Heisenberg and the chiral ones, lie on or very near the boundary of this
region. The large-$N$ antichiral point lies well outside the 'allowed' region,
which is consistent with the expectation that the antichiral theory is
unstable, and thus has an additional relevant scalar singlet operator. We also
find a sharp kink in the boundary of the 'allowed' region at values of the
scaling dimensions that do not correspond to the $(N,M)=(15,3)$ instance of any
large-$N$-predicted $O(N) \otimes O(M)$ critical theory.
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Time-reparametrization invariance and Hamilton-Jacobi approach to the
cosmological sigma-model: The construction of physical models with local time-reparametrization
invariance is reviewed. Negative-energy contributions to the hamiltonian are
shown to be crucial for the realization of this reparametrization symmetry. The
covariant formulation of the dynamics is used to develop a time and gauge
invariant Hamilton-Jacobi theory. This formalism is applied to solve for the
cosmology of a homogeneous universe of the Friedmann-Lemaitre-Robertson-Walker
type. After a discussion of empty universes, the FLRW theory is extended with
homogeneous scalar fields generically described by a $\sg$-model on some scalar
manifold. An explicit gauge-invariant solution is constructed for the
non-linear O(N)-models.
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String Amplitudes from Moyal String Field Theory: We illustrate a basic framework for analytic computations of Feynman graphs
using the Moyal star formulation of string field theory. We present efficient
methods of computation based on (a) the monoid algebra in noncommutative space
and (b) the conventional Feynman rules in Fourier space. The methods apply
equally well to perturbative string states or nonperturbative string states
involving D-branes. The ghost sector is formulated using Moyal products with
fermionic (b,c) ghosts. We also provide a short account on how the purely cubic
theory and/or VSFT proposals may receive some clarification of their midpoint
structures in our regularized framework.
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Collective Field Theory of the Fractional Quantum Hall Edge State and
the Calogero-Sutherland Model: \noindent Using hydrodynamic collective field theory approach we show that
one-particle density matrix of the $\nu=1/m$ fractional quantum Hall edge state
interpolates between chiral Luttinger liquid behavior $\langle
\psi^{\dagger}(r) \psi(0) \rangle \sim r^{-m} $ and Calogero-Sutherland model
behavior $\langle \psi^{\dagger}(r) \psi(0) \rangle \sim r^{-(m+1/m)/2} $ as
the droplet width is varied continuously. Low-energy excitations are described
by $c=1$ conformal field theory of a compact boson of radius $\sqrt m$. The
result suggests complementary relation between the two-dimensional quantum Hall
droplet and the one-dimensional Calogero-Sutherland model.
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New bi-harmonic superspace formulation of $4D, \mathcal{N}=4$ SYM theory: We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the
$\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) in four dimensions. In
this approach, the $\mathcal{N}=4$ SYM superfield constraints are solved in
terms of on-shell $\mathcal {N}=2$ harmonic superfields. Such an approach
provides a convenient tool of constructing the manifestly $\mathcal{N}=4$
supersymmetric invariants and further rewriting them in $\mathcal{N}= 2$
harmonic superspace. In particular, we present $\mathcal{N}=4$ superfield form
of the leading term in the $\mathcal{N}=4$ SYM effective action which was known
previously in $\mathcal{N}=2$ superspace formulation.
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Inflation in supergravity from field redefinitions: Supergravity (SUGRA) theories are specified by a few functions, most notably
the real K\"ahler function denoted by $G(T_i, \bar {T}_i) = K + \log |W|^2$,
where K is a real K\"ahler potential, and W is a holomorphic superpotential. A
field redefinition $T_i \rightarrow f_1(T_i)$ does not change neither the
theory, nor the K\"ahler geometry. Similarly, the K\"ahler transformation, $K
\rightarrow K + f_2 + \bar f_2, W \rightarrow e^{-f_2} W$ where $f_2$ is
holomorphic also leaves G and hence the theory and the geometry invariant.
However, if we perform a field redefinition only in $K(T_i,\bar{T}_i)
\rightarrow K(f(T_i),f(\bar{T}_i))$, while keeping the same superpotential
$W(T_i)$, we get a different theory, as G is not invariant under such a
transformation while maintaining the same K\"ahler geometry. This freedom of
choosing $f(T_i)$ allows constructing an infinite number of new theories given
a fixed K\"ahler geometry and a predetermined superpotential W. Our
construction generalizes previous ones that were limited by the holomorphic
property of $W$. In particular it allows for novel inflationary SUGRA models
and particle phenomenology model building, where the different models
correspond to different choices of field redefinitions. We demonstrate this
possibility by constructing several prototypes of inflationary models (hilltop,
Starobinsky-like, plateau, log-squared and bell-curve) all in flat K\"ahler
geometry and an originally renormalizable superpotential $W$. The models are in
accord with current observations and predict $r\in[10^{-6},0.06]$ spanning
several decades that can be easily obtained. In the bell-curve model, there
also exists a built-in gravitational reheating mechanism with $T_R\sim
\mathcal{O}( 10^7 GeV)$.
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Entanglement entropy and non-local duality: quantum channels and quantum
algebras: We investigate the transformation of entanglement entropy under dualities,
using the Kramers-Wannier duality present in the transverse field Ising model
as our example. Entanglement entropy between local spin degrees of freedom is
not generically preserved by the duality; instead, entangled states may be
mapped to states with no local entanglement. To understand the fate of this
entanglement, we consider two quantitative descriptions of degrees of freedom
and their transformation under duality. The first involves Kraus operators
implementing the partial trace as a quantum channel, while the second utilizes
the algebraic approach to quantum mechanics, where degrees of freedom are
encoded in subalgebras. Using both approaches, we show that entanglement of
local degrees of freedom is not lost; instead it is transferred to non-local
degrees of freedom by the duality transformation.
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Imaginary-Scaling versus Indefinite-Metric Quantization of the
Pais-Uhlenbeck Oscillator: Using the Pais-Uhlenbeck Oscillator as a toy model, we outline a consistent
alternative to the indefinite-metric quantization scheme that does not violate
unitarity. We describe the basic mathematical structure of this method by
giving an explicit construction of the Hilbert space of state vectors and the
corresponding creation and annihilation operators. The latter satisfy the usual
bosonic commutation relation and differ from those of the indefinite-metric
theories by a sign in the definition of the creation operator. This change of
sign achieves a definitization of the indefinite-metric that gives life to the
ghost states without changing their contribution to the energy spectrum.
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The one-loop form factors in the effective action, and production of
coherent gravitons from the vacuum: We present the solution of the problem of the $1/\Box, \Box \to 0,$
asymptotic terms discovered in the one-loop form factors of the gravitational
effective action. Owing to certain constraints among their coefficients, which
we establish, these terms cancel in the vacuum stress tensor and do not violate
the asymptotic flatness of the expectation value of the metric. They reappear,
however, in the Riemann tensor of this metric and stand for a new effect: a
radiation of gravitational waves induced by the vacuum stress. This coherent
radiation caused by the backreaction adds to the noncoherent radiation caused
by the pair creation in the case where the initial state provides the vacuum
stress tensor with a quadrupole moment.
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Generalized Weierstrass-Enneper inducing, conformal immersions, and
gravity: Basic quantities related to 2-D gravity, such as Polyakov extrinsic action,
Nambu-Goto action, geometrical action, and Euler characteristic are studied
using generalized Weierstrass-Enneper (GWE) inducing of surfaces. Connection of
the GWE inducing with conformal immersion is made and varius aspects of the
theory are shown to be invariant under the modified Veselov-Novikov hierarchy
of flows. The geometry of certain surfaces is shown to be connected with the
dynamics of infinite and finite dimensional integrable systems. Connections to
Liouville-Beltrami gravity are indicated.
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Nonperturbative aspects of ABJM theory: Using the matrix model which calculates the exact free energy of ABJM theory
on S^3 we study non-perturbative effects in the large N expansion of this
model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We
propose a general prescription to extract spacetime instanton actions from
general matrix models, in terms of period integrals of the spectral curve, and
we use it to determine them explicitly in the ABJM matrix model, as exact
functions of the 't Hooft coupling. We confirm numerically that these
instantons control the asymptotic growth of the genus expansion. Furthermore,
we find that the dominant instanton action at strong coupling determined in
this way exactly matches the action of an Euclidean D2-brane instanton wrapping
RP^3.
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Discrete Gravity on Random Tensor Network and Holographic Rényi
Entropy: In this paper we apply the discrete gravity and Regge calculus to tensor
networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We
construct the boundary many-body quantum state $|\Psi\rangle$ using random
tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave
function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement
R\'enyi entropy of $|\Psi\rangle$ is shown to holographically relate to the
on-shell action of Einstein gravity on a branch cover bulk manifold. The
resulting R\'enyi entropy $S_n$ of $|\Psi\rangle$ approximates with high
precision the R\'enyi entropy of ground state in 2-dimensional conformal field
theory (CFT). In particular it reproduces the correct $n$ dependence. Our
results develop the framework of realizing the AdS$_3$/CFT$_2$ correspondence
on random tensor networks, and provide a new proposal to approximate CFT ground
state.
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Geometrical model of massive spinning particle in four-dimensional
Minkowski space: We propose the model of massive spinning particle traveling in
four-dimensional Minkowski space. The equations of motion of the particle
follow from the fact that all the classical paths of the particle lie on a
cylinder whose position in Minkowski space is determined by the particle's
linear momentum and total angular momentum. All the paths on one and the same
cylinder are gauge equivalent. The equations of motion are found in implicit
form for general time-like paths, and they are non-Lagrangian. The explicit
equations of motion are found for trajectories with small curvature and
helices. The momentum and total angular momentum are expressed in terms of
characteristics of the path in all the cases. The constructed model of the
spinning particle has geometrical character, with no additional variables in
the space of spin states being introduced.
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Separation of variables for the classical and quantum Neumann model: The method of separation of variables is shown to apply to both the classical
and quantum Neumann model. In the classical case this nicely yields the
linearization of the flow on the Jacobian of the spectral curve. In the quantum
case the Schr\"odinger equation separates into one--dimensional equations
belonging to the class of generalized Lam\'e differential equations.
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Perturbative Confinement in a 4-d Lorentzian Complex Structure Dependent
YM-like Model: I continue the study of a renormalizable four-dimensional generally covariant
Yang-Mills-like action, which depends on the Lorentzian complex structure of
spacetime and not its metric. The field equations and their integrability
conditions are written down explicitly. The model is studied with the presence
of two static external sources in the trivial cylindrical complex structure.
The energy of two static "colored" sources is found to increase linearly with
respect to their distance, providing an explicit proof of their perturbative
confinement. In the present model, confinement is not a concequence of the
non-Abelian character of the gauge group, but it is implied by the complex
structure dependence of the model.
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Canonical Structure of Noncommutative Quantum Mechanics as Constraint
System: Starting with the first-order singular Lagrangian, the canonical structure in
the noncommutative quantum mechanics with the noncommutativities both of
coordinates and momenta is investgated. Using the projection operator method
(POM) for the constraint systems and the constraint star-product, the
noncommutative quantum system is constructed and the commutator algebra of {\it
projected} canonically conjugate set(CCS) of the system is derived in the form
including all orders of the noncommutativity parameters. We discuss the
alternative CCS, which obeys the ordinary noncommutative commutator algebra.
The {\it exact} CCS is constructed in the framework of the POM, and which is
shown to be equivalent to the CCS constructed through the Seiberg-Witten map
and the Bopp shift. We further discess the alternative Lagrangian to realize
the noncommutativities both of coordinates and momenta.
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Cosmology With Negative Potentials: We investigate cosmological evolution in models where the effective potential
V(\phi) may become negative for some values of the field \phi. Phase portraits
of such theories in space of variables (\phi,\dot\phi,H) have several
qualitatively new features as compared with phase portraits in the theories
with V(\phi) > 0. Cosmological evolution in models with potentials with a
"stable" minimum at V(\phi)<0 is similar in some respects to the evolution in
models with potentials unbounded from below. Instead of reaching an AdS regime
dominated by the negative vacuum energy, the universe reaches a turning point
where its energy density vanishes, and then it contracts to a singularity with
properties that are practically independent of V(\phi). We apply our methods to
investigation of the recently proposed cyclic universe scenario. We show that
in addition to the singularity problem there are other problems that need to be
resolved in order to realize a cyclic regime in this scenario. We propose
several modifications of this scenario and conclude that the best way to
improve it is to add a usual stage of inflation after the singularity and use
that inflationary stage to generate perturbations in the standard way.
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Dynamical Origin of Duality between Gauge Theory and Gravity: Dynamical origin of duality between gauge theory and gravity is studied using
the dual transformation and the formation of graviton as a collective
excitation of dual gauge bosons. In this manner, electric-magnetic duality in
gauge theory is reduced to the duality between gauge theory and gravity.
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Renormalization in quantum field theory and the Riemann-Hilbert problem
II: the $β$-function, diffeomorphisms and the renormalization group: We showed in part I (hep-th/9912092) that the Hopf algebra ${\cal H}$ of
Feynman graphs in a given QFT is the algebra of coordinates on a complex
infinite dimensional Lie group $G$ and that the renormalized theory is obtained
from the unrenormalized one by evaluating at $\ve=0$ the holomorphic part
$\gamma_+(\ve)$ of the Riemann-Hilbert decomposition
$\gamma_-(\ve)^{-1}\gamma_+(\ve)$ of the loop $\gamma(\ve)\in G$ provided by
dimensional regularization. We show in this paper that the group $G$ acts
naturally on the complex space $X$ of dimensionless coupling constants of the
theory. More precisely, the formula $g_0=gZ_1Z_3^{-3/2}$ for the effective
coupling constant, when viewed as a formal power series, does define a Hopf
algebra homomorphism between the Hopf algebra of coordinates on the group of
formal diffeomorphisms to the Hopf algebra ${\cal H}$. This allows first of all
to read off directly, without using the group $G$, the bare coupling constant
and the renormalized one from the Riemann-Hilbert decomposition of the
unrenormalized effective coupling constant viewed as a loop of formal
diffeomorphisms. This shows that renormalization is intimately related with the
theory of non-linear complex bundles on the Riemann sphere of the dimensional
regularization parameter $\ve$. It also allows to lift both the renormalization
group and the $\beta$-function as the asymptotic scaling in the group $G$. This
exploits the full power of the Riemann-Hilbert decomposition together with the
invariance of $\gamma_-(\ve)$ under a change of unit of mass. This not only
gives a conceptual proof of the existence of the renormalization group but also
delivers a scattering formula in the group $G$ for the full higher pole
structure of minimal subtracted counterterms in terms of the residue.
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Magnetoconductivity in chiral Lifshitz hydrodynamics: In this paper, based on the principles of linear response theory, we compute
the longitudinal DC conductivity associated with Lifshitz like fixed points in
the presence of chiral anomalies in ($ 3+1 $) dimensions. In our analysis,
apart from having the usual anomalous contributions due to chiral anomaly, we
observe an additional and pure \textit{parity odd} effect to the
magnetoconductivity which has its origin in the broken Lorentz (boost)
invariance at a Lifshitz fixed point. We also device a holographic set up in
order to compute ($ z=2 $) Lifshitz contributions to the magnetoconductivity
precisely at strong coupling and low charge density limit.
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Defect Branes: We discuss some general properties of "defect branes", i.e. branes of
co-dimension two, in (toroidally compactified) IIA/IIB string theory. In
particular, we give a full classification of the supersymmetric defect branes
in dimensions 2 < D < 11 as well as their higher-dimensionalstring and M-theory
origin as branes and a set of "generalized" Kaluza-Klein monopoles. We point
out a relation between the generalized Kaluza-Klein monopole solutions and a
particular type of mixed-symmetry tensors. These mixed-symmetry tensors can be
defined at the linearized level as duals of the supergravity potentials that
describe propagating degrees of freedom. It is noted that the number of
supersymmetric defect branes is always twice the number of corresponding
central charges in the supersymmetry algebra.
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Chiral bosonization for non-commutative fields: A model of chiral bosons on a non-commutative field space is constructed and
new generalized bosonization (fermionization) rules for these fields are given.
The conformal structure of the theory is characterized by a level of the
Kac-Moody algebra equal to $(1+ \theta^2)$ where $\theta$ is the
non-commutativity parameter and chiral bosons living in a non-commutative
fields space are described by a rational conformal field theory with the
central charge of the Virasoro algebra equal to 1. The non-commutative chiral
bosons are shown to correspond to a free fermion moving with a speed equal to $
c^{\prime} = c \sqrt{1+\theta^2} $ where $c$ is the speed of light. Lorentz
invariance remains intact if $c$ is rescaled by $c \to c^{\prime}$. The
dispersion relation for bosons and fermions, in this case, is given by $\omega
= c^{\prime} | k|$.
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Is nonsymmetric gravity related to string theory?: In this work we raise the question whether nonsymmetric gravity and string
theory are related. We start making the observation, that the gravitational
field $ g_{\mu\nu}$ and the nonsymmetric gauge field $ A_{\mu\nu}$ arising in
the low energy limit in the string theory are exactly the same two basic fields
used in four dimensions in nonsymmetric gravity. We argue, that this connection
between nonsymmetric gravity and string theory at the level of the gauge fields
$ g_{\mu\nu}$ and $ A_{\mu\nu}$ is not, however, reflected at the level of the
corresponding associated actions. In an effort to find a connection between
such an actions we discover a new gravitational action, which suggests an
alternative version of the bosonic string in which the target and the
world-volume metrics are unified.
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A Note On Boundary Conditions In Euclidean Gravity: We review what is known about boundary conditions in General Relativity on a
spacetime of Euclidean signature. The obvious Dirichlet boundary condition, in
which one specifies the boundary geometry, is actually not elliptic and in
general does not lead to a well-defined perturbation theory. It is
better-behaved if the extrinsic curvature of the boundary is suitably
constrained, for instance if it is positive- or negative-definite. A different
boundary condition, in which one specifies the conformal geometry of the
boundary and the trace of the extrinsic curvature, is elliptic and always leads
formally to a satisfactory perturbation theory. These facts might have
interesting implications for semiclassical approaches to quantum gravity.
(Submitted to a volume in honor of Roman Jackiw.)
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The enhancon mechanism for fractional branes: We study the enhancon mechanism for fractional D-branes in conifold and
orbifold backgrounds and show how it can resolve the repulson singularity of
these geometries. In particular we show that the consistency of the excision
process requires that the interior space be not empty. In the orbifold case, we
exploit the boundary state formalism to obtain an explicit conformal
description and emphasize the non trivial role of the volume of the internal
manifold.
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Stringy Corrections to the Classical Tests of General Relativity: String theory imposes modifications to Einstein's equations of classical
general relativity. Consequently, we calculate the additional corrections to
the classical tests: the perihelion precession of Mercury, the deflection of
light rays by the sun, and the gravitational redshift which should be present
if these modified equations hold. In each case, we determine --- quite
consistently with expectations --- that the stringy effects are much too small
to be measured.
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Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme: It can be expected that the respective endpoints of the Gregory-Laflamme
black brane instability and the Rayleigh-Plateau membrane instability are
related because the bifurcation diagrams of the black hole-black string system
and the liquid drop-liquid bridge system display many similarities. In this
paper, we investigate the non-linear dynamics of the Rayleigh-Plateau
instability in a range of dimensions, including the critical dimension at which
the phase structure changes. We show that near the critical dimension and
above, depending on a parameter in initial conditions an unstable cylinder will
either pinch off or converge to an equilibrium state. The equilibrium state is
apparently non-uniform but has a constant mean curvature everywhere. The
results suggest that in the gravity side, near the critical dimension and
above, the final state of an unstable black string (which is not too long) is a
non-uniform black string. The equation of motion adopted to describe the
dynamics is the surface diffusion equation, which was originally proposed to
describe a grooving process of heated metal surfaces. An interesting
correspondence between the diffusion dynamics and black hole (thermo)dynamics
is discussed.
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On a gauge-invariant deformation of a classical gauge-invariant theory: We consider a general gauge theory with independent generators and study the
problem of gauge-invariant deformation of initial gauge-invariant classical
action. The problem is formulated in terms of BV-formalism and is reduced to
describing the general solution to the classical master equation. We show that
such general solution is determined by two arbitrary generating functions of
the initial fields. As a result, we construct in explicit form the deformed
action and the deformed gauge generators in terms of above functions. We argue
that the deformed theory must in general be non-local. The developed
deformation procedure is applied to Abelian vector field theory and we show
that it allows to derive non-Abelain Yang-Mills theory. This procedure is also
applied to free massless integer higher spin field theory and leads to local
cubic interaction vertex for such fields.
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Refined Chern-Simons Theory and Topological String: We show that refined Chern-Simons theory and large N duality can be used to
study the refined topological string with and without branes. We derive the
refined topological vertex of hep-th/0701156 and hep-th/0502061 from a link
invariant of the refined SU(N) Chern-Simons theory on S^3, at infinite N.
Quiver-like Chern-Simons theories, arising from Calabi-Yau manifolds with
branes wrapped on several minimal S^3's, give a dual description of a large
class of toric Calabi-Yau. We use this to derive the refined topological string
amplitudes on a toric Calabi-Yau containing a shrinking P^2 surface. The result
is suggestive of the refined topological vertex formalism for arbitrary toric
Calabi-Yau manifolds in terms of a pair of vertices and a choice of a Morse
flow on the toric graph, determining the vertex decomposition. The dependence
on the flow is reminiscent of the approach to the refined topological string in
upcoming work of Nekrasov and Okounkov. As a byproduct, we show that large N
duality of the refined topological string explains the ``mirror symmetry`` of
the refined colored HOMFLY invariants of knots.
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On energy extraction from Q-balls and other fundamental solitons: Energy exchange mechanisms have important applications in particle physics,
gravity, fluid mechanics, and practically every field in physics. In this
letter we show, both in frequency and time domain, that energy enhancement is
possible for waves scattering off fundamental solitons (time-periodic localized
structures of bosonic fields), without the need for rotation nor translational
motion. We use two-dimensional Q-balls as a testbed, providing the correct
criteria for energy amplification, as well as the respective amplification
factors, and we discuss possible instability mechanisms. Our results lend
support to the qualitative picture drawn in ( arXiv:2212.03269 [gr-qc] );
however we show that this enhancement mechanism is not of superradiant-type,
but instead a "blueshift-like" energy exchange between scattering states
induced by the background Q-ball, which should occur generically for any
time-periodic fundamental soliton. This mechanism does not seem to lead to
instabilities.
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Mirror Fermions in Noncommutative Geometry: In a recent paper we pointed out the presence of extra fermionic degrees of
freedom in a chiral gauge theory based on Connes Noncommutative Geometry. Here
we propose a mechanism which provides a high mass to these mirror states, so
that they decouple from low energy physics.
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Gauging the Wess-Zumino term of a sigma model with boundary: We investigate the gauging of the Wess-Zumino term of a sigma model with
boundary. We derive a set of obstructions to gauging and we interpret them as
the conditions for the Wess-Zumino term to extend to a closed form in a
suitable equivariant relative de Rham complex. We illustrate this with the
two-dimensional sigma model and we show that the new obstructions due to the
boundary can be interpreted in terms of Courant algebroids. We specialise to
the case of the Wess-Zumino-Witten model, where it is proved that there always
exist suitable boundary conditions which allow gauging any subgroup which can
be gauged in the absence of a boundary. We illustrate this with two natural
classes of gaugings: (twisted) diagonal subgroups with boundary conditions
given by (twisted) conjugacy classes, and chiral isotropic subgroups with
boundary conditions given by cosets.
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Loop Calculations for the Non-Commutative U(1) Gauge Field Model with
Oscillator Term: Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar
model, a non-commutative U(1) gauge field theory including an oscillator-like
term in the action has been put forward in arXiv:0705.4205. The aim of the
current work is to analyze whether that action can lead to a fully
renormalizable gauge model on non-commutative Euclidean space. In a first step,
explicit one-loop graph computations are hence presented, and their results as
well as necessary modifications of the action are successively discussed.
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Fast Scramblers, Democratic Walks and Information Fields: We study a family of weighted random walks on complete graphs. These
`democratic walks' turn out to be explicitly solvable, and we find the
hierarchy window for which the characteristic time scale saturates the
so-called fast scrambling conjecture. We show that these democratic walks
describe well the properties of information spreading in systems in which every
degree of freedom interacts with every other degree of freedom, such as Matrix
or infinite range models. The argument is based on the analysis of suitably
defined `Information fields' ($\mathcal{I}$), which are shown to evolve
stochastically towards stationarity due to unitarity of the microscopic model.
The model implies that in democratic systems, stabilization of one subsystem is
equivalent to global scrambling. We use these results to study scrambling of
infalling perturbations in black hole backgrounds, and argue that the near
horizon running coupling constants are connected to entanglement evolution of
single particle perturbations in democratic systems.
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The Higgs Mechanism in Heterotic Orbifolds: We study spontaneous gauge symmetry breaking in the framework of orbifold
compactifcations of heterotic string theory. In particular we investigate the
electroweak symmetry breakdown via the Higgs mechanism. Such a breakdown can be
achieved by continuous Wilson lines. Exploiting the geometrical properties of
this scheme we develop a new technique which simplifies the analysis used in
previous discussions.
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Topological Invariants, Instantons and Chiral Anomaly on Spaces with
Torsion: In a spacetime with nonvanishing torsion there can occur topologically stable
configurations associated with the frame bundle which are independent of the
curvature. The relevant topological invariants are integrals of local scalar
densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y
form $N= (T^a \wedge T_a - R_{ab} \wedge e^a \wedge e^b)$ is the only closed
4-form invariant under local Lorentz rotations associated with the torsion of
the manifold. The integral of $N$ over a compact D-dimensional (Euclidean)
manifold is shown to be a topological invariant related to the Pontryagin
classes of SO(D+1) and SO(D). An explicit example of a topologically nontrivial
configuration carrying nonvanishing instanton number proportional to $\int N$
is costructed. The chiral anomaly in a four-dimensional spacetime with torsion
is also shown to contain a contribution proportional to $N$, besides the usual
Pontryagin density related to the spacetime curvature. The violation of chiral
symmetry can thus depend on the instanton number of the tangent frame bundle of
the manifold. Similar invariants can be constructed in D>4 dimensions and the
existence of the corresponding nontrivial excitations is also discussed.
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SO(10) GUT Models and Cosmology: $SO(10)$ grand unified models have an intermediate symmetry group in between
$SO(10)$ and $SU(3)_{C} \otimes SU(2)_{L} \otimes U(1)_{Y}$. Hence they lead to
a prediction for proton lifetime in agreement with the experimental lower
limit. This paper reviews the recent work on the tree-level potential and the
one-loop effective potential for such models, with application to inflationary
cosmology. The open problems are the use of the most general form of tree-level
potential for $SO(10)$ models in the reheating stage of the early universe, and
the analysis of non-local effects in the semiclassical field equations for such
models in Friedmann-Robertson-Walker backgrounds.
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Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups: The general structure of trace anomaly, suggested recently by Deser and
Shwimmer, is argued to be the consequence of the Wess-Zumino consistency
condition. The response of partition function on a finite Weyl transformation,
which is connected with the cocycles of the Weyl group in $d=2k$ dimensions is
considered, and explicit answers for $d=4,6$ are obtained. Particularly, it is
shown, that addition of the special combination of the local counterterms leads
to the simple form of that cocycle, quadratic over Weyl field $\sigma$, i.e.
the form, similar to the two-dimensional Lioville action. This form also
establishes the connection of the cocycles with conformal-invariant operators
of order $d$ and zero weight. Beside that, the general rule for transformation
of that cocycles into the cocycles of diffeomorphisms group is presented.
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The Tachyon does Matter: We review the concept of S-branes introduced by Gutperle and Strominger
hep-th/0202210. Using the effective spacetime description of the rolling
tachyon worldsheets discussed by Sen, we analyze the possibility that the
gravitational backreaction of tachyon matter is important in the time-dependent
process. We show that this is indeed the case in the example of the S0-brane in
4-dimensional Einstein-Maxwell theory. This talk is based on hep-th/0207235.
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Local supersymmetry and the square roots of Bondi-Metzner-Sachs
supertranslations: Super-BMS$_4$ algebras -- also called BMS$_4$ superalgebras -- are graded
extensions of the BMS$_4$ algebra. They can be of two different types: they can
contain either a finite number or an infinite number of fermionic generators.
We show in this letter that, with suitable boundary conditions on the graviton
and gravitino fields at spatial infinity, supergravity on asymptotically flat
spaces possesses as superalgebra of asymptotic symmetries a (nonlinear)
super-BMS$_4$ algebra containing an infinite number of fermionic generators,
which we denote SBMS$_4$. These boundary conditions are not only invariant
under SBMS$_4$, but also lead to a fully consistent canonical description of
the supersymmetries, which have in particular well-defined Hamiltonian
generators that close according to the nonlinear SBMS$_4$ algebra. One finds in
particular that the graded brackets between the fermionic generators yield all
the BMS$_4$ supertranslations, of which they provide therefore "square roots".
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2-form gauge theory dual to scalar-tensor theory: We generalize the electromagnetic duality between a massless, canonical
scalar field and a 2-form gauge field in 4-dimensional spacetime to
scalar-tensor theories. We derive the action of 2-form gauge field that is dual
to two kinds of scalar-tensor theories: shift symmetric K-essence theory and
the shift symmetric Horndeski theory up to quadratic in scalar field. The
former case, the dual 2-form has a nonlinear kinetic term. The latter case, the
dual 2-form has non-trivial interactions with gravity through Einstein tensor.
In both case, the duality relation is modified from usual case, that is, the
dual 2-form field is not simply given by the Hodge dual of the gradient of the
scalar field.
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Higher abelian gauge theory associated to gerbes on noncommutative
deformed M5-branes and S-duality: We enhance the action of higher abelian gauge theory associated to a gerbe on
an M5-brane with an action of a torus ${\mathbb T}^n (n\ge 2)$, by a
noncommutative ${\mathbb T}^n$-deformation of the M5-brane. The ingredients of
the noncommutative action and equations of motion include the deformed Hodge
duality, deformed wedge product, and the noncommutative integral over the
noncommutative space obtained by strict deformation quantization. As an
application we then introduce a variant model with an enhanced action in which
we show that the corresponding partition function is a modular form, which is a
purely noncommutative geometry phenomenon since the usual theory only has a
$\mathbb Z_2$-symmetry. In particular, S-duality in this 6-dimensional higher
abelian gauge theory model is shown to be, in this sense, on par with the usual
4-dimensional case.
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On the pulsating strings in AdS_5 x T^{1,1}: We study the class of pulsating strings in AdS_5 x T^{1,1}. Using a
generalized ansatz for pulsating string configurations we find new solutions of
this class. Further we semiclassically quantize the theory and obtain the first
correction to the energy. The latter, due to AdS/CFT correspondence, is
supposed to give the anomalous dimensions of operators in the dual N=1
superconformal gauge field theory.
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Remarks on mod-2 elliptic genus: For physicists: For supersymmetric quantum mechanics, there are cases when a
mod-2 Witten index can be defined, even when a more ordinary
$\mathbb{Z}$-valued Witten index vanishes. Similarly, for 2d supersymmetric
quantum field theories, there are cases when a mod-2 elliptic genus can be
defined, even when a more ordinary elliptic genus vanishes. We study such mod-2
elliptic genera in the context of $\mathcal{N}=(0,1)$ supersymmetry, and show
that they are characterized by mod-2 reductions of integral modular forms,
under some assumptions.
For mathematicians: We study the image of the standard homomorphism $\pi_n
\mathrm{TMF}\to \pi_n \mathrm{KO}((q))\simeq \mathbb{Z}/2((q))$ for $n=8k+1$ or
$8k+2$, by relating them to the mod-2 reductions of integral modular forms.
|
Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker
metric: A general class of cosmological models driven by a nonlocal scalar field
inspired by the string field theory is studied. Using the fact that the
considering linear nonlocal model is equivalent to an infinite number of local
models we have found an exact special solution of the nonlocal Friedmann
equations. This solution describes a monotonically increasing Universe with the
phantom dark energy.
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$\mathbb{Z}_2$ boundary twist fields and the moduli space of D-branes: We revisit the boundary conformal field theory of twist fields. Based on the
equivalence between twisted bosons on a circle and the orbifold theory at the
critical radius, we provide a bosonized representation of boundary twist fields
and thus a free field representation of the latter. One advantage of this
formulation is that it considerably simplifies the calculation of correlation
functions involving twist fields. At the same time this also gives access to
higher order terms in the operator product expansions of the latter which, in
turn, allows to explore the moduli space of marginal deformation of bound
states of D-branes. In the process we also generalize some results on
correlation functions with excited twist fields.
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The elliptic Gaudin system with spin: The elliptic Gaudin model was obtained as the Hitchin system on an elliptic
curve with two fixed points. In the present paper the algebraic-geometrical
structure of the system with two fixed points is clarified. We identify this
system with poles dynamics of the finite gap solutions of Davey-Stewartson
equation. The solutions of this system in terms of theta-functions and the
action-angle variables are constructed. We also discuss the geometry of its
degenerations.
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Kalb-Ramond scalar QED multiple vacua: We study a model of interacting vector and Kalb-Ramond gauge fields in a
non-trivial Higgs vacuum generated by a charged and a neutral scalar field. The
system admits different vacua for different v.e.v. of the two Higgs fields. Our
primary interest in this paper regards the "mixed phase" where both the photon
and the Kalb-Ramond acquire a mass. In this phase we compute the interaction
potential energy between static test charges. It turns out that the limit in
which the photon becomes massless, while the Kalb-Ramond remains massive, leads
to a Cornell confining potential between test charges.
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Erratum to `Instability in cosmological topologically massive gravity at
the chiral point', arXiv:0805.2610: We correct a sign in the first variation of the on-shell action of
cosmological topologically massive gravity at the chiral point and present the
three equations affected by that sign. While this does not change any of the
main conclusions of arXiv:0805.2610, it modifies the finite part of the
Brown-York stress tensor. Our corrected Brown-York stress tensor is still
finite, conserved and traceless, but no longer coincides with that of global
AdS_3. It agrees with results found in recent literature.
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Time dependent action in $φ^6$ potential: The false vacuum decay in field theory from a coherently oscillating initial
state is studied for $\phi^6$ potential. An oscillating bubble solution is
obtained. The instantaneous bubble nucleation rate is calculated.
|
Cohomology of Line Bundles: Proof of the Algorithm: We present a proof of the algorithm for computing line bundle valued
cohomology classes over toric varieties conjectured by R.~Blumenhagen, B.~Jurke
and the authors (arXiv:1003.5217) and suggest a kind of Serre duality for
combinatorial Betti numbers that we observed when computing examples.
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Holographic Entanglement Entropy in flat limit of the Generalized
Minimal Massive Gravity model: Previously we have studied the Generalized Minimal Massive Gravity (GMMG) in
asymptotically $AdS_3$ background, and have shown that the theory is free of
negative-energy bulk modes. Also we have shown GMMG avoids the aforementioned
bulk-boundary unitarity clash. Here instead of $AdS_3$ space we consider
asymptotically flat space, and study this model in the flat limit. The dual
field theory of GMMG in the flat limit is a $BMS_3$ invariant field theory,
dubbed (BMSFT) and we have BMS algebra asymptotically instead of Virasoro
algebra. In fact here we present an evidence for this claim. Entanglement
entropy of GMMG is calculated in the background in the flat null infinity. Our
evidence for mentioned claim is the result for entanglement entropy in filed
theory side and in the bulk (in the gravity side). At first using Cardy formula
and Rindler transformation, we calculate entanglement entropy of BMSFT in three
different cases. Zero temperature on the plane and on the cylinder, and
non-zero temperature case. Then we obtain the entanglement entropy in the bulk.
Our results in gravity side are exactly in agreement with field theory
calculations.
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Static Monopoles and Their Anti-Configurations: Recently, we have reported on the existence of some monopoles, multimonopole,
and antimonopoles configurations. In this paper we would like to present more
monopoles, multimonopole, and antimonopoles configurations of the magnetic
ansatz of Ref.\cite{kn:9} when the parameters $p$ and $b$ of the solutions
takes different serial values. These exact solutions are a different kind of
BPS solution. They satisfy the first order Bogomol'nyi equation but possess
infinite energy. They can have radial, axial, or rotational symmetry about the
z-axis. We classified these serial solutions as (i) the multimonopole at the
origin; (ii) the finitely separated 1-monopoles; (iii) the screening solutions
of multimonopole and (iv) the axially symmetric monopole solutions. We also
give a construction of their anti-configurations with all the magnetic charges
of poles in the configurations reversed. Half-integer topological magnetic
charge multimonopole also exist in some of these series of solutions.
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Chern-Simons-Higgs Theory with Visible and Hidden Sectors and its ${\cal
N}=2$ SUSY Extension: We study vortex solutions in Abelian Chern-Simons-Higgs theories with visible
and hidden sectors. We first consider the case in which the two sectors are
connected through a BF-like gauge mixing term with no explicit interaction
between the the two scalars. Since first order Bogomolny equations do not exist
in this case, we derive the second order field equations. We then proceed to an
${\cal N}=2$ supersymmetric extension including a Higgs portal mixing among the
visible and hidden charged scalars. As expected, Bogomolnyi equations do exist
in this case and we study their string-like solutions numerically.
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On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal
SL(2,R)/U(1) Model: II. The Quantum Case: This paper is devoted to constructing a quantum version of the famous KP
hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear
$\hat{W}_{\infty}$ algebra. This is achieved by quantizing the conformal
noncompact $SL(2,R)_{k}/U(1)$ coset model, in which $\hat{W}_{\infty}$ appears
as a hidden current algebra. For the quantum $\hat{W}_{\infty}$ algebra at
level $k=1$, we have succeeded in constructing an infinite set of commuting
quantum charges in explicit and closed form. Using them a completely integrable
quantum KP hierarchy is constructed in the Hamiltonian form. A two boson
realization of the quantum $\hat{W}_{\infty}$ currents has played a crucial
role in this exploration.
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T-duality for the sigma model with boundaries: We derive the most general local boundary conditions necessary for T-duality
to be compatible with superconformal invariance of the two-dimensional N=1
supersymmetric nonlinear sigma model with boundaries. To this end, we construct
a consistent gauge invariant parent action by gauging a U(1) isometry, with and
without boundary interactions. We investigate the behaviour of the boundary
conditions under T-duality, and interpret the results in terms of D-branes.
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Effect of Self-Interaction on Vacuum Energy for Yang-Mills System in
Kaluza-Klein Theory: We calculate the vacuum energy for Yang--Mills (YM) system in the background
space-time $M^4 \times S^3$, taking the effect of self-interaction of the YM
fields into account. The compactification scale obtained by Candelas--Weinberg
mechanism becomes large if the YM coupling is large. The case with an extra
space $S^3/Z_2$ is also considered, and it is shown that the vacuum associated
with broken gauge symmetry is unstable.
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Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory: In previous investigations, it was found that four-sided polygonal light-like
Wilson loops in ABJM theory calculated to two-loop order have the same form as
the corresponding Wilson loop in N = 4 SYM at one-loop order. Here we study
light-like polygonal Wilson loops with n cusps in planar three-dimensional
Chern-Simons and ABJM theory to two loops. Remarkably, the result in ABJM
theory precisely agrees with the corresponding Wilson loop in N = 4 SYM at
one-loop order for arbitrary n. In particular, anomalous conformal Ward
identites allow for a so-called remainder function of conformal cross ratios,
which is found to be trivial at two loops in ABJM theory in the same way as it
is trivial in N = 4 SYM at one-loop order. Furthermore, the result for
arbitrary n obtained here, allows for a further investigation of a Wilson loop
/ amplitude duality in ABJM theory, for which non-trivial evidence was recently
found by a calculation of four-point amplitudes that match the Wilson loop in
ABJM theory.
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Abelian Chern-Simons field theory and anyon equation on a torus: We quantize the abelian Chern-Simons theory coupled to non-relativistic
matter field on a torus without invoking the flux quantization. Through a
series of canonical transformations which is equivalent to solving the Gauss
constraint, we obtain an effective hamiltonian density with periodic matter
field. We also obtain the many-anyon Schr\"odinger equation with periodic
Aharonov-Bohm potentials and analyze the periodic property of the wavefunction.
Some comments are given on the different features of our approach from the
previous ones.
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Selberg Integral and SU(N) AGT Conjecture: An intriguing coincidence between the partition function of super Yang-Mills
theory and correlation functions of 2d Toda system has been heavily studied
recently. While the partition function of gauge theory was explored by
Nekrasov, the correlation functions of Toda equation have not been completely
understood. In this paper, we study the latter in the form of Dotsenko-Fateev
integral and reduce it in the form of Selberg integral of several Jack
polynomials. We conjecture a formula for such Selberg average which satisfies
some consistency conditions and show that it reproduces the SU(N) version of
AGT conjecture.
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A manifestly N=2 supersymmetric Born-Infeld action: A manifestly N=2 supersymmetric completion of the four-dimensional
Nambu-Goto-Born-Infeld action, which is self-dual with respect to
electric-magnetic duality, is constructed in terms of the abelian N=2
superfield strength W in the conventional N=2 superspace. A relation to the
known N=1 supersymmetric Born-Infeld action in N=1 superspace is established.
The action found can be considered either as the Goldstone action associated
with partial breaking of N=4 supersymmetry down to N=2, with the N=2 vector
superfield being a Goldstone field, or, equivalently, as the gauge-fixed
superfield action of a D-3-brane in flat six-dimensional ambient spacetime.
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WMAP5 Observationnal Constraints on Braneworld New Inflation Model: We study a new inflation potential in the framework of the Randall-Sundrum
type 2 Braneworld model. Using the technic developped in(Phys. Rev. D75, 123504
(2007).1), we consider both an monomial and a new inflation potentials and
apply the Slow-Roll approximation in high energy limit, to derive analytical
expression of relevant perturabtion spectrum. We show that for some values of
the parameter n of the potential, we obtain an perturbation spectrum wich
present a good agreement with recent WMAP5 observations.
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Haldane limits via Lagrangian embeddings: In the present paper we revisit the so-called Haldane limit, i.e. a
particular continuum limit, which leads from a spin chain to a sigma model. We
use the coherent state formulation of the path integral to reduce the problem
to a semiclassical one, which leads us to the observation that the Haldane
limit is closely related to a Lagrangian embedding into the classical phase
space of the spin chain. Using this property, we find a spin chain whose limit
produces a relativistic sigma model with target space the manifold of complete
flags U(N)/U(1)^N. We discuss possible other future applications of
Lagrangian/isotropic embeddings in this context.
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Tachyon Vacuum Solution in Open String Field Theory with Constant B
Field: We show that Schnabl's tachyon vacuum solution is an exact solution of the
equation of motion of Witten's open bosonic string field theory in the
background of constant antisymmetric two-form field. The action computed at the
vacuum solution is given by the Dirac-Born-Infeld factor multiplied to that
without the antisymmetric tensor field.
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Worldvolume Uncertainty Relations for D-Branes: By quantizing an open string ending on a D-brane in a nontrivial supergravity
background, we argue that there is a new kind of uncertainty relation on a
D-brane worldvolume. Furthermore, we fix the form of the uncertainty relations
and their dependence on the string coupling constant by requiring them to be
consistent with various string theory and M theory dualities. In this way we
find a web of uncertainties of spacetime for all kinds of brane probes,
including fundamental strings, D-branes of all dimensions as well as M theory
membranes and fivebranes.
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Revisiting Conserved Charges in Higher Curvature Gravitational Theories: Restricting the covariant gravitational phase spaces to the manifold of
parametrized families of solutions, the mass, angular momenta, entropies, and
electric charges can be calculated by a single and simple method. In this
method, which has been called "solution phase space method," conserved charges
are unambiguous and regular. Moreover, assuming the generators of the charges
to be exact symmetries, entropies and other conserved charges can be calculated
on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence,
the first law of thermodynamics would be a local identity relating the exact
symmetries to which the mass, angular momentum, electric charge, and entropy
are attributed. In this paper, we apply this powerful method to the $f(R)$
gravitational theories accompanied by the terms quadratic in the Riemann and
Ricci tensors. Furthermore, conserved charges and the first law of
thermodynamics for some of their black hole solutions are exemplified. The
examples include warped AdS$_3$, charged static BTZ, and 3-dimensional $z=3$
Lifshitz black holes.
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Conformal spacelike-timelike correspondence in QCD: This paper is a study of a spacelike-timelike conformal correspondence in
QCD. When the times at vertices are fixed in an A_+ = 0 gauge calculation the
distribution of gluons in a highly virtual decay have an exact correspondence
with the gluons in the lightcone wavefunction of a high energy dipole with the
identification of angles in the timelike case and transverse coordinates in the
lightcone wavefunction. Divergences show up when the time integrals are done. A
procedure for dropping these divergences, analogous to the Gell-Mann Low
procedure in QED, allows one to define a conformal QCD, at least through NLO.
Possible uses of such a conformal QCD are discussed.
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Normal Coordinates and Primitive Elements in the Hopf Algebra of
Renormalization: We introduce normal coordinates on the infinite dimensional group $G$
introduced by Connes and Kreimer in their analysis of the Hopf algebra of
rooted trees. We study the primitive elements of the algebra and show that they
are generated by a simple application of the inverse Poincar\'e lemma, given a
closed left invariant 1-form on $G$. For the special case of the ladder
primitives, we find a second description that relates them to the Hopf algebra
of functionals on power series with the usual product. Either approach shows
that the ladder primitives are given by the Schur polynomials. The relevance of
the lower central series of the dual Lie algebra in the process of
renormalization is also discussed, leading to a natural concept of
$k$-primitiveness, which is shown to be equivalent to the one already in the
literature.
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Classification of BPS instantons in N=4 D=4 supergravity: This talk is based on the recent work in collaboration with M.
Azreg-A\"{\i}nou and G. Cl\'ement devoted to extremal instantons in the
one-vector truncation of the Euclidean $\mathcal{N}=4,\, D=4$ theory. Extremal
solutions satisfying the no-force condition can be associated with null
geodesic curves in the homogeneous target space of the three-dimensional sigma
model arising in toroidal reduction of the four-dimensional theory. Here we
(preliminarily) discuss the case of two vector fields sufficient to find all
relevant metrics in the full $\mathcal{N}=4,\, D=4$ theory. Classification of
instanton solutions is given along the following lines. The first is their
possible asymptotic structure: asymptotically locally flat (ALF),
asymptotically locally Euclidean (ALE) and ALF or ALE with the dilaton growing
at infinity. The second is the algebraic characterization of matrix generators
according to their rank and the nature of the charge vectors in an associated
Lorentzian space. Finally, solutions are distinguished by the number of
independent harmonic functions with unequal charges (up to four).
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Non-Lorentzian RG flows and Supersymmetry: We describe a general process where a non-Lorentzian rescaling of a
supersymmetric field theory leads to a scale-invariant fixed point action
without Lorentz invariance but where the supersymmetry is preserved or even
enhanced. We apply this procedure to five-dimensional maximally supersymmetric
super-Yang-Mills, leading to a field theory with 24 super(conformal)
symmetries. We also apply this procedure to the BLG model with 32
super(conformal) symmetries and ABJM models with 24 super(conformal)
symmetries.
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Influence functionals, decoherence and conformally coupled scalars: Some of the simplest modifications to general relativity involve the coupling
of additional scalar fields to the scalar curvature. By making a Weyl rescaling
of the metric, these theories can be mapped to Einstein gravity with the
additional scalar fields instead being coupled universally to matter. The
resulting couplings to matter give rise to scalar fifth forces, which can evade
the stringent constraints from local tests of gravity by means of so-called
screening mechanisms. In this talk, we derive evolution equations for the
matrix elements of the reduced density operator of a toy matter sector by means
of the Feynman-Vernon influence functional. In particular, we employ a novel
approach akin to the LSZ reduction more familiar to scattering-matrix theory.
The resulting equations allow the analysis, for instance, of decoherence
induced in atom-interferometry experiments by these classes of modified
theories of gravity.
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An effective field theory of damped ferromagnetic systems: Using the in-in formalism, we generalize the recently constructed
magnetoelastic EFT arXiv:2112.13873 [hep-th] to describe the damping dynamics
of ferromagnetic systems at long wavelengths. We find that the standard Gilbert
damping term naturally arises as the simplest leading-order symmetry-consistent
non-conservative contribution within the in-in framework. The EFT is easily
generalized to scenarios with anisotropy and inhomogeneity. In particular, we
find the classic Landau-Lifshitz damping term emerges when isotropy is broken
by a constant external background field. This provides a first principle
explanation for distinguishing the two types of damping dynamics that were
originally constructed phenomenologically. Furthermore, the EFT framework could
also incorporate intrinsic anisotropy of the material in a straightforward way
using the spurion method. For systems with inhomogeneity such as nontrivial
spin textures, we find that the leading order derivative correction yields the
generalized Gilbert damping equations that were found in condensed matter
literature. This shows that the EFT approach enables us to derive the form of
higher-derivative-order corrections in a systematic way. Lastly, using the
phonon-magnon coupling deduced in the magnetoelastic EFT, we are able to make a
prediction for the generic form of the phononic contribution to the damping
equation.
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Scattering with partial information: We study relativistic scattering when one only has access to a subset of the
particles, using the language of quantum measurement theory. We give an exact,
non-perturbative formula for the von Neumann entanglement entropy of an
apparatus particle scattered off an arbitrary set of system particles, in
either the elastic or inelastic regime, and show how to evaluate it
perturbatively. We give general formulas for the late-time expectation values
of apparatus observables. Some simple example applications are included: in
particular, a protocol to verify preparation of coherent superpositions of
spatially localized system states using position-space information in the
outgoing apparatus state, at lowest order in perturbation theory in a weak
apparatus-system coupling.
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Duality Between String Junctions and D-Branes on Del Pezzo Surfaces: We revisit local mirror symmetry associated with del Pezzo surfaces in
Calabi-Yau threefolds in view of five-dimensional N=1 E_N theories compactified
on a circle. The mirror partner of singular Calabi-Yau with a shrinking del
Pezzo four-cycle is described as the affine 7-brane backgrounds probed by a
D3-brane. Evaluating the mirror map and the BPS central charge we relate
junction charges to RR charges of D-branes wrapped on del Pezzo surfaces. This
enables us to determine how the string junctions are mapped to D-branes on del
Pezzo surfaces.
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Emerging Hawking-like Radiation from Gravitational Bremsstrahlung Beyond
the Planck Scale: We argue that, as a consequence of the graviton's spin-2, its bremsstrahlung
in trans-planckian-energy ($E\gg M_P$) gravitational scattering at small
deflection angle can be nicely expressed in terms of helicity-transformation
phases and their transfer within the scattering process. The resulting spectrum
exhibits deeply sub-planckian characteristic energies of order $M_P^2/E \ll
M_P$ (reminiscent of Hawking radiation), a suppressed fragmentation region, and
a reduced rapidity plateau, in broad agreement with recent classical estimates.
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Twistors and the massive spinning particle: Gauge-invariant twistor variables are found for the massive spinning particle
with N-extended local worldline supersymmetry, in spacetime dimensions D=3,4,6.
The twistor action is manifestly Lorentz invariant but the anticommuting spin
variables appear exactly as in the non-relativistic limit. This allows a simple
confirmation that the quantum N=2 spinning particle has either spin one or spin
zero, and that N>2 is quantum inconsistent for D=4,6.
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Comments on twisted indices in 3d supersymmetric gauge theories: We study three-dimensional ${\mathcal N}=2$ supersymmetric gauge theories on
${\Sigma_g \times S^1}$ with a topological twist along $\Sigma_g$, a genus-$g$
Riemann surface. The twisted supersymmetric index at genus $g$ and the
correlation functions of half-BPS loop operators on $S^1$ can be computed
exactly by supersymmetric localization. For $g=1$, this gives a simple UV
computation of the 3d Witten index. Twisted indices provide us with a clean
derivation of the quantum algebra of supersymmetric Wilson loops, for any
Yang-Mills-Chern-Simons-matter theory, in terms of the associated Bethe
equations for the theory on ${\mathbb R}^2 \times S^1$. This also provides a
powerful and simple tool to study 3d ${\mathcal N}=2$ Seiberg dualities.
Finally, we study A- and B-twisted indices for ${\mathcal N}=4$ supersymmetric
gauge theories, which turns out to be very useful for quantitative studies of
three-dimensional mirror symmetry. We also briefly comment on a relation
between the $S^2 \times S^1$ twisted indices and the Hilbert series of
${\mathcal N}=4$ moduli spaces.
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The information paradox and the locality bound: Hawking's argument for information loss in black hole evaporation rests on
the assumption of independent Hilbert spaces for the interior and exterior of a
black hole. We argue that such independence cannot be established without
incorporating strong gravitational effects that undermine locality and
invalidate the use of quantum field theory in a semiclassical background
geometry. These considerations should also play a role in a deeper
understanding of horizon complementarity.
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Symplectic and Poisson Geometry on Loop Spaces of Manifolds and
Nonlinear Equations: We consider some differential geometric classes of local and nonlocal Poisson
and symplectic structures on loop spaces of smooth manifolds which give natural
Hamiltonian and multihamiltonian representations for some important nonlinear
equations of mathematical physics and field theory such as nonlinear sigma
models with torsion, degenerate Lagrangian systems of field theory, systems of
hydrodynamic type, N-component systems of Heisenberg magnet type,
Monge-Amp\`ere equations, the Krichever-Novikov equation and others. In
addition, we shall prove integrability of some class of nonhomogeneous systems
of hydrodynamic type and give a description of nonlinear partial differential
equations of associativity in $2D$ topological field theories (for some special
type solutions of the Witten-Dijkgraaf-E.Verlinde-H.Verlinde (WDVV) system) as
integrable nondiagonalizable weakly nonlinear homogeneous systems of
hydrodynamic type.
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Electroweak vacuum decay in metric-affine gravity: We investigate the stability of the electroweak vacuum in metric-affine
gravity in which the Standard Model Higgs boson can be non-minimally coupled to
both the Ricci scalar and the Holst invariant. We find that vacuum stability is
improved in this framework across a wide range of model parameters.
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Gauging Unbroken Symmetries in F-theory: F-theory attempts to include all U-dualities manifestly. Unlike its T-dual
manifest partner, which is based on string current algebra, F-theory is based
on higher dimensional brane current algebra. Like the T-dual manifest theory,
which has $O(D-1,1)^2$ unbroken symmetry, the F-theory vacuum also enjoys
certain symmetries ("$H$"). One of its important and exotic properties is that
worldvolume indices are also spacetime indices. This makes the global brane
current algebra incompatible with $H$ symmetry currents. The solution is to
introduce worldvolume covariant derivatives, which depend on the $H$
coordinates even in a "flat" background. We will also give as an explicit
example the 5-brane case.
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Non-local observables at finite temperature in AdS/CFT: Within gauge/gravity duality, we consider the AdS-Schwarzschild metric in
arbitrary dimensions. We obtain analytical closed-form results for the
two-point function, Wilson loop and entanglement entropy for strip geometries
in the finite-temperature field-theory dual. According to the duality, these
are given by the area of minimal surfaces of different dimension in the gravity
background. Our analytical results involve generalised hypergeometric
functions. We show that they reproduce known numerical results to great
accuracy. Our results allow to identify new physical behaviour: For instance,
we consider the entanglement density, i.e. the difference of entanglement
entropies at finite and vanishing temperature divided by the volume of the
entangling region. For field theories of dimension seven or higher, we find
that the entanglement density displays non-monotonic behaviour as function of
l*T, with l the strip width and T the temperature. This implies that the area
theorem, proven for RG flows in general dimensions, does not apply here. This
may signal the emergence of new degrees of freedom for AdS Schwarzschild black
holes in eight or more dimensions.
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From relativistic quantum fields to condensed matter and back again:
Updating the Gross-Neveu phase diagram: During the last few years, the phase diagram of the large N Gross-Neveu model
in 1+1 dimensions at finite temperature and chemical potential has undergone a
major revision. Here we present a streamlined account of this development,
collecting the most important results. Quasi-one-dimensional condensed matter
systems like conducting polymers provide real physical systems which can be
approximately described by the Gross-Neveu model and have played some role in
establishing its phase structure. The kink-antikink phase found at low
temperatures is closely related to inhomogeneous superconductors in the
Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at
hand, the Gross-Neveu model can now serve as a firm testing ground for new
algorithms and theoretical ideas.
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CPT anomaly in two-dimensional chiral U(1) gauge theories: The CPT anomaly, which was first seen in perturbation theory for certain
four-dimensional chiral gauge theories, is also present in the exact result for
a class of two-dimensional chiral U(1) gauge theories on the torus.
Specifically, the chiral determinant for periodic fermion fields changes sign
under a CPT transformation of the background gauge field. There is, in fact, an
anomaly of Lorentz invariance, which allows for the CPT theorem to be
circumvented.
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String Junctions and Holographic Interfaces: In this paper we study half-BPS type IIB supergravity solutions with multiple
$AdS_3\times S^3\times M_4$ asymptotic regions, where $M_4$ is either $T^4$ or
$K_3$. These solutions were first constructed in [1] and have geometries given
by the warped product of $AdS_2 \times S^2 \times M_4 $ over $\Sigma$, where
$\Sigma$ is a Riemann surface. We show that the holographic boundary has the
structure of a star graph, i.e. $n$ half-lines joined at a point. The attractor
mechanism and the relation of the solutions to junctions of self-dual strings
in six-dimensional supergravity are discussed. The solutions of [1] are
constructed introducing two meromorphic and two harmonic functions defined on
$\Sigma$. We focus our analysis on solutions corresponding to junctions of
three different conformal field theories and show that the conditions for
having a solution charged only under Ramond-Ramond three-form fields reduce to
relations involving the positions of the poles and the residues of the relevant
harmonic and meromorphic functions. The degeneration limit in which some of the
poles collide is analyzed in detail. Finally, we calculate the holographic
boundary entropy for a junction of three CFTs and obtain a simple expression in
terms of poles and residues.
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Cosmology at the end of the world: In the last two decades the Anti-de Sitter/Conformal Field Theory
correspondence (AdS/CFT) has emerged as focal point of many research interests.
In particular, it functions as a stepping stone to a still missing full quantum
theory of gravity. In this context, a pivotal question is if and how
cosmological physics can be studied using AdS/CFT. Motivated by string theory,
braneworld cosmologies propose that our universe is a four-dimensional membrane
embedded in a bulk five-dimensional AdS spacetime. We show how such a scenario
can be microscopically realized in AdS/CFT using special field theory states
dual to an "end-of-the-world brane" moving in a charged black hole spacetime.
Observers on the brane experience cosmological physics and approximately
four-dimensional gravity, at least locally in spacetime. This result opens a
new path towards a description of quantum cosmology and the simulation of
cosmology on quantum machines.
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Low Energy Dynamics of Monopoles in Supersymmetric Yang-Mills Theories
with Hypermultiplets: We derive the low energy dynamics of monopoles and dyons in N=2
supersymmetric Yang-Mills theories with hypermultiplets in arbitrary
representations by utilizing a collective coordinate expansion. We consider the
most general case that Higgs fields both in the vector multiplet and in the
hypermultiplets have nonzero vacuum expectation values. The resulting theory is
a supersymmetric quantum mechanics which has been obtained by a nontrivial
dimensional reduction of two-dimensional (4,0) supersymmetric sigma models with
potentials.
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Viability of f(R) Theories with Additional Powers of Curvature: We consider a modified gravity theory, f(R)=R-a/R^n+bR^m, in the metric
formulation, which has been suggested to produce late time acceleration in the
Universe, whilst satisfying local fifth-force constraints. We investigate the
parameter range for this theory, considering the regimes of early and late-time
acceleration, Big Bang Nucleosynthesis and fifth-force constraints. We conclude
that it is difficult to find a unique range of parameters for consistency of
this theory.
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Consistent truncation of eleven-dimensional supergravity on $S^8\times
S^1$: Eleven-dimensional supergravity on $S^8\times S^1$ is conjectured to be dual
to the M-theory matrix model. We prove that the dynamics of a subset of
fluctuations around this background is consistently described by D=2 SO(9)
gauged maximal supergravity. We provide the full non-linear uplift formulae for
all bosonic fields. We also present a further truncation to the
SO(3)$\times$SO(6) invariant sector and discuss its relation to the BMN matrix
model at finite temperature. The construction relies on the framework of
generalised Scherk-Schwarz reductions, established for E$_9$ exceptional field
theory in a companion paper. As a by-product, we severely constrain the most
general gauge deformations in D=2 admitting an uplift to higher dimensions.
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Scaling in quantum gravity: The 2-point function is the natural object in quantum gravity for extracting
critical behavior: The exponential fall off of the 2-point function with
geodesic distance determines the fractal dimension $d_H$ of space-time. The
integral of the 2-point function determines the entropy exponent $\gamma$, i.e.
the fractal structure related to baby universes, while the short distance
behavior of the 2-point function connects $\gamma$ and $d_H$ by a quantum
gravity version of Fisher's scaling relation. We verify this behavior in the
case of 2d gravity by explicit calculation.
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Supersymmetry and non-Abelian T-duality in type II supergravity: We study the effect of T-duality on supersymmetry in the context of type II
supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we
demonstrate that the supersymmetry variations after T-duality are related to
the variations before T-duality through the Kosmann spinorial Lie derivative,
which vanishes when the Killing spinors are independent of the T-duality
directions. As a byproduct of our analysis, we present closed expressions for
SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and
comment on specific examples of T-dual geometries, including a novel AdS3
geometry with large N = (0,4) superconformal symmetry.
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Noncommutative Solitons on Orbifolds: In the noncommutative field theory of open strings in a B-field, D-branes
arise as solitons described as projection operators or partial isometries in a
$C^*$ algebra. We discuss how D-branes on orbifolds fit naturally into this
algebraic framework, through the examples of $R^n/G$, $T^n=R^n/Z^n$, and
$T^n/G$. We also propose a framework for formulating D-branes on asymmetric
orbifolds.
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Critical Wilson Lines in Toroidal Compactifications of Heteroric Strings: Critical values of Wilson lines and general background fields for toroidal
compactifications of heterotic string theories are constructed systematically
using Dynkin diagrams.
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Warped Resolved L^{a,b,c} Cones: We construct supergravity solutions describing a stack of D3-branes localized
at a point on a blown-up cycle of a resolved L^{a,b,c} cone. The geometry flows
from AdS_5 x L^{a,b,c} to AdS_5 x S^5/Z_k. The corresponding quiver gauge
theory undergoes an RG flow between two superconformal fixed points, which
leads to semi-infinite chains of flows between the various L^{a,b,c} fixed
points. The general system is described by a triplet of Heun equations which
can each be solved by an expansion with a three-term recursion relation, though
there are closed-form solutions for certain cases. This enables us to read off
the operators which acquire non-zero vacuum expectation values as the quiver
gauge theory flows away from a fixed point.
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An Implication of "Gravity as the Weakest Force": The negative specific heat of a radiating black hole is indicative of a
cataclysmic endpoint to the evaporation process. In this letter, we suggest a
simple mechanism for circumventing such a dramatic outcome. The basis for our
argument is a conjecture that was recently proposed by Arkani-Hamed and
collaborators. To put it another way, we use their notion of ``Gravity as the
Weakest Force'' as a means of inhibiting the process of black hole evaporation.
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String theory as a diffusing system: Recent results on the effective non-local dynamics of the tachyon mode of
open string field theory (OSFT) show that approximate solutions can be
constructed which obey the diffusion equation. We argue that this structure is
inherited from the full theory, where it admits a universal formulation. In
fact, all known exact OSFT solutions are superpositions of diffusing surface
states. In particular, the diffusion equation is a spacetime manifestation of
OSFT gauge symmetries.
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Cosmic censorship in Lovelock theory: In analyzing maximally symmetric Lovelock black holes with non-planar horizon
topologies, many novel features have been observed. The existence of finite
radius singularities, a mass gap in the black hole spectrum and solutions
displaying multiple horizons are noteworthy examples. Naively, in all these
cases, the appearance of naked singularities seems unavoidable, leading to the
question of whether these theories are consistent gravity theories. We address
this question and show that whenever the cosmic censorship conjecture is
threaten, an instability generically shows up driving the system to a new
configuration with presumably no naked singularities. Also, the same kind of
instability shows up in the process of spherical black holes evaporation in
these theories, suggesting a new phase for their decay. We find circumstantial
evidence indicating that, contrary to many claims in the literature, the cosmic
censorship hypothesis holds in Lovelock theory.
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Higgs Mass and Noncommutative Geometry: We show that the description of the electroweak interactions based on
noncommutative geometry of a continuous and a discrete space gives no special
relations between the Higgs mass and other parameters of the model. We prove
that there exists a gauge invariant term, linear in the curvature, which is
trivial in the standard differential geometry but nontrivial in the case of the
discrete geometry. The relations could appear only if one neglects this term,
otherwise one gets the Lagrangian of the Standard model with the exact number
of free parameters.
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Q-operators, Yangian invariance and the quantum inverse scattering
method: Inspired by the integrable structures appearing in weakly coupled planar N=4
super Yang-Mills theory, we study Q-operators and Yangian invariants of
rational integrable spin chains. We review the quantum inverse scattering
method along with the Yang-Baxter equation which is the key relation in this
systematic approach to study integrable models. Our main interest concerns
rational integrable spin chains and lattice models. We recall the relation
among them and how they can be solved using Bethe ansatz methods incorporating
so-called Q-functions. In order to remind the reader how the Yangian emerges in
this context, an overview of its so-called RTT-realization is provided. The
main part is based on the author's original publications. Firstly, we construct
Q-operators whose eigenvalues yield the Q-functions for rational homogeneous
spin chains. The Q-operators are introduced as traces over certain monodromies
of R-operators. Our construction allows us to derive the hierarchy of commuting
Q-operators and the functional relations among them. We study how the
nearest-neighbor Hamiltonian and in principle also higher local charges can be
extracted from the Q-operators directly. Secondly, we formulate the Yangian
invariance condition, also studied in relation to scattering amplitudes of N=4
super Yang-Mills theory, in the RTT-realization. We find that Yangian
invariants can be interpreted as special eigenvectors of certain inhomogeneous
spin chains. This allows us to apply the algebraic Bethe ansatz and derive the
corresponding Bethe equations that are relevant to construct the invariants. We
examine the connection between the Yangian invariant spin chain eigenstates
whose components can be understood as partition functions of certain 2d lattice
models and tree-level scattering amplitudes of the four-dimensional gauge
theory. Finally, we conclude and discuss some future directions.
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An extended model for monopole catalysis of nucleon decay: A new model for monopole catalysis of nucleon decay is proposed. Unlike in
the earlier one, the only light fields in this model are the photon and Skyrme
(pion) field. The model admits the 't Hooft- Polyakov monopole and Skyrmion as
classical solutions, while baryon number non-conservation occurs through an
anomaly involving an intermediate mass axial vector field resembling W- and
Z-bosons. By considering spherically symmetric monopole-Skyrmion
configurations, we find that the Skyrmion looses essentially all its mass when
interacting with the monopole, which is phenomenologically identical to the
monopole catalysis of nucleon decay. Short-distance monopole-Skyrmion physics
in this model is interesting too, as there exist almost degenerate metastable
monopole-Skyrmion bound states separated by substantial energy barriers. Yet
the heights of the latter are much smaller than the physical nucleon mass, so
the complete disappearance of the normal undeformed Skyrmion remains perfectly
possible in Skyrmion-monopole scattering.
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Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes: We study 1-loop MHV amplitudes in N=4 super Yang-Mills theory and in N=8
supergravity. For Yang-Mills we find that the simple form for the full
amplitude presented by Del Duca, Dixon and Maltoni naturally leads to one that
has physical residues on all compact contours. After expanding the simple form
in terms of standard scalar integrals, we introduce redundancies under certain
symmetry considerations to impose the color-kinematics duality of Bern,
Carrasco and Johansson (BCJ). For five particles we directly find the results
of Carrasco and Johansson as well as a new compact form for the supergravity
amplitude. For six particles we find that all kinematic dual Jacobi identities
are encapsulated in a single functional equation relating the expansion
coefficients. By the BCJ double-copy construction we obtain a formula for the
corresponding N=8 supergravity amplitude. Quite surprisingly, all physical
information becomes independent of the expansion coefficients modulo the
functional equation. In other words, there is no need to solve the functional
equation at all. This is quite welcome as the functional equation we find,
using our restricted set of redundancies, actually has no solutions. For this
reason we call these results virtual color-kinematics duality. We end with
speculations about the meaning of an interesting global vs. local feature of
the functional equation and the situation at higher points.
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Gravitational Lorentz Violation and Superluminality via AdS/CFT Duality: A weak quantum mechanical coupling is constructed permitting superluminal
communication within a preferred region of a gravitating AdS_5 spacetime. This
is achieved by adding a spatially non-local perturbation of a special kind to
the Hamiltonian of a four-dimensional conformal field theory with a
weakly-coupled AdS dual, such as maximally supersymmetric Yang-Mills theory. In
particular, two issues are given careful treatment: (1) the UV-completeness of
our deformed CFT, guaranteeing the existence of a ``deformed string theory''
AdS dual, and (2) the demonstration that superluminal effects can take place in
AdS, both on its boundary as well as in the bulk. Exotic Lorentz-violating
properties such as these may have implications for tests of General Relativity,
addressing the cosmological constant problem, or probing "behind'' horizons.
Our construction may give insight into the interpretation of wormhole solutions
in Euclidean AdS gravity.
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Complex instantons in sigma models with chemical potential: We analyze two-dimensional nonlinear sigma models at nonzero chemical
potentials, which are governed by a complex action. In the spirit of contour
deformations (thimbles) we extend the fields into the complex plane, which
allows to incorporate the chemical potentials mu as twisted boundary
conditions. We write down the equations of motion and find exact BPS-like
solutions in terms of pairs of (anti)holomorphic functions, in particular
generalizations of unit charge and fractional instantons to generic mu. The
decay of these solutions is controled by the imaginary part of mu and a
vanishing imaginary part causes jumps in the action. We analyze how the total
charge is distributed into localized objects and to what extent these are
characterized by topology.
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A universal conformal field theory approach to the chiral persistent
currents in the mesoscopic fractional quantum Hall states: We propose a general and compact scheme for the computation of the periods
and amplitudes of the chiral persistent currents, magnetizations and magnetic
susceptibilities in mesoscopic fractional quantum Hall disk samples threaded by
Aharonov--Bohm magnetic field. This universal approach uses the effective
conformal field theory for the edge states in the quantum Hall effect to derive
explicit formulas for the corresponding partition functions in presence of
flux. We point out the crucial role of a special invariance condition for the
partition function, following from the Bloch-Byers-Yang theorem, which
represents the Laughlin spectral flow. As an example we apply this procedure to
the Z_k parafermion Hall states and show that they have universal non-Fermi
liquid behavior without anomalous oscillations. For the analysis of the
high-temperature asymptotics of the persistent currents in the parafermion
states we derive the modular S-matrices constructed from the S matrices for the
u(1) sector and that for the neutral parafermion sector which is realized as a
diagonal affine coset.
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Chiral anomaly induces superconducting baryon crystal: It was previously shown within chiral perturbation theory that the ground
state of QCD in a sufficiently large magnetic field and at nonvanishing, but
not too large, baryon chemical potential is a so-called chiral soliton lattice.
The crucial ingredient of this observation was the chiral anomaly in the form
of a Wess-Zumino-Witten term, which couples the baryon chemical potential to
the magnetic field and the gradient of the neutral pion field. It was also
shown that the chiral soliton lattice becomes unstable towards charged pion
condensation at larger magnetic fields. We point out that this instability
bears a striking resemblance to the second critical magnetic field of a type-II
superconductor, however with the superconducting phase appearing upon
increasing the magnetic field. The resulting phase has a periodically varying
charged pion condensate that coexists with a neutral pion supercurrent. We
construct this phase analytically in the chiral limit and show that it is
energetically preferred. Just like an ordinary type-II superconductor, it
exhibits a hexagonal array of magnetic flux tubes, and, due to the chiral
anomaly, a spatially oscillating baryon number of the same crystalline
structure.
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The orthogonality relations for the supergroup $U(m|n)$: Starting from the generalization of the Itzykson-Zuber integral for $U(m|n)$
we determine the orthogonality relations for this supergroup.
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On perturbative instability of Pope-Warner solutions on Sasaki-Einstein
manifolds: Given a Sasaki-Einstein manifold, M_7, there is the N=2 supersymmetric AdS_4
x M_7 Freund-Rubin solution of eleven-dimensional supergravity and the
corresponding non-supersymmetric solutions: the perturbatively stable
skew-whiffed solution, the perturbatively unstable Englert solution, and the
Pope-Warner solution, which is known to be perturbatively unstable when M_7 is
the seven-sphere or, more generally, a tri-Sasakian manifold. We show that
similar perturbative instability of the Pope-Warner solution will arise for any
Sasaki-Einstein manifold, M_7, admitting a basic, primitive, transverse
(1,1)-eigenform of the Hodge-de Rham Laplacian with the eigenvalue in the range
between 2(9-4\sqrt 3) and 2(9+4\sqrt 3). Existence of such (1,1)-forms on all
homogeneous Sasaki-Einstein manifolds can be shown explicitly using the Kahler
quotient construction or the standard harmonic expansion. The latter shows that
the instability arises from the coupling between the Pope-Warner background and
Kaluza-Klein scalar modes that at the supersymmetric point lie in a long
Z-vector supermultiplet. We also verify that the instability persists for the
orbifolds of homogeneous Sasaki-Einstein manifolds that have been discussed
recently.
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Effective action of three-dimensional extended supersymmetric matter on
gauge superfield background: We study the low-energy effective actions for gauge superfields induced by
quantum N=2 and N=4 supersymmetric matter fields in three-dimensional Minkowski
space. Analyzing the superconformal invariants in the N=2 superspace we propose
a general form of the N=2 gauge invariant and superconformal effective action.
The leading terms in this action are fixed by the symmetry up to the
coefficients while the higher order terms with respect to the Maxwell field
strength are found up to one arbitrary function of quasi-primary N=2
superfields constructed from the superfield strength and its covariant spinor
derivatives. Then we find this function and the coefficients by direct quantum
computations in the N=2 superspace. The effective action of N=4 gauge multiplet
is obtained by generalizing the N=2 effective action.
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On the Problem of Extended Special Relativity Creation: This paper presents an approach to the creation of a variant of Extended
Special Relativity that takes into consideration the existence of limiting
relativistically invariant quantities (Planck parameters). It shows the
possibility of excluding unphysical predictions of relativity theories thanks
to the use of the concept of the maximum velocity of the observed motion of
objects. It proposes a model of a vacuum-like medium with a kinematical
property of relativistically invariant rest. The Planck quantities are
considered as fundamental physical constants related to the structure of this
medium.
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$\mathcal{N}=3$ conformal superspace in four dimensions: We develop a superspace formulation for ${\cal N}=3$ conformal supergravity
in four spacetime dimensions as a gauge theory of the superconformal group
$\mathsf{SU}(2,2|3)$. Upon imposing certain covariant constraints, the algebra
of conformally covariant derivatives $\nabla_A =
(\nabla_a,\nabla_\alpha^i,\bar{\nabla}_i^{\dot \alpha})$ is shown to be
determined in terms of a single primary chiral spinor superfield, the
super-Weyl spinor $W_\alpha$ of dimension $+1/2$ and its conjugate. Associated
with $W_\alpha$ is its primary descendant $B^i{}_j$ of dimension $+2$, the
super-Bach tensor, which determines the equation of motion for conformal
supergravity. As an application of this construction, we present two different
but equivalent action principles for ${\cal N}=3$ conformal supergravity. We
describe the model for linearised $\mathcal{N}=3$ conformal supergravity in an
arbitrary conformally flat background and demonstrate that it possesses
$\mathsf{U}(1)$ duality invariance. Additionally, upon degauging certain local
symmetries, our superspace geometry is shown to reduce to the $\mathsf{U}(3)$
superspace constructed by Howe more than four decades ago. Further degauging
proves to lead to a new superspace formalism, called $\mathsf{SU}(3) $
superspace, which can also be used to describe ${\mathcal N}=3$ conformal
supergravity. Our conformal superspace setting opens up the possibility to
formulate the dynamics of the off-shell ${\mathcal N}=3$ super Yang-Mills
theory coupled to conformal supergravity.
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Exponential fall-off Behavior of Regge Scatterings in Compactified Open
String Theory: We calculate massive string scattering amplitudes of compactified open string
in the Regge regime. We extract the complete infinite ratios among high-energy
amplitudes of different string states in the fixed angle regime from these
Regge string scattering amplitudes. The complete ratios calculated by this
indirect method include and extend the subset of ratios calculated previously
(Lee and Yang, 2007, and Lee, Takimi, and Yang, 2008) by the more difficult
direct fixed angle calculation. In this calculation of compactified open string
scattering, we discover a realization of arbitrary real values L in the
identity Eq.(4.18), rather than integer value only in all previous high-energy
string scattering amplitude calculations. The identity in Eq.(4.18) was
explicitly proved recently in Lee, Yan, and Yang to link fixed angle and Regge
string scattering amplitudes. In addition, we discover a kinematic regime with
stringy highly winding modes, which shows the unusual exponential fall-off
behavior in the Regge string scattering. This is in complementary with a
kenematic regime discovered previously (Lee, Takimi, and Yang, 2008), which
shows the unusual power-law behavior in the high-energy fixed angle
compactified string scatterings. Key words: Regge string scatterings;
High-energy String
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The String Worldsheet as the Holographic Dual of SYK State: Recent studies of the fluctuations of an open string in AdS space show some
pieces of evidence that the string with a worldsheet horizon could be a dual
description of SYK model, as they saturate universal chaos bound and share the
same symmetry. An open string hangs from the AdS boundary to the horizon of
black brane could be dual to a 0+1 dimensional boundary state. To be specific,
we find that the fluctuation of the string in charged BTZ black hole has an
asymptotic scaling symmetry, and its Euclidean IR fixed point is governed by
the quadratic order of Schwarzian action, which is just the low energy
effective theory of the SYK model. Considering the open string worldsheet also
has natural reparametrization symmetry, we conjecture that the action of the
string worldsheet is a dual description of SYK state.
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Holographic Conductivity for Logarithmic Charged Dilaton-Lifshitz
Solutions: We disclose the effects of the logarithmic nonlinear electrodynamics on the
holographic conductivity of Lifshitz dilaton black holes/branes. We analyze
thermodynamics of these solutions as a necessary requirement for applying
gauge/gravity duality, by calculating conserved and thermodynamic quantities
such as the temperature, entropy, electric potential and mass of the black
holes/branes. We calculate the holographic conductivity for a
$(2+1)$-dimensional brane boundary and study its behavior in terms of the
frequency per temperature. Interestingly enough, we find out that, in contrast
to the Lifshitz-Maxwell-dilaton black branes which has conductivity for all
$z$, here in the presence of nonlinear gauge field, the holographic
conductivity do exist provided $z\leq3$ and vanishes for $z>3$. It is shown
that independent of the nonlinear parameter $\beta$, the real part of the
conductivity is the same for a specific value of frequency per temperature in
both AdS and Lifshitz cases. Besides, the behavior of real part of conductivity
for large frequencies has a positive slope with respect to large frequencies
for a system with Lifshitz symmetry whereas it tends to a constant for a system
with AdS symmetry. This behavior may be interpreted as existence of an
additional charge carrier rather than the AdS case, and is due to the presence
of the scalar dilaton field in model. Similar behavior for optical conductivity
of single-layer graphene induced by mild oxygen plasma exposure has been
reported.
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Vacuum polarization in Schwarzschild space-time by anomaly induced
effective actions: The characteristic features of $<T_{\mu\nu}>$ in the Boulware, Unruh and
Hartle-Hawking states for a conformal massless scalar field propagating in the
Schwarzschild space-time are obtained by means of effective actions deduced by
the trace anomaly. The actions are made local by the introduction of auxiliary
fields and boundary conditions are carefully imposed on them in order to select
the different quantum states.
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Black Holes and Attractors in Supergravity: We discuss some of the basic features of extremal black holes in
four-dimensional extended supergravities. Firstly, all regular solutions
display an attractor behavior for the scalar field evolution towards the black
hole horizon. Secondly, they can be obtained by solving first order flow
equations even when they are not supersymmetric, provided one identifies a
suitable superpotential W which also gives the black hole entropy at the
horizon and its ADM mass at spatial infinity. We focus on N=8 supergravity and
we review the basic role played by U-duality of the underlying supergravity in
determining the attractors, their entropies, their masses and in classifying
both regular and singular extremal black holes.
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Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons
Theory on Torus Bundles: We study the relations between two-dimensional Yang-Mills theory on the
torus, topological string theory on a Calabi-Yau threefold whose local geometry
is the sum of two line bundles over the torus, and Chern-Simons theory on torus
bundles. The chiral partition function of the Yang-Mills gauge theory in the
large N limit is shown to coincide with the topological string amplitude
computed by topological vertex techniques. We use Yang-Mills theory as an
efficient tool for the computation of Gromov-Witten invariants and derive
explicitly their relation with Hurwitz numbers of the torus. We calculate the
Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation
of the conjectured nonperturbative relation between two-dimensional Yang-Mills
theory and topological string theory. We also demonstrate how the gauge theory
leads to a simple combinatorial solution for the Donaldson-Thomas theory of the
Calabi-Yau background. We match the instanton representation of Yang-Mills
theory on the torus with the nonabelian localization of Chern-Simons gauge
theory on torus bundles over the circle. We also comment on how these results
can be applied to the computation of exact degeneracies of BPS black holes in
the local Calabi-Yau background.
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Diffeomorphism-invariant observables and their nonlocal algebra: Gauge-invariant observables for quantum gravity are described, with explicit
constructions given primarily to leading order in Newton's constant, analogous
to and extending constructions first given by Dirac in quantum electrodynamics.
These can be thought of as operators that create a particle, together with its
inseparable gravitational field, and reduce to usual field operators of quantum
field theory in the weak-gravity limit; they include both Wilson-line
operators, and those creating a Coulombic field configuration. We also describe
operators creating the field of a particle in motion; as in the electromagnetic
case, these are expected to help address infrared problems. An important
characteristic of the quantum theory of gravity is the algebra of its
observables. We show that the commutators of the simple observables of this
paper are nonlocal, with nonlocality becoming significant in strong field
regions, as predicted previously on general grounds.
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Electric-Magnetic Duality, Matrices, & Emergent Spacetime: This is a rough transcript of talks given at the Workshop on Groups &
Algebras in M Theory at Rutgers University, May 31--Jun 04, 2005. We review the
basic motivation for a pre-geometric formulation of nonperturbative String/M
theory, and for an underlying eleven-dimensional electric-magnetic duality,
based on our current understanding of the String/M Duality Web. We explain the
concept of an emerging spacetime geometry in the large N limit of a U(N) flavor
matrix Lagrangian, distinguishing our proposal from generic proposals for
quantum geometry, and explaining why it can incorporate curved spacetime
backgrounds. We assess the significance of the extended symmetry algebra of the
matrix Lagrangian, raising the question of whether our goal should be a duality
covariant, or merely duality invariant, Lagrangian. We explain the conjectured
isomorphism between the O(1/N) corrections in any given large N scaling limit
of the matrix Lagrangian, and the corresponding alpha' corrections in a string
effective Lagrangian describing some weak-coupling limit of the String/M
Duality Web.
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Late-time cosmology in (phantom) scalar-tensor theory: dark energy and
the cosmic speed-up: We consider late-time cosmology in a (phantom) scalar-tensor theory with an
exponential potential, as a dark energy model with equation of state parameter
close to -1 (a bit above or below this value). Scalar (and also other kinds of)
matter can be easily taken into account. An exact spatially-flat FRW cosmology
is constructed for such theory, which admits (eternal or transient)
acceleration phases for the current universe, in correspondence with
observational results. Some remarks on the possible origin of the phantom,
starting from a more fundamental theory, are also made. It is shown that
quantum gravity effects may prevent (or, at least, delay or soften) the cosmic
doomsday catastrophe associated with the phantom, i.e. the otherwise
unavoidable finite-time future singularity (Big Rip). A novel dark energy model
(higher-derivative scalar-tensor theory) is introduced and it is shown to admit
an effective phantom/quintessence description with a transient acceleration
phase. In this case, gravity favors that an initially insignificant portion of
dark energy becomes dominant over the standard matter/radiation components in
the evolution process.
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The Relation Between KMOC and Worldline Formalisms for Classical Gravity: We demonstrate the equivalence between KMOC and worldline formalisms for
classical general relativity, highlighting how the Keldysh-Schwinger in-in
formalism is contained in both of them even though the KMOC representation
conventionally leads to the evaluation of scattering amplitudes with Feynman
propagators. The relationship between the two approaches is illustrated in
detail for the momentum kick at second Post-Minkowskian order.
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Instantons, Fermions and Chern-Simons Terms: In five spacetime dimensions, instantons are finite energy, solitonic
particles. We describe the dynamics of these objects in the presence of a
Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons
term induces a corresponding Chern-Simons term in the ADHM quantum mechanics.
For SU(N) instantons, we provide a description in terms of geodesic motion on
the instanton moduli space, modified by the presence of a magnetic field. We
show that this magnetic field is equal to the first Chern character of an index
bundle. All of these results are derived by a simple method which follows the
fate of zero modes as fermions are introduced, made heavy, and subsequently
integrated out.
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Perturbation expansions at large order: Results for scalar field
theories revisited: The question of the asymptotic form of the perturbation expansion in scalar
field theories is reconsidered. Renewed interest in the computation of terms in
the epsilon-expansion, used to calculate critical exponents, has been
frustrated by the differing and incompatible results for the high-order
behaviour of the perturbation expansion reported in the literature. We identify
the sources of the errors made in earlier papers, correct them, and obtain a
consistent set of results. We focus on phi^4 theory, since this has been the
most studied and is the most widely used, but we also briefly discuss analogous
results for phi^N theory, with N>4. This reexamination of the structure of
perturbation expansions raises issues concerning the renormalisation of
non-perturbative effects and the nature of the Feynman diagrams at large order,
which we discuss.
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(Non-)Abelian Gauged Supergravities in Nine Dimensions: We construct five different two-parameter massive deformations of the unique
nine-dimensional N=2 supergravity. All of these deformations have a
higher-dimensional origin via Scherk-Schwarz reduction and correspond to gauged
supergravities. The gauge groups we encounter are SO(2), SO(1,1)^+, R, R^+ and
the two-dimensional non-Abelian Lie group A(1), which consists of scalings and
translations in one dimension.
We make a systematic search for half-supersymmetric domain walls and
non-supersymmetric de Sitter space solutions. Furthermore, we discuss in which
sense the supergravities we have constructed can be considered as low-energy
limits of compactified superstring theory.
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Hamilton's equations in a non-associative quantum theory: A new non-associative algebra for the quantization of strongly interacting
fields is proposed. The full set of quantum $(\pm)$associators for the product
of three operators is offered. An algorithm for the calculation of some
$(\pm)$associators for the product of some four operators is offered. The
possible generalization of Hamilton's equations for a non-associative quantum
theory is proposed. Some arguments are given that a non-associative quantum
theory can be a fundamental unifying theory.
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The Problem of Large-N Phase Transition in Kazakov-Migdal Model of
Induced QCD: We study the lattice gauge model proposed recently by Kazakov and Migdal for
inducing QCD. We discuss an extra local Z_N which is a symmetry of the model
and propose of how to construct observables. We discuss the role of the large-N
phase transition which should occur before the one associated with the
continuum limit in order that the model describes continuum QCD. We formulate
the mean field approach to study the large-N phase transition for an arbitrary
potential and show that no first order phase transition occurs for the
quadratic potential.
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The Hamiltonian Approach to Yang-Mills (2+1): An Update and Corrections
to String Tension: Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial
gauge theories in their own right and as effective theories of QCD at high
temperatures. I shall review the basics of our Hamiltonian approach to this
theory, emphasizing symmetries with a short update on its status. We will show
that the calculation of the vacuum wave function for Yang-Mills theory in 2+1
dimensions is in the lowest order of a systematic expansion. Expectation values
of observables can be calculated using an effective interacting chiral boson
theory, which also leads to a natural expansion as a double series in the
coupling constant (to be interpreted within a resummed perturbation series) and
a particular kinematical factor. The calculation of the first set of
corrections in this expansion shows that the string tension is modified by
about -0.3% to -2.8% compared to the lowest order value. This is in good
agreement with lattice estimates.
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Koopman-von Neumann Formulation of Classical Yang-Mills Theories: I: In this paper we present the Koopman-von Neumann (KvN) formulation of
classical non-Abelian gauge field theories. In particular we shall explore the
functional (or classical path integral) counterpart of the KvN method. In the
quantum path integral quantization of Yang-Mills theories concepts like
gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We
will prove that these same objects are needed also in this classical path
integral formulation for Yang-Mills theories. We shall also explore the
classical path integral counterpart of the BFV formalism and build all the
associated universal and gauge charges. These last are quite different from the
analog quantum ones and we shall show the relation between the two. This paper
lays the foundation of this formalism which, due to the many auxiliary fields
present, is rather heavy. Applications to specific topics outlined in the paper
will appear in later publications.
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Cosmological consequences of a principle of finite amplitudes: Over 30 years ago, Barrow & Tipler proposed the principle according to which
the action integrated over the entire 4-manifold describing the universe should
be finite. Here we explore the cosmological consequences of a related
criterion, namely that semi-classical transition amplitudes from the early
universe up to current field values should be well defined. On a classical
level, our criterion is weaker than the Barrow-Tipler principle, but it has the
advantage of being sensitive to quantum effects. We find significant
consequences for early universe models, in particular: eternal inflation and
strictly cyclic universes are ruled out. Within general relativity, the first
phase of evolution cannot be inflationary, and it can be ekpyrotic only if the
scalar field potential is trustworthy over an infinite field range. Quadratic
gravity eliminates all non-accelerating backgrounds near a putative big bang
(thus imposing favourable initial conditions for inflation), while the expected
infinite series of higher-curvature quantum corrections eliminates Lorentzian
big bang spacetimes altogether. The scenarios that work best with the principle
of finite amplitudes are the no-boundary proposal, which gives finite
amplitudes in all dynamical theories that we have studied, and string-inspired
loitering phases. We also comment on the relationship of our proposal to the
swampland conjectures.
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On Perturbative Quantum Gravity with a Cosmological Constant: We discuss how the incorporation of a cosmological constant affects the
perturbative quantization of (effective) Quantum General Relativity. To this
end, we derive the gravitational Slavnov--Taylor identities and appropriate
renormalization conditions for the cosmological constant. Additionally, we
calculate the corresponding Feynman rules for any vertex valence and with
general gauge parameter. Furthermore, we provide the BRST setup and generate
the Faddeev--Popov ghost and the symmetric ghost via a gauge fixing fermion and
a gauge fixing boson, respectively. Finally, we study the transversality of the
graviton propagator and the graviton three-valent vertex.
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Integral representations of thermodynamic 1PI Green functions in the
world-line formalism: The issue discussed is a thermodynamic version of the Bern-Kosower master
amplitude formula, which contains all necessary one-loop Feynman diagrams. It
is demonstrated how the master amplitude at finite values of temperature and
chemical potential can be formulated within the framework of the world-line
formalism. In particular we present an elegant method how to introduce a
chemical potential for a loop in the master formula. Various useful integral
formulae for the master amplitude are then obtained. The non-analytic property
of the master formula is also derived in the zero temperature limit with the
value of chemical potential kept finite.
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Stochastic trailing string and Langevin dynamics from AdS/CFT: Using the gauge/string duality, we derive a set of Langevin equations
describing the dynamics of a relativistic heavy quark moving with constant
average speed through the strongly-coupled N=4 SYM plasma at finite
temperature. We show that the stochasticity arises at the string world-sheet
horizon, and thus is causally disconnected from the black hole horizon in the
space-time metric. This hints at the non-thermal nature of the fluctuations, as
further supported by the fact that the noise term and the drag force in the
Langevin equations do not obey the Einstein relation. We propose a physical
picture for the dynamics of the heavy quark in which dissipation and
fluctuations are interpreted as medium-induced radiation and the associated
quantum-mechanical fluctuations. This picture provides the right parametric
estimates for the drag force and the (longitudinal and transverse) momentum
broadening coefficients.
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Graviton correlator and metric perturbations in de Sitter brane-world: We consider de Sitter brane-world motivated by dS/CFT correspondence where
both bulk and brane are de Sitter spaces. The brane tension is fixed by
holographic RG. The 4d effective action for metric perturbations and 4d
graviton correlator are explicitly found. The induced values of cosmological
and Newton constants are calculated. The short distance behaviour of the
graviton correlator (when no brane matter presents) turns out to be
significally stronger than in the case of General Relativity. It is shown that
quantum brane CFT gives the dominant contribution to graviton correlator on
small scales like in Brane New World scenario.
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Thermal CFTs in momentum space: We study some aspects of conformal field theories at finite temperature in
momentum space. We provide a formula for the Fourier transform of a thermal
conformal block and study its analytic properties. In particular we show that
the Fourier transform vanishes when the conformal dimension and spin are those
of a "double twist" operator $\Delta = 2\Delta_\phi + \ell + 2n$. By
analytically continuing to Lorentzian signature we show that the spectral
density at high spatial momenta has support on the spectrum condition $|\omega|
> |k|$. This leads to a series of sum rules. Finally, we explicitly match the
thermal block expansion with the momentum space Green's function at finite
temperature in several examples.
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Exceptional complex structures and the hypermultiplet moduli of 5d
Minkowski compactifications of M-theory: We present a detailed study of a new mathematical object in
$\mathrm{E}_{6(6)}\times \mathbb{R}^{+}$ generalised geometry called an
`exceptional complex structure' (ECS). It is the extension of a conventional
complex structure to one that includes all the degrees of freedom of M-theory
or type IIB supergravity in six or five dimensions, and as such characterises,
in part, the geometry of generic supersymmetric compactifications to
five-dimensional Minkowkski space. We define an ECS as an integrable
$\mathrm{U}^{*}(6)\times \mathbb{R}^{+}$ structure and show it is equivalent to
a particular form of involutive subbundle of the complexified generalised
tangent bundle $L_{1} \subset E_{\mathbb{C}}$. We also define a refinement, an
$\mathrm{SU}^{*}(6)$ structure, and show that its integrability requires in
addition a vanishing moment map on the space of structures. We are able to
classify all possible ECSs, showing that they are characterised by two numbers
denoted `type' and `class'. We then use the deformation theory of ECS to find
the moduli of any $\mathrm{SU}^{*}(6)$ structure. We relate these structures to
the geometry of generic minimally supersymmetric flux backgrounds of M-theory
of the form $\mathbb{R}^{4,1}\times M$, where the $\mathrm{SU}^{*}(6)$ moduli
correspond to the hypermultiplet moduli in the lower-dimensional theory. Such
geometries are of class zero or one. The former are equivalent to a choice of
(non-metric-compatible) conventional $\mathrm{SL}(3,\mathbb{C})$ structure and
strikingly have the same space of hypermultiplet moduli as the fluxless
Calabi--Yau case.
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The Chiral Heat Effect: We consider the thermal response of a (3+1)-dimensional theory with a chiral
anomaly on a curved space motivated by the chiral magnetic effect. We find a
new phenomenon, called the chiral heat effect, such that the thermal current is
induced transverse to a gradient of the temperature even on a flat space. This
effect is expected to be observed in QCD experiment as well as the chiral
magnetic effect. We study a similar topological effect on the spacetime with a
torsion. A holographic construction is also discussed with the D3/D7 and the
Sakai-Sugimoto models.
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An iterative method for spherical bounces: We develop a new iterative method for finding approximate solutions for
spherical bounces associated with the decay of the false vacuum in scalar field
theories. The method works for any generic potential in any number of
dimensions, contains Coleman's thin-wall approximation as its first iteration,
and greatly improves its accuracy by including higher order terms.
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Space-time S-matrix and Flux-tube S-matrix III. The two-particle
contributions: We consider light-like Wilson loops with hexagonal geometry in the planar
limit of N=4 Super-Yang-Mills theory. Within the Operator-Product-Expansion
framework these loops receive contributions from all states that can propagate
on top of the colour flux tube sourced by any two opposite edges of the loops.
Of particular interest are the two-particle contributions. They comprise
virtual effects like the propagation of a pair of scalars, fermions, and
gluons, on top of the flux tube. Each one of them is thoroughly discussed in
this paper. Our main result is the prediction of all the twist-2 corrections to
the expansion of the dual 6-gluons MHV amplitude in the near-collinear limit at
finite coupling. At weak coupling, our result was recently used by Dixon,
Drummond, Duhr and Pennington to predict the full amplitude at four loops. At
strong coupling, it allows us to make contact with the classical string
description and to recover the (previously elusive) AdS(3) mode from the
continuum of two-fermion states. More generally, the two-particle contributions
serve as an exemplar for all the multi-particle corrections.
|
Thermodynamics of Fuzzy Spheres in PP-wave Matrix Model: We discuss thermodynamics of fuzzy spheres in a matrix model on a pp-wave
background. The exact free energy in the fuzzy sphere vacuum is computed in the
\mu -> \infty limit for an arbitrary matrix size N. The trivial vacuum
dominates the fuzzy sphere vacuum at low temperature while the fuzzy sphere
vacuum is more stable than the trivial vacuum at sufficiently high temperature.
Our result supports that the fluctuations around the trivial vacuum would
condense to form an irreducible fuzzy sphere above a certain temperature.
|
Phase transitions in a $Φ^4$ matrix model on a curved noncommutative
space: In this contribution, we summarize our recent studies of the phase structure
of the Grosse-Wulkenhaar model and its connection to renormalizability. Its
action contains a special term that couples the field to the curvature of the
noncommutative background space. We first analyze the numerically obtained
phase diagram of the model and its three phases: the ordered, the disordered,
and the noncommutative stripe phase. Afterward, we discuss the analytical
derivation of the effective action and the ordered-to-stripe transition line,
and how the obtained expression successfully explains the curvature-induced
shift of the triple point compared to the model without curvature. This shift
also causes the removal of the stripe phase and makes the model renormalizable.
|
Worldsheet Form Factors in AdS/CFT: We formulate a set of consistency conditions appropriate to worldsheet form
factors in the massive, integrable but non-relativistic, light-cone gauge fixed
AdS(5) x S**5 string theory. We then perturbatively verify that these
conditions hold, at tree level in the near-plane-wave limit and to one loop in
the near-flat (Maldacena-Swanson) limit, for a number of specific cases. We
further study the form factors in the weakly coupled dual description,
verifying that the relevant conditions naturally hold for the one-loop
Heisenberg spin-chain. Finally, we note that the near-plane-wave expressions
for the form factors, when further expanded in small momentum or, equivalently,
large charge density, reproduce the thermodynamic limit of the spin-chain
results at leading order.
|
Particle thermalization entropy and Unruh effect: We propose the method for estimation of entropy generated during the string
breaking in high energy collisions. The approach is highly based on the ideas
proposed by Kharzeev D et al and may be useful in thermalization problem.
|
Holographic insulator/superconductor phase transition with Weyl
corrections: We analytically investigate the phase transition between the holographic
insulator and superconductor with Weyl corrections by using the variational
method for the Sturm-Liouville eigenvalue problem. We find that similar to the
curvature corrections, in p-wave model, the higher Weyl couplings make the
insulator/superconductor phase transition harder to occur. However, in s-wave
case the Weyl corrections do not influence the critical chemical potential,
which is in contrast to the effect caused by the curvature corrections.
Moreover, we observe that the Weyl corrections will not affect the critical
phenomena and the critical exponent of the system always takes the mean-field
value in both models. Our analytic results are found to be in good agreement
with the numerical findings.
|
Komar Integrals in Higher (and Lower) Derivative Gravity: The Komar integral relation of Einstein gravity is generalized to Lovelock
theories of gravity. This includes, in particular, a new boundary integral for
the Komar mass in Einstein gravity with a nonzero cosmological constant, which
has a finite result for asymptotically AdS black holes, without the need for an
infinite background subtraction. Explicit computations of the Komar mass are
given for black holes in pure Lovelock gravities of all orders and in general
Gauss-Bonnet theories.
|
Curved non-relativistic spacetimes, Newtonian gravitation and massive
matter: There is significant recent work on coupling matter to Newton-Cartan
spacetimes with the aim of investigating certain condensed matter phenomena. To
this end, one needs to have a completely general spacetime consistent with
local non-relativisitic symmetries which supports massive matter fields. In
particular, one can not impose a priori restrictions on the geometric data if
one wants to analyze matter response to a perturbed geometry. In this paper we
construct such a Bargmann spacetime in complete generality without any prior
restrictions on the fields specifying the geometry. The resulting spacetime
structure includes the familiar Newton-Cartan structure with an additional
gauge field which couples to mass. We illustrate the matter coupling with a few
examples. The general spacetime we construct also includes as a special case
the covariant description of Newtonian gravity, which has been thoroughly
investigated in previous works. We also show how our Bargmann spacetimes arise
from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion
paper [arXiv:1503.02680] we use this Bargmann spacetime structure to
investigate the details of matter couplings, including the Noether-Ward
identities, and transport phenomena and thermodynamics of non-relativistic
fluids.
|
Thermodynamics of 5D dilaton-gravity: We calculate the free energy, spatial string tension and Polyakov loop of the
gluon plasma using the dilaton potential of Ref. arXiv:0911.0627[hep-ph] in the
dilaton-gravity theory of AdS/QCD. The free energy is computed from the Black
Hole solutions of the Einstein equations in two ways: first, from the
Bekenstein-Hawking proportionality of the entropy with the area of the horizon,
and secondly from the Page-Hawking computation of the free energy. The finite
temperature behaviour of the spatial string tension and Polyakov loop follow
from the corresponding string theory in AdS_5. Comparison with lattice data is
made.
|
Lifshitz and Schrodinger Vacua, Superstar Resolution in Gauged Maximal
Supergravities: We consider the subset of gauged maximal supergravities that consists of the
SO(n+1) gauge fields A^{ij} and the scalar deformation T^{ij} of the S^n in the
spherical reduction of M-theory or type IIB. We focus on the Abelian Cartan
subgroup and the diagonal entries of T^{ij}. The resulting theories can be
viewed as the STU models with additional hyperscalars. We find that the
theories with only one or two such vectors can be generalized naturally to
arbitrary dimensions. The same is true for the D=4 or 5 Einstein-Maxwell theory
with such a hyperscalar. The gauge fields become massive, determined by
stationary points of the hyperscalars a la the analogous Abelian Higgs
mechanism. We obtain classes of Lifshitz and Schrodinger vacua in these
theories. The scaling exponent z turns out to be rather restricted, taking
fractional or irrational numbers. Tweaking the theories by relaxing the mass
parameter or making a small change of the superpotential, we find that
solutions with z=2 can emerge. In a different application, we find that the
resolution of superstar singularity in the STU models by using bubbling-AdS
solitons can be generalized to arbitrary dimensions in our theories. In
particular, we obtain the smooth AdS solitons that can be viewed as the
resolution of the Reissner-Nordstrom superstars in general dimensions.
|
Monstrous Moonshine and the uniqueness of the Moonshine module: In this talk we consider the relationship between the conjectured uniqueness
of the Moonshine module of Frenkel, Lepowsky and Meurman and Monstrous
Moonshine, the genus zero property for Thompson series discovered by Conway and
Norton. We discuss some evidence to support the uniqueness of the Moonshine
module by considering possible alternative orbifold constructions from a Leech
lattice compactified string. Within these constructions we find a new
relationship between the centralisers of the Monster group and the Conway group
generalising an observation made by Conway and Norton. We also relate the
uniqueness of the Moonshine module to Monstrous Moonshine and argue that given
this uniqueness, then the genus zero properties hold if and only if orbifolding
the Moonshine module with respect to a Monster element reproduces the Moonshine
module or the Leech theory. (Talk presented at the Nato Advanced Research
Workshop on `Low dimensional topology and quantum field theory`, Cambridge,
6-13 Sept 1992)
|
Correlators of Giant Gravitons from dual ABJ(M) Theory: We generalize the operators of ABJM theory, given by Schur polynomials, in
ABJ theory by computing the two point functions in the free field and at finite
$(N_1,N_2)$ limits. These polynomials are then identified with the states of
the dual gravity theory. Further, we compute correlators among giant gravitons
as well as between giant gravitons and ordinary gravitons through the
corresponding correlators of ABJ(M) theory. Finally, we consider a particular
non-trivial background produced by an operator with an $\cal R$-charge of
$O(N^2)$ and find, in presence of this background, due to the contribution of
the non-planar corrections, the large $(N_1,N_2)$ expansion is replaced by
$1/(N_1+M)$ and $1/(N_2+M)$ respectively.
|
Heavy Probes in Strongly Coupled Plasmas With Chemical Potential: We study the properties of heavy probes moving in strongly coupled plasmas at
finite chemical potential. Using the gauge/gravity duality we consider large
classes of gravity models consisting in deformed AdS5 spacetimes endowed with
Reissner-Nordstr\"om-type black holes. We report on our analysis of the
screening distance of a quark-antiquark pair, its free energy, and the running
coupling. These observables show a certain insensitivity as to which model and
deformation is used, pointing to strong-coupling universal behavior. Thus, the
results may be relevant for modeling heavy quarkonia traversing a quark-gluon
plasma at finite net baryon density, and their suppression by melting.
|
On the Number of Chiral Generations in Z2 X Z2 Orbifolds: The data from collider experiments and cosmic observatories indicates the
existence of three light matter generations. In some classes of string
compactifications the number of generations is related to a topological
quantity, the Euler characteristic. However, these do not explain the existence
of three generations. In a class of free fermionic string models, related to
the Z2 X Z2 orbifold compactification, the existence of three generations is
correlated with the existence of three twisted sectors in this class of
compactifications. However, the three generation models are constructed in the
free fermionic formulation and their geometrical correspondence is not readily
available. In this paper we classify quotients of the Z2 X Z2 orbifold by
additional symmetric shifts on the three complex tori. We show that three
generation vacua are not obtained in this manner, indicating that the
geometrical structures underlying the free fermionic models are more esoteric.
|
Statistical nature of Skyrme-Faddeev models in $2+1$ dimensions and
normalizable fermions: The Skyrme-Faddeev model has planar soliton solutions with target space
$\mathbb{C}P^N$. An Abelian Chern-Simons term (the Hopf term) in the Lagrangian
of the model plays a crucial role for the statistical properties of the
solutions. Because $\Pi_3(\mathbb{C}P^1)=\mathbb{Z}$, the term becomes an
integer for $N=1$. On the other hand, for $N>1$, it becomes perturbative
because $\Pi_3(\mathbb{C}P^N)$ is trivial. The prefactor $\Theta$ of the Hopf
term is not quantized, and its value depends on the physical system. We study
the spectral flow of the normalizable fermions coupled with the baby-Skyrme
model ($\mathbb{C}P^N$ Skyrme-Faddeev model). We discuss whether the
statistical nature of solitons can be explained using their constituents, i.e.,
the quarks.
|
The ground state of reduced Yang-Mills theory: For the simplest membrane matrix model (corresponding to reduced 3
dimensional SU(2) Yang Mills theory) the form of the ground state wave function
is given.
|
Stochastic growth of quantum fluctuations during inflation: The standard field-theoretical approach to the slow-roll inflation is
introduced. We then show as, in order to calculate the mean square of the
canonical gauge invariant quantum fluctuations associated to a generic field,
the logarithm of the scale factor has to be used as the time variable in the
Fokker-Planck equation in the stochastic approach. Then we compute the growth
of different test fields with a small effective mass during slow-roll
inflationary models, comparing the results with the one for the gauge invariant
canonical fluctuation associated to the inflaton, the Mukhanov variable. We
find that in most of the single fields inflationary models such fluctuation
grows faster than any test field with a non-negative effective mass, with the
exception of hybrid models.
|
Gauging Isometries on Hyperkahler Cones and Quaternion-Kahler Manifolds: We extend our previous results on the relation between quaternion-Kahler
manifolds and hyperkahler cones and we describe how isometries, moment maps and
scalar potentials descend from the cone to the quaternion-Kahler space. As an
example of the general construction, we discuss the gauging and the
corresponding scalar potential of hypermultiplets with the unitary Wolf spaces
as target spaces. This class includes the universal hypermultiplet.
|
On the Landau Background Gauge Fixing and the IR Properties of YM Green
Functions: We analyse the complete algebraic structure of the background field method
for Yang--Mills theory in the Landau gauge and show several structural
simplifications within this approach. In particular we present a new way to
study the IR behavior of Green functions in the Landau gauge and show that
there exists a unique Green function whose IR behaviour controls the IR
properties of the gluon and the ghost propagators.
|
Effective action of gauged WZW model and exact string solutions: We suggest how to derive the exact (all order in $\a'$) expressions for the
background fields for string solutions corresponding to gauged WZW models
directly at the $2d$ field theory level. One is first to replace the classical
gauged WZW action by the quantum effective one and then to integrate out the
gauge field. We find the explicit expression for the gauge invariant non-local
effective action of the gauged WZW model. The two terms (corresponding to the
group and subgroup) which appear with the same coefficients in the classical
action get different $k$-dependent coefficients in the effective one. The
procedure of integrating out the gauge field is considered in detail for the
$SL(2,R)/U(1)$ model and the exact expressions for the $D=2$ metric and the
dilaton (originally found in the conformal field theory approach) are
reproduced.
|
Wave function of the quantum black hole: We show that the Wald Noether charge entropy is canonically conjugate to the
opening angle at the horizon. Using this canonical relation we extend the
Wheeler-DeWitt equation to a Schroedinger equation in the opening angle,
following Carlip and Teitelboim. We solve the equation in the semiclassical
approximation by using the correspondence principle and find that the solutions
are minimal uncertainty wavefunctions with a continuous spectrum for the
entropy and therefore also of the area of the black hole horizon. The fact that
the opening angle fluctuates away from its classical value of 2 pi indicates
that the quantum black hole is a superposition of horizonless states. The
classical geometry with a horizon serves only to evaluate quantum expectation
values in the strict classical limit.
|
Dirac Equation in $κ$-Minkowski space-time: In this paper, we derive the Dirac equation in the $\kappa$-deformed
Minkowski space-time. We start with $\kappa$-deformed Minkowski space-time and
investigate the undeformed $\kappa$-Lorentz transformation valid to all order
in the deformation parameter $a$. Using the undeformed $\kappa$-Lorentz
algebra, we obtain the $\kappa$-deformed Dirac equation, valid to all order in
the deformation parameter $a$. In limit $a\rightarrow$0, we get back the
correct commutative result.
|
Colour-Twist Operators I: Spectrum and Wave Functions: We introduce a new class of operators in any theory with a 't Hooft large-$N$
limit that we call colour-twist operators. They are defined by twisting the
colour-trace with a global symmetry transformation and are continuously linked
to standard, un-twisted single-trace operators. In particular, correlation
functions between operators that are twisted by an R-symmetry of ${\cal N}=4$
SYM extend those in the $\gamma$-deformed theory. The most general deformation
also breaks the Lorentz symmetry but preserves integrability in the examples we
consider. In this paper, we focus on colour-twist operators in the fishnet
model. We exemplify our approach for the simplest colour-twist operators with
one and two scalar fields, which we study non-perturbatively using
field-theoretical as well as integrability methods, finding a perfect match. We
also propose the quantisation condition for the Baxter equation appearing in
the integrability calculation in the fishnet model. The results of this paper
constitute a crucial step towards building the separation of variable
construction for the correlation functions by means of the Quantum Spectral
Curve approach.
|
Universal Mass Scale for Bosonic Fields in Multi-Brane Worlds: In this paper we find an universal mass scale for all $p-$forms in
multi-brane worlds model. It is a known fact the this model provides an
ultralight mode for the fields. However, to get this, the Lagrangians
considered in the literature are not covariant. In order to solve this, we
propose a covariant version to multi-localize $q-$form fields. As a consequence
of the covariance, we show that all the $q$-form fields have an ultralight mode
with the same mass that the gravitational one. That way we show that there is
an universal mass scale for the ultralight modes of the bosonic fields. This
suggests that a new physics must emerge, for all theses fields, at the same
scale. After that, we revisit the results that consider a crystal manyfold
background in the Randall-Sundrum scenary (RS), and add the discussion related
to geometrical couplings in such a configuration. The wave functions of fields
trapped in the crystal are Bloch-like waves, and their behavior is very similar
to electrons inside a lattice, just like in the Kronig-Penney model (KP). We
compute the mass dispersion relations for those fields with and without a
dilaton coupling. It leads to new results for the band gap structure of these
fields. In the case of the Kalb-Ramond field, and with the correct dispersion
relation, there is no gap between the mass bands. Also, always that the field
is coupled with the dilaton, its first mass mode decreases. When the
generalization to the $q-$form is done, we show that it is not possible to
suppress or generate mass for the fields by controlling the dilaton coupling,
differently of what was argued previously.
|
The holographic dark energy in non-flat Brans-Dicke cosmology: In this paper we study cosmological application of holographic dark energy
density in the Brans-Dicke framework. We employ the holographic model of dark
energy to obtain the equation of state for the holographic energy density in
non-flat (closed) universe enclosed by the event horizon measured from the
sphere of horizon named $L$. Our calculation show, taking
$\Omega_{\Lambda}=0.73$ for the present time, the lower bound of $w_{\rm
\Lambda}$ is -0.9. Therefore it is impossible to have $w_{\rm \Lambda}$
crossing -1. This implies that one can not generate phantom-like equation of
state from a holographic dark energy model in non-flat universe in the
Brans-Dicke cosmology framework. In the other hand, we suggest a correspondence
between the holographic dark energy scenario in flat universe and the phantom
dark energy model in framework of Brans-Dicke theory with potential.
|
On the consistent interactions in D=11 among a graviton, a massless
gravitino and a three-form: The couplings that can be introduced between a massless Rarita-Schwinger
field, a Pauli-Fierz field and an Abelian three-form gauge field in eleven
spacetime dimensions are analyzed in the context of the deformation of the
solution of the master equation.
|
Holographic three-point correlators in the Schrodinger/dipole CFT
correspondence: We calculate, for the first time, three-point correlation functions involving
"heavy" operators in the Schrodinger/null-dipole CFT correspondence at strong
coupling. In particular, we focus on the three-point functions of the dilaton
modes and two "heavy" operators. The heavy states are dual to the single spin
and dyonic magnon, the single spin and dyonic spike solutions or to two novel
string solutions which do not have an undeformed counterpart. Our results
provide the leading term of the correlators in the large $\lambda$ expansion
and are in perfect agreement with the form of the correlator dictated by
non-relativistic conformal invariance. We also specify the scaling function
which can not be fixed by using conformal invariance.
|
Emergence of Fluctuations from a Tachyonic Big Bang: It has recently been speculated that the end state of a collapsing universe
is a tachyonic big crunch. The time reversal of this process would be the
emergence of an expanding universe from a tachyonic big bang. In this
framework, we study the emergence of cosmological fluctuations. In particular,
we compare the amplitude of the perturbations at tne end of the tachyon phase
with what would be obtained assuming the usual vacuum initial conditions. We
find that cosmological fluctuations emerge in a thermal state. We comment on
the relation to the trans-Planckian problem of inflationary cosmology.
|
Euclidean Supersymmetry, Twisting and Topological Sigma Models: We discuss two dimensional N-extended supersymmetry in Euclidean signature
and its R-symmetry. For N=2, the R-symmetry is SO(2)\times SO(1,1), so that
only an A-twist is possible. To formulate a B-twist, or to construct Euclidean
N=2 models with H-flux so that the target geometry is generalised Kahler, it is
necessary to work with a complexification of the sigma models. These issues are
related to the obstructions to the existence of non-trivial twisted chiral
superfields in Euclidean superspace.
|
Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent: The Moyal and Wick-Voros planes A^{M,V}_{\theta} are *-isomorphic. On each of
these planes the Poincar\'e group acts as a Hopf algebra symmetry if its
coproducts are deformed by twist factors. We show that the *-isomorphism T:
A^M_{\theta} to A^V_{\theta} does not also map the corresponding twists of the
Poincar\'e group algebra. The quantum field theories on these planes with
twisted Poincar\'e-Hopf symmetries are thus inequivalent. We explicitly verify
this result by showing that a non-trivial dependence on the non-commutative
parameter is present for the Wick-Voros plane in a self-energy diagram whereas
it is known to be absent on the Moyal plane (in the absence of gauge fields).
Our results differ from these of (arXiv:0810.2095 [hep-th]) because of
differences in the treatments of quantum field theories.
|
Superalgebras from D-brane actions: The Noether charge algebras of D-brane actions contain two anomalous terms
which modify the standard supertranslation algebra. We use a cocycle approach
to derive associated spectra of topological charge algebras. The formalism is
applied to $(p,q)$-strings and the D-membrane. The resulting spectra contain
known algebras which allow the construction of extended superspace actions.
|
Brane cosmology: an introduction: These notes give an introductory review on brane cosmology. This subject
deals with the cosmological behaviour of a brane-universe, i.e. a
three-dimensional space, where ordinary matter is confined, embedded in a
higher dimensional spacetime. In the tractable case of a five-dimensional bulk
spacetime, the brane (modified) Friedmann equation is discussed in detail, and
various other aspects are presented, such as cosmological perturbations, bulk
scalar fields and systems with several branes.
|
The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs: 2-group symmetries arise when 1-form symmetries and 0-form symmetries of a
theory mix with each other under group multiplication. We discover the
existence of 2-group symmetries in 5d N=1 abelian gauge theories arising on the
(non-extended) Coulomb branch of 5d superconformal field theories (SCFTs),
leading us to argue that the UV 5d SCFT itself admits a 2-group symmetry.
Furthermore, our analysis determines the global forms of the 0-form flavor
symmetry groups of 5d SCFTs, irrespective of whether or not the 5d SCFT admits
a 1-form symmetry. As a concrete application of our method, we analyze 2-group
symmetries of all 5d SCFTs, which reduce in the IR, after performing mass
deformations, to 5d N=1 non-abelian gauge theories with simple, simply
connected gauge groups. For rank-1 Seiberg theories, we check that our
predictions for the flavor symmetry groups match with the superconformal and
ray indices available in the literature. We also comment on the mixed 't Hooft
anomaly between 1-form and 0-form symmetries arising in 5d N=1 non-abelian
gauge theories and its relation to the 2-groups.
|
Singular eigenstates in the even(odd) length Heisenberg spin chain: We study the implications of the regularization for the singular solutions on
the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In
particular, the analytic expressions of the Bethe eigenstates for three
down-spin sector have been obtained along with their numerical forms in some
fixed length chains. For an even-length chain if the singular solutions
\{\lambda_\alpha\} are invariant under the sign changes of their rapidities
{\lambda_\alpha\}=\{-\lambda_\alpha\} , then the Bethe ansatz equations are
reduced to a system of (M-2)/2 ((M-3)/2) equations in an even (odd) down-spin
sector. For an odd N length chain in the three down-spin sector, it has been
analytically shown that there exist singular solutions in any finite length of
the spin chain of the form N= 3\left(2k+1\right) with k=1, 2, 3, \cdots. It is
also shown that there exist no singular solutions in the four down-spin sector
for some odd-length spin-1/2 XXX chains.
|
On rank two theories with eight supercharges part II: Lefschetz pencils: The global Seiberg-Witten (SW) geometries for rank two theories with eight
supercharges are studied. The theory is deformed generically so that there are
only simplest $I_1$ or $\tilde{I}_1$ singularities on the Coulomb branch, which
then geometrically gives the so-called Lefchetz pencils, The local singularity
was shown to be determined by the conjugacy class of mapping class group (MCG);
The global study is then reduced to the questions about MCG: a) Find the
factorization of the MCG element of the singular fiber into positive products
of Dehn twists (which gives the $I_1$ singularity or $\tilde{I}_1$
singularity); b) Find the factorization of identity element in terms of Dehn
twists. We solved above two MCG problems for most rank two theories.The results
are very helpful in determining IR physics for all vacua of 4d SCFTs. Our
approach is combinatorial and many aspects can be straightforwardly generalized
to the study of higher rank theory.
|
Representation theory of the affine Lie superalgebra sl(2|1) at
fractional level: N=2 noncritical strings are closely related to the $\Slr/\Slr$ Wess-Zumino-
Novikov-Witten model, and there is much hope to further probe the former by
using the algebraic apparatus provided by the latter. An important ingredient
is the precise knowledge of the $\hslc$ representation theory at fractional
level. In this paper, the embedding diagrams of singular vectors appearing in
$\hslc$ Verma modules for fractional values of the level ($k=p/q-1$, p and q
coprime) are derived analytically. The nilpotency of the fermionic generators
in $\hslc$ requires the introduction of a nontrivial generalisation of the MFF
construction to relate singular vectors among themselves. The diagrams reveal a
striking similarity with the degenerate representations of the $N=2$
superconformal algebra.
|
On N=1,2,4 Higher Spin Gauge Theories in Four Dimensions: We study N=1,2,4 higher spin superalgebras in four dimensions and higher spin
gauge theories based on them. We extend the existing minimal N=2,4 theories and
find a minimal N=1 theory. Utilizing the basic structure of the minimal N=8
theory, we express the full field equations for the N=1,2,4 theories in a
universal form without introducing Kleinian operators. We also use a
non-minimal N=4 higher spin algebra tensored with U(3) to describe a higher
spin extension of N=4 supergravity coupled to the massless vector multiplets
arising in the KK spectrum of 11D supergravity on the N=3 supersymmetric AdS_4
x N^{010} background. The higher spin theory also contains a triplet of vector
multiplets which may play a role in the super-Higgs effect in which N=4 is
broken down to N=3.
|
Higher Order Perturbations Around Backgrounds with One Non-Homogeneous
Dimension: It is shown that perturbations around backgrounds with one non-homogeneous
dimension, namely of co-homogeneity 1, can be canonically simplified, a
property that is shown to hold to any order in perturbation theory. Recalling
that the problem naturally reduces to 1d, a procedure is described whereby for
each gauge function in 1d two 1d fields are eliminated from the action - one is
gauge and can be eliminated without a constraint and the other is auxiliary.
These results generalize the results of hep-th/0609001 from linear to
non-linear perturbations and they unify two cases of physical interest:
cosmological perturbations and perturbations to static spherically symmetric
backgrounds. An application to black strings is discussed in some detail.
|
Epsilon-expansion in quantum field theory in curved spacetime: We discuss epsilon-expansion in curved spacetime for asymptotically free and
asymptotically non-free theories. The esistence of stable and unstable fixed
points is investigated for $f \phi^4$ and SU(2) gauge theory. It is shown that
epsilon-expansion maybe compatible with asymptotic freedom on special solutions
of the RG equations in a special case (supersymmetric theory). Using
epsilon-expansion RG technique the effective Lagrangian for covariantly
constant gauge SU(2) field and effective potential for gauged NJL-model are
found in 4-epsilon- dimensional curved space (in linear curvature
approximation). The curvature- induced phase transitions from symmetric phase
to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase,
respectively) are discussed for the above two models.
|
Nonlocal Effective Gravitational Field Equations and the Running of
Newton's G: Non-perturbative studies of quantum gravity have recently suggested the
possibility that the strength of gravitational interactions might slowly
increase with distance. Here a set of generally covariant effective field
equations are proposed, which are intended to incorporate the gravitational,
vacuum-polarization induced, running of Newton's constant $G$. One attractive
feature of this approach is that, from an underlying quantum gravity
perspective, the resulting long distance (or large time) effective
gravitational action inherits only one adjustable parameter $\xi$, having the
units of a length, arising from dimensional transmutation in the gravitational
sector. Assuming the above scenario to be correct, some simple predictions for
the long distance corrections to the classical standard model Robertson-Walker
metric are worked out in detail, with the results formulated as much as
possible in a model-independent framework. It is found that the theory, even in
the limit of vanishing renormalized cosmological constant, generally predicts
an accelerated power-law expansion at later times $t \sim \xi \sim 1/H$.
|
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