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On The Construction of Zero Energy States in Supersymmetric Matrix
Models III: For a supersymmetric Hamiltonian appearing in the matrix model related to 11
dimensional supermembranes, zero energy states are constructed. A useful
symmetry, and an energy-equipartition property is pointed out.
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Coalescence of Rotating Black Holes on Eguchi-Hanson Space: We obtain new charged rotating multi-black hole solutions on the
Eguchi-Hanson space in the five-dimensional Einstein-Maxwell system with a
Chern-Simons term and a positive cosmological constant. In the two-black holes
case, these solutions describe the coalescence of two rotating black holes with
the spatial topologies of S^3 into a single rotating black hole with the
spatial topology of the lens space S^3/Z_2. We discuss the differences in the
horizon areas between our solutions and the two-centered Klemm-Sabra solutions
which describe the coalescence of two rotating black holes with the spatial
topologies of S^3 into a single rotating black hole with the spatial topology
of S^3.
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Two-loop corrections to the QCD propagators within the Curci-Ferrari
model: We evaluate all two-point correlation functions of the Curci-Ferrari (CF)
model in four dimensions and in the presence of mass-degenerate fundamental
quark flavors, as a natural extension of an earlier investigation in the
quenched approximation. In principle, the proper account of chiral symmetry
breaking ($\chi$SB) and the corresponding dynamical generation of a quark mass
function within the CF model requires one to go beyond perturbation theory
\cite{Pelaez:2020ups}. However, it is interesting to assess whether a
perturbative description applies to correlation functions that are not directly
sensitive to $\chi$SB, such as the gluon, ghost and quark dressing functions.
We compare our two-loop results for these form factors to QCD lattice data in
the two flavor case for two different values of the pion mass, one that is
relatively far from the chiral limit, and one that is closer to the physical
value. Our results confirm that the QCD gluon and ghost dressing functions are
well described by a perturbative approach within the CF model, as already
observed at one-loop order in Ref. \cite{Pelaez:2014mxa}. Our new main result
is that the quark dressing function is also well captured by the perturbative
approach, but only starting at two-loop order, as also anticipated in Ref.
\cite{Pelaez:2014mxa}. The quark mass function predicted by the CF model at
two-loop order is in good agreement with the data if the quarks are not too
light but shows some clear tension with respect to the two-loop CF dressing
functions in the close to physical case, as expected. Interestingly, however,
we find that there is much less tension between the non-perturbative quark mass
function, as it can be obtained from lattice simulations or from
\cite{Pelaez:2020ups}, and the two-loop CF dressing functions, which confirms
the perturbative nature of the latter.
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Quantum criticality and duality in the SYK/AdS$_2$ chain: We show that the quantum critical point (QCP) between a diffusive metal and
ferromagnetic (or antiferromagnetic) phases in the SYK chain has a
gravitational description corresponding to the double-trace deformation in an
AdS$_2$ chain. Specifically, by studying a double-trace deformation of a $Z_2$
scalar in an AdS$_2$ chain where the $Z_2$ scalar is dual to the order
parameter in the SYK chain, we find that the susceptibility and renormalization
group equation describing the QCP in the SYK chain can be exactly reproduced in
the holographic model. Our results suggest that the infrared geometry in the
gravity theory dual to the diffusive metal of the SYK chain is also an AdS$_2$
chain. We further show that the transition in SYK model captures universal
information about double-trace deformation in generic black holes with near
horizon AdS$_2$ spacetime.
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Finite higher spin transformations from exponentiation: We study the exponentiation of elements of the gauge Lie algebras ${\rm
hs}(\lambda)$ of three-dimensional higher spin theories. Exponentiable elements
generate one-parameter groups of finite higher spin symmetries. We show that
elements of ${\rm hs}(\lambda)$ in a dense set are exponentiable, when pictured
in certain representations of ${\rm hs}(\lambda)$, induced from representations
of $SL(2,\mathbb{R})$ in the complementary series. We also provide a geometric
picture of higher spin gauge transformations clarifying the physical origin of
these representations. This allows us to construct an infinite-dimensional
topological group $HS(\lambda)$ of finite higher spin symmetries.
Interestingly, this construction is possible only for $0 \leq \lambda \leq 1$,
which are the values for which the higher spin theory is believed to be unitary
and for which the Gaberdiel-Gopakumar duality holds. We exponentiate explicitly
various commutative subalgebras of ${\rm hs}(\lambda)$. Among those, we
identify families of elements of ${\rm hs}(\lambda)$ exponentiating to the unit
of $HS(\lambda)$, generalizing the logarithms of the holonomies of BTZ black
hole connections. Our techniques are generalizable to the Lie algebras relevant
to higher spin theories in dimensions above three.
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Gravitational Positive Energy Theorems from Information Inequalities: In this paper we argue that classical, asymptotically AdS spacetimes that
arise as states in consistent ultraviolet completions of Einstein gravity
coupled to matter must satisfy an infinite family of positive energy
conditions. To each ball-shaped spatial region $B$ of the boundary spacetime,
we can associate a bulk spatial region $\Sigma_B$ between $B$ and the bulk
extremal surface $\tilde{B}$ with the same boundary as $B$. We show that there
exists a natural notion of a gravitational energy for every such region that is
non-negative, and non-increasing as one makes the region smaller. The results
follow from identifying this gravitational energy with a quantum relative
entropy in the associated dual CFT state. The positivity and monotonicity
properties of the gravitational energy are implied by the positivity and
monotonicity of relative entropy, which holds universally in all quantum
systems.
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Holographic subregion complexity of boosted black brane and Fisher
information: In this paper, we have studied the holographic subregion complexity for
boosted black brane for strip like subsystem. The holographic subregion
complexity has been computed for a subsystem chosen along and perpendicular to
the boost direction. We have observed that there is an asymmetry in the result
due to the boost parameter which can be attributed to the asymmetry in the
holographic entanglement entropy. The Fisher information metric and the
fidelity susceptibility have also been computed using bulk dual prescriptions.
It is observed that the two metrics computed holographically are not related
for both the pure black brane as well as the boosted black brane. This is one
of the main findings in this paper and the holographic results have been
compared with the results available in the quantum information literature where
it is known that the two distances are related to each other in general.
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Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3: We study the thermodynamics of U(N) N=4 Super Yang-Mills (SYM) on RxS^3 with
non-zero chemical potentials for the SU(4) R-symmetry. We find that when we are
near a point with zero temperature and critical chemical potential, N=4 SYM on
RxS^3 reduces to a quantum mechanical theory. We identify three such critical
regions giving rise to three different quantum mechanical theories. Two of them
have a Hilbert space given by the SU(2) and SU(2|3) sectors of N=4 SYM of
recent interest in the study of integrability, while the third one is the
half-BPS sector dual to bubbling AdS geometries. In the planar limit the three
quantum mechanical theories can be seen as spin chains. In particular, we
identify a near-critical region in which N=4 SYM on RxS^3 essentially reduces
to the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find furthermore a
limit in which this relation becomes exact.
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A-Model Correlators from the Coulomb Branch: We compute the contribution of discrete Coulomb vacua to A-Model correlators
in toric Gauged Linear Sigma Models. For models corresponding to a compact
variety, this determines the correlators at arbitrary genus. For non-compact
examples, our results imply the surprising conclusion that the quantum
cohomology relations break down for a subset of the correlators.
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Thermodynamic Bethe Ansatz of the Homogeneous Sine-Gordon models: We apply the thermodynamic Bethe Ansatz to investigate the high energy
behaviour of a class of scattering matrices which have recently been proposed
to describe the Homogeneous sine-Gordon models related to simply laced Lie
algebras. A characteristic feature is that some elements of the suggested
S-matrices are not parity invariant and contain resonance shifts which allow
for the formation of unstable bound states. From the Lagrangian point of view
these models may be viewed as integrable perturbations of WZNW-coset models and
in our analysis we recover indeed in the deep ultraviolet regime the effective
central charge related to these cosets, supporting therefore the S-matrix
proposal. For the $SU(3)_k$-model we present a detailed numerical analysis of
the scaling function which exhibits the well known staircase pattern for
theories involving resonance parameters, indicating the energy scales of stable
and unstable particles. We demonstrate that, as a consequence of the interplay
between the mass scale and the resonance parameter, the ultraviolet limit of
the HSG-model may be viewed alternatively as a massless
ultraviolet-infrared-flow between different conformal cosets. For $k=2$ we
recover as a subsystem the flow between the tricritical Ising and the Ising
model.
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Q-balls in Maxwell-Chern-Simons theory: We examine the energetics of Q-balls in Maxwell-Chern-Simons theory in two
space dimensions. Whereas gauged Q-balls are unallowed in this dimension in the
absence of a Chern-Simons term due to a divergent electromagnetic energy, the
addition of a Chern-Simons term introduces a gauge field mass and renders
finite the otherwise-divergent electromagnetic energy of the Q-ball. Similar to
the case of gauged Q-balls, Maxwell-Chern-Simons Q-balls have a maximal charge.
The properties of these solitons are studied as a function of the parameters of
the model considered, using a numerical technique known as relaxation. The
results are compared to expectations based on qualitative arguments.
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Vortex counting and the quantum Hall effect: We provide evidence for conjectural dualities between nonrelativistic
Chern-Simons-matter theories and theories of (fractional, nonAbelian) quantum
Hall fluids in $2+1$ dimensions. At low temperatures, the dynamics of
nonrelativistic Chern-Simons-matter theories can be described in terms of a
nonrelativistic quantum mechanics of vortices. At critical coupling, this may
be solved by geometric quantisation of the vortex moduli space. Using
localisation techniques, we compute the Euler characteristic
${\chi}(\mathcal{L}^\lambda)$ of an arbitrary power $\lambda$ of a quantum line
bundle $\mathcal{L}$ on the moduli space of vortices in $U(N_c)$ gauge theory
with $N_f$ fundamental scalar flavours on an arbitrary closed Riemann surface.
We conjecture that this is equal to the dimension of the Hilbert space of
vortex states when the area of the metric on the spatial surface is
sufficiently large. We find that the vortices in theories with $N_c = N_f =
\lambda$ behave as fermions in the lowest nonAbelian Landau level, with
strikingly simple quantum degeneracy. More generally, we find evidence that the
quantum vortices may be regarded as composite objects, made of dual anyons. We
comment on potential links between the dualities and three-dimensional mirror
symmetry. We also compute the expected degeneracy of local Abelian vortices on
the $\Omega$-deformed sphere, finding it to be a $q$-analog of the undeformed
case.
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Collinearity constraints for on-shell massless particle three-point
functions, and implications for allowed-forbidden $n+1$-point functions: A simple collinearity argument implies that the massless particle three-point
function of helicities $h_1, h_2, h_3$ with corresponding real-valued
four-momenta $k_1, k_2, k_3$ taken as all incoming or all outgoing (i.e., $k_1
+k_2 +k_3=0$), vanishes by helicity conservation unless $h_1+h_2+h_3=0$. When
any one particle with four-momentum $k$ is off mass shell, this constraint no
longer applies; a forbidden amplitude with $h_1+h_2+h_3\neq 0$ on-shell can be
nonzero off-shell, but vanishes proportionally to $k^2$ as $k$ approaches mass
shell. When an on-shell forbidden amplitude is coupled to an allowed $n$-point
amplitude to form an $n+1$ point function, this $k^2$ factor in the forbidden
amplitude cancels the $k^2$ in the propagator, leading to a $n+1$-point
function that has no pole at $k^2=0$. We relate our results for real-valued
four-momenta to the corresponding selection rules that have been derived in the
on-shell literature for complexified four-momenta.
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The one example of Lorentz group: The aim of this work is to show, on the example of the behaviour of the
spinless charged particle in the homogeneous electric field, that one can
quantized the velocity of particle by the special gauge fixation. The work
gives also the some information about the theory of second quantisation in the
space of Hilbert- Fock and the theory of projectors in the Hilbert space. One
consider in Appendix the theory of the spinless charged particle in the
homogeneous addiabatical changed electrical field.
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The Standard Model as an extension of the noncommutative algebra of
forms: The Standard Model of particle physics can be deduced from a small number of
axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New
J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra
extension in the sense of Eilenberg. By doing so, they could deduce three
axioms of the NCG Standard Model (i.e. order zero, order one and massless
photon) from the single requirement that the extended algebra be associative.
However, their approach was only applied to the finite algebra and fails the
full model. By taking into account the differential graded structure of the
algebra of noncommutative differential forms, we obtain a formulation where the
same three axioms are deduced from the associativity of the extended
differential graded algebra, but which is now also compatible with the full
Standard Model. Finally, we present a Lorentzian version of the noncommutative
geometry of the Standard Model and we show that the three axioms still hold if
the four-dimensional manifold has a Lorentzian metric.
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Stochastic tunneling for strongly non-Gaussian inflationary theories: We reconsider the dynamics of stochastic or thermal tunneling in theories
like Dirac-Born-Infeld inflation that have non-minimal kinetic terms and, as a
result, strongly non-Gaussian perturbations. We first describe a local
description of the tunneling process which gives results consistent with the
standard Hawking-Moss tunneling. This result is under perturbative control as
long as the fluctuation determinant is well approximated by a one-loop
integral. We then move to a global description, using the methodology of
stochastic inflation and the in-in path integral formalism. This approach shows
clearly that the tunneling process becomes strongly coupled whenever the sound
speed of the tunneling trajectory departs sufficiently from unity. We argue
that these two very different perspectives are nevertheless consistent, and may
imply the existence of a simple resummation of the strongly coupled
interactions of the field.
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On the Moduli Space of the Cascading SU(M+p)xSU(p) Gauge Theory: We carry out a thorough analysis of the moduli space of the cascading gauge
theory found on p D3-branes and M wrapped D5-branes at the tip of the conifold.
We find various mesonic branches of the moduli space whose string duals involve
the warped deformed conifold with different numbers of mobile D3-branes. The
branes that are not mobile form a BPS bound state at threshold. In the special
case where p is divisible by M there also exists a one-dimensional baryonic
branch whose family of supergravity duals, the resolved warped deformed
conifolds, was constructed recently. The warped deformed conifold is a special
case of these backgrounds where the resolution parameter vanishes and a Z_2
symmetry is restored. We study various brane probes on the resolved warped
deformed conifolds, and successfully match the results with the gauge theory.
In particular, we show that the radial potential for a D3-brane on this space
varies slowly, suggesting a new model of D-brane inflation.
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Double Horizon Limit, AdS Geometry and Entropy Function: We start from a generic metric which describes four dimensional stationary
black holes in an arbitrary theory of gravity and show that the AdS_2 part of
the near horizon geometry is a consequence of the double-horizon limit and
finiteness . We also show that the field configurations of the near horizon are
determined if the same conditions are applied to the equations of motion. This
is done by showing that in the double-horizon limit field equations at the
horizon decouple from the bulk of the space. Solving these equations gives the
near horizon field configurations. It is shown that these decoupled equations
can be obtained from an action derived from the original action by applying the
double-horizon condition. Our results agree with the entropy function method.
|
Scattering Amplitudes and Conservative Binary Dynamics at ${\cal
O}(G^4)$: Using scattering amplitudes, we obtain the potential contributions to
conservative binary dynamics in general relativity at fourth post-Minkowskian
order, ${\cal O}(G^4)$. As in previous lower-order calculations, we harness
powerful tools from the modern scattering amplitudes program including
generalized unitarity, the double copy, and advanced multiloop integration
methods, in combination with effective field theory. The classical amplitude
involves polylogarithms with up to transcendental weight two and elliptic
integrals. We derive the radial action directly from the amplitude, and
determine the corresponding Hamiltonian in isotropic gauge. Our results are in
agreement with known overlapping terms up to sixth post-Newtonian order, and
with the probe limit. We also determine the post-Minkowskian energy loss from
radiation emission at ${\cal O}(G^3)$ via its relation to the tail effect.
|
Twist Symmetry and Gauge Invariance: By applying properly the concept of twist symmetry to the gauge invariant
theories, we arrive at the conclusion that previously proposed in the
literature noncommutative gauge theories, with the use of $\star$-product, are
the correct ones, which possess the twisted Poincar\'e symmetry. At the same
time, a recent approach to twisted gauge transformations is in contradiction
with the very concept of gauge fields arising as a consequence of {\it local}
internal symmetry. Detailed explanations of this fact as well as the origin of
the discrepancy between the two approaches are presented.
|
On New Bulk Singularity Structures, RR Couplings in Asymmetric Picture
and Their All Order $α'$ Corrections: We have analyzed in detail four and five point functions of the string theory
amplitudes, including a closed string Ramond-Ramond (RR) in an asymmetric
picture and either two or three transverse scalar fields in both IIA and IIB.
The complete forms of these S-matrices are derived and these asymmetric
S-matrices are also compared with their own symmetric results. This leads us to
explore two different kinds of bulk singularity structures as well as various
new couplings in asymmetric picture of the amplitude in type II string theory.
All order $\alpha'$ higher derivative corrections to these new couplings have
been discovered as well. Several remarks for these two new bulk singularity
structures and for contact interactions of the S-Matrix have also been made.
|
Winding String Dynamics in a Time-Dependent Beta Deformed Background: We study string theory on the analytically continued $\beta$ deformed
background proposed in hep-th/0509036. This non-static model provides a
solvable conformal field theory which describes time-dependent twisted string
dynamics. With the mini-superspace approach, we examine disk one-point
correlators of D-branes and compute the winding string pair production rate. We
find that these results are consistent with the CFT computation.
|
Brane Junctions in the Randall-Sundrum Scenario: We present static solutions to Einstein's equations corresponding to branes
at various angles intersecting in a single 3-brane. Such configurations may be
useful for building models with localized gravity via the Randall-Sundrum
mechanism. We find that such solutions may exist only if the mechanical forces
acting on the junction exactly cancel. In addition to this constraint there are
further conditions that the parameters of the theory have to satisfy. We find
that at least one of these involves only the brane tensions and cosmological
constants, and thus can not have a dynamical origin. We present these
conditions in detail for two simple examples. We discuss the nature of the
cosmological constant problem in the framework of these scenarios, and outline
the desired features of the brane configurations which may bring us closer
towards the resolution of the cosmological constant problem.
|
Self-Dual Chern-Simons Solitons with Non-Compact Groups: It is shown how to couple non-relativistic matter with a Chern--Simons gauge
field that belongs to a non-compact group. We treat in some details the
$SL(2,{\bf R})$ and the Poincar\'e $ISO(2,1)$ groups. For suitable
self-interactions, we are able to exhibit soliton solutions.
|
Notes on Ramond-Ramond spinors and bispinors in double field theory: The Ramond-Ramond sector of double field theory (DFT) can be described either
as an O(D,D) spinor or an O(D-1,1) x O(1,D-1) bispinor. Both formulations may
be related to the standard polyform expansion in terms of even or odd rank
field strengths corresponding to IIA or IIB duality frames. The spinor approach
is natural in a (bosonic) metric formulation of DFT, while the bispinor is
indispensable for supersymmetric DFT. In these notes, we show how these two
approaches may be covariantly connected using a spinorial version of the DFT
vielbein, which flattens an O(D,D) spinor into a bispinor. We also elaborate on
details of the bispinor formulation in both even and odd D and elaborate on the
distinction between the IIA/IIB/IIA*/IIB* duality frames.
|
Effective Action and Phase Structure of Multi-Layer Sine-Gordon Type
Models: We analyze the effective action and the phase structure of N-layer
sine-Gordon type models, generalizing the results obtained for the two-layer
sine-Gordon model found in [I. Nandori, S. Nagy, K. Sailer and U. D.
Jentschura, Nucl. Phys. B725, 467-492 (2005)]. Besides the obvious field
theoretical interest, the layered sine-Gordon model has been used to describe
the vortex properties of high transition temperature superconductors, and the
extension of the previous analysis to a general N-layer model is necessary for
a description of the critical behaviour of vortices in realistic multi-layer
systems. The distinction of the Lagrangians in terms of mass eigenvalues is
found to be the decisive parameter with respect to the phase structure of the
N-layer models, with neighbouring layers being coupled by quadratic terms in
the field variables. By a suitable rotation of the field variables, we identify
the periodic modes (without explicit mass terms) in the N-layer structure,
calculate the effective action and determine their Kosterlitz-Thouless type
phase transitions to occur at a coupling parameter \beta^2_{c} = 8 N \pi, where
N is the number of layers (or flavours in terms of the multi-flavour Schwinger
model).
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Faddeev-Jackiw Quantization of Christ-Lee Model: We analyze the constraints of Christ-Lee model by the means of modified
Faddeev-Jackiw formalism in Cartesian as well as polar coordinates. Further, we
accomplish quantization \`{a} la Faddeev-Jackiw by choosing appropriate gauge
conditions in both the coordinate systems. Finally, we establish gauge
symmetries of Christ-Lee model with the help of zero modes of the symplectic
matrix.
|
Double scaling limit of N=2 chiral correlators with Maldacena-Wilson
loop: We consider $\mathcal N=2$ conformal QCD in four dimensions and the one-point
correlator of a class of chiral primaries with the circular $\frac{1}{2}$-BPS
Maldacena-Wilson loop. We analyze a recently introduced double scaling limit
where the gauge coupling is weak while the R-charge of the chiral primary
$\Phi$ is large. In particular, we consider the case
$\Phi=(\text{tr}\varphi^{2})^{n}$ , where $\varphi$ is the complex scalar in
the vector multiplet. The correlator defines a non-trivial scaling function at
fixed $\kappa = n\,g_{\rm YM}^{2}$ and large $n$ that may be studied by
localization. For any gauge group $SU(N)$ we provide the analytic expression of
the first correction $\sim \zeta(3)\,\kappa^{2}$ and prove its universality. In
the $SU(2)$ and $SU(3)$ theories we compute the scaling functions at order
$\mathcal O(\kappa^{6})$. Remarkably, in the $SU(2)$ case the scaling function
is equal to an analogous quantity describing the chiral 2-point functions
$\langle\Phi\overline\Phi\rangle$ in the same large R-charge limit. We
conjecture that this $SU(2)$ scaling function is computed at all-orders by a
$\mathcal N=4$ SYM expectation value of a matrix model object characterizing
the one-loop contribution to the 4-sphere partition function. The conjecture
provides an explicit series expansion for the scaling function and is checked
at order $\mathcal O(\kappa^{10})$ by showing agreement with the available data
in the sector of chiral 2-point functions.
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Renormalization of the bilocal sine-Gordon model: The functional renormalization group treatment is presented for the
two-dimensional sine-Gordon model by including a bilocal term in the potential,
which contributes to the flow at tree level. It is shown that the flow of the
bilocal term can substitute the evolution of the wave function renormalization
constant, and then the Kosterlitz-Thouless type phase transition can be
recovered.
|
On the Limits of Effective Quantum Field Theory: Eternal Inflation,
Landscapes, and Other Mythical Beasts: We recapitulate multiple arguments that Eternal Inflation, and the String
Landscape are actually part of the Swampland: ideas in Effective Quantum Field
Theory that do not have a counterpart in genuine models of Quantum Gravity.
|
Field Theoretical Quantum Effects on the Kerr Geometry: We study quantum aspects of the Einstein gravity with one time-like and one
space-like Killing vector commuting with each other. The theory is formulated
as a $\coset$ nonlinear $\sigma$-model coupled to gravity. The quantum analysis
of the nonlinear $\sigma$-model part, which includes all the dynamical degrees
of freedom, can be carried out in a parallel way to ordinary nonlinear
$\sigma$-models in spite of the existence of an unusual coupling. This means
that we can investigate consistently the quantum properties of the Einstein
gravity, though we are limited to the fluctuations depending only on two
coordinates. We find the forms of the beta functions to all orders up to
numerical coefficients. Finally we consider the quantum effects of the
renormalization on the Kerr black hole as an example. It turns out that the
asymptotically flat region remains intact and stable, while, in a certain
approximation, it is shown that the inner geometry changes considerably however
small the quantum effects may be.
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Quantum aspects of a noncommutative supersymmetric kink: We consider quantum corrections to a kink of noncommutative supersymmetric
phi^4 theory in 1+1 dimensions. Despite the presence of an infinite number of
time derivatives in the action, we are able to define supercharges and a
Hamiltonian by using an unconventional canonical formalism. We calculate the
quantum energy E of the kink (defined as a half-sum of the eigenfrequencies of
fluctuations) which coincides with its' value in corresponding commutative
theory independently of the noncommutativity parameter. The renormalization
also proceeds precisely as in the commutative case. The vacuum expectation
value of the new Hamiltonian is also calculated and appears to be consistent
with the value of the quantum energy E of the kink.
|
Massive fermion between two parallel chiral plates: We study the system of a massive fermion field confined between two parallel
plates, where the properties of both plates are discussed under chiral MIT
boundary conditions. We investigate the effects of the chiral angle on the
Casimir energy for a massive fermion field with the general momentum. We find
that the Casimir energy as a function of the chiral angle is generally
symmetric, and the attractive Casimir force in the chiral case is stronger than
that in the nonchiral case. In addition, we investigate the approximate Casimir
energy for light and heavy mass cases. The behavior of the discrete momentum
and changes of spin orientation are also discussed.
|
On Wilson Criterion: U(1) gauge theory with the Villain action on a cubic lattice approximation of
three- and four-dimensional torus is considered. The naturally chosen
correlation functions converge to the correlation functions of the R-gauge
electrodynamics on three- and four-dimensional torus as the lattice spacing
approaches zero only for the special scaling. This special scaling depends on a
choice of a correlation function system. Another scalings give the degenerate
continuum limits. The Wilson criterion for the confinement is ambiguous. The
asymptotics of the smeared Wilson loop integral for the large loop perimeters
is defined by the density of the loop smearing over a torus which is
transversal to the loop plane. When the initial torus radius tends to infinity
the correlation functions converge to the correlation functions of the R-gauge
Euclidean electrodynamics.
|
On the ambiguity of field correlators represented by asymptotic
perturbation expansions: Starting from the divergence pattern of perturbation expansions in Quantum
Field Theory and the (assumed) asymptotic character of the series, we address
the problem of ambiguity of a function determined by the perturbation
expansion. We consider functions represented by an integral of the
Laplace-Borel type along a general contour in the Borel complex plane. Proving
a modified form of the Watson lemma, we obtain a large class of functions
having the same asymptotic perturbation expansion. Some remarks on perturbative
QCD are made, using the particular case of the Adler function.
|
Modular invariance and entanglement entropy: We study the Renyi and entanglement entropies for free 2d CFT's at finite
temperature and finite size, with emphasis on their properties under modular
transformations of the torus. We address the issue of summing over fermion spin
structures in the replica trick, and show that the relation between
entanglement and thermal entropy determines two different ways to perform this
sum in the limits of small and large interval. Both answers are modular
covariant, rather than invariant. Our results are compared with those for a
free boson at unit radius in the two limits and complete agreement is found,
supporting the view that entanglement respects Bose-Fermi duality. We extend
our computations to multiple free Dirac fermions having correlated spin
structures, dual to free bosons on the Spin(2d) weight lattice.
|
Conformal Field Theory as Microscopic Dynamics of Incompressible Euler
and Navier-Stokes Equations: We consider the hydrodynamics of relativistic conformal field theories at
finite temperature. We show that the limit of slow motions of the ideal
hydrodynamics leads to the non-relativistic incompressible Euler equation. For
viscous hydrodynamics we show that the limit of slow motions leads to the
non-relativistic incompressible Navier-Stokes equation. We explain the physical
reasons for the reduction and discuss the implications. We propose that
conformal field theories provide a fundamental microscopic viewpoint of the
equations and the dynamics governed by them.
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Evolution of the Chern-Simons Vortices: Based on the gauge potential decomposition theory and the $\phi $-mapping
theory, the topological inner structure of the Chern-Simons-Higgs vortex has
been showed in detail. The evolution of CSH vortices is studied from the
topological properties of the Higgs scalar field. The vortices are found
generating or annihilating at the limit points and encountering, splitting or
merging at the bifurcation points of the scalar field $\phi .$
|
Dilaton-Axion hair for slowly rotating Kerr black holes: Campbell et al. demonstrated the existence of axion ``hair'' for Kerr black
holes due to the non-trivial Lorentz Chern-Simons term and calculated it
explicitly for the case of slow rotation. Here we consider the dilaton coupling
to the axion field strength, consistent with low energy string theory and
calculate the dilaton ``hair'' arising from this specific axion source.
|
3+1 Approach to the Long Wavelength Iteration Scheme: Large-scale inhomogeneities and anisotropies are modeled using the Long
Wavelength Iteration Scheme. In this scheme solutions are obtained as
expansions in spatial gradients, which are taken to be small. It is shown that
the choice of foliation for spacetime can make the iteration scheme more
effective in two respects: (i) the shift vector can be chosen so as to dilute
the effect of anisotropy on the late-time value of the extrinsic curvature of
the spacelike hypersurfaces of the foliation; and (ii) pure gauge solutions
present in a similar calculation using the synchronous gauge vanish when the
spacelike hypersurfaces have extrinsic curvature with constant trace. We
furthermore verify the main conclusion of the synchronous gauge calculation
which is large-scale inhomogeneity decays if the matter--considered to be that
of a perfect-fluid with a barotropic equation of state--violates the
strong-energy condition. Finally, we obtain the solution for the lapse function
and discuss its late-time behaviour. It is found that the lapse function is
well-behaved when the matter violates the strong energy condition.
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Causal diamonds in 2+1 dimensional quantum gravity: We develop the reduced phase space quantization of causal diamonds in pure
2+1 dimensional gravity with a non-positive cosmological constant. The system
is defined as the domain of dependence of a topological disc with fixed
boundary metric. By solving the initial value constraints in a
constant-mean-curvature time gauge and removing all the spatial gauge
redundancy, we find that the phase space is the cotangent bundle of
Diff^+(S^1)/PSL(2,R). To quantize this phase space we apply Isham's
group-theoretic quantization scheme, with respect to a BMS_3 group, and find
that the quantum theory can be realized by wavefunctions on some coadjoint
orbit of the Virasoro group, with labels in irreducible unitary representations
of the corresponding little group. We find that the twist of the diamond
boundary loop is quantized in integer or half-integer multiples of the ratio of
the Planck length to the boundary length.
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The BFV Approach for a Nonlocal Symmetry of QED: In this paper we use the Batalin-Fradkin-Vilkovisky formalism to study a
recently proposed nonlocal symmetry of QED. In the BFV extended phase space we
show that this symmetry stems from a canonical transformation in the ghost
sector.
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Yang-Mills theories with an arbitrary number of compactified extra
dimensions: The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra
dimension (UED) is generalized to an arbitrary number of spatial extra
dimensions through a novel compactification scheme. In this paper, the
Riemannian flat based manifold under consideration contains $ n $ spatial extra
dimensions defined by $ n $ copies of the orbifold $ S^{1} / Z_{2}$. In this
approach, we present the gauge structure and the mass spectrum of the effective
four-dimensional theory. We introduce the concept of standard and nonstandard
gauge transformations of the effective theory, and explicitly identify the
emergence of massive vector fields in the same number as massless
('pseudo-Goldstone') scalars in the compactified theory, verifying that a
Higgs-like mechanism operates in the compactification process. It is found
that, in contrast with the one UED scenario, in cases with two or more UEDs
there emerge massive scalar fields. Besides, at phase-space level, the
Hamiltonian analysis yields that the higher-dimensional and compactified
theories are classically equivalent using the fundamental concept of canonical
transformation. This work lays the ground for a wider study on these theories
concerning their quantization and predictive power at the level of quantum
fluctuations.
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Differential Renormalization-Group Approach to the Layered sine-Gordon
Model: New qualitative picture of vortex length-scale dependence has been found in
recent electrical transport measurements performed on strongly anisotropic
BSCCO single crystals in zero magnetic field. This indicates the need for a
better description of the 3D/2D crossover in vortex dimensionality. The
vortex-dominated properties of high transition temperature superconductors with
extremely high anisotropy (layered systems) are reasonably well described in
the framework of the layered XY model which can be mapped onto the layered
sine-Gordon model. For the latter we derive an exact renormalization group (RG)
equation using Wegner's and Houghton's approach in the local potential
approximation. The agreement of the UV scaling laws find by us by linearizing
the RG equations with those obtained previously in the literature in the dilute
gas approximation makes the improvement appearant which can be achieved by
solving our RG equations numerically.
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Fluid description of gravity on a timelike cut-off surface: beyond
Navier-Stokes equation: Over the past few decades, a host of theoretical evidence have surfaced that
suggest a connection between theories of gravity and Navier-Stokes (NS)
equation of fluid dynamics. It emerges out that gravity theory can be treated
as some kind of fluid on a particular surface. Motivated by the work carried
out by Bredberg et al (JHEP 1207, 146 (2012)) \cite{Bredberg:2011jq}, our paper
focuses on including certain modes to the metric which are consistent with the
so called hydrodynamic scaling and discuss the consequences, one of which
appear in the form of Damour Navier Stokes (DNS) equation with the
incompressibility condition. We also present an alternative route to the
results by considering the metric as a perturbative expansion in the
hydrodynamic scaling parameter $\epsilon$ and with a specific gauge choice,
thus modifying the metric. It is observed that the inclusion of certain modes
in the metric corresponds to the solution of Einstein's equations in presence
of a particular type of matter in the spacetime. This analysis reveals that
gravity has both the NS and DNS description not only on a null surface, but
also on a timelike surface. So far we are aware of, this analysis is the first
attempt to illuminate the possibility of presenting the gravity dual of DNS
equation on a timelike surface. In addition, an equivalence between the
hydrodynamic expansion and the near-horizon expansion has also been studied in
the present context.
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*-Products on Quantum Spaces: In this paper we present explicit formulas for the *-product on quantum
spaces which are of particular importance in physics, i.e., the q-deformed
Minkowski space and the q-deformed Euclidean space in 3 and 4 dimensions,
respectively. Our formulas are complete and formulated using the deformation
parameter q. In addition, we worked out an expansion in powers of h=lnq up to
second order, for all considered cases.
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Gauges in the bulk: We present a general framework for nonparallel brane worlds and use it to
discuss the nonlinear radion problem. By imposing the Einstein frame as a gauge
condition we are able to give the effective action for both Minkowski and
(A)dS$_{4}$ branes. In particular we find the nonlinear radion does not
disappear in the second Randall-Sundrum model.
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BPS equations in N=2, D=5 supergravity with hypermultiplets: With the general aim to classify BPS solutions in N=2, D=5 supergravities
interacting with an arbitrary number of vector, tensor and hypermultiplets,
here we begin considering the most general electrostatic, spherical-symmetric
BPS solutions in the presence of hypermultiplet couplings. We discuss the
properties of the BPS equations and the restrictions imposed by their
integrability conditions. We exhibit explicit solutions for the case of static
BPS black-holes coupled to one (the so called universal) hypermultiplet.
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Euclidean Black Hole Vortices: We argue the existence of solutions of the Euclidean Einstein equations that
correspond to a vortex sitting at the horizon of a black hole. We find the
asymptotic behaviours, at the horizon and at infinity, of vortex solutions for
the gauge and scalar fields in an abelian Higgs model on a Euclidean
Schwarzschild background and interpolate between them by integrating the
equations numerically. Calculating the backreaction shows that the effect of
the vortex is to cut a slice out of the Euclidean Schwarzschild geometry.
Consequences of these solutions for black hole thermodynamics are discussed.
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Extensions of Conformal Nets and Superselection Structures: Starting with a conformal Quantum Field Theory on the real line, we show that
the dual net is still conformal with respect to a new representation of the
Moebius group. We infer from this that every conformal net is normal and
conormal, namely the local von Neumann algebra associated with an interval
coincides with its double relative commutant inside the local von Neumann
algebra associated with any larger interval. The net and the dual net give
together rise to an infinite dimensional symmetry group, of which we study a
class of positive energy irreducible representations. We mention how
superselsection sectors extend to the dual net and we illustrate by examples
how, in general, this process generates solitonic sectors. We describe the free
theories associated with the lowest weight n representations of PSL(2,R),
showing that they violate 3-regularity for n>2. When n>1, we obtain examples of
non Moebius-covariant sectors of a 3-regular (non 4-regular) net.
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On a geometric derivation of Witten's identity for Chern-Simons theory: We present a formal but simple calculational scheme to relate the expectation
value of Wilson loops in Chern-Simons theory to the Jones polynomial. We
consider the exponential of the generator of homotopy transformations which
produces the finite loop deformations that define the crossing change formulas
of knot polynomials. Applying this operator to the expectation value of Wilson
loops for an unspecified measure we find a set of conditions on the measure and
the regularization such that the Jones polynomial is obtained.
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Ashtekar's Approach to Quantum Gravity: A review is given of work by Abhay Ashtekar and his colleagues Carlo Rovelli,
Lee Smolin, and others, which is directed at constructing a nonperturbative
quantum theory of general relativity.
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Entropy Function for Heterotic Black Holes: We use the entropy function formalism to study the effect of the Gauss-Bonnet
term on the entropy of spherically symmetric extremal black holes in heterotic
string theory in four dimensions. Surprisingly the resulting entropy and the
near horizon metric, gauge field strengths and the axion-dilaton field are
identical to those obtained by Cardoso et. al. for a supersymmetric version of
the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet
term. We also study the effect of holomorphic anomaly on the entropy using our
formalism. Again the resulting attractor equations for the axion-dilaton field
and the black hole entropy agree with the corresponding equations for the
supersymmetric version of the theory. These results suggest that there might be
a simpler description of supergravity with curvature squared terms in which we
supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.
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D-brane Solitons in Supersymmetric Sigma-Models: Massive D=4 N=2 supersymmetric sigma models typically admit domain wall
(Q-kink) solutions and string (Q-lump) solutions, both preserving 1/2
supersymmetry. We exhibit a new static 1/4 supersymmetric `kink-lump' solution
in which a string ends on a wall, and show that it has an effective realization
as a BIon of the D=4 super DBI-action. It is also shown to have a
time-dependent Q-kink-lump generalization which reduces to the Q-lump in a
limit corresponding to infinite BI magnetic field. All these 1/4 supersymmetric
sigma-model solitons are shown to be realized in M-theory as calibrated, or
`Q-calibrated', M5-branes in an M-monopole background.
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Operator Krylov complexity in random matrix theory: Krylov complexity, as a novel measure of operator complexity under Heisenberg
evolution, exhibits many interesting universal behaviors and also bounds many
other complexity measures. In this work, we study Krylov complexity
$\mathcal{K}(t)$ in Random Matrix Theory (RMT). In large $N$ limit: (1) For
infinite temperature, we analytically show that the Lanczos coefficient
$\{b_n\}$ saturate to constant plateau $\lim\limits_{n\rightarrow\infty}b_n=b$,
rendering a linear growing complexity $\mathcal{K}(t)\sim t$, in contrast to
the exponential-in-time growth in chaotic local systems in thermodynamic limit.
After numerically comparing this plateau value $b$ to a large class of chaotic
local quantum systems, we find that up to small fluctuations, it actually
bounds the $\{b_n\}$ in chaotic local quantum systems. Therefore we conjecture
that in chaotic local quantum systems after scrambling time, the speed of
linear growth of Krylov complexity cannot be larger than that in RMT. (2) For
low temperature, we analytically show that $b_n$ will first exhibit linear
growth with $n$, whose slope saturates the famous chaos bound. After hitting
the same plateau $b$, $b_n$ will then remain constant. This indicates
$\mathcal{K}(t)\sim e^{2\pi t/\beta}$ before scrambling time $t_*\sim
O(\beta\log\beta)$, and after that it will grow linearly in time, with the same
speed as in infinite temperature. We finally remark on the effect of finite $N$
corrections.
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Gravitons in a gravitational plane wave: Gravitational plane waves (when Ricci flat) belong to the VSI family. The
achronym VSI stands for vanishing scalar invariants, meaning that all scalar
invariants built out of Riemann tensor and its derivatives vanish, although the
Riemann tensor itself does not. In the particular case of plane waves many
interesting phenomena have been uncovered for strings propagating in this
background. Here we comment on gravitons propagating in such a spacetime, which
itself presumably consists of an Avogadro number of such gravitons.
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The massless supersymmetric ladder with L rungs: We show that in the massless N=1 supersymmetric Wess-Zumino theory it is
possible to devise a computational strategy by which the x-space calculation of
the ladder 4-point correlators can be carried out without introducing any
regularization. As an application we derive a representation valid at all loop
orders in terms of conformal invariant integrals. We obtain an explicit
expression of the 3-loop ladder diagram for collinear external points.
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World Sheet Superstring and Superstring Field Theory: a new solution
using Ultradistributions of Exponential Type: In this paper we show that Ultradistributions of Exponential Type (UET) are
appropriate for the description in a consistent way world sheet superstring and
superstring field theories. A new Lagrangian for the closed world sheet
superstring is obtained. We also show that the superstring field is a linear
superposition of UET of compact support (CUET), and give the notion of
anti-superstring. We evaluate the propagator for the string field, and
calculate the convolution of two of them.
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Superconductivity in Anyon Fluid at Finite Temperature and Density: The boundary effects in the screening of an applied magnetic field in a
charged anyon fluid at finite temperature and density are investigated. By
analytically solving the extremum equations of the sytem and minimizing the
free energy density, we find that in a sample with only one boundary (the half
plane), a total Meissner effect takes place; while the sample with two
boundaries (the infinite strip) exhibits a partial Meissner effect. The
short-ranges modes of propagation of the magnetic field inside the fluid are
characterized by two temp erature dependent penetration lengths.
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Partial D-operators for the generalized IBP reduction: Empirical evidence reveals existence of partial D-operators for the
generalized IBP (BT) reduction algorithms that are, counterintuitively, much
simpler and much easier to find than the complete D-operators from the
foundational Bernstein theorem, allowing one to construct first true two-loop
examples of generalized IBP identities.
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Non Abelian Toda Theory : A Completely Integrable Model for Strings on a
Black Hole Background: The present paper studies a completely integrable conformally invariant model
in 1+1 dimensions that corresponds to string propagation on the two-dimensional
black hole background (semi-ininite cigar). Besides the two space-time string
fields there is a third (internal) field with a very specific Liouville-type
interaction leading to the complete integrability. This system is known as
non-abelian Toda theory. I give the general explicit classical solution. It
realizes a rather involved transformation expressing the interacting string
fields in terms of (three) functions $\varphi_j(u)$ and $\bar\varphi_j(v)$ of
one light-cone variable only. The latter are shown to lead to standard harmonic
oscillator (free field) Poisson brackets thus paving the way towards
quantization. There are three left-moving and three right-moving conserved
quantities. The right (left)-moving conserved quantities form a new closed
non-linear, non-local Poisson bracket algebra. This algebra is a Virasoro
algebra extended by two conformal dimension-two primaries.
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Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II.
Oscillator Realization: Following the general formalism presented in arXiv:0812.3615 -- referred to
as Paper I -- we derive the unfolded equations of motion for tensor fields of
arbitrary shape and mass in constantly curved backgrounds by radial reduction
of Skvortsov's equations in one higher dimension. The complete unfolded system
is embedded into a single master field, valued in a tensorial Schur module
realized equivalently via either bosonic (symmetric basis) or fermionic
(anti-symmetric basis) vector oscillators. At critical masses the reduced Weyl
zero-form modules become indecomposable. We explicitly project the latter onto
the submodules carrying Metsaev's massless representations. The remainder of
the reduced system contains a set of Stueckelberg fields and dynamical
potentials that leads to a smooth flat limit in accordance with the
Brink--Metsaev--Vasiliev (BMV) conjecture. In the unitary massless cases in
AdS, we identify the Alkalaev--Shaynkman--Vasiliev frame-like potentials and
explicitly disentangle their unfolded field equations.
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Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann
surface: We study and classify quarter-BPS AdS5 systems in M-theory, whose internal
six-dimensional geometry is a T2 bundle over a Riemann surface and two interval
directions. The general system presented, provides a unified description of all
known AdS5 solutions in M-theory. These systems are governed by two functions,
one that corresponds to the conformal factor of the Riemann surface and another
that describes the T2 fibration. We find solutions that can be organized into
two classes. In the first one, solutions are specified by the conformal factor
of the Riemann surface which satisfies a warped generalization of the
SU(infinity) Toda equation. The system in the second class requires the Riemann
surface to be S2, H2 or T2. Class one contains the M-theory AdS5 solutions of
Lin, Lunin and Maldacena; the solutions of Maldacena and Nunez; the solutions
of Gauntlett, Martelli, Sparks and Waldram; and the eleven-dimensional uplift
of the Y(p,q) metrics. The second includes the recently found solutions of
Beem, Bobev, Wecht and the author. Within each class there are new solutions
that will be studied in a companion paper.
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Higher Spin Symmetries, Star-Product and Relativistic Equations in AdS
Space: We discuss general properties of the theory of higher spin gauge fields in
$AdS_4$ focusing on the relationship between the star-product origin of the
higher spin symmetries, AdS geometry and the concept of space-time locality. A
full list of conserved higher spin currents in the flat space of arbitrary
dimension is presented.
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On quasinormal modes of small Schwarzschild-Anti-de-Sitter black hole: We compute the quasinormal modes associated with decay of the massless scalar
filed around a small Schwarzschild-Anti-de-Sitter black hole. The computations
shows that when the horizon radius is much less than the anti-de-Sitter radius,
the imaginary part of the frequency goes to zero as $r_+^{d-2}$ while the real
part of $\omega$ decreases to its minimum and then goes to $d-1$. Thus the
quasinormal modes approach the usual AdS modes in the limit $r_+ -> 0$. This
agrees with suggestions of Horowitz et al (Phys.Rev. D62 024027 (2000)).
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Lorentzian Goldstone modes shared among photons and gravitons: It has long been known that photons and gravitons may appear as vector and
tensor Goldstone modes caused \ by spontaneous Lorentz invariance violation
(SLIV). Usually this approach is considered for photons and gravitons
separately. We develop the emergent electrogravity theory consisting of the
ordinary QED and the tensor field gravity model which mimics the linearized
general relativity in Minkowski spacetime. In this theory, Lorentz symmetry
appears incorporated into higher global symmetries of the length-fixing
constraints put on the vector and tensor fields involved, $A_{\mu }^{2}=\pm
M_{A}^{2}$ and $H_{\mu \nu }^{2}=\pm M_{H}^{2}$ ($M_{A}$ and $M_{H}$ are the
proposed symmetry breaking scales). We show that such a SLIV pattern being
related to breaking of global symmetries underlying these constraints induces
the massless Goldstone and pseudo-Goldstone modes shared among photon and
graviton. While for a vector field case the symmetry of the constraint
coincides with Lorentz symmetry $SO(1,3)$ of the electrogravity Lagrangian, the
tensor field constraint itself possesses much higher global symmetry $SO(7,3)$,
whose spontaneous violation provides a sufficient number of zero modes
collected in a graviton. Accordingly, while photon may only contain true
Goldstone modes, graviton appears at least partially composed from
pseudo-Goldstone modes rather than from pure Goldstone ones. When expressed in
terms of these modes, the theory looks essentially nonlinear and contains a
variety of Lorentz and $CPT$ violating couplings. However, all SLIV effects
turn out to be strictly cancelled in the lowest order processes that is
considered in some detail. How this emergent electrogravity theory could be
observationally differed from conventional QED and GR theories is also briefly
discussed.
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RG and logarithmic CFT multicritical properties of randomly diluted
Ising models: We discuss how a spin system, which is subject to quenched disorder, might
exhibit multicritical behaviors at criticality if the distribution of the
impurities is arbitrary. In order to provide realistic candidates for such
multicritical behaviors, we discuss several generalizations of the standard
randomly diluted Ising's universality class adopting the $\epsilon$-expansion
close to several upper critical dimensions. In the presentation, we spend a
special effort in bridging between CFT and RG results and discuss in detail the
computation of quantities, which are of prominent interest in the case of
logarithmic CFT.
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The String Measure and Spectral Flow of Critical N=2 Strings: The general structure of N=2 moduli space at arbitrary genus and instanton
number is investigated. The N=2 NSR string measure is calculated, yielding
picture- and U(1) ghost number-changing operator insertions. An explicit
formula for the spectral flow operator acting on vertex operators is given, and
its effect on N=2 string amplitudes is discussed.
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Fermionic and bosonic pair creation in an external electric field at
finite temperature using the functional Schrödinger representation: We solve the time evolution of the density matrix both for fermions and
bosons in the presence of a homogeneous but time dependent external electric
field. The number of particles produced by the external field, as well as their
distribution in momentum space is found for finite times. Furthermore, we
calculate the probability of finding a given number of particles in the
ensemble. In all cases, there is a nonvanishing thermal contribution. The
bosonic and the fermionic density matrices are expressed in a "functional field
basis". This constitutes an extension of the "field basis" concept to fermions.
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On the stability problem in the O(N) nonlinear sigma model: The stability problem for the O(N) nonlinear sigma model in the 2+\epsilon
dimensions is considered. We present the results of the 1/N^{2} order
calculations of the critical exponents (in the 2<d<4 dimensions) of the
composite operators relevant for this problem. The arguments in the favor of
the scenario with the conventional fixed point are given.
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On Charged Fields with Group Symmetry and Degeneracies of Verlinde's
Matrix S: We consider the complete normal field net with compact symmetry group
constructed by Doplicher and Roberts starting from a net of local observables
in >=2+1 spacetime dimensions and its set of localized (DHR) representations.
We prove that the field net does not possess nontrivial DHR sectors, provided
the observables have only finitely many sectors. Whereas the superselection
structure in 1+1 dimensions typically does not arise from a group, the DR
construction is applicable to `degenerate sectors', the existence of which (in
the rational case) is equivalent to non-invertibility of Verlinde's S-matrix.
We prove Rehren's conjecture that the enlarged theory is non-degenerate, which
implies that every degenerate theory is an `orbifold' theory. Thus, the
symmetry of a generic model `factorizes' into a group part and a pure quantum
part which still must be clarified.
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The R^2 phase-diagram of QEG and its spectral dimension: Within the gravitational asymptotic safety program, the RG flow of the R^2
truncation in three and four spacetime dimensions is analyzed in detail. In
particular, we construct RG trajectories which emanate from the non-Gaussian UV
fixed point and possess long classical regimes where the effective average
action is well approximated by the classical Einstein-Hilbert action. As an
application we study the spectral dimension of the effective QEG spacetimes
resulting from these trajectories, establishing that the picture of a
multi-fractal spacetime is robust under the extension of the truncated theory
space. We demonstrate that regimes of constant spectral dimensions can either
be attributed to universal features of RG fixed points or singular loci in the
\beta functions.
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Absorption cross section and Hawking radiation in two-dimensional AdS
black hole: We calculate the absorption coefficient of scalar field on the background of
the two-dimensional AdS black hole, which is of relevance to Hawking radiation.
For the massless scalar field, we find that there does not exist any massless
radiation.
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Description of the Heterotic String Solutions in the M Model: We continue the study of heterotic non-Abelian BPS-saturated flux tubes
(strings). Previously, such solutions were obtained in U(N) gauge theories: N=2
supersymmetric QCD deformed by superpotential terms \mu A^2 breaking N=2
supersymmetry down to N=1. In these models one cannot consider the limit
\mu\to\infty which would eliminate adjoint fields: the bulk theory develops a
Higgs branch; the emergence of massless particles in the bulk precludes one
from taking the limit \mu\to\infty. This drawback is absent in the M model
(hep-th/0701040) where the matter sector includes additional "meson" fields M
introduced in a special way. We generalize our previous results to the M model,
derive the heterotic string (the string world-sheet theory is a heterotic
N=(2,0) sigma model, with the CP(N-1) target space for bosonic fields and an
extra right-handed fermion coupled to the fermion fields of the N=(2,2) CP(N-1)
model), and then explicitly obtain all relevant zero modes. This allows us to
relate parameters of the microscopic M model to those of the world-sheet
theory. The limit \mu\to\infty is perfectly smooth. Thus, the full-blown and
fully analyzed heterotic string emerges, for the first time, in the N=1 theory
with no adjoint fields. The fate of the confined monopoles is discussed.
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Universal results from an alternate random matrix model for QCD with a
baryon chemical potential: We introduce a new non-Hermitian random matrix model for QCD with a baryon
chemical potential. This model is a direct chiral extension of a previously
studied model that interpolates between the Wigner-Dyson and Ginibre ensembles.
We present exact results for all eigenvalue correlations for any number of
quark flavors using the orthogonal polynomial method. We also find that the
parameters of the model can be scaled to remove the effects of the chemical
potential from all thermodynamic quantities until the finite density phase
transition is reached. This makes the model and its extensions well suited for
studying the phase diagram of QCD.
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Establishing strongly-coupled 3D AdS quantum gravity with Ising dual
using all-genus partition functions: We study 3D pure Einstein quantum gravity with negative cosmological
constant, in the regime where the AdS radius $l$ is of the order of the Planck
scale. Specifically, when the Brown-Henneaux central charge $c=3l/2G_N$ ($G_N$
is the 3D Newton constant) equals $c=1/2$, we establish duality between 3D
gravity and 2D Ising conformal field theory by matching gravity and conformal
field theory partition functions for AdS spacetimes with general asymptotic
boundaries. This duality was suggested by a genus-one calculation of Castro et
al. [Phys. Rev. D {\bf 85}, 024032 (2012)]. Extension beyond genus-one requires
new mathematical results based on 3D Topological Quantum Field Theory; these
turn out to uniquely select the $c=1/2$ theory among all those with $c<1$,
extending the previous results of Castro et al..
Previous work suggests the reduction of the calculation of the gravity
partition function to a problem of summation over the orbits of the mapping
class group action on a "vacuum seed". But whether or not the summation is
well-defined for the general case was unknown before this work. Amongst all
theories with Brown-Henneaux central charge $c<1$, the sum is finite and unique
{\it only} when $c=1/2$, corresponding to a dual Ising conformal field theory
on the asymptotic boundary.
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Real analytic solutions for marginal deformations in open superstring
field theory: We construct analytic solutions for marginal deformations satisfying the
reality condition in open superstring field theory formulated by Berkovits when
operator products made of the marginal operator and the associated
superconformal primary field are regular. Our strategy is based on the recent
observation by Erler that the problem of finding solutions for marginal
deformations in open superstring field theory can be reduced to a problem in
the bosonic theory of finding a finite gauge parameter for a certain pure-gauge
configuration labeled by the parameter of the marginal deformation. We find a
gauge transformation generated by a real gauge parameter which infinitesimally
changes the deformation parameter and construct a finite gauge parameter by its
path-ordered exponential. The resulting solution satisfies the reality
condition by construction.
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Heterotic Standard Model Moduli: In previous papers, we introduced a heterotic standard model and discussed
its basic properties. The Calabi-Yau threefold has, generically, three Kahler
and three complex structure moduli. The observable sector of this vacuum has
the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate
fields. The hidden sector has no charged matter in the strongly coupled string
and only minimal matter for weak coupling. Additionally, the spectrum of both
sectors will contain vector bundle moduli. The exact number of such moduli was
conjectured to be small, but was not explicitly computed. In this paper, we
rectify this and present a formalism for computing the number of vector bundle
moduli. Using this formalism, the number of moduli in both the observable and
strongly coupled hidden sectors is explicitly calculated.
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Dualities in the classical supergravity limits: Duality symmetries of supergravity theories are powerful tools to restrict
the number of possible actions, to link different dimensions and number of
supersymmetries and might help to control quantisation.
(Hodge-Dirac-)Dualisation of gauge potentials exchanges Noether and topological
charges, equations of motion and Bianchi identities, internal rigid symmetries
and gauge symmetries, local transformations with nonlocal ones and most
exciting particles and waves. We compare the actions of maximally dualised
supergravities (ie with gauge potential forms of lowest possible degree) to the
non-dualised actions coming from 11 (or 10) dimensions by plain dimensional
reduction as well as to other theories with partial dualisations. The effect on
the rigid duality group is a kind of contraction resulting from the elimination
of the unfaithful generators associated to the (inversely) dualised scalar
fields. New gauge symmetries are introduced by these (un)dualisations and it is
clear that a complete picture of duality (F(ull)-duality) should include all
gauge symmetries at the same time as the rigid symmetries and the spacetime
symmetries. We may read off some properties of F-duality on the internal rigid
Dynkin diagram: field content, possible dualisations, increase of the rank
according to the decrease of space dimension... Some recent results are
included to suggest the way towards unification via a universal twisted
self-duality (TS) structure. The analysis of this structure had revealed
several profound differences according to the parity mod 4 of the dimension of
spacetime (to be contrasted with the (Bott) period 8 of spinor properties).
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Holographic Aspects of Even-Dimensional Topological Gravity: In an odd-dimensional spacetime, gravity can be formulated as a proper gauge
theory based on the Chern-Simons action for a suitable gauge group. Performing
dimensional reduction, one obtains, as an effective theory, Chamseddine's
even-dimensional topological gravity with the reduced gauge symmetry. This
theory involves a multiplet of scalar fields that appear as a result of the
dimensional reduction, and it is topological in the sense that its action does
not depend on the metric. Focusing primarily on the four-dimensional case, we
use the holographic dictionary to compute one-point correlation functions of
the relevant boundary operators and find that the spin-current can have a
nonzero expectation value in the dual quantum field theory. We also consider
the generalized holographic Weyl anomaly and find that it vanishes. Finally, we
propose a way of computing two-point correlation functions using the
gravitational Wilson lines.
|
Orientifold Calabi-Yau Threefolds with Divisor Involutions and String
Landscape: We establish an orientifold Calabi-Yau threefold database for $h^{1,1}(X)
\leq 6$ by considering non-trivial $\mathbb{Z}_{2}$ divisor exchange
involutions, using a toric Calabi-Yau database
(http://www.rossealtman.com/toriccy/). We first determine the topology for each
individual divisor (Hodge diamond), then identify and classify the proper
involutions which are globally consistent across all disjoint phases of the
K\"ahler cone for each unique geometry. Each of the proper involutions will
result in an orientifold Calabi-Yau manifold. Then we clarify all possible
fixed loci under the proper involution, thereby determining the locations of
different types of $O$-planes. It is shown that under the proper involutions,
one typically ends up with a system of $O3/O7$-planes, and most of these will
further admit naive Type IIB string vacua.The geometries with freely acting
involutions are also determined. We further determine the splitting of the
Hodge numbers into odd/even parity in the orbifold limit. The final result is a
class of orientifold Calabi-Yau threefolds with non-trivial odd class
cohomology $h^{1,1}_{-}(X / \sigma^*) \neq 0$.
|
Jordan meets Freudenthal. A Black Hole Exceptional Story: Within the extremal black hole attractors arising in ungauged
$\mathcal{N}\geqslant 2$-extended Maxwell Einstein supergravity theories in
$3+1$ space-time dimensions, we provide an overview of the stratification of
the electric-magnetic charge representation space into "large" orbits and
related "moduli spaces", under the action of the (continuous limit of the)
non-compact $U$-duality Lie group. While each "large" orbit of the $U$-duality
supports a class of attractors, the corresponding "moduli space" is the proper
subspace of the scalar manifold spanned by those scalar fields on which the
Attractor Mechanism is inactive. We present the case study concerning
$\mathcal{N}=2$ supergravity theories with symmetric vector multiplets' scalar
manifold, which in all cases (with the exception of the minimally coupled
models) have the electric-magnetic charge representation of $U$-duality fitting
into a reduced Freudenthal triple system over a cubic (simple or semi-simple)
Jordan algebra.
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Functional Renormalization of Noncommutative Scalar Field Theory: In this paper we apply the Functional Renormalization Group Equation (FRGE)
to the non-commutative scalar field theory proposed by Grosse and Wulkenhaar.
We derive the flow equation in the matrix representation and discuss the theory
space for the self-dual model. The features introduced by the external
dimensionful scale provided by the non-commutativity parameter, originally
pointed out in \cite{Gurau:2009ni}, are discussed in the FRGE context. Using a
technical assumption, but without resorting to any truncation, it is then shown
that the theory is asymptotically safe for suitably small values of the
$\phi^4$ coupling, recovering the result of \cite{disertori:2007}. Finally, we
show how the FRGE can be easily used to compute the one loop beta-functions of
the duality covariant model.
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Scaling results for charged sectors of near conformal QCD: We provide the leading near conformal corrections on a cylinder to the
scaling dimension $\Delta_Q^\ast$ of fixed isospin charge $Q$ operators defined
at the lower boundary of the Quantum Chromodynamics conformal window:
\begin{equation}
\Delta_Q = \Delta_Q^\ast +\left(\frac{m_{\sigma}}{4 \pi \nu}\right)^2 \,
Q^{\frac{\Delta}{3}} B_1 + \left(\frac{m_\pi(\theta)}{4\pi \nu} \right)^4\
Q^{\frac{2}{3}(1-\gamma)} B_2 + \mathcal{O}\left ( m_\sigma^4 , m_\pi^8,
m_\sigma^2 m_\pi^4\right) \ . \nonumber
\end{equation} The results are expressed in powers of the dilaton and pion
masses in units of the chiral symmetry breaking scale $4\pi \nu$ with the
theta-angle dependence encoded directly in the pion mass. The characteristic
$Q$-scaling is dictated by the quark mass operator anomalous dimension $\gamma$
and the one characterising the dilaton potential $\Delta$. The coefficients
$B_i$ with $i=1,2$ depend on the geometry of the cylinder and properties of the
nearby conformal field theory.
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Vector-tensor supermultiplets in AdS and supergravity: In N = 2 Poincare supersymmetry in four space-time dimensions, there exist
off-shell supermultiplets with intrinsic central charge, including the
important examples of the Fayet-Sohnius hypermultiplet, the linear and the
nonlinear vector-tensor (VT) multiplets. One can also define similar
supermultiplets in the context of N = 2 anti-de Sitter (AdS) supersymmetry,
although the origin of the central charge becomes somewhat obscure. In this
paper we develop a general setting for N = 2 AdS supersymmetric theories with
central charge. We formulate a supersymmetric action principle in N = 2 AdS
superspace and then reformulate it in terms of N = 1 superfields. We prove that
N = 2 AdS supersymmetry does not allow existence of a linear VT multiplet. For
the nonlinear VT multiplet, we derive consistent superfield constraints in the
presence of any number of N = 2 Yang-Mills vector multiplets, give the
supersymmetric action and elaborate on the N = 1 superfield and component
descriptions of the theory. Our description of the nonlinear VT multiplet in
AdS is then lifted to N = 2 supergravity. Moreover, we derive consistent
superfield constraints and Lagrangian that describe the linear VT multiplet in
N = 2 supergravity in the presence of two vector multiplets, one of which
gauges the central charge. These supergravity constructions thus provide the
first superspace formulation for the component results derived in
arXiv:hep-th/9710212. We also construct higher-derivative couplings of the VT
multiplet to any number of N = 2 tensor multiplets.
|
Gravity Induced Chiral Condensate Formation and the Cosmological
Constant: It is well known that the covariant coupling of fermionic matter to gravity
induces a four-fermion interaction. The presence of this term in a homogenous
and isotropic space-time results in a BCS-like Hamiltonian and the formation of
a chiral condensate with a mass gap. We calculate the gap ($\Delta$) via a
mean-field approximation for minimally coupled fermionic fields in a FRW
background and find that it depends on the scale factor. The calculation also
yields a correction to the bare cosmological constant ($\Lambda_0$), and a
non-zero vev for $<\psi^\dag\psi>$ which then behaves as a scalar field. Hence
we conjecture that the presence of fermionic matter in gravity provides a
natural mechanism for relaxation of the $\Lambda_0$ and explains the existence
of a scalar field from (almost) first principles.
|
The Cosmological Switchback Effect: The volume behind the black hole horizon was suggested as a holographic dual
for the quantum computational complexity of the boundary state in AdS/CFT. This
identification is strongly motivated by the switchback effect: a characteristic
delay of complexity growth in reaction to an inserted perturbation, modelled as
a shockwave in the bulk. Recent proposals of de Sitter (dS) holography suggest
that a dual theory could be living on a stretched horizon near the cosmological
horizon. We study how the spacetime volume behind the cosmological horizon in
Schwarzschild-dS space reacts to the insertion of shockwaves in an attempt to
characterize the properties of this dual theory. We demonstrate that a
switchback effect can be observed in dS space. That is, the growth of
complexity is delayed in reaction to a perturbation. This delay is longer for
earlier shocks and depends on a scrambling time which is logarithmic in the
strength of the shockwave and proportional to the inverse temperature of the
cosmological dS horizon. This behavior is very similar to what happens for AdS
black holes, albeit the geometric origin of the effect is different.
|
No-scale D=5 supergravity from Scherk-Schwarz reduction of D=6 theories: We perform a generalized dimensional reduction of six dimensional
supergravity theories to five dimensions. We consider the minimal $(2,0)$ and
the maximal $(4,4)$ theories. In each case the reduction allows us to obtain
gauged supergravities of no-scale type in dimension five with gauge groups that
escape previous classifications. In the minimal case, the geometric data of the
reduced theory correspond to particular cases of the D=5 real special geometry.
In the maximal case we find a four parameter solution which allows partial
breaking of supersymmetry.
|
A No-Go Theorem for the Consistent Quantization of Spin 3/2 Fields on
General Curved Spacetimes: It is well-known that coupling a spin $\frac32$-field to a gravitational or
electromagnetic background leads to potential problems both in the classical
and in the quantum theory. Various solutions to these problems have been
proposed so far, which are all restricted to a limited class of backgrounds. On
the other hand, negative results for general gravitational backgrounds have
been reported only for a limited set of couplings to the background to date.
Hence, to our knowledge, a comprehensive analysis of all possible couplings to
the gravitational field and general gravitational backgrounds including
off-shell ones has not been performed so far. In this work we analyse whether
it is possible to couple a spin $\frac32$-field to a gravitational field in
such a way that the resulting quantum theory is consistent on arbitrary
gravitational backgrounds. We find that this is impossible as all couplings
require the background to be an Einstein spacetime for consistency. This
enforces the widespread belief that supergravity theories are the only
meaningful models which contain spin $\frac32$ fields as in these models such
restrictions of the gravitational background appear naturally as on-shell
conditions.
|
Little String Origin of Surface Defects: We derive the codimension-two defects of 4d $\mathcal{N} = 4$ Super
Yang-Mills (SYM) theory from the (2, 0) little string. The origin of the little
string is type IIB theory compactified on an ADE singularity. The defects are
D-branes wrapping the 2-cycles of the singularity. We use this construction to
make contact with the description of SYM defects due to Gukov and Witten
[arXiv:hep-th/0612073]. Furthermore, we derive from a geometric perspective the
complete nilpotent orbit classification of codimension-two defects, and the
connection to ADE-type Toda CFT. The only data needed to specify the defects is
a set of weights of the algebra obeying certain constraints, which we give
explicitly. We highlight the differences between the defect classification in
the little string theory and its (2, 0) CFT limit.
|
Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like
Matter Fields: The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely
reproduces the geometric data such as volume of Sasaki-Einstein manifolds in
the large-$N$ limit, at least for vector-like models. The validity of
chiral-like models is not established yet, due to technical problems in both
analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested
that the counting of chiral operators can be used to find the eigenvalue
distribution of quiver matrix models. In this paper we apply this method to
some vector-like or chiral-like quiver theories, including the triangular
quivers with generic Chern-Simons levels which are dual to in-homogeneous
Sasaki-Einstein manifolds $Y^{p,k}(\mathbb{CP}^2)$. The result is consistent
with AdS/CFT and the volume formula. We discuss the implication of our
analysis.
|
Hawking Radiation, Covariant Boundary Conditions and Vacuum States: The basic characteristics of the covariant chiral current $<J_{\mu}>$ and the
covariant chiral energy-momentum tensor $<T_{\mu\nu}>$ are obtained from a
chiral effective action. These results are used to justify the covariant
boundary condition used in recent approaches
\cite{Isowilczek,Isoumtwilczek,shailesh,shailesh2,Banerjee} of computing the
Hawking flux from chiral gauge and gravitational anomalies. We also discuss a
connection of our results with the conventional calculation of nonchiral
currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware)
states.
|
Moduli Space for Kink Collisions with Moving Center of Mass: We apply the collective coordinate model framework to describe collisions of
a kink and an antikink with nonzero total momentum, i.e., when the solitons
possess different velocities. The minimal moduli space with only two
coordinates (the mutual distance and the position of the center of mass) is of
a wormhole type, whose throat shrinks to a point for symmetric kinks. In this
case, a singularity is formed. For non-zero momentum, it prohibits solutions
where the solitons pass through each other. We show that this unphysical
feature can be cured by enlarging the dimension of the moduli space, e.g., by
the inclusion of internal modes.
|
A Comment on Duality in SUSY SU(N) Gauge Theory with a Symmetric Tensor: We suggest an alternative approach to deconfine N =1 SU(N) supersymmetric
gauge theory with a symmetric tensor, fundamentals, anti-fundamentals, and no
superpotential. It is found that although the dual prescription derived by this
new method of deconfinement is different from that by the original method, both
dual prescriptions are connected by duality transformations. By deforming the
theory, it is shown that both dual theories flow properly so that the Seiberg's
duality is preserved.
|
Short distance properties of cascading gauge theories: We study the short distance (large momentum) properties of correlation
functions of cascading gauge theories by performing a tree-level computation in
their dual gravitational background. We prove that these theories are
holographically renormalizable; the correlators have only analytic ultraviolet
divergences, which may be removed by appropriate local counterterms. We find
that n-point correlation functions of properly normalized operators have the
expected scaling in the semi-classical gravity (large N) limit: they scale as
N_{eff}^{2-n} with N_{eff} proportional to ln(k/Lambda) where k is a typical
momentum. Our analysis thus confirms the interpretation of the cascading gauge
theories as renormalizable four-dimensional quantum field theories with an
effective number of degrees of freedom which logarithmically increases with the
energy.
|
Conformal supergravity in five dimensions: New approach and applications: We develop a new off-shell formulation for five-dimensional (5D) conformal
supergravity obtained by gauging the 5D superconformal algebra in superspace.
An important property of the conformal superspace introduced is that it reduces
to the superconformal tensor calculus (formulated in the early 2000's) upon
gauging away a number of superfluous fields. On the other hand, a different
gauge fixing reduces our formulation to the SU(2) superspace of
arXiv:0802.3953, which is suitable to describe the most general off-shell
supergravity-matter couplings. Using the conformal superspace approach, we show
how to reproduce practically all off-shell constructions derived so far,
including the supersymmetric extensions of $R^2$ terms, thus demonstrating the
power of our formulation. Furthermore, we construct for the first time a
supersymmetric completion of the Ricci tensor squared term using the standard
Weyl multiplet coupled to an off-shell vector multiplet. In addition, we
present several procedures to generate higher-order off-shell invariants in
supergravity, including higher-derivative ones. The covariant projective
multiplets proposed in arXiv:0802.3953 are lifted to conformal superspace, and
a manifestly superconformal action principle is given. We also introduce
unconstrained prepotentials for the vector multiplet, the ${\cal{O}}(2)$
multiplet (i.e., the linear multiplet without central charge) and
${\cal{O}}(4+n)$ multiplets, with $n=0,1,\dots$ Superform formulations are
given for the BF action and the non-abelian Chern-Simons action. Finally, we
describe locally supersymmetric theories with gauged central charge in
conformal superspace.
|
Effective dynamics of an electrically charged string with a current: Equations of motion for an electrically charged string with a current in an
external electromagnetic field with regard to the first correction due to the
self-action are derived. It is shown that the reparametrization invariance of
the free action of the string imposes constraints on the possible form of the
current. The effective equations of motion are obtained for an absolutely
elastic charged string in the form of a ring (circle). Equations for the
external electromagnetic fields that admit stationary states of such a ring are
revealed. Solutions to the effective equations of motion of an absolutely
elastic charged ring in the absence of external fields as well as in an
external uniform magnetic field are obtained. In the latter case, the frequency
at which one can observe radiation emitted by the ring is evaluated. A model of
an absolutely nonstretchable charged string with a current is proposed. The
effective equations of motion are derived within this model, and a class of
solutions to these equations is found.
|
Cayley-Klein Algebras as Graded Contractions of so(N+1): We study $\Bbb Z_2^{\otimes N}$ graded contractions of the real compact
simple Lie algebra $so(N+1)$, and we identify within them the Cayley-Klein
algebras as a naturally distinguished subset.
|
Graviton and gluon scattering from first principles: Graviton and gluon scattering are studied from minimal physical assumptions
such as Poincare and gauge symmetry as well as unitarity. The assumptions lead
to an interesting and surprisingly restrictive set of linear equations. This
shows gluon and graviton scattering to be related in many field and string
theories, explaining and extending several known results. By systematic
analysis exceptional graviton scattering amplitudes are derived which in
general dimensions can not be related to gluon amplitudes. The simplicity of
the formalism guarantees wide further applicability to gauge and gravity
theories.
|
Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz
symmetry: We study nonlinear vacuum electrodynamics in a first-order formulation
proposed by Pleba\'nski. By applying a Dirac constraint analysis, we derive an
effective Hamiltonian, together with the equations of motion. We show that
there exists a large class of potentials for which the effective Hamiltonian is
bounded from below, while at the same time possessing stationary points in
which the field strength acquires a nonzero vacuum expectation value. The
associated spontaneous breaking of Lorentz symmetry can in principle be
detected by coupling the model to a suitable external current, or to gravity.
We show that the possible vacua can be classified in four classes. We study
some of their properties, using explicit examples for illustration.
|
Infinite Braided Tensor Products and 2-D quantum Gravity: Braided tensor products have been introduced by the author as a systematic
way of making two quantum-group-covariant systems interact in a covariant way,
and used in the theory of braided groups. Here we study infinite braided tensor
products of the quantum plane (or other constant Zamolodchikov algebra). It
turns out that such a structure precisely describes the exchange algebra in 2D
quantum gravity in the approach of Gervais. We also consider infinite braided
tensor products of quantum groups and braided groups.
|
All-order consistency of 5d sugra vacua: We show that the maximally supersymmetric vacua of d=5 N=1 sugra remain
maximally supersymmetric solutions when taking into account higher order
corrections.
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A light dilaton in a metastable vacuum: We identify a parametrically light dilaton by studying the perturbations of
metastable vacua along a branch of regular supergravity backgrounds that are
dual to four-dimensional confining field theories. The branch includes also
stable and unstable solutions. The former encompass, as a special case, the
geometry proposed by Witten as a holographic model of confinement. The latter
approach a supersymmetric solution, by enhancing a condensate in the dual field
theory. A phase transition separates the space of stable backgrounds from the
metastable ones. In proximity of the phase transition, one of the lightest
scalar states inherits some of the properties of the dilaton, despite not being
particularly light.
|
Noncommutative Field Theories and (Super)String Field Theories: In this lecture notes we explain and discuss some ideas concerning
noncommutative geometry in general, as well as noncommutative field theories
and string field theories. We consider noncommutative quantum field theories
emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's
conjectures on open string tachyon condensation and their application to the
D-brane physics have led to wide investigations of the covariant string field
theory proposed by Witten about 15 years ago. We review main ingredients of
cubic (super)string field theories using various formulations: functional,
operator, conformal and the half string formalisms. The main technical tools
that are used to study conjectured D-brane decay into closed string vacuum
through the tachyon condensation are presented. We describe also methods which
are used to study the cubic open string field theory around the tachyon vacuum:
construction of the sliver state, ``comma'' and matrix representations of
vertices.
|
Non-trivial 2d space-times from matrices: Solutions of matrix quantum mechanics have been shown to describe time
dependent backgrounds in the holographically dual two dimensional closed string
theory. We review some recent work dealing with non-trivial space-times which
arise in this fashion and discuss aspects of physical phenomena in them.
|
Relativistic gyratons in asymptotically AdS spacetime: We study the gravitational field of a spinning radiation beam-pulse (a
gyraton) in a D-dimensional asymptotically AdS spacetime. It is shown that the
Einstein equations for such a system reduce to a set of two linear equations in
a (D-2)-dimensional space. By solving these equations we obtain a metric which
is an exact solution of gravitational equations with the (negative)
cosmological constant. The explicit metrics for 4D and 5D gyratons in
asymptotically AdS spacetime are given and their properties are discussed.
|
Nonsingular multidimensional cosmologies without fine tuning: Exact cosmological solutions for effective actions in D dimensions inspired
by the tree-level superstring action are studied. For a certain range of free
parameters existing in the model, nonsingular bouncing solutions are found.
Among them, of particular interest can be open hyperbolic models, in which,
without any fine tuning, the internal scale factor and the dilaton field
(connected with string coupling in string theories) tend to constant values at
late times. A cosmological singularity is avoided due to nonminimal
dilaton-gravity coupling and, for D > 11, due to pure imaginary nature of the
dilaton, which conforms to currently discussed unification models. The
existence of such and similar solutions supports the opinion that the Universe
had never undergone a stage driven by full-scale quantum gravity.
|
Fermionic String from Abelian Higgs Model with monopoles and
$Θ$-term: The four dimensional Abelian Higgs model with monopoles and $\Theta$-term is
considered in the limit of the large mass of the higgs boson. We show that for
$\Theta=2 \pi$ the theory is equivalent, at large distances, to summation over
all possible world-sheets of fermionic strings with Dirichlet type boundary
conditions on string coordinates.
|
Spacetime Superalgebra in AdS_4 \times S^7 via Supermembrane Probe: The spacetime superalgebra via the supermembrane probe in the background of
AdS_4 \times S^7 is discussed to the lowest order in the spinor coordinate
$\t$. To obtain the correct spacetime superalgebras, all $\t^2$ order
corrections for supervielbein and super 3-form gauge potential have to be
included. The central extension of the superalgebra OSp(8|4) of the super
isometries for AdS_4 \times S^7 is found.
|
Thermodynamic Bethe Ansatz for N = 1 Supersymmetric Theories: We study a series of $N\!=\!1$ supersymmetric integrable particle theories in
$d=1+1$ dimensions. These theories are represented as integrable perturbations
of specific $N\!=\!1$ superconformal field theories. Starting from the
conjectured $S$-matrices for these theories, we develop the Thermodynamic Bethe
Ansatz (TBA), where we use that the 2-particle $S$-matrices satisfy a free
fermion condition. Our analysis proves a conjecture by E.~Melzer, who proposed
that these $N\!=\!1$ supersymmetric TBA systems are ``folded'' versions of
$N\!=\!2$ supersymmetric TBA systems that were first studied by P.~Fendley and
K.~Intriligator.
|
Static M-horizons: We determine the geometry of all static black hole horizons of M-theory
preserving at least one supersymmetry. We demonstrate that all such horizons
are either warped products R^{1,1} *_w S or AdS_2 *_w S, where S admits an
appropriate Spin(7) or SU(4) structure respectively; and we derive the
conditions imposed by supersymmetry on these structures. We show that for
electric static horizons with Spin(7) structure, the near horizon geometry is a
product R^{1,1} * S, where S is a compact Spin(7) holonomy manifold. For
electric static solutions with SU(4) structure, we show that the horizon
section S is a circle fibration over an 8-dimensional Kahler manifold which
satisfies an additional condition involving the Ricci scalar and the length of
the Ricci tensor. Solutions include AdS_2 * S^3 * CY_6 as well as many others
constructed from taking the 8-dimensional Kahler manifold to be a product of
Kahler-Einstein and Calabi-Yau spaces.
|
Replication Regulates Volume Weighting in Quantum Cosmology: Probabilities for observations in cosmology are conditioned both on the
universe's quantum state and on local data specifying the observational
situation. We show the quantum state defines a measure for prediction through
such conditional probabilities that is well behaved for spatially large or
infinite universes when the probabilities that our data is replicated are taken
into account. In histories where our data are rare volume weighting connects
top-down probabilities conditioned on both the data and the quantum state to
the bottom-up probabilities conditioned on the quantum state alone. We apply
these principles to a calculation of the number of inflationary e-folds in a
homogeneous, isotropic minisuperspace model with a single scalar field moving
in a quadratic potential. We find that volume weighting is justified and the
top-down probabilities favor a large number of e-folds.
|
The Complete Brane Solution in D-dimensional Coupled Gravity System: In this letter we present the complete explicit brane solution in
D-dimensional coupled gravity system.
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Quantum geometry and quiver gauge theories: We study macroscopically two dimensional $\mathcal{N}=(2,2)$ supersymmetric
gauge theories constructed by compactifying the quiver gauge theories with
eight supercharges on a product $\mathbb{T}^{d} \times
\mathbb{R}^{2}_{\epsilon}$ of a $d$-dimensional torus and a two dimensional
cigar with $\Omega$-deformation. We compute the universal part of the effective
twisted superpotential. In doing so we establish the correspondence between the
gauge theories, quantization of the moduli spaces of instantons on
$\mathbb{R}^{2-d} \times \mathbb{T}^{2+d}$ and singular monopoles on
$\mathbb{R}^{2-d} \times \mathbb{T}^{1+d}$, for $d=0,1,2$, and the Yangian
$\mathbf{Y}_{\epsilon}(\mathfrak{g}_{\Gamma})$, quantum affine algebra
$\mathbf{U}^{\mathrm{aff}}_q(\mathfrak{g}_{\Gamma})$, or the quantum elliptic
algebra $\mathbf{U}^{\mathrm{ell}}_{q,p}(\mathfrak{g}_{\Gamma})$ associated to
Kac-Moody algebra $\mathfrak{g}_{\Gamma}$ for quiver $\Gamma$.
|
Geometric Kac-Moody Modularity: It is shown how the arithmetic structure of algebraic curves encoded in the
Hasse-Weil L-function can be related to affine Kac-Moody algebras. This result
is useful in relating the arithmetic geometry of Calabi-Yau varieties to the
underlying exactly solvable theory. In the case of the genus three Fermat curve
we identify the Hasse-Weil L-function with the Mellin transform of the twist of
a number theoretic modular form derived from the string function of a
non-twisted affine Lie algebra. The twist character is associated to the number
field of quantum dimensions of the conformal field theory.
|
Note About Unstable D-Brane with Dynamical Tension: We propose an action for unstable Dp-brane with dynamical tension. We show
that the equations of motion are equivalent to the equations of motion derived
from DBI and WZ actions for non-BPS Dp-brane. We also find Hamiltonian
formulation of this action and analyze properties of the solutions
corresponding to the tachyon vacuum and zero tension solution.
|
Descent Relations Among Bosonic D-branes: We show that the tachyonic kink solution on a pair of D-p-branes in the
bosonic string theory can be identified with the D-(p-1)-brane of the same
theory. We also speculate on the possibility of obtaining the D-(p-1)-brane as
a tachyonic lump on a single D-p-brane. We suggest a possible reinterpretation
of the first result which unifies these two apparently different descriptions
of the D-(p-1) brane.
|
Modified-gravity theories with nondynamical background fields: We study the dynamics of a modified-gravity theory, which is supplemented by
an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism
violation through nondynamical background fields denoted as $u$ and
$s^{\mu\nu}$ in the literature. An ADM decomposition allows us to project the
modified Einstein equations into purely spacelike hypersurfaces, which implies
the field equations for the induced dynamical three-metric. We also obtain the
Hamilton-Jacobi equations of motion for the canonical variables of the theory
based on its Hamiltonian, which was derived in a previous work. The
computations show that the dynamical field equations obtained from the
Lagrangian and Hamiltonian approaches are consistent with each other.
Connections to Brans-Dicke theory and ghost-free massive gravity are
established.
|
On kappa-deformation and triangular quasibialgebra structure: We show that, up to terms of order 1/kappa^5, the kappa-deformed Poincare
algebra can be endowed with a triangular quasibialgebra structure. The
universal R matrix and coassociator are given explicitly to the first few
orders. In the context of kappa-deformed quantum field theory, we argue that
this structure, assuming it exists to all orders, ensures that states of any
number of identical particles, in any representation, can be defined in a
kappa-covariant fashion.
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Lorentzian Vacuum Transitions: Open or Closed Universes?: We consider the generalisation of quantum tunneling transitions in the WKB
approximation to the time-independent functional Schr\"odinger and
Wheeler-DeWitt equations. Following a Lorentzian approach, we compute the
transition rates among different scalar field vacua and compare with those
performed by Coleman and collaborators using the Euclidean approach. For
gravity, we develop a general formalism for computing transition rates in
Wheeler's superspace. This is then applied to computing decays in flat space
and then to transitions in the presence of gravity. In the latter case we point
out the complexities arising from having non-positive definite kinetic terms
illustrating them in the simplified context of mini-superspace. This
corresponds to a generalisation of the well-known `tunneling from nothing'
scenarios. While we can obtain the leading term for the transitions obtained by
Euclidean methods we also point out some differences and ambiguities. We show
that there is no obstruction to keeping the spherically ($SO(4)$) symmetric
closed slicing for the new vacuum after a de Sitter to de Sitter transition. We
argue that this is the natural Lorentzian realisation of the Coleman-De Luccia
instanton and that a closed universe is also obtained if the mini-superspace
assumption is relaxed. This is contrary to the open universe predicted by
Coleman-De Luccia which relies on an analytic continuation performed after
bubble nucleation. Our findings may have important cosmological implications
related to the origin of inflation and to the string landscape. In particular,
they question the widespread belief that evidence for a closed universe would
rule out the string landscape.
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Finite temperature fermionic charge and current densities induced by a
cosmic string with magnetic flux: We investigate the finite temperature expectation values of the charge and
current densities for a massive fermionic field with nonzero chemical
potential, $\mu$, in the geometry of a straight cosmic string with a magnetic
flux running along its axis. These densities are decomposed into the vacuum
expectation values and contributions coming from the particles and
antiparticles. The charge density is an even periodic function of the magnetic
flux with the period equal to the quantum flux and an odd function of the
chemical potential. The only nonzero component of the current density
corresponds to the azimuthal current. The latter is an odd periodic function of
the magnetic flux and an even function of the chemical potential. At high
temperatures, the parts in the charge density and azimuthal current induced by
the planar angle deficit and magnetic flux are exponentially small. The
asymptotic behavior at low temperatures crucially depends whether the value
$|\mu|$ is larger or smaller than the mass of the field quanta, $m$. For
$|\mu|<m$ the charge density and the contributions into the azimuthal current
coming from the particles and antiparticles are exponentially suppressed at low
temperatures. In the case $|\mu|>m$, the charge and current densities receive
two contributions coming from the vacuum expectation values and from particles
or antiparticles (depending on the sign of chemical potential). At large
distances from the string the latter exhibits a damping oscillatory behavior
with the amplitude inversely proportional to the square of the distance.
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CFT's From Calabi-Yau Four-folds: We consider F/M/Type IIA theory compactified to four, three, or two
dimensions on a Calabi-Yau four-fold, and study the behavior near an isolated
singularity in the presence of appropriate fluxes and branes. We analyze the
vacuum and soliton structure of these models, and show that near an isolated
singularity, one often generates massless chiral superfields and a
superpotential, and in many instances in two or three dimensions one obtains
nontrivial superconformal field theories. In the case of two dimensions, we
identify some of these theories with certain Kazama-Suzuki coset models, such
as the N=2 minimal models.
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Hermitian Matrix Model with Plaquette Interaction: We study a hermitian $(n+1)$-matrix model with plaquette interaction,
$\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the
model as an $O(n)$ model on a random lattice with a non polynomial potential.
This allows us to solve the model exactly. We investigate the critical
properties of the plaquette model and find that for $n\in]-2,2]$ the model
belongs to the same universality class as the $O(n)$ model on a random lattice.
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Dirac equation in very special relativity for hydrogen atom: In this work, we study the modified Dirac equation in the framework of very
special relativity (VSR). The low-energy regime is accessed and the
nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is
similar to that achieved from the Standard Model Extension (SME) via coupling
of the spinor field to a Lorentz-violating term, but new features arise
inherited from the non-local character of the VSR. In addition, the
implications of the VSR-modified Lorentz symmetry on the spectrum of a hydrogen
atom are determined by calculating the first-order energy corrections in the
context of standard quantum mechanics. Among the results, we highlight that the
modified Hamiltonian provides non-vanishing corrections which lift the
degeneracy of the energy levels and allow us to find an upper bound upon the
VSR-parameter.
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Comments on Born-Infeld Theory: The low-energy effective action of supersymmetric D-brane systems consists of
two terms, one of which is of the Born-Infeld type and one of which is of the
Chern-Simons type. I briefly review the status of our understanding of these
terms for both the Abelian and non-Abelian cases.
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On the Six-dimensional Kerr Theorem and Twistor Equation: The Kerr theorem is revisited as part of the twistor program in six
dimensions. The relationship between pure spinors and integrable 3-planes is
investigated. The real condition for Lorentzian spacetimes is seen to induce a
projective property in the space of solutions, reminiscent of the quaternionic
structure of the 6-dimensional Lorentz group. The twistor equation (or Killing
spinor equations generically) also has an interpretation as integrable null
planes and a family of Einstein spacetimes with this property are presented in
the Kerr-Schild fashion.
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Anomalous Chiral Superfluidity: We discuss both the anomalous Cartan currents and the energy-momentum tensor
in a left chiral theory with flavour anomalies as an effective theory for
flavored chiral phonons in a chiral superfluid with the gauged
Wess-Zumino-Witten term. In the mean-field (leading tadpole) approximation the
anomalous Cartan currents and the energy momentum tensor take the form of
constitutive currents in the chiral superfluid state. The pertinence of higher
order corrections and the Adler-Bardeen theorem is briefly noted.
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Conformal Regge Theory at Finite Boost: The Operator Product Expansion is a useful tool to represent correlation
functions. In this note we extend Conformal Regge theory to provide an exact
OPE representation of Lorenzian four-point correlators in conformal field
theory, valid even away from Regge limit. The representation extends
convergence of the OPE by rewriting it as a double integral over continuous
spins and dimensions, and features a novel "Regge block". We test the formula
in the conformal fishnet theory, where exact results involving nontrivial Regge
trajectories are available.
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On the Derivation of the Exact Slope Function: In this note we give a simple derivation of the exact slope function
conjectured by Basso for the anomalous dimensions of Wilson operators in the
sl2 sector of planar N=4 Super-Yang-Mills theory. We also discuss
generalizations of this result for higher charges and other sectors.
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The volume of a soliton: There exists, in general, no unique definition of the size (volume, area,
etc., depending on dimension) of a soliton. Here we demonstrate that the
geometric volume (area etc.) of a soliton is singled out in the sense that it
exactly coincides with the thermodynamical or continuum-mechanical volume. In
addition, this volume may be defined uniquely for rather arbitrary solitons in
arbitrary dimensions.
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The Matrix Model for M Theory as an Exemplar of Trace (or Generalized
Quantum) Dynamics: We show that the recently proposed matrix model for M theory obeys the cyclic
trace assumptions underlying generalized quantum or trace dynamics. This
permits a verification of supersymmetry as an operator calculation, and a
calculation of the supercharge density algebra by using the generalized Poisson
bracket, in a basis-independent manner that makes no reference to individual
matrix elements. Implications for quantization of the model are discussed. Our
results are a special case of a general result presented elsewhere, that all
rigid supersymmetry theories can be extended to give supersymmetric trace
dynamics theories, in which the supersymmetry algebra is represented by the
generalized Poisson bracket of trace supercharges, constructed from fields that
form a noncommutative trace class graded operator algebra.
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Boundary three-point function on AdS2 D-branes: Using the H3+-Liouville relation, I explicitly compute the boundary
three-point function on AdS2 D-branes in H3+, and check that it exhibits the
expected symmetry properties and has the correct geometrical limit. I then find
a simple relation between this boundary three-point function and certain fusing
matrix elements, which suggests a formal correspondence between the AdS2
D-branes and discrete representations of the symmetry group. Concluding
speculations deal with the fuzzy geometry of AdS2 D-branes, strings in the
Minkowskian AdS3, and the hypothetical existence of new D-branes in H3+.
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N=4 SYM to Two Loops: Compact Expressions for the Non-Compact Symmetry
Algebra of the su(1,1|2) Sector: We begin a study of higher-loop corrections to the dilatation generator of
N=4 SYM in non-compact sectors. In these sectors, the dilatation generator
contains infinitely many interactions, and therefore one expects very
complicated higher-loop corrections. Remarkably, we find a short and simple
expression for the two-loop dilatation generator. Our solution for the
non-compact su(1,1|2) sector consists of nested commutators of four O(g)
generators and one simple auxiliary generator. Moreover, the solution does not
require the planar limit; we conjecture that it is valid for any gauge group.
To obtain the two-loop dilatation generator, we find the complete O(g^3)
symmetry algebra for this sector, which is also given by concise expressions.
We check our solution using published results of direct field theory
calculations. By applying the expression for the two-loop dilatation generator
to compute selected anomalous dimensions and the bosonic sl(2) sector internal
S-matrix, we confirm recent conjectures of the higher-loop Bethe ansatz of
hep-th/0412188.
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Conformal Invariance of the Pure Spinor Superstring in a Curved
Background: It is shown that the pure spinor formulation of the heterotic superstring in
a generic gravitational and super Yang-Mills background has vanishing one-loop
beta functions.
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Sequestering the Standard Model Vacuum Energy: We propose a very simple reformulation of General Relativity, which
completely sequesters from gravity {\it all} of the vacuum energy from a matter
sector, including all loop corrections and renders all contributions from phase
transitions automatically small. The idea is to make the dimensional parameters
in the matter sector functionals of the 4-volume element of the universe. For
them to be nonzero, the universe should be finite in spacetime. If this matter
is the Standard Model of particle physics, our mechanism prevents any of its
vacuum energy, classical or quantum, from sourcing the curvature of the
universe. The mechanism is consistent with the large hierarchy between the
Planck scale, electroweak scale and curvature scale, and early universe
cosmology, including inflation. Consequences of our proposal are that the
vacuum curvature of an old and large universe is not zero, but very small, that
$w_{DE} \simeq -1$ is a transient, and that the universe will collapse in the
future.
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A Quantum Rosetta Stone for the Information Paradox: The black hole information loss paradox epitomizes the contradictions between
general relativity and quantum field theory. The AdS/CFT correspondence
provides an implicit answer for the information loss paradox in black hole
physics by equating a gravity theory with an explicitly unitary field theory.
Gravitational collapse in asymptotically AdS spacetimes is generically
turbulent. Given that the mechanism to read out the information about
correlations functions in the field theory side is plagued by deterministic
classical chaos, we argue that quantum chaos might provide the true Rosetta
Stone for answering the information paradox in the context of the AdS/CFT
correspondence.
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Quantum phantom cosmology: We apply the formalism of quantum cosmology to models containing a phantom
field. Three models are discussed explicitly: a toy model, a model with an
exponential phantom potential, and a model with phantom field accompanied by a
negative cosmological constant. In all these cases we calculate the classical
trajectories in configuration space and give solutions to the Wheeler-DeWitt
equation in quantum cosmology. In the cases of the toy model and the model with
exponential potential we are able to solve the Wheeler-DeWitt equation exactly.
For comparison, we also give the corresponding solutions for an ordinary scalar
field. We discuss in particular the behaviour of wave packets in
minisuperspace. For the phantom field these packets disperse in the region that
corresponds to the Big Rip singularity. This thus constitutes a genuine quantum
region at large scales, described by a regular solution of the Wheeler-DeWitt
equation. For the ordinary scalar field, the Big-Bang singularity is avoided.
Some remarks on the arrow of time in phantom models as well as on the relation
of phantom models to loop quantum cosmology are given.
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Some aspects of a Chern-Simons-like coupling in an external magnetic
field: For a gauge theory which includes a light massive vector field interacting
with the familiar photon U(1)_{QED} via a Chern-Simons- like coupling, we study
the static quantum potential. Our analysis is based on the gauge-invariant, but
path-dependent, variables formalism. The result is that the theory describes an
exactly screening phase. Interestingly enough, this result displays a marked
departure of a qualitative nature from the axionic elctrodynamics result.
However, the present result is analogous to that encountered in the coupling
between the familiar photon U(1)_{QED} and a second massive gauge field living
in the so-called hidden-sector U(1)_h, inside a superconducting box.
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Note on correlation functions in conformal quantum mechanics: We suggest a method to compute the correlation functions in conformal quantum
mechanics (CFT$_1$) for the fields that transform under a non-local
representation of $\mathfrak{sl}(2)$ basing on the invariance properties.
Explicit calculations of 2- and 3-point correlation functions are presented.
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Nonlinear hidden symmetries in General Relativity and String Theory: a
matrix generalization of the Ernst potentials: In this paper we recall a simple formulation of the stationary electrovacuum
theory in terms of the famous complex Ernst potentials, a pair of functions
which allows one to generate new exact solutions from known ones by means of
the so-called nonlinear hidden symmetries of Lie-Backlund type. This formalism
turned out to be very useful to perform a complete classification of all 4D
solutions which present two spacetime symmetries or possess two Killing
vectors. Curiously enough, the Ernst formalism can be extended and applied to
stationary General Relativity as well as the effective heterotic string theory
reduced down to three spatial dimensions by means of a (real) matrix
generalization of the Ernst potentials. Thus, in this theory one can also make
use of nonlinear matrix hidden symmetries in order to generate new exact
solutions from seed ones. Due to the explicit independence of the matrix Ernst
potential formalism of the original theory (prior to dimensional reduction) on
the dimension D, in the case when the theory initially has D>=5, one can
generate new solutions like charged black holes, black rings and black Saturns,
among others, starting from uncharged field configurations.
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Mass gap for gravity localized on Weyl thick branes: We study the properties of a previously found family of thick brane
configurations in a pure geometric Weyl integrable 5D space time, a
non-Riemannian generalization of Kaluza-Klein (KK) theory involving a geometric
scalar field. Thus the 5D theory describes gravity coupled to a
self-interacting scalar field which gives rise to the structure of the thick
branes. Analyzing the graviton spectrum for this class of models, we find that
a particularly interesting situation arises for a special case in which the 4D
graviton is separated from the KK gravitons by a mass gap. The corresponding
effective Schroedinger equation has a modified Poeschl-Teller potential and can
be solved exactly. Apart from the massless 4D graviton, it contains one massive
KK bound state, and the continuum spectrum of delocalized KK modes. We discuss
the mass hierarchy problem, and explicitly compute the corrections to Newton's
law in the thin brane limit.
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An interpolation between Bose, Fermi and Maxwell-Boltzmann statistics
based on Jack Polynomials: An interpolation between the canonical partition functions of Bose, Fermi and
Maxwell-Boltzmann statistics is proposed. This interpolation makes use of the
properties of Jack polynomials and leads to a physically appealing
interpolation between the statistical weights of the three statistics. This, in
turn, can be used to define a new exclusion statistics in the spirit of the
work of Haldane.
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Remarks on the exotic central extension of the planar Galilei group: Some issues in relating the central extensions of the planar Galilei group to
parameters in the corresponding relativistic theory are discussed.
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On the Null Energy Condition and Causality in Lifshitz Holography: We use a WKB approximation to establish a relation between the wavefront
velocity in a strongly coupled theory and the local speed of light in a
holographic dual, with our main focus put on systems with Lifshitz scaling with
dynamical exponent z. We then use Einstein equations to relate the behavior of
the local speed of light in the bulk with the null energy condition (NEC) for
bulk matter, and we show that it is violated for Lifshitz backgrounds with z<1.
We study signal propagation in the gravity dual and show that violations of the
NEC are incompatible with causality in the strongly coupled theory, ruling out
as holographic models Lifshitz backgrounds with z<1. We argue that causality
violations in z<1 theories will show up in correlators as superluminal modes
and confirm this for a particular example with z=1/2. Finally, as an
application, we use z<1 solutions to uncover regions of the parameter space of
curvature squared corrections to gravity where the NEC can be violated.
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Commuting quantities and exceptional W-algebras: Sets of commuting charges constructed from the current of a U(1) Kac-Moody
algebra are found. There exists a set S_n of such charges for each positive
integer n > 1; the corresponding value of the central charge in the
Feigin-Fuchs realization of the stress tensor is c = 13-6n-6/n. The charges in
each series can be written in terms of the generators of an exceptional
W-algebra.
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Free Boson Representation of $U_{q}(\hat{sl_{2}})$: A representation of the quantum affine algebra $U_{q}(\hat{sl_{2}})$ of an
arbitrary level $k$ is realized in terms of three boson fields, whose $q
\rightarrow 1$ limit becomes the Wakimoto representation. An analogue of the
screening current is also obtained. It commutes with the action of
$U_{q}(\hat{sl_{2}})$ modulo total difference of some fields.
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On the Consistency of Orbifolds: Modular invariance is a necessary condition for the consistency of any closed
string theory. In particular, it imposes stringent constraints on the spectrum
of orbifold theories, and in principle determines their spectrum uniquely up to
discrete torsion classes. In practice, however, there are often ambiguities in
the construction of orbifolds that are a consequence of the fact that the
action of the orbifold elements on degenerate ground states is not unambiguous.
We explain that there exists an additional consistency condition, related to
the spectrum of D-branes in the theory, which eliminates these ambiguities. For
supersymmetric orbifolds this condition turns out to be equivalent to the
condition that supersymmetry is unbroken in the twisted sectors, but for
non-supersymmetric orbifolds it appears to be a genuinely new consistency
condition.
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N=2 supersymmetric extension of l-conformal Galilei algebra: N=2 supersymmetric extension of the l-conformal Galilei algebra is
constructed. A relation between its representations in flat spacetime and in
Newton-Hooke spacetime is discussed. An infinite-dimensional generalization of
the superalgebra is given.
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Operator Product Expansion for Pure Spinor Superstring on AdS(5)*S(5): The tree-level operator product expansion coefficients of the matter currents
are calculated in the pure spinor formalism for type IIB superstring in the
AdS(5)*S(5) background.
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Continuous non-perturbative regularization of QED: We regularize in a continuous manner the path integral of QED by construction
of a non-local version of its action by means of a regularized form of Dirac's
$\delta$ functions. Since the action and the measure are both invariant under
the gauge group, this regularization scheme is intrinsically non-perturbative.
Despite the fact that the non-local action converges formally to the local one
as the cutoff goes to infinity, the regularized theory keeps trace of the
non-locality through the appearance of a quadratic divergence in the transverse
part of the polarization operator. This term which is uniquely defined by the
choice of the cutoff functions can be removed by a redefinition of the
regularized action. We notice that as for chiral fermions on the lattice, there
is an obstruction to construct a continuous and non ambiguous regularization in
four dimensions. With the help of the regularized equations of motion, we
calculate the one particle irreducible functions which are known to be
divergent by naive power counting at the one loop order.
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Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons: Type IIA string theory compactified on a rigid Calabi-Yau threefold gives
rise to a classical moduli space that carries an isometric action of U(2,1).
Various quantum corrections break this continuous isometry to a discrete
subgroup. Focussing on the case where the intermediate Jacobian of the
Calabi-Yau admits complex multiplication by the ring of quadratic imaginary
integers O_d, we argue that the remaining quantum duality group is an
arithmetic Picard modular group PU(2,1;O_d). Based on this proposal we
construct an Eisenstein series invariant under this duality group and study its
non-Abelian Fourier expansion. This allows the prediction of non-perturbative
effects, notably the contribution of D2- and NS5-brane instantons. The present
work extends our previous analysis in 0909.4299 which was restricted to the
special case of the Gaussian integers O_1=Z[i].
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Massive Fields of Arbitrary Half-Integer Spin in Constant
Electromagnetic Field: We study the interaction of gauge fields of arbitrary half-integer spins with
the homogeneous electromagnetic field. We reduce the problem of obtaining the
gauge-invariant Lagrangian and transformations of the half-integer spin fields
in the external field to an algebraic problem of search for a set of operators
with certain algebraical features using the representation of the higher-spin
fields as vectors in a pseudo-Hilbert space. We consider such construction at
linear order in the external electromagnetic field and also present an explicit
form of interaction Lagrangians and gauge transformations for the massive
particles of spins 3/2 and 5/2 in terms of symmetric spin-tensor fields. The
obtained result is valid for space-time of arbitrary even dimension.
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Composite Fermion Metals from Dyon Black Holes and S-Duality: We propose that string theory in the background of dyon black holes in
four-dimensional anti-de Sitter spacetime is holographic dual to conformally
invariant composite Dirac fermion metal. By utilizing S-duality map, we show
that thermodynamic and transport properties of the black hole match with those
of composite fermion metal, exhibiting Fermi liquid-like. Built upon
Dirac-Schwinger-Zwanziger quantization condition, we argue that turning on
magnetic charges to electric black hole along the orbit of Gamma(2) subgroup of
SL(2,Z) is equivalent to attaching even unit of statistical flux quanta to
constituent fermions. Being at metallic point, the statistical magnetic flux is
interlocked to the background magnetic field. We find supporting evidences for
proposed holographic duality from study of internal energy of black hole and
probe bulk fermion motion in black hole background. They show good agreement
with ground-state energy of composite fermion metal in Thomas-Fermi
approximation and cyclotron motion of a constituent or composite fermion
excitation near Fermi-point.
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Transport Properties of QCD at Large $N_c$ and the Gauge/String Duality: Below the deconfinement phase transition large $N_c$ QCD is expected to be a
very viscous hadronic fluid because both the shear and bulk viscosity to
entropy density ratio, $\eta/s,\zeta/s \sim N_c^2$. In this letter I show that
$\eta/s \sim N_c^2$ in the confined phase of holographic models of QCD at large
$N_c$ defined in the supergravity approximation. Our results show that the
gauge/string duality can be used to describe not only nearly perfect fluids but
also extremely viscous systems such as a cold gas of glueballs.
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Soliton, breather and shockwave solutions of the Heisenberg and the
$T\bar T$ deformations of scalar field theories in 1+1 dimensions: In this note we study soliton, breather and shockwave solutions in certain
two dimensional field theories. These include: (i) Heisenberg's model suggested
originally to describe the scattering of high energy nucleons (ii) $T\bar T$
deformations of certain canonical scalar field theories with a potential. We
find explicit soliton solutions of these models with sine-Gordon and Higgs-type
potentials. We prove that the $T\bar T$ deformation of a theory of a given
potential does not correct the mass of the soliton of the undeformed one. We
further conjecture the form of breather solutions of these models. We show that
certain $T\bar T$ deformed actions admit shockwave solutions that generalize
those of Heisenberg's Lagrangian.
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Brighter Branes, enhancement of photon production by strong magnetic
fields in the gauge/gravity correspondence: We use the gauge/gravity correspondence to calculate the rate of photon
production in a strongly coupled N=4 plasma in the presence of an intense
magnetic field. We start by constructing a family of back reacted geometries
that include the black D3-brane solution, as a smooth limiting case for B=0,
and extends to backgrounds with an arbitrarily large constant magnetic field.
This family provides the gravitational dual of a field theory in the presence
of a very strong magnetic field which intensity can be fixed as desired and
allows us to study its effect on the photon production of a quark-gluon plasma.
The inclusion of perturbations in the electromagnetic field on these
backgrounds is consistent only if the metric is perturbed as well, so we use
methods developed to treat operator mixing to manage these general
perturbations. Our results show a clear enhancement of photon production with a
significant anisotropy, which, in qualitative agreement with the experiments of
heavy ion collisions, is particularly noticeable for low P.
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One-loop vacuum energy in 10D super-Yang-Mills theory on magnetized tori
with/without 4D N=1 supersymmetric completion: We discuss the behavior of the one-loop vacuum energy of 10 dimensional (10D)
super Yang-Mills theory on magnetized tori $\mathbb{R}^{1,3}\times
(\mathbb{T}^2)^3$ in the presence of the Abelian magnetic fluxes, including all
the contributions from Kaluza-Klein (KK) modes. Higher-dimensional super
Yang-Mills action is known to be repackaged in terms of 4D $\mathcal{N}=1$
superfield. We, however, find that such a superspace action differs from the
original 10D super Yang-Mills action in the presence of magnetic fluxes. We
show that the KK mass spectrum and hence the vacuum energy computed from these
two actions differ from each other. In particular, we find that the UV
divergence of the vacuum energy based on the original action precisely cancels
independently of flux configuration whereas that based on the superspace
completion does only when flux configuration preserves supersymmetry, which
implies spontaneous or explicit breaking of hidden extended supersymmetry.
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Predictions of quantum gravity in inflationary cosmology: effects of the
Weyl-squared term: We derive the predictions of quantum gravity with fakeons on the amplitudes
and spectral indices of the scalar and tensor fluctuations in inflationary
cosmology. The action is $R+R^{2}$ plus the Weyl-squared term. The ghost is
eliminated by turning it into a fakeon, that is to say a purely virtual
particle. We work to the next-to-leading order of the expansion around the de
Sitter background. The consistency of the approach puts a lower bound ($
m_{\chi }>m_{\phi }/4$) on the mass $m_{\chi }$ of the fakeon with respect to
the mass $m_{\phi }$ of the inflaton. The tensor-to-scalar ratio $r$ is
predicted within less than an order of magnitude ($4/3<N^{2}r<12$ to the
leading order in the number of $e$-foldings $N$). Moreover, the relation
$r\simeq -8n_{T}$ is not affected by the Weyl-squared term. No vector and no
other scalar/tensor degree of freedom is present.
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A Solvable Model of Two-Dimensional Dilaton-Gravity Coupled to a
Massless Scalar Field: We present a solvable model of two-dimensional dilaton-gravity coupled to a
massless scalar field. We locally integrate the field equations and briefly
discuss the properties of the solutions. For a particular choice of the
coupling between the dilaton and the scalar field the model can be interpreted
as the two-dimensional effective theory of 2+1 cylindrical gravity minimally
coupled to a massless scalar field.
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Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$
SYM theory at multi-Regge kinematics: Conformal Regge pole contribution: We investigate the analytic structure of the $2\to5$ scattering amplitude in
the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics in all
physical regions. We demonstrate the close connection between Regge pole and
Regge cut contributions: in a selected class of kinematic regions (Mandelstam
regions) the usual factorizing Regge pole formula develops unphysical
singularities which have to be absorbed and compensated by Regge cut
contributions. This leads, in the corrections to the BDS formula, to conformal
invariant 'renormalized' Regge pole expressions in the remainder function. We
compute these renormalized Regge poles for the $2\to5$ scattering amplitude.
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Quantization of Fayet-Iliopoulos Parameters in Supergravity: In this short note we discuss quantization of the Fayet-Iliopoulos parameter
in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos
parameter determines a lift of the group action to a line bundle, and such
lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted
in terms of moment maps and symplectic reductions, we argue that in
supergravity the quantization of the Fayet-Iliopoulos parameter has a natural
understanding in terms of linearizations in geometric invariant theory (GIT)
quotients, the algebro-geometric version of symplectic quotients.
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Asymptotic Freedom and Confinement from Type 0 String Theory: We argue that there are generic solutions to the type 0 gravity equations of
motion that are confining in the infrared and have log scaling in the
ultraviolet. The background curvature generically diverges in the IR.
Nevertheless, there exist solutions where higher order string corrections
appear to be exponentially suppressed in the IR with respect to the leading
type 0 gravity terms. For these solutions the tachyon flows to a fixed value.
We show that the generic solutions lead to a long range linear quark
potential, magnetic screening and a discrete glueball spectrum. We also
estimate some WKB glueball mass ratios and compare them to ratios found using
finite temperature models and lattice computations.
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The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV
Amplitude in Multi-Regge Kinematics: The precise form of the multi-Regge asymptotics of the two-loop six-point MHV
amplitude in N = 4 Super-Yang-Mills theory has been a subject of recent
controversy. In this paper we utilize the amplitude/Wilson loop correspondence
to obtain precise numerical results for the imaginary part of these
asymptotics. The region of phase-space that we consider is interesting because
it allowed Bartels, Lipatov, and Sabio Vera to determine that the two-loop
six-point MHV amplitude is not fixed by the BDS ansatz. They proceeded by
working in the framework of a high energy effective action, thus side-stepping
the need for an arduous two-loop calculation. Our numerical results are
consistent with the predictions of Bartels, Lipatov, and Sabio Vera for the
leading-log asymptotics.
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Vortex loop operators and quantum M2-branes: We study M2-branes in $AdS_4\times S^7/{\mathbb Z}_k$ dual to 1/2 and 1/3 BPS
vortex loop operators in ABJM theory and compute their one-loop correction
beyond the classical M2-brane action. The correction depends only on the parity
of $k$ and is independent of all continues parameters in the definition of the
vortex loops. The result for odd $k$ agrees with the answers for the 1/2 BPS
Wilson loop in the $k=1$ theory and for even $k$ with the one in the $k = 2$
theory. Combining with the classical part, we find that the natural expansion
parameter seems to be $1/\sqrt{kN}$ rather than $1/\sqrt{N}$. This provides a
further setting where semiclassical quantisation can be applied to M2-branes
and produces new results inaccessible by other methods.
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D-branes and Near Extremal Black Holes at Low Energies: It has been observed recently that many properties of some near extremal
black holes can be described in terms of bound states of D-branes. Using a
non-renormalization theorem we argue that the D-brane description is the
correct quantum gravity description of the black hole at low energies. The low
energy theory includes the black hole degrees of freedom that account for the
entropy and describes also Hawking radiation. The description is unitary and
there seems to be no information loss at low energies.
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Generalised matter couplings in massive bigravity: We investigate matter couplings in massive bigravity. We find a new family of
such consistent couplings, including and extending known consistent matter
couplings, and we investigate their decoupling limits, ADM decompositions,
Higuchi bounds and further aspects. We show that differences to previous known
consistent couplings only arise beyond the $\Lambda_3$ decoupling limit and
discuss the uniqueness of consistent matter couplings and how this is related
to the so-called symmetric vielbein condition. Since we work in a vielbein
formulation, these results easily generalise to multi-gravity.
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On the non-abelian superalgebra spanned by the conserved quantities of
N=1 supersymmetric Korteweg-de Vries equation: We obtain an infinite sequence of bosonic non-local conserved quantities for
the N=1 supersymmetric Korteweg-de Vries equation. It is generated from a
bosonic non-local conserved quantity of Super Gardner equation. In distinction
to the already known one with odd parity and dimension 1/2, it has even parity
and dimension 1. It fits exactly in the supersymmetric cohomology in the space
of conserved quantities that we also introduce here. Using results from this
cohomology we obtain the Poisson bracket of several non-local conserved
quantities, including the already known odd ones and the new even ones. The
algebra closes in terms of polynomials of local and non-local conserved
quantities. We prove that the bosonic non-local conserved quantities cannot be
expressed as functions of the already known local and non-local conserved
quantities of Super KdV equation.
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Instanton effects in N=1 brane models and the Kahler metric of twisted
matter: We consider locally consistent systems of magnetized D9 branes on an
orbifolded six-torus which support N=1 gauge theories. In such realizations,
the matter multiplets arise from "twisted" strings connecting different stacks
of branes. The introduction of Euclidean 5 branes (E5) wrapped on the
six-dimensional compact space leads to instanton effects. For instance, if the
system is engineered so as to yield SQCD, a single E5 brane may account for the
ADS/TVY superpotential. We discuss the subtle interplay that exists between the
annuli diagrams with an E5 boundary and the holomorphicity properties of the
effective low-energy action of the N=1 theory. The consistency of this picture
allows to obtain information on the Kahler metric of the chiral matter
multiplets arising from twisted strings.
|
Fluid Dynamical Profiles and Constants of Motion from D-Branes: Various fluid mechanical systems, governed by nonlinear differential
equations, enjoy a hidden, higher-dimensional dynamical Poincar\'e symmetry,
which arises owing to their descent from a Nambu-Goto action. Also, for the
same reason, there are equivalence transformations between different models.
These interconnections are discussed in this lecture, and are summarized in
Fig. 3.
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From Coxeter Higher-Spin Theories to Strings and Tensor Models: A new class of higher-spin gauge theories associated with various Coxeter
groups is proposed. The emphasize is on the $B_p$--models. The cases of $B_1$
and its infinite graded-symmetric product $sym\,(\times B_1)^\infty$ correspond
to the usual higher-spin theory and its multi-particle extension, respectively.
The multi-particle $B_2$--higher-spin theory is conjectured to be associated
with String Theory. $B_p$--higher-spin models with $p>2$ are anticipated to be
dual to the rank-$p$ boundary tensor sigma-models. $B_p$ higher-spin models
with $p\geq 2$ possess two coupling constants responsible for higher-spin
interactions in $AdS$ background and stringy/tensor effects, respectively. The
brane-like idempotent extension of the Coxeter higher-spin theory is proposed
allowing to unify in the same model the fields supported by space-times of
different dimensions. Consistency of the holographic interpretation of the
boundary matrix-like model in the $B_2$-higher-spin model is shown to demand
$N\geq 4$ SUSY, suggesting duality with the $N=4$ SYM upon spontaneous breaking
of higher-spin symmetries. The proposed models are shown to admit unitary
truncations.
|
Massive and massless higher spinning particles in odd dimensions: We study actions for massive bosonic particles of higher spins by
dimensionally reducing an action for massless particles. For the latter we take
a model with a SO(N) extended local supersymmetry on the worldline, that is
known to describe massless (conformal) particles of higher spins in flat
spacetimes of even dimensions. Dimensional reduction produces an action for
massive spinning particles in odd dimensions. The field equations that emerge
in a quantization a la Dirac are shown to be equivalent to the Fierz-Pauli
ones. The massless limit generates a multiplet of massless states with higher
spins, whose first quantized field equations have a geometric form with fields
belonging to various types of Young tableaux. These geometric equations can be
partially integrated to show their equivalence with the standard
Fronsdal-Labastida equations. We covariantize our model to check whether an
extension to curved spacetimes can be achieved. Restricting to (A)dS spaces, we
find that the worldline gauge algebra becomes nonlinear, but remains first
class. This guarantees consistency on such backgrounds. A light cone analysis
confirms the presence of the expected propagating degrees of freedom. A
covariant analysis is worked out explicitly for the massive case, which is seen
to give rise to the Fierz-Pauli equations extended to (A)dS spaces. It is worth
noting that in D=3 the massless limit of our model when N goes to infinity has
the same field content of the Vasiliev's theory that accommodates each spin
exactly once.
|
The renormalization group flow of the dilaton potential: We consider a scalar-metric gauge theory of gravity with independent metric,
connection and dilaton. The role of the dilaton is to provide the scale of all
masses, via its vacuum expectation value. In this theory, we study the
renormalization group flow of the dilaton potential, taking into account
threshold effects at the Planck scale. Due to the running of the VEV of the
dilaton all particles that would naively seem to have masses larger than
Planck's mass, may actually not propagate. This could solve the problem of
unitarity in these theories.
|
Perturbative expansions of Rényi relative divergences and holography: In this paper, we develop a novel way to perturbatively calculate R\'enyi
relative divergences $D_{\gamma}(\rho|| \sigma) ={\rm tr} \rho^{\gamma}
\sigma^{1-\gamma}$ and related quantities without using replica trick as well
as analytic continuation. We explicitly determine the form of the perturbative
term at any order by an integral along the modular flow of the unperturbed
state. By applying the prescription to a class of reduced density matrices in
conformal field theory, we find that the second order term of certain linear
combination of the divergences has a holographic expression in terms of bulk
symplectic form, which is a one parameter generalization of the statement
"Fisher information = Bulk canonical energy".
|
Algebraic Aspects of Interactions of Massive Spinning Particles in Three
Dimensions: The most general 2+1 dimensional spinning particle model is considered. The
action functional may involve all the possible first order Poincare invariants
of world lines, and the particular class of actions is specified thus the
corresponding gauge algebra to be unbroken by inhomogeneous external fields.
Nevertheless, the consistency problem reveals itself as a requirement of the
global compatibility between first and second class constraints. These
compatibility conditions, being unnoticed before in realistic second class
theories, can be satisfied for a particle iff the gyromagnetic ratio takes the
critical value g=2. The quantization procedure is suggested for a particle in
the generic background field by making use of a Darboux co-ordinates, being
found by a perturbative expansion in the field multipoles and the general
procedure is described for constructing of the respective transformation in any
order.
|
Squeezing, Chaos and Thermalization in Periodically Driven Quantum
Systems: The Case of Bosonic Preheating: The phenomena of Squeezing and chaos have recently been studied in the
context of inflation. We apply this formalism in the post-inflationary
preheating phase. During this phase, inflaton field undergoes quasi-periodic
oscillation, which acts as a driving force for the resonant growth of quantum
fluctuation or particle production. Furthermore, the quantum state of the
fluctuations is known to have evolved into a squeezed state. In this
submission, we explore the underlying connection between the resonant growth,
squeezing, and chaos by computing the Out of Time Order Correlator (OTOC) of
phase space variables and establishing a relation among the Lyapunov, Floquet
exponents, and squeezing parameters. For our study, we consider observationally
favored $\alpha$-attractor E-model of inflaton which is coupled with the
bosonic field. After the production, the system of produced bosonic
fluctuations/particles from the inflaton is supposed to thermalize, and that is
believed to have an intriguing connection to the nature of chaos of the system
under perturbation. %By using this we calculated approximate lower bound of
temperature ${\bar T}_{\rm MSS}$. We conjecture a relation between the
thermalization temperature $({\bar T}_{\rm SS})$ of the system and quantum
squeezing, which is further shown to be consistent with the well-known
Rayleigh-Jeans formula for the temperature symbolized as ${\bar T}_{\rm RJ}$,
and that is ${\bar T}_{\rm SS} \simeq {\bar T}_{\rm RJ}$. Finally, we show that
the system temperature is in accord with the well-known lower bound on the
temperature of a chaotic system proposed by Maldacena-Shenker-Stanford (MSS).
|
Gauge Independent Reduction of a Solvable Model with Gribov-Like
Ambiguity: We present a gauge independent Lagrangian method of abstracting the reduced
space of a solvable model with Gribov-like ambiguity, recently proposed by
Friedberg, Lee, Pang and Ren. The reduced space is found to agree with the
explicit solutions obtained by these authors. Complications related to gauge
fixing are analysed. The Gribov ambiguity manifests by a nonuniqueness in the
canonical transformations mapping the hamiltonian in the afflicted gauge with
that obtained gauge independently. The operator ordering problem in this gauge
is investigated and a prescription is suggested so that the results coincide
with the usual hamiltonian formalism using the Schr\"odinger representation.
Finally, a Dirac analysis of the model is elaborated. In this treatment it is
shown how the existence of a nontrivial canonical set in the ambiguity-ridden
gauge yields the connection with the previous hamiltonian formalism.
|
High energy bosons do not propagate: We discuss the propagation of bosons (scalars, gauge fields and gravitons) at
high energy in the context of the spectral action. Using heat kernel
techniques, we find that in the high-momentum limit the quadratic part of the
action does not contain positive powers of the derivatives. We interpret this
as the fact that the two point Green functions vanish for nearby points, where
the proximity scale is given by the inverse of the cutoff.
|
No vDVZ Discontinuity in Non-Fierz-Pauli Theories: In theories of massive gravity with Fierz-Pauli mass term at the linearized
level, perturbative radially symmetric asymptotic solutions are singular in the
zero mass limit, hence van Dam-Veltman-Zakharov (vDVZ) discontinuity. In this
note, in the context of gravitational Higgs mechanism, we argue that in
non-Fierz-Pauli theories, which non-perturbatively are unitary, perturbative
radially symmetric asymptotic solutions have a smooth massless limit, hence no
vDVZ discontinuity. Perturbative vDVZ discontinuity as an artifact of the
Fierz-Pauli mass term becomes evident in the language of constrained gravity,
which is the massless limit of gravitational Higgs mechanism.
|
Curvature relations in almost product manifolds: New relations involving curvature components for the various connections
appearing in the theory of almost product manifolds are given and the conformal
behaviour of these connections are studied. New identities for the irreducible
parts of the deformation tensor are derived. Some direct physical applications
in Kaluza-Klein and gauge theory are discussed.
|
Effective action and black hole solutions in asymptotically safe quantum
gravity: We derive the quantum effective action and the respective quantum equations
of motion from multi-graviton correlation functions in asymptotically safe
quantum gravity. The fully momentum-dependent couplings of three- and
four-graviton scatterings are computed within the functional renormalisation
group approach and the effective action is reconstructed from these vertices.
The resulting quantum equations of motion are solved numerically for quantum
black hole geometries. Importantly, the black hole solutions show signatures of
quantum gravity outside the classical horizon, which manifest in the behaviour
of the temporal and radial components of the metric. Three different types of
solutions with distinct causal structures are identified and the phase
structure of the solution space is investigated.
|
The dS/dS Correspondence: We present a holographic duality for the de Sitter static patch which
consolidates basic features of its geometry and the behavior of gravity and
brane probes, valid on timescales short compared to the decay or Poincare
recurrence times. Namely de Sitter spacetime $dS_d(R)$ in $d$ dimensions with
curvature radius $R$ is holographically dual to two conformal field theories on
$dS_{d-1}(R)$, cut off at an energy scale 1/R where they couple to each other
and to $d-1$ dimensional gravity. As part of our analysis, we study brane
probes in de Sitter and thermal Anti de Sitter spaces, and interpret the terms
in the corresponding DBI action via strongly coupled thermal field theory. This
provides a dual field theoretic interpretation of the fact that probes take
forever to reach a horizon in general relativity.
|
Five-dimensional vector-coupled supergravity on a manifold with boundary: We consider the bosonic and fermionic symmetries of five-dimensional Maxwell-
and Yang-Mills-Einstein supergravity theories on a spacetime with boundaries
(isomorphic to M x S1/Z2). Due to the appearance of the "Chern-Simons" term,
the classical action is not generally invariant under gauge and
supersymmetries. Once bulk vector fields are allowed to propagate on the
boundaries, there is an "inflow" governed by the rank-3 symmetric tensor that
defines the five-dimensional theories. We discuss the requirements that
invariance of the action imposes on new matter content and boundary conditions.
|
Higgs-free confinement hierarchy in five colour QCD: I consider the monopole condensate of five color QCD. The naive lowest energy
state is unobtainable at one-loop for five or more colors due to simple
geometric considerations. The consequent adjustment of the vacuum condensate
generates a hierarchy of confinement scales in a natural Higgs-free manner. The
accompanying symmetry hierarchy contains hints of standard model phenomenology.
|
Killing Horizons and Spinors: We study the near horizon geometry of generic Killing horizons constructing
suitable coordinates and taking the appropriate scaling limit. We are able to
show that the geometry will always show an enhancement of symmetries, and, in
the extremal case, will develop a causally disconnected "throat" as expected.
We analyze the implications of this to the Kerr/CFT conjecture and the
attractor mechanism. We are also able to construct a set of special (pure)
spinors associated with the horizon structure using their interpretation as
maximally isotropic planes. The structure generalizes the usual reduced
holonomy manifold in an interesting way and may be fruitful to the search of
new types of compactification backgrounds.
|
Scattering approach for calculating one-loop effective action and vacuum
energy: We propose an approach for calculating one-loop effective actions and vacuum
energies in quantum field theory. Spectral functions are functions defined by
the eigenvalues of an operator. One-loop effective actions and vacuum energies
in quantum field theory, as well as scattering phase shifts and scattering
amplitudes in quantum mechanics, are all spectral functions. If a
transformation between different spectral functions is identified, we can
obtain a spectral function from another through the transformation. In this
paper, we convert quantum mechanical methods for calculating scattering phase
shifts and scattering amplitudes into quantum field theory methods for
calculating one-loop effective actions and vacuum energies. As examples, the
Born approximation and the WKB approximation in quantum mechanics are converted
into quantum field theory methods. We also calculate the one-loop effective
action and vacuum energy of scalar fields in the Schwarzschild spacetime and
the Reissner-Nordstr\"{o}m spacetime as examples. Some integral representations
of the Bessel function are given in appendices.
|
A Note on Noncompact and Nonmetricit Quadratic Curvature Gravity
Theories: In this note, we evaluate the Weyl-invariant quadratic curvature tensors for
the particular Weyl's gauge field constructed in the $3+1$-dimensional
noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to
its higher curvature version. Here, we also compute Weyl-invariant extension of
topological Gauss-Bonnet term for this specific choice of vector field.
|
BRST Anomaly and Superspace Constraints of the Pure Spinor Heterotic
String in a Curved Background: The pure spinor heterotic string in a generic super Yang-Mills and
supergravity background is considered. We determine the one-loop BRST anomaly
at the cohomological level. We prove that it can be absorbed by consistent
corrections of the classical constraints due to Berkovits and Howe, in
agreement with the Green-Schwarz cancelation mechanism.
|
Dimensional reduction of the ABJM model: We dimensionally reduce the ABJM model, obtaining a two-dimensional theory
that can be thought of as a 'master action'. This encodes information about
both T- and S-duality, i.e. describes fundamental (F1) and D-strings (D1) in 9
and 10 dimensions. The Higgsed theory at large VEV and large k yields D1-brane
actions in 9d and 10d, depending on which auxiliary fields are integrated out.
For N=1 there is a map to a Green-Schwarz string wrapping a nontrivial circle
in C^4/Z_k.
|
Bi-scalar integrable CFT at any dimension: We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal
quantum field theory recently introduced by G\"{u}rdogan and one of the authors
as a strong-twist double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM
theory. Similarly to the $4D$ case, this D-dimensional CFT is also dominated by
"fishnet" Feynman graphs and is integrable in the planar limit. The dynamics of
these graphs is described by the integrable conformal $SO(D+1,1)$ spin chain.
In $2D$ it is the analogue of L. Lipatov's $SL(2,\mathbb{C})$ spin chain for
the Regge limit of $QCD$, but with the spins $s=1/4$ instead of $s=0$.
Generalizing recent $4D$ results of Grabner, Gromov, Korchemsky and one of the
authors to any $D$ we compute exactly, at any coupling, a four point
correlation function, dominated by the simplest fishnet graphs of cylindric
topology, and extract from it exact dimensions of R-charge 2 operators with any
spin and some of their OPE structure constants.
|
An action principle for Vasiliev's four-dimensional higher-spin gravity: We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge
fields in four spacetime dimensions with an action principle. We first extend
Vasiliev's original system with differential forms in degrees higher than one.
We then derive the resulting duality-extended equations of motion from a
variational principle based on a generalized Hamiltonian sigma-model action.
The generalized Hamiltonian contains two types of interaction freedoms: One set
of functions that appears in the Q-structure of the generalized curvatures of
the odd forms in the duality-extended system; and another set depending on the
Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of
polyvector fields of ranks two or higher in target space. We find that at least
one of the two sets of interaction-freedom functions must be linear in order to
ensure gauge invariance. We discuss consistent truncations to the minimal Type
A and B models (with only even spins), spectral flows on-shell and provide
boundary conditions on fields and gauge parameters that are compatible with the
variational principle and that make the duality-extended system equivalent, on
shell, to Vasiliev's original system.
|
No-hair conjectures, primordial shear and protoinflationary initial
conditions: Anisotropic inflationary background geometries are analyzed in the context of
an extended gauge action where the electric and magnetic susceptibilities are
not bound to coincide and depend on the inflaton field. After deriving various
classes of solutions with electric and magnetic hairs, we discuss the problem
of the initial boundary conditions of the shear parameter and consider a
globally neutral plasma as a possible relic of a preinflationary stage of
expansion. While electric hairs are washed out by the finite value of the
protoinflationary conductivity, magnetic hairs can persist and introduce a tiny
amount of shear causing a different inflationary rate of expansion along
orthogonal spatial directions. The plasma interactions are a necessary
criterion to discriminate between physical and unphysical initial conditions
but they are not strictly sufficient to warrant the stability of a given
magnetic solution.
|
How $\mathcal N=1$, $D=4$ SYM domain walls look like: We review main features of the pure $\mathcal N=1$, $D=4$ SYM and its
effective description by the Veneziano-Yankielowicz generalized sigma-model. We
then indicate that the construction of BPS domain walls interpolating between
different SYM vacua requires the presence of a dynamical membrane source. We
will show how such a membrane is coupled to the SYM and present the explicit
form of BPS domain walls which it creates in the Veneziano-Yankielowicz
effective theory. In particular, we will describe 1/2 BPS domain wall
configurations with $|k|\leq N/3$, where $k$ is the membrane charge that sets
the "distance" between two distinct SUSY vacua.
|
Categorical Symmetry of the Standard Model from Gravitational Anomaly: In the Standard Model, some combination of the baryon $\bf B$ and lepton $\bf
L$ number symmetry is free of mixed anomalies with strong and electroweak
$su(3) \times su(2) \times u(1)_{\tilde Y}$ gauge forces. However, it can still
suffer from a mixed gravitational anomaly, hypothetically pertinent to
leptogenesis in the very early universe. This happens when the total "sterile
right-handed" neutrino number $n_{\nu_R}$ is not equal to the family number
$N_f$. Thus the invertible $\bf B - L$ symmetry current conservation can be
violated quantum mechanically by gravitational backgrounds such as
gravitational instantons. In specific, we show that a noninvertible categorical
$\bf B - L$ generalized symmetry still survives in gravitational backgrounds.
In general, we propose a construction of noninvertible symmetry charge
operators as topological defects derived from invertible anomalous symmetries
that suffer from mixed gravitational anomalies. Examples include the
perturbative local and nonperturbative global anomalies classified by
$\mathbb{Z}$ and $\mathbb{Z}_{16}$ respectively. For this construction, we
utilize the anomaly inflow bulk-boundary correspondence, the 4d Pontryagin
class and the gravitational Chern-Simons 3-form, the 3d
Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding
to a 2d rational conformal field theory with an appropriate rational chiral
central charge, and the 4d $\mathbb{Z}_4^{\rm TF}$-time-reversal symmetric
topological superconductor with 3d boundary topological order.
|
Holographic relations for OPE blocks in excited states: We study the holographic duality between boundary OPE blocks and geodesic
integrated bulk fields in quotients of AdS$_3$ dual to excited CFT states. The
quotient geometries exhibit non-minimal geodesics between pairs of spacelike
separated boundary points which modify the OPE block duality. We decompose OPE
blocks into quotient invariant operators and propose a duality with bulk fields
integrated over individual geodesics, minimal or non-minimal. We provide
evidence for this relationship by studying the monodromy of asymptotic maps
that implement the quotients.
|
Classical Limit of Large N Gauge Theories with Conformal Symmetry: In this paper we study classical limit of conformal field theories realized
by large N gauge theories using the generalized coherent states. For generic
large N gauge theories with conformal symmetry, we show that the classical
limit of them is described by the classical Einstein gravity. This may be
regarded as a kind of derivation of the AdS/CFT correspondence.
|
Kinks in the relativistic model with logarithmic nonlinearity: We study the properties of a relativistic model with logarithmic
nonlinearity. We show that such model allows two types of solutions:
topologically trivial (gaussons) and topologically non-trivial (kinks),
depending on a sign of the nonlinear coupling. We focus primarily on the kinks'
case and study their scattering properties. For the kink-antikink scattering,
we have found a critical value of the initial velocity, which separates two
different scenarios of scattering. For the initial velocities below this
critical value, the kinks form a bound state, which then decays slowly. If the
initial velocities are above the critical value, the kinks collide, bounce and
eventually escape to infinities. During this process, the higher initial
velocity is, the greater is the elasticity of the collision. We also study
excitation spectrum of the kink solution.
|
Mimetic Curvaton: In this paper, we investigate the primordial perturbations of inflation model
induced from the multi-field mimetic gravity, where there are two field during
inflation, and thus both adiabatic and isocurvature perturbation modes are
generated. We show that although it is true that the original adiabatic
perturbation mode loses the kinetic term due to the constraint equation, by
applying the curvaton mechanism where one of the field is viewed as curvaton
field, the adiabatic perturbation can actually be transferred from the
isocurvature one at the end of inflation. Detailed calculations are performed
for both inflationary and the consequent matter-dominant epochs. Therefore, the
so-called "non-propagating problem" of the adiabatic mode will actually do no
harm to the multi-field mimetic inflation models.
|
Is Eternal Inflation Past-Eternal? And What if It Is?: As a result of discussions with Bousso and Vilenkin I want to return to the
question of whether the multiverse is past-eternal or if there was a beginning.
Not surprisingly, given three people, there were three answers. However, the
discussions have led to some common ground.
The multiverse being past-eternal, or at least extremely old has content and
potential phenomenological implications. I will discuss how the oldness of the
multiverse is connected with recent speculations of Douglas.
|
The Collinear Limit of the Four-Point Energy Correlator in $\mathcal{N}
= 4$ Super Yang-Mills Theory: We present a compact formula, expressed in terms of classical polylogarithms
up to weight three, for the leading order four-point energy correlator in
maximally supersymmetric Yang-Mills theory, in the limit where the four
detectors are collinear. This formula is derived by combining a simplified,
manifestly dual conformal invariant form of the 1 -> 4 splitting function
obtained from the square of the tree-level five-particle form factor of
stress-tensor multiplet operators, with a novel integration-by-parts algorithm
operating directly on Feynman parameter integrals. Our results provide valuable
data for exploring the structure of physical observables in perturbation
theory, and for calculations of jet substructure observables in quantum
chromodynamics.
|
One-loop Double Copy Relation from Twisted (Co)homology: We propose a geometric relation between closed and open string amplitudes at
one-loop. After imposing a homological splitting on the world-sheet torus
twisted intersection theory is used to establish a one-loop double copy
relation. The latter expresses a closed string amplitude by a pair of open
string amplitudes and twisted intersection numbers. These inner products on the
vector space of allowed differential forms are related to the twisted homology
and cohomology groups associated with the Riemann-Wirtinger integral.
|
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