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Comments on "Entropy of 2D Black Holes from Counting Microstates": In a recent letter, Cadoni and Mignemi proposed a formulation for the
statistical computation of the 2D black holes entropy. We present a criticism
about their formulation. | Spontaneous scalarization in (A)dS gravity at zero temperature: We study spontaneous scalarization of electrically charged extremal black
holes in $D\geq 4$ spacetime dimensions. Such a phenomenon is caused by the
symmetry breaking due to quartic interactions of the scalar -- Higgs potential
and Stueckelberg interaction with electromagnetic and gravitational fields,
characterized by the couplings $a$ and $b$, respectively. We use the entropy
representation of the states in the vicinity of the horizon, apply the inverse
attractor mechanism for the scalar field, and analyze analytically the
thermodynamic stability of the system using the laws of thermodynamics. As a
result, we obtain that the scalar field condensates on the horizon only in
spacetimes which are asymptotically non-flat, $\Lambda \neq 0$ (dS or AdS), and
whose extremal black holes have non-planar horizons $k=\pm 1$, provided that
the mass $m$ of the scalar field belongs to a mass interval (area code)
different for each set of the boundary conditions specified by $(\Lambda ,k)$.
A process of scalarization describes a second order phase transition of the
black hole, from the extremal Reissner-Nordstr\"{o}m (A)dS one, to the
corresponding extremal hairy one. Furthermore, for the transition to happen,
the interaction has to be strong enough, and all physical quantities on the
horizon depend at most on the effective Higgs-Stueckelberg interaction
$am^2-2b$. Most of our results are general, valid for any parameter and any
spacetime dimension. |
Cosmology of Rolling Tachyon: We study dynamics of rolling tachyon and Abelian gauge field on unstable
D-branes, of which effective action is given by Born-Infeld type nonlocal
action. Possible cosmological evolutions are also discussed. In the Einstein
frame of string cosmology, every expanding flat universe is proven to be
decelerating. | A direct proof of AGT conjecture at beta = 1: The AGT conjecture claims an equivalence of conformal blocks in 2d CFT and
sums of Nekrasov functions (instantonic sums in 4d SUSY gauge theory). The
conformal blocks can be presented as Dotsenko-Fateev beta-ensembles, hence, the
AGT conjecture implies the equality between Dotsenko-Fateev beta-ensembles and
the Nekrasov functions. In this paper, we prove it in a particular case of
beta=1 (which corresponds to c = 1 at the conformal side and to epsilon_1 +
epsilon_2 = 0 at the gauge theory side) in a very direct way. The central role
is played by representation of the Nekrasov functions through correlators of
characters (Schur polynomials) in the Selberg matrix models. We mostly
concentrate on the case of SU(2) with 4 fundamentals, the extension to other
cases being straightforward. The most obscure part is extending to an arbitrary
beta: for beta \neq 1, the Selberg integrals that we use do not reproduce
single Nekrasov functions, but only sums of them. |
On Solutions to the "Faddeev-Niemi" Equations: Recently it has been pointed out that the "Faddeev-Niemi" equations that
correspond to the Yang-Mills equations of motion for a decomposed gauge field,
can have solutions that obey the standard Yang-Mills equations with a source
term. Here we present a general class of such gauge field configurations. | Semiclassical Tunneling in 1+1 Dimensional String Theory: We describe time-dependent tunneling of massless particles in 1+1 dimensional
string field theory. Polchinski's description of the classical solutions in
terms of the Fermi sea is used to identify the leading instanton contribution
connecting the two half-lines. The field theory lagrangian is proportional to
$1/g^2$, where $g$ is the string coupling constant, but the $S$-matrix for
tunneling from one half-line to the other behaves as $\exp(-C/g)$. We note the
constant~$C$ involves curious boundary contributions and observe that a
prescription connecting the two half-lines unifies treatments of the Fermi
level above and below the barrier. We also note the relation to recent work of
Brustein and Ovrut. |
On the first law of entanglement for Quasi-Topological gravity: The first law of entanglement has been used to obtain the linearized Einstein
equations of the holographic dual spacetimes. In the present paper, the first
law of entanglement in quasi-topological gravity is explicitly derived by using
the Iyer-Wald formalism. In addition, we investigate the extended first law of
entanglement for the special case in Quasi-Topological gravity. | Moduli-Space Approximation for BPS Brane-Worlds: We develop the moduli-space approximation for the low energy regime of
BPS-branes with a bulk scalar field to obtain an effective four-dimensional
action describing the system. An arbitrary BPS potential is used and account is
taken of the presence of matter in the branes and small supersymmetry breaking
terms. The resulting effective theory is a bi-scalar tensor theory of gravity.
In this theory, the scalar degrees of freedom can be stabilized naturally
without the introduction of additional mechanisms other than the appropriate
BPS potential. We place observational constraints on the shape of the potential
and the global configuration of branes. |
Radiation from the non-extremal fuzzball: The fuzzball proposal says that the information of the black hole state is
distributed throughout the interior of the horizon in a `quantum fuzz'. There
are special microstates where in the dual CFT we have `many excitations in the
same state'; these are described by regular classical geometries without
horizons. Jejjala et.al constructed non-extremal regular geometries of this
type. Cardoso et. al then found that these geometries had a classical
instability. In this paper we show that the energy radiated through the
unstable modes is exactly the Hawking radiation for these microstates. We do
this by (i) starting with the semiclassical Hawking radiation rate (ii) using
it to find the emission vertex in the CFT (iii) replacing the Boltzman
distributions of the generic CFT state with the ones describing the microstate
of interest (iv) observing that the emission now reproduces the classical
instability. Because the CFT has `many excitations in the same state' we get
the physics of a Bose-Einstein condensate rather than a thermal gas, and the
usually slow Hawking emission increases, by Bose enhancement, to a classically
radiated field. This system therefore provides a complete gravity description
of information-carrying radiation from a special microstate of the nonextremal
hole. | S-duality and the Double Copy: The double copy formalism provides an intriguing connection between gauge
theories and gravity. It was first demonstrated in the perturbative context of
scattering amplitudes but recently the formalism has been applied to exact
classical solutions in gauge theories such as the monopole and instanton.
In this paper we will investigate how duality symmetries in the gauge theory
double copy to gravity and relate these to solution generating transformations
and the action of $Sl(2,R)$ in general relativity. |
Spectral function of the Bloch-Nordsieck model at finite temperature: In this paper we determine the exact fermionic spectral function of the
Bloch-Nordsieck model at finite temperature. Analytic results are presented for
some special parameters, for other values we have numerical results. The
spectral function is finite and normalizable for any nonzero temperature
values. The real time dependence of the retarded Green's function is power-like
for small times and exhibits exponential damping for large times. Treating the
temperature as an infrared regulator, we can also give a safe interpretation of
the zero temperature result. | Low-energy U(1) x USp(2M) gauge theory from simple high-energy gauge
group: We give an explicit example of the embedding of a near BPS low-energy (U(1) x
USp(2M))/Z_2 gauge theory into a high-energy theory with a simple gauge group
and adjoint matter content. This system possesses degenerate monopoles arising
from the high-energy symmetry breaking as well as non-Abelian vortices due to
the symmetry breaking at low energies. These solitons of different codimensions
are related by the exact homotopy sequences. |
Chaos in Celestial CFT: Celestial holography proposes a duality between gravitational scattering in
asymptotically flat space-time and a conformal field theory living on the
celestial sphere. Its dictionary relates the infinite dimensional space-time
symmetry group to Ward identities of the CFT. The spontaneous breaking of these
asymptotic symmetries governs the dynamics of the soft sector in the CFT. Here
we show that this sector encodes non-trivial backreaction effects that exhibit
characteristics of maximal quantum chaos. A key element in the derivation is
the identification of the Hilbert space of celestial CFT, defined through
radial quantization, with that of a constantly accelerating Rindler observer.
From the point of view of the bulk, Rindler particles exhibit Lyapunov behavior
due to shockwave interactions that shift the observer horizon. From the point
of view of the boundary, the superrotation Goldstone modes affect the relevant
representations of the celestial Virasoro symmetry in a manner that induces
Lyapunov behavior of out-of-time-ordered celestial correlators. | Generalising the matter coupling in massive gravity: a search for new
interactions: Massive gravity theory introduced by de Rham, Gabadadze, Tolley (dRGT) is
restricted by several uniqueness theorems that protect the form of the
potential and kinetic terms, as well as the matter coupling. These restrictions
arise from the requirement that the degrees of freedom match the expectation
from Poincar\'e representations of a spin--2 field. Any modification beyond the
dRGT form is known to invalidate a constraint that the theory enjoys and revive
a dangerous sixth mode. One loophole is to exploit the effective nature of the
theory by pushing the sixth mode beyond the strong coupling scale without
completely removing it. In this paper, we search for modifications to dRGT
action by coupling the matter sector to an arbitrary metric constructed out of
the already existing degrees of freedom in the dRGT action. We formulate the
conditions that such an extension should satisfy in order to prevent the sixth
mode from contaminating the effective theory. Our approach provides a new
perspective for the "composite coupling" which emerges as the unique extension
up to four-point interactions. |
Harmonicity in N=4 supersymmetry and its quantum anomaly: The holomorphicity property of N=1 superpotentials or of N=2 F-terms
involving vector multiplets is generalized to the case of N=4 1/2-BPS effective
operators defined in harmonic superspace. The resulting harmonicity equations
are shown to control the moduli dependence of the couplings of higher
dimensional operators involving powers of the N=4 Weyl superfield, computed by
N=4 topological amplitudes. These equations can also be derived on the string
side, exhibiting an anomaly from world-sheet boundary contributions that leads
to recursion relations for the non-analytic part of the couplings. | 6d surface defects from massive type IIA: We present a new BPS flow within minimal $\mathcal{N}=1$ supergravity in
seven dimensions describing a warped $\textrm{AdS}_{3}$ background supported by
a "dyonic" profile of the three-form. Furthermore, we discuss the holographic
interpretation of the above solution in terms of a defect $\textrm{SCFT}_{2}$
inside the 6d $(1,0)$ theory dual to the AdS in the asymptotic region. Finally
we provide the brane picture of the aforementioned defect CFT as D2- and
wrapped D4-branes ending on a D6 - NS5 - D8 funnel in massive type IIA string
theory. |
$T^{1,1}$ truncation on the spindle: We study the compactification of the $\mathcal{N}=2$ AdS$_5$ consistent
truncation of the conifold, in presence of a Betti vector multiplet, on the
spindle. We derive the BPS equations and solve them at the poles, computing the
central charge for both the twist and the anti-twist class, turning on the
magnetic charge associated to the baryonic symmetry. Then, in the anti-twist
class, where there are choices of the quantized flux that give origin to a
positive central charge, we numerically solve the BPS equations interpolating
between the poles of the spindle. We conclude by comparing our results with the
one obtained from the analysis of the dual field theory, finding an exact
agreement. | Pole-skipping and hydrodynamic analysis in Lifshitz, AdS$_2$ and Rindler
geometries: The "pole-skipping" phenomenon reflects that the retarded Green's function is
not unique at a pole-skipping point in momentum space $(\omega,k)$. We explore
the universality of the pole-skipping in different geometries. In holography,
near horizon analysis of the bulk equation of motion is a simpler way to derive
a pole-skipping point and we use this method in Lifshitz, AdS$_2$ and Rindler
geometries. We also study the complex hydrodynamic analyses and find that the
dispersion relations in terms of dimensionless variables $\frac{\omega}{2\pi
T}$ and $\frac{\vert k\vert}{2\pi T}$ pass through pole-skipping points
$(\frac{\omega_n}{2\pi T}, \frac{\vert k_n\vert}{2\pi T}$) at small $\omega$
and $k$ in Lifshitz background. We verify that the position of the
pole-skipping points does not depend on the standard quantization or
alternative quantization in the boundary theory in
AdS$_2\times\mathbb{R}^{d-1}$ geometry. In Rindler geometry, we cannot find the
corresponding Green's function to calculate pole-skipping points because it is
difficult to impose the boundary condition. However we can obtain "special
points" near horizon where bulk equations of motion have two incoming
solutions. These "special points" correspond to nonunique of the Green's
function in physical meaning from the perspective of holography. |
Transcending the ensemble: baby universes, spacetime wormholes, and the
order and disorder of black hole information: In the 1980's, work by Coleman and by Giddings and Strominger linked the
physics of spacetime wormholes to `baby universes' and an ensemble of theories.
We revisit such ideas, using features associated with a negative cosmological
constant and asymptotically AdS boundaries to strengthen the results, introduce
a change in perspective, and connect with recent replica wormhole discussions
of the Page curve. A key new feature is an emphasis on the role of null states.
We explore this structure in detail in simple topological models of the bulk
that allow us to compute the full spectrum of associated boundary theories. The
dimension of the asymptotically AdS Hilbert space turns out to become a random
variable $Z$, whose value can be less than the naive number $k$ of independent
states in the theory. For $k>Z$, consistency arises from an exact degeneracy in
the inner product defined by the gravitational path integral, so that many a
priori independent states differ only by a null state. We argue that a similar
property must hold in any consistent gravitational path integral. We also
comment on other aspects of extrapolations to more complicated models, and on
possible implications for the black hole information problem in the individual
members of the above ensemble. | Scattering of Topological Solitons on Barriers and Holes in Two λ
φ^4 Models: We present results of our studies of various scattering properties of
topological solitons on obstructions in the form of holes and barriers in 1+1
dimensions. Our results are based on two models involving a \phi^4 potential.
The obstructions are characterised by a potential parameter, \lambda which has
a non-zero value in a certain region of space and zero elsewhere. In the first
model the potential parameter is included in the potential and in the second
model the potential parameter is included in the metric. Our results are based
on numerical simulations and analytical considerations. |
WZNW Models and Gauged WZNW Models Based on a Family of Solvable Lie
Algebras: A family of solvable self-dual Lie algebras that are not double extensions of
Abelian algebras and, therefore, cannot be obtained through a Wigner
contraction, is presented. We construct WZNW and gauged WZNW models based on
the first two algebras in this family. We also analyze some general phenomena
arising in such models. | Quantum Kaluza-Klein Cosmologies (V): In the No-boundary Universe with $d=11$ supergravity, under the $S_n \times
S_{11-n}$ Kaluza-Klein ansatz, the only seed instanton for the universe
creation is a $S_7 \times S_4$ space. It is proven that for the Freund-Rubin,
Englert and Awada-Duff-Pope models the macroscopic universe in which we are
living must be 4- instead of 7-dimensional without appealing to the anthropic
principle. |
Fermion on Curved Spaces, Symmetries, and Quantum Anomalies: We review the geodesic motion of pseudo-classical spinning particles in
curved spaces. Investigating the generalized Killing equations for spinning
spaces, we express the constants of motion in terms of Killing-Yano tensors.
Passing from the spinning spaces to the Dirac equation in curved backgrounds we
point out the role of the Killing-Yano tensors in the construction of the
Dirac-type operators. The general results are applied to the case of the
four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. The gravitational
and axial anomalies are studied for generalized Euclidean Taub-NUT metrics
which admit hidden symmetries analogous to the Runge-Lenz vector of the
Kepler-type problem. Using the Atiyah-Patodi-Singer index theorem for manifolds
with boundaries, it is shown that the these metrics make no contribution to the
axial anomaly. | Dynamical Description of Spectral Flow in N=2 Superconformal Field
Theories: We show how the spectral flow between the Neveu-Schwarz and Ramond sectors of
N=2 superconformal field theories can be described in three dimensions in terms
of the propagation of charged particles coupled to a a Chern-Simons gauge
theory. Quantum mechanical mixing between the degenerate Chern-Simons vacua
interpolates between the different boundary conditions of the two sectors and
so provides a dynamical picture for the GSO-projection. |
Picard-Fuchs Equations and Prepotentials in $N=2$ Supersymmetric QCD: The Picard-Fuchs equations for $N=2$ supersymmetric $SU(N_{c})$ Yang-Mills
theories with massless hypermultiplets are obtained for $N_{c}=2$ and $3$. For
$SU(2)$ we derive the non-linear differential equations for the prepotentials
and calculate full non-perturbative corrections to the effective gauge coupling
constant in the weak and strong coupling regions. | The global gravitational anomaly of the self-dual field theory: We derive a formula for the global gravitational anomaly of the self-dual
field theory on an arbitrary compact oriented Riemannian manifold. Along the
way, we uncover interesting links between the theory of determinant line
bundles of Dirac operators, Siegel theta functions and a functor constructed by
Hopkins and Singer. We apply our result to type IIB supergravity and show that
in the naive approximation where the Ramond-Ramond fields are treated as
differential cohomology classes, the global gravitational anomaly vanishes on
all 10-dimensional spin manifolds. We sketch a few other important physical
applications. |
Warped anti-de Sitter in 3d (2,0) Supergravity: We comment on the ubiquity of the so-called warped anti-de Sitter spacetimes
in three-dimensional (2,0) supergravity theory. By using isometry-invariant
tensors and simple counting, we prove their existence for arbitrary $(2,0)$
supergravity models suitably defined close to a minimal model. We also analyze
their offshell supersymmetry and the supersymmetry of two geometric orbifolds. | Gauge Theories with Time Dependent Couplings and their Cosmological
Duals: We consider the N=4 SYM theory in flat 3+1 dimensional spacetime with a time
dependent coupling constant which vanishes at $t=0$, like $g_{YM}^2=t^p$. In an
analogous quantum mechanics toy model we find that the response is singular.
The energy diverges at $t=0$, for a generic state. In addition, if $p>1$ the
phase of the wave function has a wildly oscillating behavior, which does not
allow it to be continued past $t=0$. A similar effect would make the gauge
theory singular as well, though nontrivial effects of renormalization could
tame this singularity and allow a smooth continuation beyond $t=0$. The gravity
dual in some cases is known to be a time dependent cosmology which exhibits a
space-like singularity at $t=0$. Our results, if applicable in the gauge theory
for the case of the vanishing coupling, imply that the singularity is a genuine
sickness and does not admit a meaningful continuation. When the coupling
remains non-zero and becomes small at $t=0$, the curvature in the bulk becomes
of order the string scale. The gauge theory now admits a time evolution beyond
this point. In this case, a finite amount of energy is produced which possibly
thermalizes and leads to a black hole in the bulk. |
The R-matrix structure of the Euler-Calogero-Moser model: We construct the $r$-matrix for the generalization of the Calogero-Moser
system introduced by Gibbons and Hermsen. By reduction procedures we obtain the
$r$-matrix for the $O(N)$ Euler-Calogero-Moser model and for the standard $A_N$
Calogero-Moser model. | Lie 2-algebra models: In this paper, we begin the study of zero-dimensional field theories with
fields taking values in a semistrict Lie 2-algebra. These theories contain the
IKKT matrix model and various M-brane related models as special cases. They
feature solutions that can be interpreted as quantized 2-plectic manifolds. In
particular, we find solutions corresponding to quantizations of R^3, S^3 and a
five-dimensional Hpp-wave. Moreover, by expanding a certain class of Lie
2-algebra models around the solution corresponding to quantized R^3, we obtain
higher BF-theory on this quantized space. |
Superfield Lagrangian Quantization with Extended BRST Symmetry: We consider possible superfield representations of extended BRST symmetry for
general gauge theories within the principle of gauge-fixing based on a
generating equation for the gauge functional. We examine admissible superfield
choices for an extended antibracket and delta-operator with given algebraic
properties and show that only one of these choices is compatible with the
requirement of extended BRST symmetry realized in terms of supertranslations
along Grassmann coordinates. We demonstrate that this realization leads to the
gauge-independence of the S-matrix. | Deformation Quantization, Superintegrability, and Nambu Mechanics: Phase Space is the framework best suited for quantizing superintegrable
systems--systems with more conserved quantities than degrees of freedom. In
this quantization method, the symmetry algebras of the hamiltonian invariants
are preserved most naturally. We illustrate the power and simplicity of the
method through new applications to nonlinear sigma-models, specifically for
Chiral Models and de Sitter N-spheres, where the symmetric quantum hamiltonians
amount to compact and elegant expressions, in accord with the Groenewold-van
Hove theorem. Additional power and elegance is provided by the use of Nambu
Brackets (linked to Dirac Brackets) involving the extra invariants of
superintegrable models. The quantization of Nambu Brackets is then successfully
compared to that of Moyal, validating Nambu's original proposal, while
invalidating other proposals. |
How useful can knot and number theory be for loop calculations?: We summarize recent results connecting multiloop Feynman diagram calculations
to different parts of mathematics, with special attention given to the Hopf
algebra structure of renormalization. | Particle with non-Abelian charge: classical and quantum: We study the action for a non-Abelian charged particle in a non-Abelian
background field in the worldline formalism, described by real bosonic
variables, leading to the well known equations given by Wong. The isospin parts
in the action can be viewed as the Lagrange multiplier term corresponding to a
non-holonomic constraint restricting the isospins to be parallel transported.
The path integration is performed over the isospin variables and as a result,
the worldlines turn out to be constrained by the classical solutions for the
isospins. We derive a wave equation from the path integral, constructed as the
constrained Hamiltonian operator acting on the wave function. The operator
ordering corresponding to the quantum Hamiltonian is found and verified by the
inverse Weyl transformation. |
Path Integral Discussion of Two and- Three-Dimensional $δ$-Function
Perturbations: The incorporation of two- and three-dimensional $\delta$-function
perturbations into the path-integral formalism is discussed. In contrast to the
one-dimensional case, a regularization procedure is needed due to the
divergence of the Green-function $G^{(V)}(\vec x,\vec y;E)$, ($\vec x,\vec
y\in\bbbr^2,\bbbr^3$) for $\vec x=\vec y$, corresponding to a potential problem
$V(\vec x)$. The known procedure to define proper self-adjoint extensions for
Hamiltonians with deficiency indices can be used to regularize the path
integral, giving a perturbative approach for $\delta$-function perturbations in
two and three dimensions in the context of path integrals. Several examples
illustrate the formalism. | N=1/2 Super Yang-Mills Theory on Euclidean AdS2xS2: We study D-branes in the background of Euclidean AdS2xS2 with a graviphoton
field turned on. As the background is not Ricci flat, the graviphoton field
must have both self-dual and antiself-dual parts. This, in general, will break
all the supersymmetries on the brane. However, we show that there exists a
limit for which one can restore half of the supersymmetries. Further, we show
that in this limit, the N=1/2 SYM Lagrangian on flat space can be lifted on to
the Euclidean AdS2xS2 preserving the same amount of supersymmetries as in the
flat case. We observe that without the C-dependent terms present in the action
this lift is not possible. |
Supersymmetry in Classical Mechanics: We briefly review the universal supersymmetry present in classical
hamiltonian systems and show its applications to field theories. | Complex Monopoles and Gribov Copies: Complex monopole solutions exist in the three dimensional Georgi-Glashow
model with the Chern-Simons term. They dominate the path integral and disorder
the Higgs vacuum. Gribov copies of the vacuum and monopole configurations are
studied in detail. |
Towards general scalar-Yukawa renormalisation group equations at
three-loop order: For arbitrary four-dimensional quantum field theories with scalars and
fermions, renormalisation group equations in the $\overline{\text{MS}}$ scheme
are investigated at three-loop order in perturbation theory. Collecting
literature results, general expressions are obtained for field anomalous
dimensions, Yukawa interactions, as well as fermion masses. The renormalisation
group evolution of scalar quartic, cubic and mass terms is determined up to a
few unknown coefficients. The combined results are applied to compute the
renormalisation group evolution of the gaugeless Litim-Sannino model. | Seiberg-Witten Geometry of Four-Dimensional $\mathcal N=2$ Quiver Gauge
Theories: Seiberg-Witten geometry of mass deformed $\mathcal N=2$ superconformal ADE
quiver gauge theories in four dimensions is determined. We solve the limit
shape equations derived from the gauge theory and identify the space $\mathfrak
M$ of vacua of the theory with the moduli space of the genus zero holomorphic
(quasi)maps to the moduli space ${\rm Bun}_{\mathbf G} (\mathcal E)$ of
holomorphic $G^{\mathbb C}$-bundles on a (possibly degenerate) elliptic curve
$\mathcal E$ defined in terms of the microscopic gauge couplings, for the
corresponding simple ADE Lie group $G$. The integrable systems $\mathfrak P$
underlying the special geometry of $\mathfrak M$ are identified. The moduli
spaces of framed $G$-instantons on ${\mathbb R}^{2} \times {\mathbb T}^{2}$, of
$G$-monopoles with singularities on ${\mathbb R}^{2} \times {\mathbb S}^{1}$,
the Hitchin systems on curves with punctures, as well as various spin chains
play an important r\^ole in our story. We also comment on the
higher-dimensional theories. |
Chromo-Natural Model in Anisotropic Background: In this work we study the chromo-natural inflation model in the anisotropic
setup. Initiating inflation from Bianchi type-I cosmology, we analyze the
system thoroughly during the slow-roll inflation, from both analytical and
numerical points of view. We show that the isotropic FRW inflation is an
attractor of the system. In other words, anisotropies are damped within few
$e$--folds and the chromo-natural model respects the cosmic no-hair conjecture.
Furthermore, we demonstrate that in the slow-roll limit, the anisotropies in
both chromo-natural and gauge-flation models share the same dynamics. | Path Integral Bosonization of the Massive Thirring Model: There is a conceptual error in the main argument of this paper (essentially a
regularization scheme is changed in the middle of a calculation), and therefore
it is withdrawn. Interested readers are instead referred to hep-th/9811137. |
Nonperturbative infrared effects for light scalar fields in de Sitter
space: We study the phi^4 scalar field theory in de Sitter space using the 2PI
effective action formalism. This formalism enables us to investigate the
nonperturbative quantum effects. We use the mean field and gap equations and
calculate the physical mass and effective potential. We find that
nonperturbative infrared effects on de Sitter space produce a curvature-induced
mass and work to restore the broken Z_2 symmetry. | Algebraic Properties of BRST Coupled Doublets: We characterize the dependence on doublets of the cohomology of an arbitrary
nilpotent differential s (including BRST differentials and classical linearized
Slavnov-Taylor (ST) operators) in terms of the cohomology of the
doublets-independent component of s. All cohomologies are computed in the space
of local integrated formal power series. We drop the usual assumption that the
counting operator for the doublets commutes with s (decoupled doublets) and
discuss the general case where the counting operator does not commute with s
(coupled doublets). The results are purely algebraic and do not rely on
power-counting arguments. |
Magnetic Moments of Branes and Giant Gravitons: We study the magnetic analogue of Myers' Dielectric Effect and, in some
cases, relate it to the blowing up of particles into branes, first investigated
by Greevy, Susskind and Toumbas. We show that $D0$ branes or gravitons in M
theory, moving in a magnetic four-form field strength background expand into a
non-commutative two sphere. Both examples of constant magnetic field and
non-constant fields in curved backgrounds generated by branes are considered.
We find, in all cases, another solution, consisting of a two-brane wrapping a
classical two-sphere, which has all the quantum numbers of the $D0$ branes.
Motivated by this, we investigate the blowing up of gravitons into branes in
backgrounds different from $AdS_m \times S^n$. We find the phenomenon is quite
general. In many cases with less or even no supersymmetry we find a brane
configuration which has the same quantum numbers and the same energy as a
massless particle in supergravity. | Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function: A systematic approach to the study of semiclassical fluctuations of strings
in AdS_5 x S^5 based on the Green-Schwarz formalism is developed. We show that
the string partition function is well defined and finite. Issues related to
different gauge choices are clarified. We consider explicitly several cases of
classical string solutions with the world surface ending on a line, on a circle
or on two lines on the boundary of AdS. The first example is a BPS object and
the partition function is one. In the third example the determinants we derive
should give the first corrections to the Wilson loop expectation value in the
strong coupling expansion of the n=4 SYM theory at large N. |
Wave zone in the Hořava-Lifshitz theory at the kinetic-conformal
point in the low energy regime: We show that in the Ho\v{r}ava-Lifshitz theory at the kinetic-conformal
point, in the low energy regime, a wave zone for asymptotically flat fields can
be consistently defined. In it, the physical degrees of freedom, the transverse
traceless tensorial modes, satisfy a linear wave equation. The Newtonian
contributions, among which there are terms which manifestly break the
relativistic invariance, are non-trivial but do not obstruct the free
propagation (radiation) of the physical degrees of freedom. For an appropriate
value of the couplings of the theory, the wave equation becomes the
relativistic one in agreement with the propagation of the gravitational
radiation in the wave zone of General Relativity. Previously to the wave zone
analysis, and in general grounds, we obtain the physical Hamiltonian of the
Ho\v{r}ava-Lifshitz theory at the kinetic-conformal point in the constrained
submanifold. We determine the canonical physical degrees of freedom in a
particular coordinate system. They are well defined fuctions of the
transverse-traceless modes of the metric and coincide with them in the wave
zone and also at linearized level. | Gravity and Yang-Mills Amplitude Relations: Using only general features of the S-matrix and quantum field theory, we
prove by induction the Kawai-Lewellen-Tye relations that link products of gauge
theory amplitudes to gravity amplitudes at tree level. As a bonus of our
analysis, we provide a novel and more symmetric form of these relations. We
also establish an infinite tower of new identities between amplitudes in gauge
theories. |
Black hole entropy reveals a 12th "dimension": The Beckenstein-Hawking black hole entropy in string theory and its
extensions, as expressed in terms of charges that correspond to central
extensions of the supersymmetry algebra, has more symmetries than U-duality. It
is invariant under transformations of the charges, involving a 12th (or 13th)
``dimension''. This is an indication that the secret theory behind string
theory has a superalgebra involving Lorentz non-scalar extensions (that are not
strictly central), as suggested in S-theory, and which could be hidden in M- or
F- theories. It is suggested that the idea of spacetime is broader than usual,
and that a larger ``spacetime" is partially present in black holes. | Reducible higher-spin multiplets in flat and AdS spaces and their
geometric frame-like formulation: We consider the frame-like formulation of reducible sets of totally symmetric
bosonic and fermionic higher-spin fields in flat and AdS backgrounds of any
dimension, that correspond to so-called higher-spin triplets resulting from the
string-inspired BRST approach. The explicit relationship of the fields of
higher-spin triplets to the higher-spin vielbeins and connections is found. The
gauge invariant actions are constructed including, in particular, the reducible
(i.e. triplet) higher-spin fermion case in AdS_D space. |
The Geometry/Gauge Theory Duality and the Dijkgraaf-Vafa Conjecture: In this dissertation we discuss various issues concerning application of the
Dijkgraaf-Vafa (DV) conjecture to the study of supersymmetric gauge theories.
The DV approach is very powerful in that it provides a systematic way of
computing the nonperturbative, often even exact, superpotential of the system,
which was possible only on a case-by-case basis in the more traditional
approach based on holomorphy and symmetry.
This conjecture has been checked for many nontrivial examples, but the range
of its applicability remained unclear. We give an explicit example, Sp(N)
theory with antisymmetric tensor, which reveals the subtleties in applying the
conjecture. We show that, the superpotential obtained by a straightforward
application of the DV approach starts to disagree with the standard gauge
theory result at N/2+1 loops. The same discrepancy is reproduced in the
generalized Konishi anomaly method.
In order to look for the physical origin of the discrepancy, we consider the
string theory realization of the gauge theories by Calabi-Yau
compactifications. By closely analyzing the physics that accompanies the
geometric transitions involved, we clarify the prescription regarding when to
include a glueball field as the physical field, and when to not. In particular,
the aforementioned discrepancy is resolved if we follow this prescription and
introduce a glueball field for the "Sp(0)" group.
Furthermore, we generalize the prescription to include flavors and
demonstrate that the matrix model computations with the generalized
prescription correctly reproduce the gauge theory results. | Generalizing the Swampland: Embedding $P(X, \varphi)$ Inflationary
Theories in a Curved Multi-field Space: We study the general embedding of a $ P(X, \varphi) $ inflationary theory
into a two-field theory with curved field space metric, which was proposed as a
possible way to examine the relation between de Sitter Swampland conjecture and
\textit{k}-inflation. We show that this embedding method fits into the special
type of two-field model in which the heavy field can be integrated out at the
full action level. However, this embedding is not exact due to the upper bound
of the effective mass of the heavy field. We quantify the deviation between the
speed of sound calculated via the $ P(X, \varphi) $ theory and the embedding
two-field picture to next leading order terms. We especially focus on the first
potential slow roll parameter defined in the two-field picture and obtain an
upper bound on it. |
String Unification and Threshold Corrections: The interpretation of the apparent unification of gauge couplings within
supersymmetric theories depends on uncertainties induced through heavy particle
thresholds. While in standard grand unified theories these effects can be
estimated easily, the corresponding calculations are quite complicated in
string unified theories and do exist only in models with unbroken $E_6$. We
present results for heavy particle thresholds in more realistic models with
gauge group $SU(3)\times SU(2)\times U(1)$. Effects of Wilson line background
fields as well as the universal part of the (rather mild) threshold corrections
indicate a strong model dependence. We discuss the consequences of our results
for the idea of string unification without a grand unified gauge group. | Statistical physics of black holes as quantum-mechanical systems: Some basic features of black-hole statistical mechanics are investigated,
assuming that black holes respect the principles of quantum mechanics. Care is
needed in defining an entropy S_bh corresponding to the number of microstates
of a black hole, given that the black hole interacts with its surroundings. An
open question is then the relationship between this entropy and the
Bekenstein-Hawking entropy S_BH. For a wide class of models with interactions
needed to ensure unitary quantum evolution, these interactions produce extra
energy flux beyond that predicted by Hawking. Arguments are then presented that
this results in an entropy S_bh that is smaller than S_BH. Correspondingly, in
such scenarios equilibrium properties of black holes are modified. We examine
questions of consistency of such an inequality; if it is not consistent, that
provides significant constraints on models for quantum-mechanical black hole
evolution. |
Non Local Observables and Confinement in BF Formulation of Yang-Mills
Theory: The vev's of the magnetic order-disorder operators in QCD are found in an
explicit calculation using the first order formulation of Yang-Mills theory. | Killing-Yano equations and G-structures: We solve the Killing-Yano equation on manifolds with a $G$-structure for
$G=SO(n), U(n), SU(n), Sp(n)\cdot Sp(1), Sp(n), G_2$ and $Spin(7)$. Solutions
include nearly-K\"ahler, weak holonomy $G_2$, balanced SU(n) and holonomy $G$
manifolds. As an application, we find that particle probes on $AdS_4\times X$
compactifications of type IIA and 11-dimensional supergravity admit a ${\cal
W}$-type of symmetry generated by the fundamental forms. We also explore the
${\cal W}$-symmetries of string and particle actions in heterotic and common
sector supersymmetric backgrounds. In the heterotic case, the generators of the
${\cal W}$-symmetries completely characterize the solutions of the gravitino
Killing spinor equation, and the structure constants of the ${\cal W}$-symmetry
algebra depend on the solution of the dilatino Killing spinor equation. |
Lagrangian quantum field theory in momentum picture. II. Free spinor
fields: Free spinor fields, with spin 1/2, are explored in details in the momentum
picture of motion in Lagrangian quantum field theory. The field equations are
equivalently written in terms of creation and annihilation operators and on
their base the anticommutation relations are derived. Some problems concerning
the vacuum and state vectors of free spinor field are discussed. Several
Lagrangians, describing free spinor fields, are considered and the basic
consequences of them are investigated. | Geometrical thermodynamics and P-V criticality of charged accelerating
AdS black holes: The unusual asymptotic structure of the accelerating black holes led to
ambiguity in their geometric characteristics and thermodynamic behavior.
Motivated by the interesting properties of such black holes and the significant
role of electric charge and string tension on their structure, we study the
thermodynamic behavior of these black holes by two methods and examine the
changes of free parameters on the thermal behavior of the black holes. First,
we investigate phase transition and thermal stability of the system through the
use of heat capacity in the non-extended phase space. We examine the effects of
electric charge, string tension and the cosmological constant on the phase
transition and stability of the system. We also find that to have a phase
transition, we have to apply some constraints on the free parameters. Then, we
employ the geometrical thermodynamic (GT) method to study phase transition and
compare the obtained results with those of the heat capacity. Next, we work in
the extended phase space by considering the cosmological constant as a
dynamical pressure and evaluate the existence of van der Waals like phase
transition. We obtain critical quantities and study the effective role of
electric charge and string tension on these quantities. Finally, we make use of
the GT method in the extended phase space and find that the results of the GT
method, heat capacity and $P-V$ diagram lead to a consistent conclusion. |
Dynamic and static properties of Quantum Hall and Harmonic Oscillator
systems on the non-commutative plane: We study two quantum mechanical systems on the noncommutative plane using a
representation independent approach. First, in the context of the Landau
problem, we obtain an explicit expression for the gauge transformation that
connects the Landau and the symmetric gauge in noncommutative space. This lead
us to conclude that the usual form of the symmetric gauge
$\vec{A}=\left(-\frac{\beta}{2}\hat{Y},\frac{\beta}{2}\hat{X}\right)$, in which
the constant $\beta$ is interpreted as the magnetic field, is not true in
noncommutative space. We also be able to establish a precise definition of
$\beta$ as function of the magnetic field, for which the equivalence between
the symmetric and Landau gauges is hold in noncommutative plane. Using the
symmetric gauge we obtain results for the spectrum of the Quantum Hall system,
its transverse conductivity in the presence of an electric field and other
static observables. These results amend the literature on Quantum Hall Effect
in noncommutative plane in which the incorrect form of the symmetric gauge, in
noncommutative space, is assumed. We also study the non-equilibrium dynamics of
simple observables for this system. On the other hand, we study the dynamics of
the harmonic oscillator in non-commutative space and show that, in general, it
exhibit quasi-periodic behavior, in striking contrast with its commutative
version. The study of the dynamics reveals itself as a most powerful tool to
characterize and understand the effects of non-commutativity. | On the stability and spectrum of non-supersymmetric AdS(5) solutions of
M-theory compactified on Kahler-Einstein spaces: Eleven-dimensional supergravity admits non-supersymmetric solutions of the
form AdS(5)xM(6) where M(6) is a positive Kahler-Einstein space. We show that
the necessary and sufficient condition for such solutions to be stable against
linearized bosonic supergravity perturbations can be expressed as a condition
on the spectrum of the Laplacian acting on (1,1)-forms on M(6). For M(6)=CP(3),
this condition is satisfied, although there are scalars saturating the
Breitenlohner-Freedman bound. If M(6) is a product S(2)xM(4) (where M(4) is
Kahler-Einstein) then there is an instability if M(4) has a continuous
isometry. We show that a potential non-perturbative instability due to 5-brane
nucleation does not occur. The bosonic Kaluza-Klein spectrum is determined in
terms of eigenvalues of operators on M(6). |
String propagation in four-dimensional dyonic black hole background: We study string propagation in an exact, four-dimensional dyonic black hole
background. The general solutions describing string configurations are obtained
by solving the string equations of motion and constraints. By using the
covariant formalism, we also investigate the propagation of physical
perturbations along the string in the given curved background. | Quantum gravity and elementary particles from higher gauge theory: We give a brief overview how to couple general relativity to the Standard
Model of elementary particles, within the higher gauge theory framework,
suitable for the spinfoam quantization procedure. We begin by providing a short
review of all relevant mathematical concepts, most notably the idea of a
categorical ladder, 3-groups and generalized parallel transport. Then, we give
an explicit construction of the algebraic structure which describes the full
Standard Model coupled to Einstein-Cartan gravity, along with the classical
action, written in the form suitable for the spinfoam quantization procedure.
We emphasize the usefulness of the 3-group concept as a superior tool to
describe gauge symmetry, compared to an ordinary Lie group, as well as the
possibility to employ this new structure to classify matter fields and study
their spectrum, including the origin of fermion families. |
A note on the Gauge Symmetries of Unimodular Gravity: The symmetries of Unimodular Gravity are clarified somewhat. | Physical ageing and new representations of some Lie algebras of local
scale-invariance: Indecomposable but reducible representations of several Lie algebras of local
scale-transformations, including the Schr\"odinger and conformal Galilean
algebras, and some of their applications in physical ageing are reviewed. The
physical requirement of the decay of co-variant two-point functions for large
distances is related to analyticity properties in the coordinates dual to the
physical masses or rapidities. |
Noncommutativity from Embedding Techniques: We apply the embedding method of Batalin-Tyutin for revealing noncommutative
structures in the generalized Landau problem. Different types of
noncommutativity follow from different gauge choices. This establishes a
duality among the distinct algebras. An alternative approach is discussed which
yields equivalent results as the embedding method. We also discuss the
consequences in the Landau problem for a non constant magnetic field. | Generalized universality in the massive sine-Gordon model: A non-trivial interplay of the UV and IR scaling laws, a generalization of
the universality is demonstrated in the framework of the massive sine-Gordon
model, as a result of a detailed study of the global behaviour of the
renormalization group flow and the phase structure. |
Phase Transitions In M-Theory And F-Theory: Phase transitions are studied in $M$-theory and $F$-theory. In $M$-theory
compactification to five dimensions on a Calabi-Yau, there are
topology-changing transitions similar to those seen in conformal field theory,
but the non-geometrical phases known in conformal field theory are absent. At
boundaries of moduli space where such phases might have been expected, the
moduli space ends, by a conventional or unconventional physical mechanism. The
unconventional mechanisms, which roughly involve the appearance of tensionless
strings, can sometimes be better understood in $F$-theory. | A Conformal Fixed-Point Equation for the Effective Average Action: A Legendre transform of the recently discovered conformal fixed-point
equation is constructed, providing an unintegrated equation encoding full
conformal invariance within the framework of the effective average action. |
Rigid Supersymmetry from Conformal Supergravity in Five Dimensions: We study the rigid limit of 5d conformal supergravity with minimal
supersymmetry on Riemannian manifolds. The necessary and sufficient condition
for the existence of a solution is the existence of a conformal Killing vector.
Whenever a certain $SU(2)$ curvature becomes abelian the backgrounds define a
transversally holomorphic foliation. Subsequently we turn to the question under
which circumstances these backgrounds admit a kinetic Yang-Mills term in the
action of a vector multiplet. Here we find that the conformal Killing vector
has to be Killing. We supplement the discussion with various appendices. | Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver
Theories: Three-dimensional Coulomb branches have a prominent role in the study of
moduli spaces of supersymmetric gauge theories with $8$ supercharges in
$3,4,5$, and $6$ dimensions. Inspired by simply laced $3$d $\mathcal{N}=4$
supersymmetric quiver gauge theories, we consider Coulomb branches constructed
from non-simply laced quivers with edge multiplicity $k$ and no flavor nodes.
In a computation of the Coulomb branch as the space of dressed monopole
operators, a center-of-mass $U(1)$ symmetry needs to be ungauged. Typically,
for a simply laced theory, all choices of the ungauged $U(1)$ (i.e. all choices
of ungauging schemes) are equivalent and the Coulomb branch is unique. In this
note, we study various ungauging schemes and their effect on the resulting
Coulomb branch variety. It is shown that, for a non-simply laced quiver,
inequivalent ungauging schemes exist which correspond to inequivalent Coulomb
branch varieties. Ungauging on any of the long nodes of a non-simply laced
quiver yields the same Coulomb branch $\mathcal{C}$. For choices of ungauging
the $U(1)$ on a short node of rank higher than $1$, the GNO dual magnetic
lattice deforms such that it no longer corresponds to a Lie group, and
therefore, the monopole formula yields a non-valid Coulomb branch. However, if
the ungauging is performed on a short node of rank $1$, the one-dimensional
magnetic lattice is rescaled conformally along its single direction and the
corresponding Coulomb branch is an orbifold of the form
$\mathcal{C}/\mathbb{Z}_k$. Ungauging schemes of $3$d Coulomb branches provide
a particularly interesting and intuitive description of a subset of actions on
the nilpotent orbits studied by Kostant and Brylinski arXiv:math/9204227. The
ungauging scheme analysis is carried out for minimally unbalanced $C_n$, affine
$F_4$, affine $G_2$, and twisted affine $D_4^{(3)}$ quivers, respectively. |
Black Holes in Supergravity and String Theory: We give an elementary introduction to black holes in supergravity and string
theory. The focus is on BPS solutions in four- and higher-dimensional
supergravity and string theory. Basic ideas and techniques are explained in
detail, including exercises with solutions. | Lorentz-violating effects on topological defects generated by two real
scalar fields: The influence of a Lorentz-violation on soliton solutions generated by a
system of two coupled scalar fields is investigated. Lorentz violation is
induced by a fixed tensor coefficient that couples the two fields. The
Bogomol'nyi method is applied and first-order differential equations are
obtained whose solutions minimize energy and are also solutions of the
equations of motion. The analysis of the solutions in phase space shows how the
stability is modified with the Lorentz violation. It is shown explicitly that
the solutions preserve linear stability despite the presence of Lorentz
violation. Considering Lorentz violation as a small perturbation, an analytical
method is employed to yield analytical solutions. |
Domain Walls for Two-Dimensional Renormalization Group Flows: Renormalization Group domain walls are natural conformal interfaces between
two CFTs related by an RG flow. The RG domain wall gives an exact relation
between the operators in the UV and IR CFTs. We propose an explicit algebraic
construction of the RG domain wall between consecutive Virasoro minimal models
in two dimensions. Our proposal passes a stringent test: it reproduces in
detail the leading order mixing of UV operators computed in the conformal
perturbation theory literature. The algebraic construction can be applied to a
variety of known RG flows in two dimensions. | Monopoles near the Planck Scale and Unification: Considering our (3+1)-dimensional space-time as, in some way, discrete or l
attice with a parameter $a=\lambda_P$, where $\lambda_P$ is the Planck length,
we have investigated the additional contributions of lattice artifact monopoles
to beta-functions of the renormalisation group equations for the running fine
structure constants $\alpha_i(\mu)$ (i=1,2,3 correspond to the U(1), SU(2) and
SU(3) gauge groups of the Standard Model) in the Family Replicated Gauge Group
Model (FRGGM) which is an extension of the Standard Model at high energies. It
was shown that monopoles have $N_{fam}$ times smaller magnetic charge in FRGGM
than in SM ($N_{fam}$ is the number of families in FRGGM). We have estimated al
so the enlargement of a number of fermions in FRGGM leading to the suppression
of the asymptotic freedom in the non-Abelian theory. We have shown that, in
contrast to the case of AntiGUT when the FRGGM undergoes the breakdown at
$\mu=\mu_G\sim 10^{18}$ GeV, we have the possibility of unification if the
FRGGM-breakdown occurs at $\mu_G\sim 10^{14}$ GeV. By numerical calculations we
obtained an example of the unification of all gauge interactions (including
gravity) at the scale $\mu_{GUT}\approx 10^{18.4}$ GeV. We discussed the
possibility of $[SU(5)]^3$ or $[SO(10)]^3$ (SUSY or not SUSY) unifications. |
Spinor description of $D=5$ massless low-spin gauge fields: Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger
and gravitational fields is elaborated. Restrictions imposed on the curvature
spinors by the dynamical equations and Bianchi identities are analyzed. In the
absence of sources symmetric curvature spinors with $2s$ indices obey
first-order equations that in the linearized limit reduce to Dirac-type
equations for massless free fields. These equations allow for a higher-spin
generalization similarly to $4d$ case. Their solution in the form of the
integral over Lorentz-harmonic variables parametrizing coset manifold
$SO(1,4)/(SO(1,1)\times ISO(3))$ isomorphic to the three-sphere is considered.
Superparticle model that contains such Lorentz harmonics as dynamical
variables, as well as harmonics parametrizing the two-sphere $SU(2)/U(1)$ is
proposed. The states in its spectrum are given by the functions on $S^3$ that
upon integrating over the Lorentz harmonics reproduce on-shell symmetric
curvature spinors for various massless supermultiplets of $D=5$ space-time
supersymmetry. | Green functions of 2-dimensional Yang-Mills theories on nonorientable
surfaces: By using the path integral method , we calculate the Green functions of field
strength of Yang-Mills theories on arbitrary nonorientable surfaces in
Schwinger-Fock gauge. We show that the non-gauge invariant correlators consist
of a free part and an almost $x$-independent part. We also show that the gauge
invariant $n$-point functions are those corresponding to the free part , as in
the case of orientable surfaces. |
On Quantum Cohomology: We discuss a general quantum theoretical example of quantum cohomology and
show that various mathematical aspects of quantum cohomology have quantum
mechanical and also observable significance. | From dS to AdS and back: We describe in more detail the general relation uncovered in our previous
work between boundary correlators in de Sitter (dS) and in Euclidean anti-de
Sitter (EAdS) space, at any order in perturbation theory. Assuming the
Bunch-Davies vacuum at early times, any given diagram contributing to a
boundary correlator in dS can be expressed as a linear combination of Witten
diagrams for the corresponding process in EAdS, where the relative coefficients
are fixed by consistent on-shell factorisation in dS. These coefficients are
given by certain sinusoidal factors which account for the change in coefficient
of the contact sub-diagrams from EAdS to dS, which we argue encode
(perturbative) unitary time evolution in dS. dS boundary correlators with
Bunch-Davies initial conditions thus perturbatively have the same singularity
structure as their Euclidean AdS counterparts and the identities between them
allow to directly import the wealth of techniques, results and understanding
from AdS to dS. This includes the Conformal Partial Wave expansion and, by
going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the
Froissart-Gribov inversion formula. We give a few (among the many possible)
applications both at tree and loop level. Such identities between boundary
correlators in dS and EAdS are made manifest by the Mellin-Barnes
representation of boundary correlators, which we point out is a useful tool in
its own right as the analogue of the Fourier transform for the dilatation
group. The Mellin-Barnes representation in particular makes manifest
factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS,
which imply Cutkosky cutting rules and dispersion formulas for boundary
correlators in (EA)dS. Our results are completely general and in particular
apply to any interaction of (integer) spinning fields. |
The lowest modes around Gaussian solutions of tensor models and the
general relativity: In the previous paper, the number distribution of the low-lying spectra
around Gaussian solutions representing various dimensional fuzzy tori of a
tensor model was numerically shown to be in accordance with the general
relativity on tori. In this paper, I perform more detailed numerical analysis
of the properties of the modes for two-dimensional fuzzy tori, and obtain
conclusive evidences for the agreement. Under a proposed correspondence between
the rank-three tensor in tensor models and the metric tensor in the general
relativity, conclusive agreement is obtained between the profiles of the
low-lying modes in a tensor model and the metric modes transverse to the
general coordinate transformation. Moreover, the low-lying modes are shown to
be well on a massless trajectory with quartic momentum dependence in the tensor
model. This is in agreement with that the lowest momentum dependence of metric
fluctuations in the general relativity will come from the R^2-term, since the
R-term is topological in two dimensions. These evidences support the idea that
the low-lying low-momentum dynamics around the Gaussian solutions of tensor
models is described by the general relativity. I also propose a renormalization
procedure for tensor models. A classical application of the procedure makes the
patterns of the low-lying spectra drastically clearer, and suggests also the
existence of massive trajectories. | Asymptotic Symmetries and Electromagnetic Memory: Recent investigations into asymptotic symmetries of gauge theory and gravity
have illuminated connections between gauge field zero-mode sectors, the
corresponding soft factors, and their classically observable counterparts -- so
called "memories." Here we complete this triad for the case of large U(1) gauge
symmetries at null infinity. |
Future Boundary Conditions in De Sitter Space: We consider asymptotically future de Sitter spacetimes endowed with an
eternal observatory. In the conventional descriptions, the conformal metric at
the future boundary I^+ is deformed by the flux of gravitational radiation. We
however impose an unconventional future "Dirichlet" boundary condition
requiring that the conformal metric is flat everywhere except at the conformal
point where the observatory arrives at I^+. This boundary condition violates
conventional causality, but we argue the causality violations cannot be
detected by any experiment in the observatory. We show that the bulk-to-bulk
two-point functions obeying this future boundary condition are not realizable
as operator correlation functions in any de Sitter invariant vacuum, but they
do agree with those obtained by double analytic continuation from anti-de
Sitter space. | Bulk locality and cooperative flows: We use the 'bit thread' formulation of holographic entanglement entropy to
highlight the distinction between the universally-valid strong subadditivity
and the more restrictive relation called monogamy of mutual information (MMI),
known to hold for geometrical states (i.e. states of holographic theories with
gravitational duals describing a classical bulk geometry). In particular, we
provide a novel proof of MMI, using bit threads directly. To this end, we
present an explicit geometrical construction of cooperative flows which we
build out of disjoint thread bundles. We conjecture that our method applies in
a wide class of configurations, including ones with non-trivial topology,
causal structure, and time dependence. The explicit nature of the construction
reveals that MMI is more deeply rooted in bulk locality than is the case for
strong subadditivity. |
Dynamical (super)symmetry vacuum properties of the supersymmetric
Chern-Simons-matter model: By computing the two-loop effective potential of the D=3 N=1 supersymmetric
Chern-Simons model minimally coupled to a massless self-interacting matter
superfield, it is shown that supersymmetry is preserved, while the internal
U(1) and the scale symmetries are broken at two-loop order, dynamically
generating masses both for the gauge superfield and for the real component of
the matter superfield. | The analytic structure of conformal blocks and the generalized
Wilson-Fisher fixed points: We describe in detail the method used in our previous work arXiv:1611.10344
to study the Wilson-Fisher critical points nearby generalized free CFTs,
exploiting the analytic structure of conformal blocks as functions of the
conformal dimension of the exchanged operator. Our method is equivalent to the
mechanism of conformal multiplet recombination set up by null states. We
compute, to the first non-trivial order in the $\epsilon$-expansion, the
anomalous dimensions and the OPE coefficients of infinite classes of scalar
local operators using just CFT data. We study single-scalar and
$O(N)$-invariant theories, as well as theories with multiple deformations. When
available we agree with older results, but we also produce a wealth of new
ones. Unitarity and crossing symmetry are not used in our approach and we are
able to apply our method to non-unitary theories as well. Some implications of
our results for the study of the non-unitary theories containing partially
conserved higher-spin currents are briefly mentioned. |
A test of the circular Unruh effect using atomic electrons: We propose a test for the circular Unruh effect using certain atoms -
fluorine and oxygen. For these atoms the centripetal acceleration of the outer
shell electrons implies an effective Unruh temperature in the range 1000 - 2000
K. This range of Unruh temperatures is large enough to shift the expected
occupancy of the lowest energy level and nearby energy levels. In effect the
Unruh temperature changes the expected pure ground state, with all the
electrons in the lowest energy level, to a mixed state with some larger than
expected occupancy of states near to the lowest energy level. Examining these
atoms at low background temperatures and finding a larger than expected number
of electrons in low lying excited levels, beyond what is expected due to the
background thermal excitation, would provide experimental evidence for the
Unruh effect. | Topological Masses From Broken Supersymmetry: We develop a formalism for computing one-loop gravitational corrections to
the effective action of D-branes. In particular, we study bulk to brane
mediation of supersymmetry breaking in models where supersymmetry is broken at
the tree-level in the closed string sector (bulk) by Scherk-Schwarz boundary
conditions, while it is realized on a collection of D-branes in a linear or
non-linear way. We compute the gravitational corrections to the fermion masses
$m_{1/2}$ (gauginos or goldstino) induced from the exchange of closed strings,
which are non-vanishing for world-sheets with Euler characteristic -1 (``genus
3/2'') due to a string diagram with one handle and one hole. We show that the
corrections have a topological origin and that in general, for a small
gravitino mass, the induced mass behaves as $m_{1/2}\propto g^4 m_{3/2}$, with
$g$ the gauge coupling. In generic orbifold compactifications however, this
leading term vanishes as a consequence of cancellations caused by discrete
symmetries, and the remainder is exponentially suppressed by a factor of
$\exp(-1/\alpha'm^2_{3/2})$. |
Dual Vector Multiplet Coupled to Dual N=1 Supergravity in 10D: We couple in superspace a `dual' vector multiplet (C_{m_1... m_7}, \l^\alpha)
to the dual version of N=1 supergravity (e_m{}^a, \psi_m{}^\alpha, M_{m_1...
m_6}, \chi_\a,\Phi) in ten-dimensions. Our new 7-form field C has its 8-form
field strength H dual to the 2-form field strength F of the conventional vector
multiplet. We have found that the H-Bianchi identity must have the form N\wedge
F, where N is the 7-form field strength in dual supergravity. We also see why
only the dual version of supergravity couples to the dual vector multiplet
consistently. The potential anomaly for the dual vector multiplet can be
cancelled for the particular gauge group U(1)^{496} by the Green-Schwarz
mechanism. As a by-product, we also give the globally supersymmetric Abelian
Dirac-Born-Infeld interactions for the dual vector multiplet for the first
time. | Charge Expulsion from Black Brane Horizons, and Holographic Quantum
Criticality in the Plane: Quantum critical behavior in 2+1 dimensions is established via holographic
methods in a 5+1-dimensional Einstein gravity theory with gauge potential form
fields of rank 1 and 2. These fields are coupled to one another via a
tri-linear Chern-Simons term with strength k. The quantum phase transition is
physically driven by the expulsion of the electric charge from inside the black
brane horizon to the outside, where it gets carried by the gauge fields which
acquire charge thanks to the Chern-Simons interaction. At a critical value
k=k_c, zero temperature, and any finite value of the magnetic field, the IR
behavior is governed by a near-horizon Lifshitz geometry. The associated
dynamical scaling exponent depends on the magnetic field. For k<k_c, the flow
towards low temperature is governed by a Reissner-Nordstrom-like black brane
whose charge and entropy density are non-vanishing at zero temperature. For k >
k_c, the IR flow is towards the purely magnetic brane in AdS_6. Its
near-horizon geometry is AdS_4 \times R^2, so that the entropy density vanishes
quadratically with temperature, and all charge is carried by the gauge fields
outside of the horizon. |
Quantum flux operators in higher spin theories: We construct Carrollian higher spin field theories by reducing the bosonic
Fronsdal theories in flat spacetime to future null infinity. We extend the
Poincar\'e fluxes to quantum flux operators which generate Carrollian
diffeomorphism, namely supertranslation and superrotation. These flux operators
form a closed symmetry algebra once including a helicity flux operator which
follows from higher spin super-duality transformation. The super-duality
transformation is an angle-dependent transformation at future null infinity
which generalizes the usual electro-magnetic duality transformation. The
results agree with the lower spin cases when restricting to $s=0,1,2$. | On Exceptional 't Hooft Lines in 4D-Chern-Simons Theory: We study 't Hooft lines and the associated $\mathcal{L}$- operators in
topological 4D Chern-Simons theory with gauge symmetry given by the exceptional
groups E$_{6}$ and E$_{7}$. We give their oscillator realisations and propose
topological gauge quivers encoding the properties of these topological lines
where Darboux coordinates are interpreted in terms of topological fundamental
matter. Other related aspects are also described. |
Deriving on-shell open string field amplitudes without using Feynman
rules: We present a series of new gauge invariant quantities in Witten's open string
field theory. They are defined for a given set of open string states which
satisfy the physical state condition around a classical solution. For known
classical solutions, we show that these gauge invariant quantities compute on
shell tree-level scattering amplitudes around the correspondent D-brane
configuration. | Conformal mechanics on rotating Bertotti-Robinson spacetime: We investigate conformal mechanics associated with the rotating
Bertotti-Robinson (RBR) geometry found recently as the near-horizon limit of
the extremal rotating Einstein-Maxwell-dilaton-axion black holes. The solution
breaks the $SL(2,R)\times SO(3)$ symmetry of Bertotti-Robinson (BR) spacetime
to $SL(2,R)\times U(1)$ and breaks supersymmetry in the sense of $N=4, d=4$
supergravity as well. However, it shares with BR such properties as confinement
of timelike geodesics and discreteness of the energy of test fields on the
geodesically complete manifold. Conformal mechanics governing the radial
geodesic motion coincides with that for a charged particle in the BR background
(a relativistic version of the De Alfaro-Fubini-Furlan model), with the
azimuthal momentum playing the role of a charge. Similarly to the BR case, the
transition from Poincar\'e to global coordinates leads to a redefinition of the
Hamiltonian making the energy spectrum discrete. Although the metric does not
split into a product space even asymptotically, it still admits an
infinite-dimensional extension of $SL(2,R)$ as asymptotic symmetry. The latter
is shown to be given by the product of one copy of the Virasoro algebra and
U(1), the same being valid for the extremal Kerr throat. |
Interaction of instantons in a gauge theory forcing their identical
orientation: A gauge theory model in which there exists a specific interaction between
instantons is considered. An effective action describing this interaction
possesses a minimum when the instantons have identical orientation. The
considered interaction might provide a phase transition into the state where
instantons have a preferred orientation. This phase of the gauge-field theory
is important because it can give the description of gravity in the framework of
the gauge theory. | Moving Mixed Branes in Compact Spacetime: In this article we present a general description of two moving branes in
presence of the $B_{\mu \nu}$ field and gauge fields $A^{(1)}_{\alpha_1}$ and
$A^{(2)}_{\alpha_2}$ on them, in spacetime in which some of its directions are
compact on tori. Some examples are considered to elucidate this general
description. Also contribution of the massless states to the interaction is
extracted. Boundary state formalism is a useful tool for these considerations. |
The vacuum state functional of interacting string field theory: We show that the vacuum state functional for both open and closed string
field theories can be constructed from the vacuum expectation values it must
generate. The method also applies to quantum field theory and as an application
we give a diagrammatic description of the equivalance between Schrodinger and
covariant repreresentations of field theory. | Supersymmetry,Shape Invariance and Exactly Solvable Noncentral
Potentials: Using the ideas of supersymmetry and shape invariance we show that the
eigenvalues and eigenfunctions of a wide class of noncentral potentials can be
obtained in a closed form by the operator method. This generalization
considerably extends the list of exactly solvable potentials for which the
solution can be obtained algebraically in a simple and elegant manner. As an
illustration, we discuss in detail the example of the potential
$$V(r,\theta,\phi)={\omega^2\over 4}r^2 + {\delta\over r^2}+{C\over r^2
sin^2\theta}+{D\over r^2 cos^2\theta} + {F\over r^2 sin^2\theta sin^2
\alpha\phi} +{G\over r^2 sin^2\theta cos^2\alpha\phi}$$ with 7 parameters.Other
algebraically solvable examples are also given. |
Two-dimensional Yang-Mills theory: perturbative and instanton
contributions, and its relation to QCD in higher dimensions: Two different scenarios (light-front and equal-time) are possible for
Yang-Mills theories in two dimensions. The exact $\bar q q$-potential can be
derived in perturbation theory starting from the light-front vacuum, but
requires essential instanton contributions in the equal-time formulation. In
higher dimensions no exact result is available and, paradoxically, only the
latter formulation (equal-time) is acceptable, at least in a perturbative
context. | Superconducting phase transitions in 2+1 dimensional quantum field
theories modeling generalized polaronic interactions. Part I: Jahn-Teller
inspired models: We review the fundamentals of Jahn-Teller interactions and their field
theoretical modelings and show that a 2+1 dimensional gauge theory where the
gauge field couples to "flavored fermions" arises in a natural way from a
two-band model describing the dynamical Jahn-Teller effect. The theory exhibits
a second order phase transition to novel finite-temperature superconductivity. |
On a Deformation of 3-Branes: We construct an explicit class of solutions of type IIB supergravity that is
a smooth deformation of the 3-brane class of solutions. The solution is
nonsupersymmetric and involves nontrivial dilaton and axion fields as well as
the standard 5-form field strength. One of the main features of the solution is
that for large values of the radius the deformation is small and it
asymptotically approaches the undeformed 3-brane solution, signaling a
restoration of conformal invariance in the UV for the dual gauge theory. We
suggest that the supergravity deformation corresponds to a massive deformation
on the dual gauge theory and consequently the deformed theory has the
undeformed one as an ultraviolet fixed point. In cases where the original
3-brane solution preserves some amount of supersymmetry we suggest that the
gauge theory interpretation is that of soft supersymmetry breaking. We discuss
the deformation for D3-branes on the conifold and the generalized conifold
explicitly. We show that the semiclassical behavior of the Wilson loop suggests
that the corresponding gauge theory duals are confining. | Conserved charges and soliton solutions in affine Toda theory: We study the conserved charges of affine Toda field theories by making use of
the conformally invariant extension of these theories. We compute the values of
all charges for the single soliton solutions, and show that these are related
to eigenvectors of the Cartan matrix of the finite-dimensional Lie algebra
underlying the theory. |
The upper critical magnetic field of holographic superconductor with
conformally invariant power-Maxwell electrodynamics: The properties of $(d-1)$-dimensional $s$-wave holographic superconductor in
the presence of power-Maxwell field is explored. We study the probe limit in
which the scalar and gauge fields do not backreact on the background geometry.
Our study is based on the matching of solutions on the boundary and on the
horizon at some intermediate point. At first, the case without external
magnetic field is considered, and the critical temperature is obtained in terms
of the charge density, the dimensionality, and the power-Maxwell exponent.
Then, a magnetic field is turned on in the $d$-dimensional bulk which can
influence the $(d-1)$-dimensional holographic superconductor at the boundary.
The phase behavior of the corresponding holographic superconductor is obtained
by computing the upper critical magnetic field in the presence of power-Maxwell
electrodynamics, characterized by the power exponent $q$. Interestingly, it is
observed that in the presence of magnetic field, the physically acceptable
phase behavior of the holographic superconductor is obtained for $q={d}/{4}$,
which guaranties the conformal invariance of the power-Maxwell Lagrangian. The
case of physical interest in five spacetime dimensions ($d=5$, and $q=5/4$) is
considered in detail, and compared with the results obtained for the usual
Maxwell electrodynamics $q=1$ in the same dimensions. | A non-rational CFT with central charge 1: Two dimensional conformal field theories with central charge one are
discussed. After a short review of theories based on one free boson, a
different CFT is described, which is obtained as a limit of minimal models. |
Relativistic Bohmian mechanics from scalar gravity: In this article we show that the fundamental equations of relativistic
Bohmian mechanics for a single particle can be derived from a scalar theory of
curved space-time. | Gauge Orbit Types for Theories with Classical Compact Gauge Group: We determine the orbit types of the action of the group of local gauge
transformations on the space of connections in a principal bundle with
structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold
of dimension 4. Complemented with earlier results on U(n) and SU(n) this
completes the classification of the orbit types for all classical compact gauge
groups over such space-time manifolds. On the way we derive the classification
of principal bundles with structure group SO(n) over these manifolds and the
Howe subgroups of SO(n). |
F-Theorem without Supersymmetry: The conjectured F-theorem for three-dimensional field theories states that
the finite part of the free energy on S^3 decreases along RG trajectories and
is stationary at the fixed points. In previous work various successful tests of
this proposal were carried out for theories with {\cal N}=2 supersymmetry. In
this paper we perform more general tests that do not rely on supersymmetry. We
study perturbatively the RG flows produced by weakly relevant operators and
show that the free energy decreases monotonically. We also consider large N
field theories perturbed by relevant double trace operators, free massive field
theories, and some Chern-Simons gauge theories. In all cases the free energy in
the IR is smaller than in the UV, consistent with the F-theorem. We discuss
other odd-dimensional Euclidean theories on S^d and provide evidence that
(-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1
this is the well-known g-theorem. | Gauge bosons and the AdS_3/LCFT_2 correspondence: We study the relationship between the gauge boson coupled to spin 2 operator
and the singleton in three-dimensional anti-de Sitter space(AdS$_3$). The
singleton can be expressed in terms of a pair of dipole ghost fields $A$ and
$B$ which couple to $D$ and $C$ operators on the boundary of AdS$_3$. These
operators form the logarithmic conformal field theory(LCFT$_2$). Using the
correlation function for logarithmic pair, we calculate the greybody factor for
the singleton. In the low temperature limit of $\omega \gg T_{\pm}$, this is
compared with the result of the bulk AdS$_3$ calculation of the gauge boson. We
find that the gauge boson cannot be realized as a model of the AdS$_3$/LCFT$_2$
correspondence. |
Massive Fields of Arbitrary Integer Spin in Symmetrical Einstein Space: We study the propagation of gauge fields with arbitrary integer spins in the
symmetrical Einstein space of any dimensionality. We reduce the problem of
obtaining a gauge-invariant Lagrangian of integer spin fields in such
background to an purely algebraic problem of finding a set of operators with
certain features using the representation of high-spin fields in the form of
some vectors of pseudo-Hilbert space. We consider such construction in the
linear order in the Riemann tensor and scalar curvature and also present an
explicit form of interaction Lagrangians and gauge transformations for massive
particles with spins 1 and 2 in terms of symmetrical tensor fields. | On the quantum matrix string: We study the behavior of matrix string theory in the strong coupling region,
where it is expected to reduce to discrete light-cone type IIA superstring. In
the large $N$ limit, the reduction corresponds to the double-dimensional
reduction from wrapped supermembranes on $R^{10}\times S^1$ to type IIA
superstrings on $R^{10}$ in the light-cone gauge, which is shown classically,
however it is not obvious quantum mechanically. We analyze the problem in
matrix string theory by using the strong coupling ($1/g$) expansion. We find
that the quantum corrections do not cancel out at $\mathcal{O}(1/g^2)$.
Detailed calculations can be seen in Ref.\cite{UY}. |
Localization of Bulk Matters on a Thick Anti-de Sitter Brane: In this paper, we investigate the localization and the mass spectra of
gravity and various bulk matter fields on a thick anti-de Sitter (AdS) brane,
by presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in
the corresponding Schr\"{o}dinger equations. For gravity, the potential of the
KK modes tends to infinity at the boundaries of the extra dimension, which
leads to an infinite number of the bound KK modes. Although the gravity zero
mode cannot be localized on the AdS brane, the massive modes are trapped on the
brane. The scalar perturbations of the thick AdS brane have been analyzed, and
the brane is stable under the scalar perturbations. For spin-0 scalar fields
and spin-1 vector fields, the potentials of the KK modes also tend to infinity
at the boundaries of the extra dimension, and the characteristic of the
localization is the same as the case of gravity. For spin-1/2 fermions, by
introducing the usual Yukawa coupling $\eta\bar{\Psi}\phi\Psi$ with the
positive coupling constant $\eta$, the four-dimensional massless left-chiral
fermion and massive Dirac fermions are obtained on the AdS thick brane. | Low Energy Processes Associated with Spontaneously Broken N=2
Supersymmetry: We consider low energy processes described by the N=2 supercurrent on its
partially (to N=1) and spontaneously broken vacuum and the attendant
Nambu-Goldstone fermion (NGF), which the presence of the electric and magnetic
Fayet-Iliopoulos (FI) terms is responsible for. We show suppressions of
amplitudes decaying into the NGF as its momentum becomes small. In the
lagrangian realization (namely, the model of arXiv:hep-th/0409060) of the
conserved supercurrent, the NGF resides in the overall U(1), which is
nonetheless not decoupled, and interacts with the SU(N) sector through
nonderivative as well as derivative couplings. The low energy suppression is
instead accomplished by a cancellation between the annihilation diagram from
the Yukawa couplings and the contact four-Fermi terms. We give a complete form
of the supercurrent and the model is recast in more transparent notation. |
New agegraphic dark energy in Horava-Lifshitz cosmology: We investigate the new agegraphic dark energy scenario in a universe governed
by Horava-Lifshitz gravity. We consider both the detailed and non-detailed
balanced version of the theory, we impose an arbitrary curvature, and we allow
for an interaction between the matter and dark energy sectors. Extracting the
differential equation for the evolution of the dark energy density parameter
and performing an expansion of the dark energy equation-of-state parameter, we
calculate its present and its low-redshift value as functions of the dark
energy and curvature density parameters at present, of the Horava-Lifshitz
running parameter $\lambda$, of the new agegraphic dark energy parameter $n$,
and of the interaction coupling $b$. We find that $w_0=-0.82^{+0.08}_{-0.08}$
and $w_1=0.08^{+0.09}_{-0.07}$. Although this analysis indicates that the
scenario can be compatible with observations, it does not enlighten the
discussion about the possible conceptual and theoretical problems of
Horava-Lifshitz gravity. | Microstates of Non-supersymmetric Black Holes: A five-dimensional dyonic black hole in Type-I theory is considered that is
extremal but non-supersymmetric. It is shown that the Bekenstein-Hawking
entropy of this black hole counts precisely the microstates of a D-brane
configuration with the same charges and mass, even though there is no apparent
supersymmetric nonrenormalization theorem for the mass. A similar result is
known for the entropy at the stretched horizon of electrically charged,
extremal, but non-supersymmetric black holes in heterotic string theory. It is
argued that classical nonrenormalization of the mass may partially explain this
result. |
D-Branes in Coset Models: The analysis of D-branes in coset models G/H provides a natural extension of
recent studies on branes in WZW-theory and it has various interesting
applications to physically relevant models. In this work we develop a reduction
procedure that allows to construct the non-commutative gauge theories which
govern the dynamics of branes in G/H. We obtain a large class of solutions and
interprete the associated condensation processes geometrically. The latter are
used to propose conservation laws for the dynamics of branes in coset models at
large level k. In super-symmetric theories, conserved charges are argued to
take their values in the representation ring of the denominator theory.
Finally, we apply the general results to study boundary fixed points in two
examples, namely for parafermions and minimal models. | Exact Geometries from Boundary Gravity: We show that the extremal Reissner-Nordstr\"{o}m type multi black holes in an
emergent scenario are exact in General Relativity. It is shown that an axion in
the bulk together with a geometric torsion ensure the required energy-momentum
to source the $(3$$+$$1)$ geometry in the Einstein tensor. Analysis reveals a
significant role of dark energy to the curved space-time. |
No-interaction theorem without Hamiltonian and Lagrangian formalism:
invariant momentum on null cones: In a previous paper (G.Yoneda, Proc.R.Soc.London, A445,(1994),221), we proved
the no-interaction theorem for four particles with the assumption that the
(linear and angular) momentum on space-like planes is invariant. In this paper,
we assume that the momentum on null cones is invariant and prove that there is
no interaction for four particles. | Holographic Entanglement Distillation from the Surface State
Correspondence: We study correlations between geometric subfactors living on the
Ryu-Takayanagi surface that bounds the entanglement wedge. Using the
surface-state correspondence and the bit threads program, we are able to
calculate mutual information and conditional mutual information between
subfactors. This enables us to count the shared Bell pairs between subfactors,
and we propose an entanglement distillation procedure over these subsystems via
a SWAP gate protocol. We comment on extending to multipartite entanglement. |
The Mathematical Footing of Non-associative Geometry: Starting with a Hilbert space endowed with a representation of a unitary Lie
algebra and an action of a generalized Dirac operator, we develop a
mathematical concept towards gauge field theories. This concept shares common
features with the non--commutative geometry a la Connes/Lott, differs from
that, however, by the implementation of unitary Lie algebras instead of
associative *-algebras. The general scheme is presented in detail and is
applied to functions $\otimes$ matrices. | From k-essence to generalised Galileons: We determine the most general scalar field theories which have an action that
depends on derivatives of order two or less, and have equations of motion that
stay second order and lower on flat space-time. We show that those theories can
all be obtained from linear combinations of Lagrangians made by multiplying a
particular form of the Galileon Lagrangian by an arbitrary scalar function of
the scalar field and its first derivatives. We also obtain curved space-time
extensions of those theories which have second order field equations for both
the metric and the scalar field. This provide the most general extension, under
the condition that field equations stay second order, of k-essence, Galileons,
k-Mouflage as well as of the kinetically braided scalars. It also gives the
most general action for a scalar classicalizer, which has second order field
equations. We discuss the relation between our construction and the Euler
hierachies of Fairlie et al, showing in particular that Euler hierachies allow
one to obtain the most general theory when the latter is shift symmetric. As a
simple application of our formalism, we give the covariantized version of the
conformal Galileon. |
Black holes from CFT: Universality of correlators at large c: Two-dimensional conformal field theories at large central charge and with a
sufficiently sparse spectrum of light states have been shown to exhibit
universal thermodynamics. This thermodynamics matches that of AdS$_3$ gravity,
with a Hawking-Page transition between thermal AdS and the BTZ black hole. We
extend these results to correlation functions of light operators. Upon making
some additional assumptions, such as large $c$ factorization of correlators, we
establish that the thermal AdS and BTZ solutions emerge as the universal
backgrounds for the computation of correlators. In particular, Witten diagrams
computed on these backgrounds yield the CFT correlators, order by order in a
large $c$ expansion, with exponentially small corrections. In pure CFT terms,
our result is that thermal correlators of light operators are determined
entirely by light spectrum data. Our analysis is based on the constraints of
modular invariance applied to the torus two-point function. | Unstable Nambu-Goldstone modes: Nambu-Goldstone (NG) modes for 0-form and higher-form symmetries can become
unstable in the presence of background fields. Examples include the instability
of a photon with a time-dependent axion background or with a chirality
imbalance, known as the chiral plasma instability, and the instability of a
dynamical axion with a background electric field. We show that all these
phenomena can be universally described by a symmetry algebra for 0-form and
higher-form symmetries. We prove a counting rule for the number of unstable NG
modes in terms of correlation functions of broken symmetry generators. Based on
our unified description, we further give a simple new example where one of the
NG modes associated with the spontaneous 0-form symmetry breaking $U(1) \times
U(1) \to \{1\}$ becomes unstable. |
Supersymmetric Janus Solutions in Four Dimensions: We use maximal gauged supergravity in four dimensions to construct the
gravity dual of a class of supersymmetric conformal interfaces in the theory on
the world-volume of multiple M2-branes. We study three classes of examples in
which the $(1+1)$-dimensional defects preserve $(4,4)$, $(0,2)$ or $(0,1)$
supersymmetry. Many of the solutions have the maximally supersymmetric $AdS_4$
vacuum dual to the $\mathcal{N}=8$ ABJM theory on both sides of the interface.
We also find new special classes of solutions including one that interpolates
between the maximally supersymmetric vacuum and a conformal fixed point with
$\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. We find another
solution that interpolates between two distinct conformal fixed points with
$\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. In eleven dimensions,
this $G_2$ to $G_2$ solution corresponds to a domain wall across which a
magnetic flux reverses orientation. | Some properties of meta-stable supersymmetry-breaking vacua in
Wess-Zumino models: As a contribution to the current efforts to understand supersymmetry-breaking
by meta-stable vacua, we study general properties of supersymmetry-breaking
vacua in Wess-Zumino models: we show that tree-level degeneracy is generic,
explore some constraints on the couplings and present a simple model with a
long-lived meta-stable vacuum, ending with some generalizations to
non-renormalizable models. |
Electric dipole moment induced by a QCD instanton in an external
magnetic field: In the chiral magnetic effect, there is a competition between a strong
magnetic field, which tends to project positively charged particles to have
spin aligned along the magnetic field, and a chirality imbalance which may be
produced locally by a topologically nontrivial gauge field such as an
instanton. We study the properties of the Euclidean Dirac equation for a light
fermion in the presence of both a constant abelian magnetic field and an SU(2)
instanton. In particular, we analyze the zero modes analytically in various
limits, both on R^4 and on the four-torus, in order to compare with recent
lattice QCD results, and study the implications for the electric dipole moment. | On Unitarity of Massive Gravity in Three Dimensions: We examine a unitarity of a particular higher-derivative extension of general
relativity in three space-time dimensions, which has been recently shown to be
equivalent to the Pauli-Fierz massive gravity at the linearized approximation
level, and explore a possibility of generalizing the model to higher space-time
dimensions. We find that the model in three dimensions is indeed unitary in the
tree-level, but the corresponding model in higher dimensions is not so due to
the appearance of non-unitary massless spin-2 modes. |
Decay constants in soft wall AdS/QCD revisited: Phenomenological AdS/QCD models, like hard wall and soft wall, provide
hadronic mass spectra in reasonable consistency with experimental and (or)
lattice results. These simple models are inspired in the AdS/CFT correspondence
and assume that gauge/ gravity duality holds in a scenario where conformal
invariance is broken through the introduction of an energy scale.
Another important property of hadrons: the decay constant, can also be
obtained from these models. However, a consistent formulation of an AdS/QCD
model that reproduces the observed behavior of decay constants of vector meson
excited states is still lacking. In particular: for radially excited states of
heavy vector mesons, the experimental data lead to decay constants that
decrease with the radial excitation level.
We show here that a modified framework of soft wall AdS/QCD involving an
additional dimensionfull parameter, associated with an ultraviolet energy
scale, provides decay constants decreasing with radial excitation level. In
this version of the soft wall model the two point function of gauge theory
operators is calculated at a finite position of the anti-de Sitter space radial
coordinate. | T-symmetry in String Geometry Theory: String geometry theory is one of the candidates of non-perturbative
formulation of string theory. In this paper, we have shown that dimensionally
reduced string geometry theories have what we call T-symmetry. In case of the
dimensional reduction in space-like directions, the T-symmetry transformation
gives the T-dual transformation between the type IIA and IIB perturbative
vacua. In case of the dimensional reduction in the direction of string geometry
time $\bar{\tau}$, the T-symmetry transformation is independent of the T-dual
transformation, and gives a symmetry that cannot be seen in the perturbative
string theories. |
Vacuum expectation value of the energy-momentum tensor in a higher
dimensional compactified cosmic string spacetime: The main objective of this paper is to analyze the vacuum expectation value
(VEV) of the energy-momentum tensor (EMT) associated with a charged scalar
quantum field in a high-dimensional cosmic string spacetime admitting the
presence of a magnetic flux running along the string's core. In addition, we
also assume that the coordinate along the string's axis is compactified to a
circle and presents an extra magnetic flux running along its center. This
compactification is implemented by imposing a quasiperiodic condition on the
field with an arbitrary phase $\beta$. The calculation of the VEV of the EMT
and field squared, are developed by using the positive-energy Wightman
function. The latter is constructed by the mode sum of the complete set of
normalized bosonic wave-functions. Due to the compactification, two distinct
contributions take place. The first one corresponds to the VEV in a cosmic
string spacetime without compactification considering the magnetic interaction.
So, this term presents a contribution due to the non-trivial topology of the
conical space, and an additional contribution due to the interaction between
the scalar field with the magnetic flux. The latter is a periodic function of
the magnetic flux with period equal to the quantum flux, $\Phi_0=2\pi/e$, and
corresponds to a Aharanov-Bhom type contribution. The second contribution is
induced by the compactification itself and depends on the magnetic flux along
the string's core. It is also an even function of the magnetic flux enclosed by
the string axis. Some asymptotic expressions for the VEVs of the
energy-momentum tensor and field squared are provided for specific limiting
cases of the physical parameter of the model. | Holographic Optics and Negative Refractive Index: In recent years a very exciting and intense activity has been devoted to the
understanding and construction of materials that enjoy exotic optical
properties, such as a negative refractive index. Motivated by these
experimental and theoretical developments, we use the string-inspired idea of
holography to study the electromagnetic response of a certain class of media:
strongly coupled relativistic systems that admit a dual gravitational
description. Our results indicate that this type of media generally have a
negative refractive index. Moreover we observe that a negative refractive index
could be a common feature of relativistic hydrodynamic systems at low
frequencies. |
Black hole entropy and quantum information: We review some recently established connections between the mathematics of
black hole entropy in string theory and that of multipartite entanglement in
quantum information theory. In the case of N=2 black holes and the entanglement
of three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant,
provides both the black hole entropy and the measure of tripartite
entanglement. In the case of N=8 black holes and the entanglement of seven
qubits, the quartic E_7 invariant of Cartan provides both the black hole
entropy and the measure of a particular tripartite entanglement encoded in the
Fano plane. | Initial states and infrared physics in locally de Sitter spacetime: The long wavelength physics in a de Sitter region depends on the initial
quantum state. While such long wavelength physics is under control for massive
fields near the Hartle-Hawking vacuum state, such initial states make unnatural
assumptions about initial data outside the region of causal contact of a local
observer. We argue that a reasonable approximation to a maximum entropy state,
one that makes minimal assumptions outside an observer's horizon volume, is one
where a cutoff is placed on a surface bounded by timelike geodesics, just
outside the horizon. For sufficiently early times, such a cutoff induces
secular logarithmic divergences with the expansion of the region. For massive
fields, these effects sum to finite corrections at sufficiently late times. The
difference between the cutoff correlators and Hartle-Hawking correlators
provides a measure of the theoretical uncertainty due to lack of knowledge of
the initial state in causally disconnected regions. These differences are
negligible for primordial inflation, but can become significant during epochs
with very long-lived de Sitter regions, such as we may be entering now. |
Causal propagation of constraints in bimetric relativity in standard 3+1
form: The goal of this work was to investigate the propagation of the constraints
in the ghost-free bimetric theory where the evolution equations are in standard
3+1 form. It is established that the constraints evolve according to a
first-order symmetric hyperbolic system whose characteristic cone consists of
the null cones of the two metrics. Consequently, the constraint evolution
equations are well-posed, and the constraints stably propagate. | The quantum algebra of superspace: We present the complete set of $N=1$, $D=4$ quantum algebras associated to
massive superparticles. We obtain the explicit solution of these algebras
realized in terms of unconstrained operators acting on the Hilbert space of
superfields. These solutions are expressed using the chiral, anti-chiral and
tensorial projectors which define the three irreducible representations of the
supersymmetry on the superfields. In each case the space-time variables are
non-commuting and their commutators are proportional to the internal angular
momentum of the representation. The quantum algebra associated to the chiral or
the anti-chiral projector is the one obtained by the quantization of the
Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new
superparticle action for the (superspin 1/2) case and show that their wave
functions are the ones associated to the irreducible tensor multiplet. |
A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices: We use the idea of a Wigner surmise to compute approximate distributions of
the first eigenvalue in chiral Random Matrix Theory, for both real and complex
eigenvalues. Testing against known results for zero and maximal non-Hermiticity
in the microscopic large-N limit we find an excellent agreement, valid for a
small number of exact zero-eigenvalues. New compact expressions are derived for
real eigenvalues in the orthogonal and symplectic classes, and at intermediate
non-Hermiticity for the unitary and symplectic classes. Such individual Dirac
eigenvalue distributions are a useful tool in Lattice Gauge Theory and we
illustrate this by showing that our new results can describe data from
two-colour QCD simulations with chemical potential in the symplectic class. | Sound waves in strongly coupled non-conformal gauge theory plasma: Gauge/string correspondence provides an efficient method to investigate gauge
theories. In this talk we discuss the results of the paper (to appear) by P.
Benincasa, A. Buchel and A. O. Starinets, where the propagation of sound waves
is studied in a strongly coupled non-conformal gauge theory plasma. In
particular, a prediction for the speed of sound as well as for the bulk
viscosity is made for the N=2* gauge theory in the high temperature limit. As
expected, the results achieved show a deviation from the speed of sound and the
bulk viscosity for a conformal theory. It is pointed out that such results
depend on the particular gauge theory considered. |
On-shell recursion for massive fermion currents: We analyze the validity of BCFW recursion relations for currents of n - 2
gluons and two massive quarks, where one of the quarks is off shell and the
remaining particles are on shell. These currents are gauge-dependent and can be
used as ingredients in the unitarity-based approach to computing one-loop
amplitudes. The validity of BCFW recursion relations is well known to depend on
the so-called boundary behavior of the currents as the momentum shift parameter
goes to infinity. With off-shell currents, a new potential problem arises,
namely unphysical poles that depend on the choice of gauge. We identify
conditions under which boundary terms are absent and unphysical poles are
avoided, so that there is a natural recursion relation. In particular, we are
able to choose a gauge in which we construct a valid shift for currents with at
least n - 3 gluons of the same helicity. We derive an analytic formula in the
case where all gluons have the same helicity. As by-products, we prove the
vanishing boundary behavior of general off-shell objects in Feynman gauge, and
we find a compact generalization of Berends-Giele gluon currents with a generic
reference spinor. | A General Framework of Automorphic Inflation: Automorphic inflation is an application of the framework of automorphic
scalar field theory, based on the theory of automorphic forms and
representations. In this paper the general framework of automorphic and modular
inflation is described in some detail, with emphasis on the resulting
stratification of the space of scalar field theories in terms of the group
theoretic data associated to the shift symmetry, as well as the automorphic
data that specifies the potential. The class of theories based on Eisenstein
series provides a natural generalization of the model of $j$-inflation
considered previously. |
Third order wave equation in Duffin-Kemmer-Petiau theory. Massive case: Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more
consistent approach to the derivation of the third order wave equation obtained
earlier by M. Nowakowski [Phys.Lett.A {\bf 244} (1998) 329] on the basis of
heuristic considerations is suggested. For this purpose an additional algebraic
object, the so-called $q$ - commutator ($q$ is a primitive cubic root of unity)
and a new set of matrices $\eta_{\mu}$ instead of the original matrices
$\beta_{\mu}$ of the DKP algebra are introduced. It is shown that in terms of
these $\eta_{\mu}$ matrices we have succeeded in reducing a procedure of the
construction of cubic root of the third order wave operator to a few simple
algebraic transformations and to a certain operation of the passage to the
limit $z \rightarrow q$, where $z$ is some complex deformation parameter
entering into the definition of the $\eta$ - matrices. A corresponding
generalization of the result obtained to the case of the interaction with an
external electromagnetic field introduced through the minimal coupling scheme
is carried out and a comparison with M. Nowakowski's result is performed. A
detailed analysis of the general structure for a solution of the first order
differential equation for the wave function $\psi(x; z)$ is performed and it is
shown that the solution is singular in the $z \rightarrow q$ limit. The
application to the problem of construction within the DKP approach of the path
integral representation in parasuperspace for the propagator of a massive
vector particle in a background gauge field is discussed. | On Smooth Time-Dependent Orbifolds and Null Singularities: We study string theory on a non-singular time-dependent orbifold of flat
space, known as the `null-brane'. The orbifold group, which involves only
space-like identifications, is obtained by a combined action of a null Lorentz
transformation and a constant shift in an extra direction. In the limit where
the shift goes to zero, the geometry of this orbifold reproduces an orbifold
with a light-like singularity, which was recently studied by Liu, Moore and
Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to
a test particle can be made arbitrarily small, and that there are scattering
processes which can be studied in the approximation of a constant background.
We quantize strings on this orbifold and calculate the torus partition
function. We construct a basis of states on the smooth orbifold whose tree
level string interactions are nonsingular. We discuss the existence of physical
modes in the singular orbifold which resolve the singularity. We also describe
another way of making the singular orbifold smooth which involves a sandwich
pp-wave. |
Confinement and Asymptotic Freedom with Cooper pairs: One of the most profound aspects of the standard model of particle physics,
the mechanism of confinement binding quarks into hadrons, is not sufficiently
understood. The only known semiclassical mechanism of confinement, mediated by
chromo-electric strings in a condensate of magnetic monopoles still lacks
experimental evidence. Here we show that the infinite resistance
superinsulating state, which emerges on the insulating side of the
superconductor-insulator transition in superconducting films offers a
realization of confinement that allows for a direct experimental access. We
find that superinsulators realize a single-color version of quantum
chromodynamics and establish the mapping of quarks onto Cooper pairs. We reveal
that the mechanism of superinsulation is the linear binding of Cooper pairs
into neutral "mesons" by electric strings. Our findings offer a powerful
laboratory for exploring and testing the fundamental implications of
confinement, asymptotic freedom, and related quantum chromodynamics phenomena
via desktop experiments on superconductors. | Some exact solutions of all f(Ricci) theories in three dimensions: We find constant scalar curvature Type-N and Type-D solutions in all higher
curvature gravity theories with actions of the form f(Ricci) that are built on
the Ricci tensor, but not on its derivatives. In our construction, these higher
derivative theories inherit some of the previously studied solutions of the
cosmological topologically massive gravity and the new massive gravity field
equations, once the parameters of the theories are adjusted. Besides the
generic higher curvature theory, we have considered in some detail the examples
of the quadratic curvature theory, the cubic curvature theory, and the
Born-Infeld extension of the new massive gravity. |
Cancellation of energy-divergences in Coulomb gauge QCD: In the Coulomb gauge of nonabelian gauge theories there are in general, in
individual graphs, 'energy-divergences' on integrating over the loop energy
variable for fixed loop momentum. These divergences are avoided in the
Hamiltonian, phase-space formulation. But, even in this formulation,
energy-divergences re-appear at 2-loop order. We show in an example how these
cancel between graphs as a consequence of Ward identities. | Bethe Ansatz in Stringy Sigma Models: We compute the exact S-matrix and give the Bethe ansatz solution for three
sigma-models which arise as subsectors of string theory in AdS(5)xS(5):
Landau-Lifshitz model (non-relativistic sigma-model on S(2)),
Alday-Arutyunov-Frolov model (fermionic sigma-model with su(1|1) symmetry), and
Faddeev-Reshetikhin model (string sigma-model on S(3)xR). |
Conformal bounds in three dimensions from entanglement entropy: The entanglement entropy of an arbitrary spacetime region $A$ in a
three-dimensional conformal field theory (CFT) contains a constant universal
coefficient, $F(A)$. For general theories, the value of $F(A)$ is minimized
when $A$ is a round disk, $F_0$, and in that case it coincides with the
Euclidean free energy on the sphere. We conjecture that, for general CFTs, the
quantity $F(A)/F_0$ is bounded above by the free scalar field result and below
by the Maxwell field one. We provide strong evidence in favor of this claim and
argue that an analogous conjecture in the four-dimensional case is equivalent
to the Hofman-Maldacena bounds. In three dimensions, our conjecture gives rise
to similar bounds on the quotients of various constants characterizing the CFT.
In particular, it implies that the quotient of the stress-tensor two-point
function coefficient and the sphere free energy satisfies $C_{
\scriptscriptstyle T} / F_0 \leq 3/ (4\pi^2 \log 2 - 6\zeta[3]) \simeq 0.14887$
for general CFTs. We verify the validity of this bound for free scalars and
fermions, general $O(N)$ and Gross-Neveu models, holographic theories,
$\mathcal{N}=2$ Wess-Zumino models and general ABJM theories. | Graviton Vertices and the Mapping of Anomalous Correlators to Momentum
Space for a General Conformal Field Theory: We investigate the mapping of conformal correlators and of their anomalies
from configuration to momentum space for general dimensions, focusing on the
anomalous correlators $TOO$, $TVV$ - involving the energy-momentum tensor $(T)$
with a vector $(V)$ or a scalar operator ($O$) - and the 3-graviton vertex
$TTT$. We compute the $TOO$, $TVV$ and $TTT$ one-loop vertex functions in
dimensional regularization for free field theories involving conformal scalar,
fermion and vector fields. Since there are only one or two independent tensor
structures solving all the conformal Ward identities for the $TOO$ or $TVV$
vertex functions respectively, and three independent tensor structures for the
$TTT$ vertex, and the coefficients of these tensors are known for free fields,
it is possible to identify the corresponding tensors in momentum space from the
computation of the correlators for free fields. This works in general $d$
dimensions for $TOO$ and $TVV$ correlators, but only in 4 dimensions for $TTT$,
since vector fields are conformal only in $d=4$. In this way the general
solution of the Ward identities including anomalous ones for these correlators
in (Euclidean) position space, found by Osborn and Petkou is mapped to the
ordinary diagrammatic one in momentum space. We give simplified expressions of
all these correlators in configuration space which are explicitly Fourier
integrable and provide a diagrammatic interpretation of all the contact terms
arising when two or more of the points coincide. We discuss how the anomalies
arise in each approach [...] |
NonMarkovian Abraham--Lorentz--Dirac Equation: Radiation Reaction
without Pathology: Motion of a point charge emitting radiation in an electromagnetic field obeys
the Abraham-Lorenz-Dirac (ALD) equation, with the effects of radiation reaction
or self-force incorporated. This class of equations describing backreaction,
including also the equations for gravitational self-force or Einstein's
equation for cosmology driven by trace anomaly, contain third-order derivative
terms. They are known to have pathologies like the possession of runaway
solutions, causality violation in pre-acceleration and the need for an extra
second-order derivative initial condition. In our current program we reexamine
this old problem from the perspective of non-Markovian dynamics in open
systems, applied earlier to backreaction problems in the early universe. Here
we consider a harmonic atom coupled to a scalar field, which acts effectively
like a supra-Ohmic environment, as in scalar electrodynamics. Our analysis
shows that a) there is no need for specifying a second derivative for the
initial condition; b) there is no pre-acceleration. These undesirable features
in conventional treatments arise from an inconsistent Markovian assumption:
these equations were regarded as Markovian ab initio, not as a limit of the
backreaction-imbued non-Markovian equation of motion. If one starts with the
full non-Markovian dynamical equation and takes the proper Markovian limit
judiciously, no harms are done. Finally, c) There is no causal relation between
the higher-derivative term in the equation of motion and the existence of
runaway solutions. If the charge has an effective size greater than this
critical value, its dynamics is stable. When this reasonable condition is met,
radiation reaction understood and treated correctly in the non-Ohmic
non-Markovian dynamics still obeys a third-order derivative equation, but it
does not require a second derivative initial condition, and there is no
pre-acceleration. | Correlation functions of boundary field theory from bulk Green's
functions and phases in the boundary theory: In the context of the bulk-boundary correspondence we study the correlation
functions arising on a boundary for different types of boundary conditions. The
most general condition is the mixed one interpolating between the Neumann and
Dirichlet conditions. We obtain the general expressions for the correlators on
a boundary in terms of Green's function in the bulk for the Dirichlet, Neumann
and mixed boundary conditions and establish the relations between the
correlation functions. As an instructive example we explicitly obtain the
boundary correlators corresponding to the mixed condition on a plane boundary
$R^d$ of a domain in flat space $R^{d+1}$. The phases of the boundary theory
with correlators of the Neumann and Dirichlet types are determined. The
boundary correlation functions on sphere $S^d$ are calculated for the Dirichlet
and Neumann conditions in two important cases: when sphere is a boundary of a
domain in flat space $R^{d+1}$ and when it is a boundary at infinity of Anti-De
Sitter space $AdS_{d+1}$. For massless in the bulk theory the Neumann
correlator on the boundary of AdS space is shown to have universal logarithmic
behavior in all AdS spaces. In the massive case it is found to be finite at the
coinciding points. We argue that the Neumann correlator may have a dual
two-dimensional description. The structure of the correlators obtained, their
conformal nature and some recurrent relations are analyzed. We identify the
Dirichlet and Neumann phases living on the boundary of AdS space and discuss
their evolution when the location of the boundary changes from infinity to the
center of the AdS space. |
A Proposal On Culling & Filtering A Coxeter Group For 4D, N = 1
Spacetime SUSY Representations: We review the mathematical tools required to cull and filter representations
of the Coxeter Group $BC_4$ into providing bases for the construction of
minimal off-shell representations of the 4D, $ {\cal N}$ = 1 spacetime
supersymmetry algebra. Of necessity this includes a description of the
mathematical mechanism by which four dimensional Lorentz symmetry appears as an
emergent symmetry in the context of one dimensional adinkras with four colors
described by the Coxeter Group $BC_4$. | Localization of nonlocal cosmological models with quadratic potentials
in the case of double roots: Nonlocal cosmological models with quadratic potentials are considered. We
study the action with an arbitrary analytic function F(\Box_g), which has both
double and simple roots. The formulae for nonlocal energy-momentum tensor,
which correspond to double roots, have been obtained. The way to find
particular solutions for nonlocal Einstein equations in the case when F(\Box_g)
has both simple and double roots has been proposed. One and the same functions
solve the initial nonlocal Einstein equations and the obtained local Einstein
equations. |
Solitons on Noncommutative Torus as Elliptic Algebras and Elliptic
Models: For the noncommutative torus ${\cal T}$, in case of the N.C. parameter
$\theta = \frac{Z}{n}$ and the area of ${\cal T}$ is an integer, we construct
the basis of Hilbert space ${\cal H}_n$ in terms of $\theta$ functions of the
positions $z_i$ of $n$ solitons. The loop wrapping around the torus generates
the algebra ${\cal A}_n$. We show that ${\cal A}_n$ is isomorphic to the $Z_n
\times Z_n$ Heisenberg group on $\theta$ functions. We find the explicit form
for the local operators, which is the generators $g$ of an elliptic $su(n)$,
and transforms covariantly by the global gauge transformation of the Wilson
loop in ${\cal A}_n$. By acting on ${\cal H}_n$ we establish the isomorphism of
${\cal A}_n$ and $g$. Then it is easy to give the projection operators
corresponding to the solitons and the ABS construction for generating solitons.
We embed this $g$ into the $L$-matrix of the elliptic Gaudin and C.M. models to
give the dynamics. For $\theta$ generic case, we introduce the crossing
parameter $\eta$ related with $\theta$ and the modulus of ${\cal T}$. The
dynamics of solitons is determined by the transfer matrix $T$ of the elliptic
quantum group ${\cal A}_{\tau, \eta}$, equivalently by the elliptic Ruijsenaars
operators $M$. The eigenfunctions of $T$ found by Bethe ansatz appears to be
twisted by $\eta$. | Brans-Dicke theory in the local potential approximation: We study the Brans-Dicke theory with arbitrary potential within a functional
renormalization group framework. Motivated by the asymptotic safety scenario of
quantum gravity and by the well-known relation between f(R) gravity and
Brans-Dicke theory at the classical level, we concentrate our analysis on the
fixed-point equation for the potential in four dimensions and with Brans-Dicke
parameter omega equal to zero. For two different choices of gauge, we study the
resulting equations by examining both local and global properties of the
solutions, by means of analytical and numerical methods. As a result of our
analysis we do not find any nontrivial fixed point in one gauge, but we find a
continuum of fixed points in the other one. We interpret such inconsistency as
a result of the restriction to omega equal to zero, and thus we suggest that it
indicates a failure of the equivalence between f(R) gravity and Brans-Dicke
theory at the quantum level. |
Low energy dynamics from deformed conformal symmetry in quantum 4D N = 2
SCFTs: We determine the one-loop deformation of the conformal symmetry of a general
N}=2 superconformally invariant Yang-Mills theory. The deformation is computed
for several explicit examples which have a realization as world-volume theories
on a stack of D3 branes. These include (i) N=4 SYM with gauge groups SU(N),
USp(2N) and SO(N); (ii) USp(2N) gauge theory with one hypermultiplet in the
traceless antisymmetric representation and four hypermultiplets in the
fundamental; (iii) quiver gauge theory with gauge group SU(N)xSU(N) and two
hypermultiplets in the bifundamental representations (N,\bar N) and (bar N,N).
The existence of quantum corrections to the conformal transformations imposes
restrictions on the effective action which we study on a subset of the Coulomb
branch corresponding to the separation of one brane from the stack. In the N=4
case, the one-loop corrected transformations provide a realization of the
conformal algebra; this deformation is shown to be one-loop exact. For the
other two models, higher-loop corrections are necessary to close the algebra.
Requiring closure, we infer the two-loop conformal deformation. | Bound States of Dimensionally Reduced {SYM}_{2+1} at Finite N: We consider the dimensional reduction of N=1 {SYM}_{2+1} to 1+1 dimensions.
The gauge groups we consider are U(N) and SU(N), where N is finite. We
formulate the continuum bound state problem in the light-cone formalism, and
show that any normalizable SU(N) bound state must be a superposition of an
infinite number of Fock states. We also discuss how massless states arise in
the DLCQ formulation for certain discretizations. |
Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions: We construct, in D=3,4,6 and 10 space-time dimensions, supersymmetric
Lagrangians for free massless higher spin fields which belong to reducible
representations of the Poincare group.The fermionic part of these models
consists of spinor-tensor fields which are totally symmetrical with respect to
their tensor indices, while the bosonic part contains totally symmetric tensor
fields as well as the simplest mixed-symmetry fields. A peculiar feature of
these models is that they describe higher- and lower-spin supermultiplets in
different dimensions in a uniform way. | Noncommutativity and logarithmic correction to the black hole entropy: We study the noncommutative corrections to the entropy of the
Reissner-Nordstr\"{o}m black hole using a $\kappa$-deformed scalar probe within
the brick-wall framework. The noncommutativity is encoded in an Abelian
Drinfeld twist constructed from the Killing vector fields of the
Reissner-Nordstr\"{o}m black hole. We show that the noncommutative effects
naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy
even at the lowest order of the WKB approximation. In contrast, such
logarithmic corrections in the commutative setup appear only after the quantum
effects are included through higher order WKB corrections or through higher
loop effects. Our analysis thus provides further evidence towards the
hypothesis that the noncommutative framework is capable of encoding quantum
effects in curved spacetime. |
Casimir effect for massless minimally coupled scalar field between
parallel plates in de Sitter spacetime: Casimir effect for massless minimally coupled scalar field is studied. An
explicit answer for de Sitter spacetime is obtained and analized. Cosmological
implications of the result are discussed. | Dirac spectrum and chiral condensate for QCD at fixed $θ$-angle: We analyze the mass dependence of the chiral condensate for QCD at nonzero
$\theta$-angle and find that in general the discontinuity of the chiral
condensate is not on the support of the Dirac spectrum. To understand this
behavior we decompose the spectral density and the chiral condensate into
contributions from the zero modes, the quenched part, and a remainder which is
sensitive to the fermion determinant and is referred to as the dynamical part.
We obtain general formulas for the contributions of the zero modes. Expressions
for the quenched part, valid for an arbitrary number of flavors, and for the
dynamical part, valid for one and two flavors, are derived in the microscopic
domain of QCD. We find that at nonzero $\theta$-angle the quenched and
dynamical part of the Dirac spectral density are strongly oscillating with an
amplitude that increases exponentially with the volume $V$ and a period of
order of $1/V$. The quenched part of the chiral condensate becomes
exponentially large at $\theta\ne0$, but this divergence is canceled by the
contribution from the zero modes. The oscillatory behavior of the dynamical
part of the density is essential for moving the discontinuity of the chiral
condensate away from the support of the Dirac spectrum. As important
by-products of this work we obtain analytical expressions for the microscopic
spectral density of the Dirac operator at nonzero $\theta$-angle for both one-
and two-flavor QCD with nonzero quark masses. |
Quasi-local conserved charges and holography: We construct a quasi-local formalism for conserved charges in a theory of
gravity in the presence of matter fields which may have slow falloff behaviors
at the asymptotic infinity. This construction depends only on equations of
motion and so it is irrespective of ambiguities in the total derivatives of the
Lagrangian. By using identically conserved currents, we show that this
formalism leads to the same expressions of conserved charges as those in the
covariant phase space approach. At the boundary of the asymptotic AdS space, we
also introduce an identically conserved boundary current which has the same
structure as the bulk current and then show that this boundary current gives us
the holographic conserved charges identical with those from the boundary stress
tensor method. In our quasi-local formalism we present a general proof that
conserved charges from the bulk potential are identical with those from the
boundary current. Our results can be regarded as the extension of the existing
results on the equivalence of conserved charges by the covariant phase space
approach and by the boundary stress tensor method. | On the equivalence between Implicit Regularization and Constrained
Differential Renormalization: Constrained Differential Renormalization (CDR) and the constrained version of
Implicit Regularization (IR) are two regularization independent techniques that
do not rely on dimensional continuation of the space-time. These two methods
which have rather distinct basis have been successfully applied to several
calculations which show that they can be trusted as practical, symmetry
invariant frameworks (gauge and supersymmetry included) in perturbative
computations even beyond one-loop order.
In this paper, we show the equivalence between these two methods at one-loop
order. We show that the configuration space rules of CDR can be mapped into the
momentum space procedures of Implicit Regularization, the major principle
behind this equivalence being the extension of the properties of regular
distributions to the regularized ones. |
Linear relations among 4-point functions in the high energy limit of
string theory: The decoupling of zero-norm states leads to linear relations among 4-point
functions in the high energy limit of string theory. Recently it was shown that
the linear relations uniquely determine ratios among 4-point functions at the
leading order. The purpose of this paper is to extend the validity of the same
approach to the next-to-leading order and higher orders. | MHz Gravitational Waves from Short-term Anisotropic Inflation: We reveal the universality of short-term anisotropic inflation. As a
demonstration, we study inflation with an exponential type gauge kinetic
function which is ubiquitous in models obtained by dimensional reduction from
higher dimensional fundamental theory. It turns out that an anisotropic
inflation universally takes place in the later stage of conventional inflation.
Remarkably, we find that primordial gravitational waves with a peak amplitude
around $10^{-26}$ ~ $10^{-27}$ are copiously produced in high-frequency bands
10MHz~100MHz. If we could detect such gravitational waves in future, we would
be able to probe higher dimensional fundamental theory. |
Lorentz Anomaly and 1+1-Dimensional Radiating Black Holes: The radiation from the black holes of a 1+1-dimensional chiral quantum
gravity model is studied. Most notably, a non-trivial dependence on a
renormalization parameter that characterizes the anomaly relations is uncovered
in an improved semiclassical approximation scheme; this dependence is not
present in the naive semiclassical approximation. | Flux-Induced Baryon Asymmetry: I propose that the primordial baryon asymmetry of the universe was induced by
the presence of a non-vanishing antisymmetric field background H_ijk across the
three space dimensions. This background creates a dilute (B-L)-number density
in the universe cancelling the contribution from baryons and leptons. This
situation naturally appears if the U(1)_{B-L} symmetry is gauged and the
corresponding gauge boson gets a Stuckelberg mass by combining with an
antisymmetric field B_ij. All these ingredients are present in D-brane models
of particle physics. None of the Sakharov conditions are required. |
On the Perturbative Equivalence Between the Hamiltonian and Lagrangian
Quantizations: The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to
be equivalent perturbatively to each other. It is shown in particular that the
quantum master equation being treated perturbatively possesses a local formal
solution. | Environment-induced uncertainties on moving mirrors in quantum critical
theories via holography: Environment effects on a $n$-dimensional mirror from the strongly coupled
d-dimensional quantum critical fields with a dynamic exponent $z$ in weakly
squeezed states are studied by the holographic approach. The dual description
is a $n+1$-dimensional probe brane moving in the $d+1$-dimensional asymptotic
Lifshitz geometry with gravitational wave perturbations. Using the holographic
influence functional method, we find that the large coupling constant of the
fields reduces the position uncertainty of the mirror, but enhances the
momentum uncertainty. As such, the product of the position and momentum
uncertainties is independent of the coupling constant. The proper choices of
the phase of the squeezing parameter might reduce the uncertainties,
nevertheless large values of its amplitude always lead to the larger
uncertainties due to the fact that more quanta are excited as compared with the
corresponding normal vacuum and thermal states. In the squeezed vacuum state,
the position and momentum of the mirror gain maximum uncertainties from the
field at the dynamic exponent $z=n+2$ when the same squeezed mode is
considered. As for the squeezed thermal state, the contributions of thermal
fluctuations to the uncertainties decrease as the temperature increases in the
case $1<z<n+2$, whereas for $z>n+2$ the contributions increase as the
temperature increases. These results are in sharp contrast with those in the
environments of the relativistic free field. Some possible observable effects
are discussed. |
Classical Scattering in $1+1$ Dimensional String Theory: We find the general solution to Polchinski's classical scattering equations
for $1+1$ dimensional string theory. This allows efficient computation of
scattering amplitudes in the standard Liouville $\times$ $c=1$ background.
Moreover, the solution leads to a mapping from a large class of time-dependent
collective field theory backgrounds to corresponding nonlinear sigma models.
Finally, we derive recursion relations between tachyon amplitudes. These may be
summarized by an infinite set of nonlinear PDE's for the partition function in
an arbitrary time-dependent background. | Duality of the Superstring in Superspace: The evolution of a closed NSR string is considered in the background of
constant graviton and antisymmetric fields. The $\sigma$-model action is
written in a manifestly supersymmetric form in terms of superfields. The first
order formalism adopted for the closed bosonic string is generalised to
implement duality transformations and the constant dual backgrounds are
obtained for the dual theory. We recover the $G \rightarrow G^{-1}$ duality for
the case when antisymmetric tensor field is set to zero. Next, the case when
the backgrounds depend on one superfield, is also analysed. This scenario is
similar to the cosmological case envisaged for the bosonic string. The explicit
form of the duality transformation is given for this case. |
Abelian Current Algebra and the Virasoro Algebra on the Lattice: We describe how a natural lattice analogue of the abelian current algebra
combined with free discrete time dynamics gives rise to the lattice Virasoro
algebra and corresponding hierarchy of conservation laws. | Ultra-spinning exotic compact objects supporting static massless scalar
field configurations: Horizonless spacetimes describing highly compact exotic objects with
reflecting (instead of absorbing) surfaces have recently attracted much
attention from physicists and mathematicians as possible quantum-gravity
alternatives to canonical classical black-hole spacetimes. Interestingly, it
has recently been proved that spinning compact objects with angular momenta in
the sub-critical regime ${\bar a}\equiv J/M^2\leq1$ are characterized by an
infinite countable set of surface radii, $\{r_{\text{c}}({\bar
a};n)\}^{n=\infty}_{n=1}$, that can support asymptotically flat static
configurations made of massless scalar fields. In the present paper we study
analytically the physical properties of ultra-spinning exotic compact objects
with dimensionless angular momenta in the complementary regime ${\bar a}>1$. It
is proved that ultra-spinning reflecting compact objects with dimensionless
angular momenta in the super-critical regime
$\sqrt{1-[{{m}/{(l+2)}}]^2}\leq|{\bar a}|^{-1}<1$ are characterized by a finite
discrete family of surface radii, $\{r_{\text{c}}({\bar
a};n)\}^{n=N_{\text{r}}}_{n=1}$, distributed symmetrically around $r=M$, that
can support spatially regular static configurations of massless scalar fields
(here the integers $\{l,m\}$ are the harmonic indices of the supported static
scalar field modes). Interestingly, the largest supporting surface radius
$r^{\text{max}}_{\text{c}}({\bar a})\equiv \text{max}_n\{r_{\text{c}}({\bar
a};n)\}$ marks the onset of superradiant instabilities in the composed
ultra-spinning-exotic-compact-object-massless-scalar-field system. |
A new two-faced scalar solution and cosmological SUSY breaking: We propose a possible new way to resolve the long standing problem of strong
supersymmetry breaking coexisting with a small cosmological constant. We
consider a scalar component of a minimally coupled N=1 supermultiplet in a
general Friedmann-Robertson-Walker (FRW) expanding universe. We argue that a
tiny term, proportional to H^2 ~ 10^(-122) in Plank's units, appearing in the
field equations due to this expansion will provide both, the small vacuum
energy and the heavy mass of the scalar supersymmetric partner. We present a
non-perturbative solution for the scalar field with an unusual dual-frequency
behavior. This solution has two characteristic mass scales related to the
Hubble parameter as H^(1/4) and H^(1/2) measured in Plank's units. | $κ$-Deformation of Poincaré Superalgebra with Classical Lorentz
Subalgebra and its Graded Bicrossproduct Structure: The $\kappa$-deformed $D=4$ Poincar{\'e} superalgebra written in Hopf
superalgebra form is transformed to the basis with classical Lorentz subalgebra
generators. We show that in such a basis the $\kappa$-deformed $D=4$ Poincare
superalgebra can be written as graded bicrossproduct. We show that the
$\kappa$-deformed $D=4$ superalgebra acts covariantly on $\kappa$-deformed
chiral superspace. |
A Three-Point Form Factor Through Five Loops: We bootstrap the three-point form factor of the chiral part of the
stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory,
obtaining new results at three, four, and five loops. Our construction employs
known conditions on the first, second, and final entries of the symbol,
combined with new multiple-final-entry conditions, ``extended-Steinmann-like''
conditions, and near-collinear data from the recently-developed form factor
operator product expansion. Our results are expected to give the maximally
transcendental parts of the $gg\to Hg$ and $H\to ggg$ amplitudes in the
heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of
functions we describe contains all transcendental functions required for
four-point amplitudes with one massive and three massless external legs, and
all massless internal lines, including processes such as $gg\to Hg$ and
$\gamma^*\to q\bar{q}g$. We expect the extended-Steinmann-like space to contain
these amplitudes at higher loops as well, although not to arbitrarily high loop
order. We present evidence that the planar $\mathcal{N}=4$ three-point form
factor can be placed in an even smaller space of functions, with no independent
$\zeta$ values at weights two and three. | Twistor Parametrization of Locally BPS Super-Wilson Loops: We consider the kinematics of the locally BPS super-Wilson loop in
$\mathcal{N}=4$ super-Yang-Mills with scalar coupling from a twistorial point
of view. We find that the kinematics can be described either as
supersymmetrized pure spinors or as a point in $G_{2\vert 2}(4\vert 4) \times
G_{2\vert 2}(4\vert 4)$. In this description of the kinematics the
scalar--scalar correlation function appearing in the one-loop evaluation of the
super-Wilson loop can be neatly written as a sum of four super-determinants. |
New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D
superspace: induced strings and 2D relativistic models: A novel feature of the ${\mathbb Z}_2\times {\mathbb Z}_2$-graded
supersymmetry which finds no counterpart in ordinary supersymmetry is the
presence of $11$-graded exotic bosons (implied by the existence of two classes
of parafermions). Their interpretation, both physical and mathematical,
presents a challenge. The role of the "exotic bosonic coordinate" was not
considered by previous works on the one-dimensional ${\mathbb Z}_2\times
{\mathbb Z}_2$-graded superspace (which was restricted to produce
point-particle models). By treating this coordinate at par with the other
graded superspace coordinates new consequences are obtained. The graded
superspace calculus of the ${\mathbb Z}_2\times {\mathbb Z}_2$-graded worldline
super-Poincar\'e algebra induces two-dimensional ${\mathbb Z}_2\times {\mathbb
Z}_2$-graded relativistic models; they are invariant under a new ${\mathbb
Z}_2\times {\mathbb Z}_2$-graded $2D$ super-Poincar\'e algebra which differs
from the previous two ${\mathbb Z}_2\times {\mathbb Z}_2$-graded $2D$ versions
of super-Poincar\'e introduced in the literature. In this new superalgebra the
second translation generator and the Lorentz boost are $11$-graded.
Furthermore, if the exotic coordinate is compactified on a circle ${\bf S}^1$,
a ${\mathbb Z}_2\times {\mathbb Z}_2$-graded closed string with periodic
boundary conditions is derived. The analysis of the irreducibility conditions
of the $2D$ supermultiplet implies that a larger $(\beta$-deformed, where
$\beta\geq 0$ is a real parameter) class of point-particle models than the ones
discussed so far in the literature (recovered at $\beta=0$) is obtained. While
the spectrum of the $\beta=0$ point-particle models is degenerate (due to its
relation with an ${\cal N}=2$ supersymmetry), this is no longer the case for
the $\beta> 0$ models. | The fate of the type I non-BPS D7-brane: We describe the fate of the Type I non-BPS D7-brane, which is tachyonic but
carries a non-trivial K-theory $\IZ_2$ charge. It decays to topologically
non-trivial gauge field configurations on the background D9-branes. In the
uncompactified theory the decay proceeds to infinity, while with a transverse
torus the decay reaches a final state, a toron gauge configuration with
vanishing Chern classes but non-trivial $\IZ_2$ charge. A similar behaviour is
obtained for the type I non-BPS D8-brane, and other related systems. We
construct explicit examples of type IIB orientifolds with non-BPS D7-branes,
which are hence non-supersymmetric, but for which supersymmetry is restored
upon condensation of the tachyon. We also report on the interesting structure
of non-BPS states of type IIA theory in the presence of an O6-plane, their
M-theory lifts, the relation between string theory K-theory and M-theory
cohomology, and its interplay with NS-NS charged objects. We discuss several
new effects, including: i) transmutation between NS-NS and RR torsion charges,
ii) non-BPS states classified by K-theory but not by cohomology in string
theory, but whose lift to M-theory is cohomological. |
R-charges, Chiral Rings and RG Flows in Supersymmetric
Chern-Simons-Matter Theories: We discuss the non-perturbative behavior of the U(1)_R symmetry in N=2
superconformal Chern-Simons theories coupled to matter in the (anti)fundamental
and adjoint representations of the gauge group, which we take to be U(N).
Inequalities constraining this behavior are obtained as consequences of
spontaneous breaking of supersymmetry and Seiberg duality. This information
reveals a web of RG flows connecting different interacting superconformal field
theories in three dimensions. We observe that a subclass of these theories
admits an ADE classification. In addition, we postulate new examples of Seiberg
duality in N=2 and N=3 Chern-Simons-matter theories and point out interesting
parallels with familiar non-perturbative properties in N=1 (adjoint) SQCD
theories in four dimensions where the exact U(1)_R symmetry can be determined
using a-maximization. | Replica Symmetry Breaking and Phase Transitions in a PT Symmetric
Sachdev-Ye-Kitaev Model: We show that the low temperature phase of a conjugate pair of uncoupled,
quantum chaotic, nonhermitian systems such as the Sachdev-Ye-Kitaev (SYK) model
or the Ginibre ensemble of random matrices are dominated by replica symmetry
breaking configurations with a nearly flat free energy that terminates in a
first order phase transition. In the case of the SYK model, we show explicitly
that the spectrum of the effective replica theory has a gap. These features are
strikingly similar to those induced by wormholes in the gravity path integral
which suggests a close relation between both configurations. For a non-chaotic
SYK, the results are qualitatively different: the spectrum is gapless in the
low temperature phase and there is an infinite number of second order phase
transitions unrelated to the restoration of replica symmetry. |
Celestial holography and AdS3/CFT2 from a scaling reduction of twistor
space: Celestial amplitudes obtained from Mellin transforming 4d momentum space
scattering amplitudes contain distributional delta functions, hindering the
application of conventional CFT techniques. In this paper, we propose to bypass
this problem by recognizing Mellin transforms as integral transforms
projectivizing certain components of the angular momentum. It turns out that
the Mellin transformed wavefunctions in the conformal primary basis can be
regarded as representatives of certain cohomology classes on the minitwistor
space of the hyperbolic slices of 4d Minkowski space. Geometrically, this
amounts to treating 4d Minkowski space as the embedding space of AdS3. By
considering scattering of such on-shell wavefunctions on the projective spinor
bundle PS of Euclidean AdS3, we bypass the difficulty of the distributional
properties of celestial correlators using the traditional AdS3/CFT2 dictionary
and find conventional 2d CFT correlators for the scaling reduced Yang-Mills
theory living on the hyperbolic slices. In the meantime, however, one is
required to consider action functionals on the auxiliary space PS, which
introduces additional difficulties. Here we provide a framework to work on the
projective spinor bundle of hyperbolic slices, obtained from a careful scaling
reduction of the twistor space of 4d Minkowski spacetime. | Generalized Integrability and two-dimensional Gravitation: We review the construction of generalized integrable hierarchies of partial
differential equations, associated to affine Kac-Moody algebras, that include
those considered by Drinfel'd and Sokolov. These hierarchies can be used to
construct new models of 2D quantum or topological gravity, as well as new $\cal
W$-algebras. |
The spin jumping in the context of a QCD effective model: The tensor formulation for the effective theory of QCD vector ressonances,
whose model we denote by TEVR, is given by an antisymmetric tensor field and
describes spin 1 particles. Our goal is to show, by diferent approaches, that
the Abelian version of this model presents the so called "spin jumping" when we
consider its massless limit. Classically we find, by the use of the equations
of motion and the Hamiltonian constraint analysis, that the massive phase of
the model describes spin 1 particles while its massless phase describes spin 0
particles. By the quantum point of view we derive these conclusions via tree
level unitarity analysis and the master action approach. | Supersymmetric Casimir energy on $\mathcal{N}=1$ conformal supergravity
backgrounds: We provide a first principles derivation of the supersymmetric Casimir energy
of $\mathcal{N}=1$ SCFTs in four dimensions using the supercharge algebra on
general conformal supergravity backgrounds that admit Killing spinors. The
superconformal Ward identities imply that there exists a continuous family of
conserved R-currents on supersymmetric backgrounds, as well as a continuous
family of conserved currents for each conformal Killing vector. These
continuous families interpolate between the consistent and covariant R-current
and energy-momentum tensor. The resulting Casimir energy, therefore, depends on
two continuous parameters corresponding to the choice of conserved currents
used to define the energy and R-charge. This ambiguity is in addition to any
possible scheme dependence due to local terms in the effective action. As an
application, we evaluate the general expression for the supersymmetric Casimir
energy we obtain on a family of backgrounds with the cylinder topology
$\mathbb{R}\times S^3$ and admitting a single Majorana supercharge. Our result
is a direct consequence of the supersymmetry algebra, yet it resembles more
known expressions for the non-supersymmetric Casimir energy on such backgrounds
and differs from the supersymmetric Casimir energy obtained from the zero
temperature limit of supersymmetric partition functions. We defer a thorough
analysis of the relation between these results to future work. |
$κ$-Poincaré-comodules, Braided Tensor Products and
Noncommutative Quantum Field Theory: We discuss the obstruction to the construction of a multiparticle field
theory on a $\kappa$-Minkowski noncommutative spacetime: the existence of
multilocal functions which respect the deformed symmetries of the problem. This
construction is only possible for a light-like version of the commutation
relations, if one requires invariance of the tensor product algebra under the
coaction of the $\kappa$-Poincar\'e group. This necessitates a braided tensor
product. We study the representations of this product, and prove that
$\kappa$-Poincar\'e-invariant N-point functions belong to an Abelian
subalgebra, and are therefore commutative. We use this construction to define
the 2-point Whightman and Pauli--Jordan functions, which turn out to be
identical to the undeformed ones. We finally outline how to construct a free
scalar $\kappa$-Poincar\'e-invariant quantum field theory, and identify some
open problems. | Low Energy Supersymmetry from Non-Geometry: We study a class of flux compactifications that have all the moduli
stabilised, a high (GUT) string scale and a low (TeV) gravitino mass that is
generated dynamically. These non-geometric compactifications correspond to type
II string theories on SU(3)xSU(3) structure orientifolds. The resulting
superpotentials admit, excluding non-perturbative effects, supersymmetric
Minkowski vacua with any number of moduli stabilised. We argue that
non-perturbative effects are present and introduce terms in the superpotential
that are exponentially suppressed by the same moduli that appear
perturbatively. These deform the supersymmetric Minkowski vacua to
supersymmetric AdS vacua with an exponentially small gravitino mass. The
resulting vacua allow for low scale supersymmetry breaking which can be
realised by a number of mechanisms. |
Anomalous Dimensions from a Spinning D5-Brane: We consider the anomalous dimension of a certain twist two operator in N=4
super Yang-Mills theory. At strong coupling and large-N it is captured by the
classical dynamics of a spinning D5-brane. The present calculation generalizes
the result of Gubser, Klebanov and Polyakov (hep-th/0204051): in order to
calculate the anomalous dimension of a bound state of k coincident strings, the
spinning closed string is replaced by a spinning D5 brane that wraps an S4
inside the S5 part of the AdS5 times S5 metric. | $U_q osp(2,2)$ Lattice Models: In this paper I construct lattice models with an underlying $U_q osp(2,2)$
superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation.
These {\it trigonometric} $R$-matrices depend on {\it three} continuous
parameters, the spectral parameter, the deformation parameter $q$ and the
$U(1)$ parameter, $b$, of the superalgebra. It must be emphasized that the
parameter $q$ is generic and the parameter $b$ does not correspond to the
`nilpotency' parameter of \cite{gs}. The rational limits are given; they also
depend on the $U(1)$ parameter and this dependence cannot be rescaled away. I
give the Bethe ansatz solution of the lattice models built from some of these
$R$-matrices, while for other matrices, due to the particular nature of the
representation theory of $osp(2,2)$, I conjecture the result. The parameter $b$
appears as a continuous generalized spin. Finally I briefly discuss the problem
of finding the ground state of these models. |
The structure of the ground ring in critical $W_3$ gravity: By explicit calculation, I determine the structure of the ground ring of the
critical $W_3$ gravity and show that there is an $su(3)$ invariant quadratic
relation among the six basic elements. By using this result, I also construct
some discrete physical states of the critical $W_3$ gravity. | Adiabatic Invariance of Oscillons/I-balls: Real scalar fields are known to fragment into spatially localized and
long-lived solitons called oscillons or $I$-balls. We prove the adiabatic
invariance of the oscillons/$I$-balls for a potential that allows periodic
motion even in the presence of non-negligible spatial gradient energy. We show
that such potential is uniquely determined to be the quadratic one with a
logarithmic correction, for which the oscillons/$I$-balls are absolutely
stable. For slightly different forms of the scalar potential dominated by the
quadratic one, the oscillons/$I$-balls are only quasi-stable, because the
adiabatic charge is only approximately conserved. We check the conservation of
the adiabatic charge of the $I$-balls in numerical simulation by slowly varying
the coefficient of logarithmic corrections. This unambiguously shows that the
longevity of oscillons/$I$-balls is due to the adiabatic invariance. |
Near horizon gravitational charges: In this paper, we study the near horizon symmetry and gravitational charges
in the Newman-Penrose formalism. In particular we investigate the effect from
topological terms. We find that the Pontryagin term and Gauss-Bonnet term have
significant influence on the near horizon charges and bring interesting novel
features. We show that the gravitational charge derived from a general class of
topological terms including the Pontryagin term and Gauss-Bonnet term can be
obtained from the ambiguities of the symplectic potential. | Untwisted Moduli and Internal Fermions in Free Fermionic Strings: We investigate the dependence of the number and type of untwisted moduli on
the boundary condition vectors of relistic free fermionic strings. The number
of moduli is given by six minus the number of complex internal world--sheet
fermions and the type of moduli is determined by the details of the
world--sheet left--right asymmetry of the boundary conditions for the internal
fermions. We give a geometrical description of our results in terms of the
transformations of the compactified dimensions of $Z_2 \times Z_2$ orbifolds.
We investigate all possible boundary conditions for the internal fermions and
prove our results in general by showing that world--sheet supersymmetry
eliminates those boundary conditions which violate our results. |
Lattice Topological Field Theory in Two Dimensions: The lattice definition of a two-dimensional topological field theory (TFT) is
given generically, and the exact solution is obtained explicitly. In
particular, the set of all lattice topological field theories is shown to be in
one-to-one correspondence with the set of all associative algebras $R$, and the
physical Hilbert space is identified with the center $Z(R)$ of the associative
algebra $R$. Perturbations of TFT's are also considered in this approach,
showing that the form of topological perturbations is automatically determined,
and that all TFT's are obtained from one TFT by such perturbations. Several
examples are presented, including twisted $N=2$ minimal topological matter and
the case where $R$ is a group ring. | Gauge k-vortices: We consider gauge vortices in symmetry breaking models with a non-canonical
kinetic term. This work extends our previous study on global topological
k-defects (hep-th/0608071), including a gauge field. The model consists of a
scalar field with a non-canonical kinetic term, while for the gauge field the
standard form of its kinetic term is preserved. Topological defects arising in
such models, k-vortices, may have quite different properties as compared to
``standard'' vortices. This happens because an additional dimensional parameter
enters the Lagrangian for the considered model -- a ``kinetic'' mass. We
briefly discuss possible consequences for cosmology, in particular, the
formation of cosmic strings during phase transitions in the early universe and
their properties. |
Lattice regularization of massive and massless integrable field theories: We show that integrable vertex and RSOS models with trigonometric Boltzmann
weights and appropriate inhomogeneities provide a convenient lattice
regularization for massive field theories and for the recently studied massless
field theories that interpolate between two non trivial conformal field
theories. Massive and massless S matrices are computed from the lattice Bethe
ansatz. | Spectral interaction between universes: We derive a perturbative formula for the direct interaction between two
four-dimensional geometries. Based on the spectral action principle we give an
explicit potential up to the third order perturbation around the flat vacua. We
present the leading terms of the interaction as polynomials of the invariants
of the two metrics and compare the expansion to the models of bimetric gravity. |
Quantum Deformation of the Poincare Supergroup and $κ$-deformed
Superspace: The classical $r$-matrix for $N=1$ superPoincar{\'e} algebra, given by
Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure
on the $N=1$ Poincar{\'e} supergroup. The standard correspondence principle
between the even (odd) Poisson brackets and (anti)commutators leads to the
consistent quantum deformation of the superPoincar{\'e} group with the
deformation parameter $q$ described by fundamental mass parameter $\kappa \quad
(\kappa^{-1}=\ln{q})$. The $\kappa$-deformation of $N=1$ superspace as dual to
the $\kappa$-deformed supersymmetry algebra is discussed. | Reply to Comment on Dirac spectral sum rules for QCD in three dimensions: I reply to the comment by Dr S. Nishigaki (hep-th/0007042) to my papers Phys.
Rev. D61 (2000) 056005 and Phys. Rev. D62 (2000) 016005. |
Wilson loops and topological phases in closed string theory: Using covariant phase space formulations for the natural topological
invariants associated with the world-surface in closed string theory, we find
that certain Wilson loops defined on the world-surface and that preserve
topological invariance, correspond to wave functionals for the vacuum state
with zero energy. The differences and similarities with the 2-dimensional QED
proposed by Schwinger early are discussed. | Complexity growth rate during phase transitions: We present evidences for the connection between the potential of different
fields and complexity growth rates both in conformal and confining cases. By
studying different models, we also establish a strong connection between phase
transitions and the discontinuities in the complexity growth rates. In the
first example, for the dyonic black holes which are dual to van der Waals
fluids, we find a similar first order phase transition in the behavior of
complexity growth rate. We then compare the Schwinger effect and also the
behavior of complexity in the AdS and AdS soliton backgrounds and comment on
the connection between them. Finally, in a general Gubser model of QCD, we
present the connections between the potentials, entropies, speed of sounds and
complexity growth rates during crossover, first and second order phase
transitions and also the behavior of quasinormal modes. |
Noncommutative Standard Modelling: We present a noncommutative gauge theory that has the ordinary Standard Model
as its low-energy limit. The model is based on the gauge group U(4) x U(3) x
U(2) and is constructed to satisfy the key requirements imposed by
noncommutativity: the UV/IR mixing effects, restrictions on representations and
charges of matter fields, and the cancellation of noncommutative gauge
anomalies. At energies well below the noncommutative mass scale our model flows
to the commutative Standard Model plus additional free U(1) degrees of freedom
which are decoupled due to the UV/IR mixing. Our model also predicts the values
of the hypercharges of the Standard Model fields. | Uniqueness of photon sphere for Einstein-Maxwell-dilaton black holes
with arbitrary coupling constant: The uniqueness of static asymptotically flat photon sphere for static black
hole solution in Einstein-Maxwell-dilaton theory with arbitrary coupling
constant was proposed. Using the conformal positive energy theorem we show that
the dilaton sphere subject to the non-extremality condition authorizes a
cylinder over a topological sphere. |
An Embedding of the BV Quantization into an N=1 Local Superfield
Formalism: We propose an N=1 superfield formulation of Lagrangian quantization in
general hypergauges by extending a reducible gauge theory to a superfield model
with a local dependence on a Grassmann parameter $\theta$. By means of
$\theta$-local functions of the quantum and gauge-fixing actions in terms of
Darboux coordinates on the antisymplectic manifold, we construct superfield
generating functionals of Green's functions, including the effective action. We
prove the gauge-independence of the S-matrix, obtain the Ward identities and
establish a relation of the proposed local quantization with the BV method and
the multilevel Batalin-Tyutin formalism. | A Numerical Study of Gluon Scattering Amplitudes in N=4 Super Yang-Mills
Theory at Strong Coupling: We study gluon scattering amplitudes in N=4 super Yang-Mills theory at strong
coupling via the AdS/CFT correspondence. We solve numerically the discretized
Euler-Lagrange equations on the square worldsheet for the minimal surface with
light-like boundaries in AdS spacetime. We evaluate the area of the surface for
the 4, 6 and 8-point amplitudes using worldsheet and radial cut-off
regularizations. Their infrared singularities in the cut-off regularization are
found to agree with the analytical results near the cusp less than 5% at
520x520 lattice points. |
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