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Double-well instantons in finite volume: Assuming a toroidal space with finite volume, we derive analytically the full
one-loop vacuum energy for a scalar field tunnelling between two degenerate
vacua, taking into account discrete momentum. The Casimir energy is computed
for an arbitrary number of dimensions using the Abel-Plana formula, while the
one-loop instanton functional determinant is evaluated using the Green's
functions for the fluctuation operators. The resulting energetic properties are
non-trivial: both the Casimir effect and tunnelling contribute to the Null
Energy Condition violation, arising from a non-extensive true vacuum energy. We
discuss the relevance of this mechanism to induce a cosmic bounce, requiring no
modified gravity or exotic matter. | Aspects of the map from Exact RG to Holographic RG in AdS and dS: In earlier work the evolution operator for the exact RG equation was mapped
to a field theory in Euclidean AdS. This gives a simple way of understanding
AdS/CFT. We explore aspects of this map by studying a simple example of a
Schroedinger equation for a free particle with time dependent mass. This is an
analytic continuation of an ERG like equation. We show for instance that it can
be mapped to a harmonic oscillator. We show that the same techniques can lead
to an understanding of dS/CFT too. |
A Comment on Quantum Distribution Functions and the OSV Conjecture: Using the attractor mechanism and the relation between the quantization of
$H^{3}(M)$ and topological strings on a Calabi Yau threefold $M$ we define a
map from BPS black holes into coherent states. This map allows us to represent
the Bekenstein-Hawking-Wald entropy as a quantum distribution function on the
phase space $H^{3}(M)$. This distribution function is a mixed
Husimi/anti-Husimi distribution corresponding to the different normal ordering
prescriptions for the string coupling and deviations of the complex structure
moduli. From the integral representation of this distribution function in terms
of the Wigner distribution we recover the Ooguri-Strominger-Vafa (OSV)
conjecture in the region "at infinity" of the complex structure moduli space.
The physical meaning of the OSV corrections are briefly discussed in this
limit. | String theory of the Omega deformation: In this article, we construct a supersymmetric real mass deformation for the
adjoint chiral multiplets in the gauge theory describing the dynamics of a
stack of D2-branes in type II string theory. We do so by placing the D2-branes
into the T-dual of a supersymmetric NS fluxbrane background. We furthermore
note that this background is the string theoretic realization of an
Omega-deformation of flat space in the directions transverse to the branes
where the deformation parameters satisfy \epsilon_1 = - \epsilon_2. This
\Omega-deformation therefore serves to give supersymmetric real masses to the
chiral multiplets of the 3D gauge theory. To illustrate the physical effect of
the real mass term, we derive BPS-saturated classical solutions for the branes
rotating in this background. Finally, we reproduce all the same structure in
the presence of NS fivebranes and comment on the relationship to the gauge
theory/spin-chain correspondence of Nekrasov and Shatashvili. |
The Green--Schwarz Superstring in Extended Configuration Space and
Infinitely Reducible First Class Constraints Problem: The Green--Schwarz superstring action is modified to include some set of
additional (on-shell trivial) variables. A complete constraints system of the
theory turns out to be reducible both in the original and in additional
variable sectors. The initial $8s$ first class constraints and $8c$ second
class ones are shown to be unified with $8c$ first and $8s$ second class
constraints from the additional variables sector, resulting with
$SO(1,9)$-covariant and linearly independent constraint sets. Residual
reducibility proves to fall on second class constraints only. | Stability of Scalar Fields in Warped Extra Dimensions: This work sets up a general theoretical framework to study stability of
models with a warped extra dimension where N scalar fields couple minimally to
gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk
scalars, and general domain-wall models. We derive the Schrodinger equation
governing the spin-0 spectrum of perturbations of such a system. This result is
specialized to potentials generated using fake supergravity, and we show that
models without branes are free of tachyonic modes. Turning to the existence of
zero modes, we prove a criterion which relates the number of normalizable zero
modes to the parities of the scalar fields. Constructions with definite parity
and only odd scalars are shown to be free of zero modes and are hence
perturbatively stable. We give two explicit examples of domain-wall models with
a soft wall, one which admits a zero mode and one which does not. The latter is
an example of a model that stabilizes a compact extra dimension using only bulk
scalars and does not require dynamical branes. |
Uniqueness theorem for stationary black hole solutions of σ-models
in five dimensions: We prove the uniqueness theorem for stationary self-gravitating non-linear
\sigma-models in five-dimensional spacetime. We show that the Myers-Perry
vacuum Kerr spacetime is the only maximally extended, stationary, axisymmetric,
asymptotically flat solution having the regular rotating event horizon with
constant mapping. | AdS$_5$ Black Hole Entropy near the BPS Limit: We analyze AdS$_5$ black holes that are nearly supersymmetric. They depart
from the BPS limit in two distinct ways: a temperature takes them above
extremality and a potential violates a certain constraint. We study the
thermodynamics of these deformations and their interplay in detail. We discuss
recent microscopic computations of BPS black hole entropy in $\mathcal{N}=4$
SYM and generalize methods to the nearBPS regime by relaxing constraints
imposed by supersymmetry. The computations recover gravitational results from
microscopics also for nearBPS black holes. |
Higher Genus Correlators for the Complex Matrix Model: We describe an iterative scheme which allows us to calculate any multi-loop
correlator for the complex matrix model to any genus using only the first in
the chain of loop equations. The method works for a completely general
potential and the results contain no explicit reference to the couplings. The
genus $g$ contribution to the $m$--loop correlator depends on a finite number
of parameters, namely at most $4g-2+m$. We find the generating functional
explicitly up to genus three. We show as well that the model is equivalent to
an external field problem for the complex matrix model with a logarithmic
potential. | F-theory and Dark Energy: Motivated by its potential use as a starting point for solving various
cosmological constant problems, we study F-theory compactified on the warped
product $\mathbb{R}_{\text{time}} \times S^3 \times Y_{8}$ where $Y_{8}$ is a
$Spin(7)$ manifold, and the $S^3$ factor is the target space of an $SU(2)$
Wess--Zumino--Witten (WZW) model at level $N$. Reduction to M-theory exploits
the abelian duality of this WZW model to an $S^3 / \mathbb{Z}_N$ orbifold. In
the large $N$ limit, the untwisted sector is captured by 11D supergravity. The
local dynamics of intersecting 7-branes in the $Spin(7)$ geometry is controlled
by a Donaldson--Witten twisted gauge theory coupled to defects. At late times,
the system is governed by a 1D quantum mechanics system with a ground state
annihilated by two real supercharges, which in four dimensions would appear as
"$\mathcal{N} = 1/2$ supersymmetry" on a curved background. This leads to a
cancellation of zero point energies in the 4D field theory but a split mass
spectrum for superpartners of order $\Delta m_\text{4D} \sim \sqrt{M_\text{IR}
M_\text{UV}}$ specified by the IR and UV cutoffs of the model. This is
suggestively close to the TeV scale in some scenarios. The classical 4D
geometry has an intrinsic instability which can produce either a collapsing or
expanding Universe, the latter providing a promising starting point for a
number of cosmological scenarios. The resulting 1D quantum mechanics in the
time direction also provides an appealing starting point for a more detailed
study of quantum cosmology. |
Canonical formulation of Pais-Ulhenbeck action and resolving the issue
of branched Hamiltonian: Shortcomings of Dirac's constrained analysis in the context of fourth order
Pais-Uhlenbeck oscillator action and the appearance of badly affected
phase-space Hamiltonian for a generalized fourth order oscillator action,
following Ostrogradski, Dirac and Horowitz's formalism, require a viable
canonical formulation. This is achieved only after fixing appropriate variables
at the end points and taking care of the counter surface terms obtained from
variational principle. In the process a one-to-one correspondence between
different higher order theories has been established. On the other hand the
issue of branched Hamiltonian appearing in the presence of velocities with
degree higher than two in the Lagrangian, has not been resolved uniquely as
yet. However, often such terms appear with higher order theory, gravity in
particular. Here we show that canonical formulation of higher order theory
takes care of the issue elegantly. | A Field Theory of Knotted Solitons: The conjecture that the elementary fermions are knotted flux tubes permit the
construction of a phenomenology that is not accessible from the standard
electroweak theory. In order to carry these ideas further we have attempted to
formulate the elements of a field theory in which local SU(2) x U(1), the
symmetry group of standard electroweak theory, is combined with global SU_q(2),
the symmetry group of knotted solitons. |
Adler-Bardeen theorem and manifest anomaly cancellation to all orders in
gauge theories: We reconsider the Adler-Bardeen theorem for the cancellation of gauge
anomalies to all orders, when they vanish at one loop. Using the
Batalin-Vilkovisky formalism and combining the dimensional-regularization
technique with the higher-derivative gauge invariant regularization, we prove
the theorem in the most general perturbatively unitary renormalizable gauge
theories coupled to matter in four dimensions, and identify the subtraction
scheme where anomaly cancellation to all orders is manifest, namely no
subtractions of finite local counterterms are required from two loops onwards.
Our approach is based on an order-by-order analysis of renormalization, and,
differently from most derivations existing in the literature, does not make use
of arguments based on the properties of the renormalization group. As a
consequence, the proof we give also applies to conformal field theories and
finite theories. | False Vacuum Decay Catalyzed by Black Holes: False vacuum states are metastable in quantum field theories, and true vacuum
bubbles can be nucleated due to the quantum tunneling effect. It was recently
suggested that an evaporating black hole (BH) can be a catalyst of bubble
nucleations and dramatically shortens the lifetime of the false vacuum. In
particular, in the context of the Standard Model valid up to a certain energy
scale, even a single evaporating BH may spoil the successful cosmology by
inducing the decay of our electroweak vacuum. In this paper, we reinterpret
catalyzed vacuum decay by BHs, using an effective action for a thin-wall bubble
around a BH to clarify the meaning of bounce solutions. We calculate bounce
solutions in the limit of a flat spacetime and in the limit of negligible
backreaction to the metric, where it is much easier to understand the physical
meaning, and compare these results with the full calculations done in the
literature. As a result, we give a physical interpretation of the enhancement
factor: it is nothing but the probability of producing states with a finite
energy. This makes it clear that all the other states such as plasma should
also be generated through the same mechanism, and calls for finite-density
corrections to the tunneling rate which tend to stabilize the false vacuum. We
also clarify that the dominant process is always consistent with the
periodicity indicated by the BH Hawking temperature after summing over all
possible remnant BH masses or bubble energies, although the periodicity of each
bounce solution as a function of a remnant BH can be completely different from
the inverse temperature of the system as mentioned in the previous literature. |
Topics in gravity SCET: the diff Wilson lines and reparametrization
invariance: Two topics in soft collinear effective theory (SCET) for gravitational
interactions are explored. First, the collinear Wilson lines---necessary
building blocks for maintaining multiple copies of diffeomorphism invariance in
gravity SCET---are extended to all orders in the SCET expansion parameter
$\lambda$, where it has only been known to $O(\lambda)$ in the literature.
Second, implications of reparametrization invariance (RPI) for the structure of
gravity SCET lagrangians are studied. The utility of RPI is illustrated by an
explicit example in which $O(\lambda^2)$ hard interactions of a collinear
graviton are completely predicted by RPI from its $O(\lambda)$ hard
interactions. It is also pointed out that the multiple diffeomorphism
invariances and RPI together require certain relations among $O(\lambda)$
terms, thereby reducing the number of $O(\lambda)$ terms that need to be fixed
by matching onto the full theory in the first place. | Topological mass generation to antisymmetric tensor matter field: We propose a mechanism to give mass to tensor matter field which preserve the
U(1) symmetry. We introduce a complex vector field that couples with the tensor
in a topological term. We also analyze the influence of the kinetic terms of
the complex vector in our mechanism. |
Smearing and Unsmearing KKLT AdS Vacua: Gaugino condensation on D-branes wrapping internal cycles gives a mechanism
to stabilize the associated moduli. According to the effective field theory,
this gives rise, when combined with fluxes, to supersymmetric AdS$_4$
solutions. In this paper we provide a ten-dimensional description of these
vacua. We first find the supersymmetry equations for type II AdS$_4$ vacua with
gaugino condensates on D-branes, in the framework of generalized complex
geometry. We then solve them for type IIB compactifications with gaugino
condensates on smeared D7-branes. We show that supersymmetry requires a
(conformal) Calabi-Yau manifold and imaginary self-dual three-form fluxes with
an additional (0,3) component. The latter is proportional to the cosmological
constant, whose magnitude is determined by the expectation value of the gaugino
condensate and the stabilized volume of the cycle wrapped by the branes. This
confirms, qualitatively and quantitatively, the results obtained using
effective field theory. We find that exponential separation between the AdS and
the KK scales seems possible as long as the three-form fluxes are such that
their (0,3) component is exponentially suppressed. As for the localized
solution, it requires going beyond SU(3)-structure internal manifolds.
Nevertheless, we show that the action can be evaluated on-shell without relying
on the details of such complicated configuration. We find that no "perfect
square" structure occurs, and the result is divergent. We compute the
four-fermion contributions, including a counterterm, needed to cancel these
divergencies. | Background charges and consistent continuous deformations of $2d$
gravity theories: We construct and discuss all background charges and continuous consistent
deformations of standard $2d$ gravity theories with scalar matter fields. It
turns out that the background charges and those deformations which change
nontrivially both the form of the action and of its gauge symmetries are
closely linked and exist only if the target space has at least one special
(`covariantly constant') Killing vector which must be a null vector in the case
of the deformations. The deformed actions provide interesting novel $2d$
gravity models. We argue that some of them lead to non-critical string
theories. |
Probing Clifford Algebras Through Spin Groups: A Standard Model
Perspective: Division algebras have demonstrated their utility in studying non-associative
algebras and their connection to the Standard Model through complex Clifford
algebras. This article focuses on exploring the connection between these
complex Clifford algebras and their corresponding real Clifford algebras
providing insight into geometric properties of bivector gauge symmetries. We
first generate gauge symmetries in the complex Clifford algebra through a
general Witt decomposition. Gauge symmetries act as a constraint on the
underlying real Clifford algebra, where they're then translated from their
complex form to their bivector counterpart. Spin group arguments allow the
identification of bivector structures which preserve the gauge symmetry
yielding the corresponding real Clifford algebra. We conclude that Standard
Model gauge groups emerge from higher-dimensional Clifford algebras carrying
Euclidean signatures, where particle states are recognized as a combination of
basis elements corresponding to complex Euclidean Clifford algebras. | Magnon like solutions for strings in I-brane background: We study the solutions for fundamental string rotating in a background
generated by a 1+1 dimensional intersection of two orthogonal stacks of
fivebranes in type IIB string theory. We show the existence of magnon like
solutions for the string moving simultaneously in the two spheres in this
background and find the relevant dispersion relation among the various
conserved charges. |
On actions for (entangling) surfaces and DCFTs: The dynamics of surfaces and interfaces describe many physical systems,
including fluid membranes, entanglement entropy and the coupling of defects to
quantum field theories. Based on the formulation of submanifold calculus
developed by Carter, we introduce a new variational principle for (entangling)
surfaces. This principle captures all diffeomorphism constraints on
surface/interface actions and their associated spacetime stress tensor. The
different couplings to the geometric tensors appearing in the surface action
are interpreted in terms of response coefficients within elasticity theory. An
example of a surface action with edges at the two-derivative level is studied,
including both the parity-even and parity-odd sectors. Its conformally
invariant counterpart restricts the type of conformal anomalies that can appear
in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics,
it is shown that classification methods can be used to constrain the stress
tensor of (entangling) surfaces at a given order in derivatives. This analysis
reveals a purely geometric parity-odd contribution to the Young modulus of a
thin elastic membrane. Extending this novel variational principle to BCFTs and
DCFTs in curved spacetimes allows to obtain the Ward identities for
diffeomorphism and Weyl transformations. In this context, we provide a formal
derivation of the contact terms in the stress tensor and of the displacement
operator for a broad class of actions. | Algebraic derivation of spectrum of the Dirac Hamiltonian for arbitrary
combination of Lorentz-scalar and Lorentz-vector Coulomb potentials: Spectrum of the Dirac Equation is obtained algebraically for arbitrary
combination of Lorentz-scalar and Lorentz-vector Coulomb potentials using the
Witten's Superalgebra approach. The result coincides with that, known from the
explicit solution of Dirac equation. |
The Physics Inside Topological Quantum Field Theories: We show that the equations of motion defined over a specific field space are
realizable as operator conditions in the physical sector of a generalized Floer
theory defined over that field space. The ghosts associated with such a
construction are found not to be dynamical. This construction is applied to
gravity on a four dimensional manifold, $M$; whereupon, we obtain Einstein's
equations via surgery, along $M$, in a five-dimensional topological quantum
field theory. | ${\cal N}=(2,2)$ AdS$_3$ from D3-branes wrapped on Riemann surfaces: We construct $\mathcal{N}=(2,2)$ supersymmetric AdS$_3$ solutions of type IIB
supergravity, dual to twisted compactifications of 4d $\mathcal{N}=4$
super-Yang--Mills on Riemann surfaces. We consider both theories with a regular
topological twist, and a twist involving the isometry group of the Riemann
surface. These solutions are interpreted as the near-horizon of black strings
asymptoting to AdS$_5\times \text{S}^5$. As evidence for the proposed duality
we compute the central charge of the gravity solutions and show that it agrees
with the field theory result. |
Left-Right Symmetric Model from Geometrical Formulation of Gauge Theory
in $M_4 \times Z_2 \times Z_2$: The left-right symmetric model (LRSM) with gauge group $SU(2)_{L} \times
SU(2)_{R} \times U(1)_{B-L}$ is reconstructed from the geometric formulation of
gauge theory in $M_4 \times Z_2 \times Z_2$ where $M_4$ is the four-dimensional
Minkowski space and $Z_2 \times Z_2$ the discrete space with four points. The
geometrical structure of this model becomes clearer compared with other works
based on noncommutative geometry. As a result, the Yukawa coupling terms and
the Higgs potential are derived in more restricted forms than in the standard
LRSM. | Gluon scattering amplitudes from gauge/string duality and integrability: We discuss gluon scattering amplitudes/null-polygonal Wilson loops of N = 4
super Yang-Mills theory at strong coupling based on the gauge/string duality
and its underlying integrability. We focus on the amplitudes/Wilson loops
corresponding to the minimal surfaces in AdS_3, which are described by the
thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon model.
Using conformal perturbation theory and an interesting relation between the
g-function (boundary entropy) and the T-function, we derive analytic expansions
around the limit where the Wilson loops become regular-polygonal. We also
compare our analytic results with those at two loops, to find that the rescaled
remainder functions are close to each other for all multi-point amplitudes. |
Gaugino Condensation and the Vacuum Expectation Value of the Dilaton: The mechanism of gaugino condensation has emerged as a prime candidate for
supersymmetry breakdown in low energy effective supergravity (string) models.
One of the open questions in this approach concerns the size of the gauge
coupling constant which is dynamically fixed through the vev of the dilaton. We
argue that a nontrivial gauge kinetic function $f(S)$ could solve the potential
problem of a runaway dilaton. The actual form of $f(S)$ might be constrained by
symmetry arguments. | Scales of String Theory: I review the arguments in favor of/against the traditional hypothesis that
the Planck, string and compactification scales are all within a couple of
orders of magnitude from each other. I explain how the extreme brane-world
scenario, with TeV type I scale and two large (near millimetric) transverse
dimensions, creates conditions analogous to those of the energy desert and is
thus naturally singled out. I comment on the puzzle of gauge coupling
unification in this context. |
Quintessence with a localized scalar field on the brane: We study issues of the quintessence in the brane cosmology. The initial bulk
spacetime consists of two 5D topological anti de Sitter black hole joined by
the brane (moving domain wall). Here we do not introduce any conventional
radiation and matter. Instead we include a localized scalar on the brane as a
stress-energy tensor, and thus we find the quintessence which gives an
accelerating universe. Importantly, we obtain a $\rho^2$-term as well as a
holographic matter term of $\alpha/a^4$ from the masses of the topological
black holes. We discuss a possibility that in the early universe, $\rho^2$-term
makes a large kinetic term which induces a decelerating universe. This may
provide a hint of avoiding from the perpetually accelerating universe of the
present-day quintessence. If a holographic matter term exists, it will plays
the role of a CFT-radiation in the early universe. | Operator Regularization and Large Noncommutative Chern Simons Theory: We examine noncommutative Chern Simons theory using operator regularization.
Both the zeta-function and the eta-function are needed to determine one loop
effects. The contributions to these functions coming from the two point
function is evaluated. The U(N) noncommutative model smoothly reduces to the
SU(N) commutative model as the noncommutative parameter theta_{mu nu} vanishes. |
Notes on AdS-Schwarzschild eikonal phase: We consider the eikonal phase associated with the gravitational scattering of
a highly energetic light particle off a very heavy object in AdS spacetime. A
simple expression for this phase follows from the WKB approximation to the
scattering amplitude and has been computed to all orders in the ratio of the
impact parameter to the Schwarzschild radius of the heavy particle. The eikonal
phase is related to the deflection angle by the usual stationary phase
relation. We consider the flat space limit and observe that for sufficiently
small impact parameters (or angular momenta) the eikonal phase develops a large
imaginary part; the inelastic cross-section is exactly the classical absorption
cross-section of the black hole. We also consider a double scaling limit where
the momentum becomes null simultaneously with the asymptotically AdS black hole
becoming very large. In the dual CFT this limit retains contributions from all
leading twist multi stress tensor operators, which are universal with respect
to the addition of higher derivative terms to the gravitational lagrangian. We
compute the eikonal phase and the associated Lyapunov exponent in the double
scaling limit. | Hawking Radiation inside Black Holes in Quantum Gravity: We study black hole radiation inside black holes within the framework of
quantum gravity. First, we review on our previous work of a canonical
quantization for a spherically symmetric geometry where one of the spatial
coordinates is treated as the time variable, since we think of the interior
region of a black hole. Based on this formalism, under physically plausible
assumptions, we solve the Wheeler-De Witt equation inside the black hole, and
show that the mass-loss rate of an evaporating black hole due to thermal
radiation is equivalent to the result obtained by Hawking in his semi-classical
approach. A remarkable point is that our assumptions make the momentum
constraint coincide with the Hamiltonian constraint up to an irrelevant overall
factor. Furthermore, for comparison, we solve the Wheeler-De Witt equation
outside the black hole as well, and see that the mass-loss rate of an
evaporating black hole has the same expression. The present analysis suggests
that the black hole radiation comes from the black hole singularity. We also
comment on the Birkhoff theorem in quantum gravity. |
On Chiral Symmetry Breaking in a Constant Magnetic Field in Higher
Dimension: Chiral symmetry breaking in the Nambu-Jona-Lasinio model in a constant
magnetic field is studied in spacetimes of dimension D > 4. It is shown that a
constant magnetic field can be characterized by [(D-1)/2] parameters. For the
maximal number of nonzero field parameters, we show that there is an effective
reduction of the spacetime dimension for fermions in the infrared region D
$\to$ 1 + 1 for even-dimensional spacetimes and D $\to$ 0 + 1 for
odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our
conclusions. | Geometric Resolution of Schwarzschild Horizon: We provide the first example of a geometric transition that resolves the
Schwarzschild black hole into a smooth microstructure in eleven-dimensional
supergravity on a seven-torus. The geometry is indistinguishable from a
Schwarzschild black hole dressed with a scalar field in four dimensions,
referred to as a Schwarzschild scalarwall. In eleven dimensions, the scalar
field arises as moduli of the torus. The resolution occurs at an infinitesimal
scale above the horizon, where it transitions to a smooth bubbling spacetime
supported by M2-brane flux. |
Generalized lagrangian of the Rarita--Schwinger field: We derive the most general lagrangian of the free massive Rarita--Schwinger
field, which generalizes the previously known ones. The special role of the
reparameterization transformation is discussed. | Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories: The expectation value of a smooth conformal line defect in a CFT is a
conformal invariant functional of its path in space-time. For example, in large
$N$ holographic theories, these fundamental observables are dual to the open
string partition function in AdS. In this paper, we develop a bootstrap method
for studying them and apply it to conformal line defects in Chern-Simons matter
theories. In these cases, the line bootstrap is based on three minimal
assumptions -- conformal invariance of the line defect, large $N$
factorization, and the spectrum of the two lowest-lying operators at the end of
the line. On the basis of these assumptions, we solve the one-dimensional CFT
on the line and systematically compute the defect expectation value in an
expansion around the straight line. We find that the conformal symmetry of a
straight defect is insufficient to fix the answer. Instead, imposing the
conformal symmetry of the defect along an arbitrary curved line leads to a
functional bootstrap constraint. The solution to this constraint is found to be
unique. |
Exotic Universal Solutions in Cubic Superstring Field Theory: We present a class of analytic solutions of cubic superstring field theory in
the universal sector on a non-BPS D-brane. Computation of the action and gauge
invariant overlap reveal that the solutions carry half the tension of a non-BPS
D-brane. However, the solutions do not satisfy the reality condition. In fact,
they display an intriguing topological structure: We find evidence that
conjugation of the solutions is equivalent to a gauge transformation that
cannot be continuously deformed to the identity. | Novel Complete Non-compact Symmetries for the Wheeler-DeWitt Equation in
a Wormhole Scalar Model and Axion-Dilaton String Cosmology: We find the full symmetries of the Wheeler-DeWitt equation for the Hawking
and Page wormhole model and an axion-dilaton string cosmology. We show that the
Wheeler-DeWitt Hamiltonian admits an U(1,1) hidden symmetry for the Hawking and
Page model and U(2,1) for the axion-dilaton string cosmology. If we consider
the existence of matter-energy renormalization, for each of these models we
find that the Wheeler-DeWitt Hamiltonian accept an additional SL(2,R) dynamical
symmetry. In this case, we show that the SL(2,R) dynamical symmetry generators
transform the states from one energy Hilbert eigensubspace to another. Some new
wormhole type-solutions for both models are found. |
Batalin-Tyutin Quantization of the Chern-Simons-Proca Theory: We quantize the Chern-Simons-Proca theory in three dimensions by using the
Batalin-Tyutin Hamiltonian method, which systematically embeds second class
constraint system into first class by introducing new fields in the extended
phase space. As results, we obtain simultaneously the St\"uckelberg scalar
term, which is needed to cancel the gauge anomaly due to the mass term, and the
new type of Wess-Zumino action, which is irrelevant to the gauge symmetry. We
also investigate the infrared property of the Chern-Simons-Proca theory by
using the Batalin-Tyutin formalism comparing with the symplectic formalism. As
a result, we observe that the resulting theory is precisely the gauge invariant
Chern-Simons-Proca quantum mechanical version of this theory. | A hidden symmetry in quantum gravity: The action integral contains more information than the equations of motion.
We have previously shown that there are signs of an extended exceptional
symmetry for N=8 supergravity in four dimensions. The symmetry is such that the
fields used in the Lagrangian are not representations of the symmetry. Instead
one has to add representations to obtain a representation of the extended
symmetry group. In this paper we discuss an extended symmetry in
four-dimensional gravity which is the Ehlers symmetry in three dimensions. It
cannot be spanned by the helicity states of four-dimensional gravity but it can
be realised once we treat the helicity states just as field variables of the
functional integral, which can be changed like variables in any integral. We
also explain how this symmetry is inherent to formulations of N=8 supergravity
in four dimensions through a truncation in the field space to pure gravity. |
A condition on the chiral symmetry breaking solution of the
Dyson-Schwinger equation in three-dimensional QED: In three-dimensional QED, which is analyzed in the 1/$N$ expansion, we obtain
a sufficient and necessary condition for a nontrivial solution of the
Dyson-Schwinger equation to be chiral symmetry breaking solution. In the
derivation, a normalization condition of the Goldstone bound state is used. It
is showed that the existent analytical solutions satisfy this condition. | Inhomogeneous Near-extremal Black Branes: It has recently been shown that there exist stable inhomogeneous neutral
black strings in higher dimensional gravity. These solutions were motivated by
the fact that the corresponding homogeneous solutions are unstable. We show
that there exist new inhomogeneous black string and black p-brane solutions
even when the corresponding translationally invariant solutions are stable. In
particular, we show there exist inhomogeneous near-extremal black strings and
p-branes. Some of these solutions remain inhomogeneous even when the size of
the compact direction (at infinity) is very small. |
On instantons as Kaluza-Klein modes of M5-branes: Instantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory
arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein
modes and winding self-dual strings, respectively. We study an index which
counts BPS instantons with electric charges in Coulomb and symmetric phases. We
first prove the existence of unique threshold bound state of (noncommutative)
U(1) instantons for any instanton number, and also show that charged instantons
in the Coulomb phase correctly give the degeneracy of SU(2) self-dual strings.
By studying SU(N) self-dual strings in the Coulomb phase, we find novel
momentum-carrying degrees on the worldsheet. The total number of these degrees
equals the anomaly coefficient of SU(N) (2,0) theory. We finally show that our
index can be used to study the symmetric phase of this theory, and provide an
interpretation as the superconformal index of the sigma model on instanton
moduli space. | A Formulation of Quantum Field Theory Realizing a Sea of Interacting
Dirac Particles: In this survey article, we explain a few ideas behind the fermionic projector
approach and summarize recent results which clarify the connection to quantum
field theory. The fermionic projector is introduced, which describes the
physical system by a collection of Dirac states, including the states of the
Dirac sea. Formulating the interaction by an action principle for the fermionic
projector, we obtain a consistent description of interacting quantum fields
which reproduces the results of perturbative quantum field theory. We find a
new mechanism for the generation of boson masses and obtain small corrections
to the field equations which violate causality. |
Generalized Calogero-Sutherland systems from many-matrix models: We construct generalizations of the Calogero-Sutherland-Moser system by
appropriately reducing a model involving many unitary matrices. The resulting
systems consist of particles on the circle with internal degrees of freedom,
coupled through modifications of the inverse-square potential. The coupling
involves SU(M) non-invariant (anti)ferromagnetic interactions of the internal
degrees of freedom. The systems are shown to be integrable and the spectrum and
wavefunctions of the quantum version are derived. | Chaotic Brane Inflation: We illustrate a framework for constructing models of chaotic inflation where
the inflaton is the position of a D3 brane along the universal cover of a
string compactification. In our scenario, a brane rolls many times around a
non-trivial one-cycle, thereby unwinding a Ramond-Ramond flux. These "flux
monodromies" are similar in spirit to the monodromies of Silverstein, Westphal,
and McAllister, and their four-dimensional description is that of Kaloper and
Sorbo. Assuming moduli stabilization is rigid enough, the large-field
inflationary potential is protected from radiative corrections by a discrete
shift symmetry. |
The Polynomial Formulation of the U(1) Non-Linear Sigma-Model in 2
Dimensions: We investigate some properties of a first-order polynomial formulation of the
U(1) non-linear sigma-model in two Euclidean dimensions. The variables in this
description are a 1-form field plus a 0-form Lagrange multiplier field. The
usual spin variables are non-local functions of the new fields. As this
construction incorporates O(2) invariance ab initio, only O(2)-invariant
correlation functions (the only non-vanishing ones in the model) can be
constructed. We show that the vortices play a dual role to the spin variables
in the partition function. The equivalent Sine-Gordon description is obtained
in a natural way, when one integrates out the 1-form field to get an effective
partition function for the Lagrange multiplier. We also show how to introduce
strings of vortices within this formulation. | Holographic Model of Dual Superconductor for Quark Confinement: We show that a hairy black hole solution can provide a holographically dual
description of quark confinement. There exists a one-parameter sensible metric
which receives the backreaction of matter contents in the holographic action,
where the scalar and gauge field are responsible for the condensation of
chromomagnetic monopoles. This model features a preconfining phase triggered by
second-order monopole condensation and a first-order confinement/deconfinement
phase transition. To confirm the confinement, the quark-antiquark potential is
calculated by probing a QCD string in both phases. At last, contribution from
Kaluza-Klein monopoles in the confining phase is discussed. |
Geometry and Energy of Non-abelian Vortices: We study pure Yang--Mills theory on $\Sigma\times S^2$, where $\Sigma$ is a
compact Riemann surface, and invariance is assumed under rotations of $S^2$. It
is well known that the self-duality equations in this set-up reduce to vortex
equations on $\Sigma$. If the Yang--Mills gauge group is $\SU{2}$, the
Bogomolny vortex equations of the abelian Higgs model are obtained. For larger
gauge groups one generally finds vortex equations involving several
matrix-valued Higgs fields. Here we focus on Yang--Mills theory with gauge
group $\SU{N}/\ZZ_N$ and a special reduction which yields only one non-abelian
Higgs field. One of the new features of this reduction is the fact that while
the instanton number of the theory in four dimensions is generally fractional
with denominator $N$, we still obtain an integral vortex number in the reduced
theory. We clarify the relation between these two topological charges at a
bundle geometric level. Another striking feature is the emergence of
non-trivial lower and upper bounds for the energy of the reduced theory on
$\Sigma$. These bounds are proportional to the area of $\Sigma$. We give
special solutions of the theory on $\Sigma$ by embedding solutions of the
abelian Higgs model into the non-abelian theory, and we relate our work to the
language of quiver bundles, which has recently proved fruitful in the study of
dimensional reduction of Yang--Mills theory. | Energy-momentum tensor for a scalar Casimir apparatus in a weak
gravitational field: Neumann conditions: We consider a Casimir apparatus consisting of two perfectly conducting
parallel plates, subject to the weak gravitational field of the Earth. The aim
of this paper is the calculation of the energy-momentum tensor of this system
for a free, real massless scalar field satisfying Neumann boundary conditions
on the plates. The small gravity acceleration (here considered as not varying
between the two plates) allows us to perform all calculations to first order in
this parameter. Some interesting results are found: a correction, depending on
the gravity acceleration, to the well-known Casimir energy and pressure on the
plates. Moreover, this scheme predicts a tiny force in the upwards direction
acting on the apparatus. These results are supported by two consistency checks:
the covariant conservation of the energy-momentum tensor and the vanishing of
its regularized trace, when the scalar field is conformally coupled to gravity. |
Non-Perturbative JT Gravity: Recently, Saad, Shenker and Stanford showed how to define the genus expansion
of Jackiw-Teitelboim quantum gravity in terms of a double-scaled Hermitian
matrix model. However, the model's non-perturbative sector has fatal
instabilities at low energy that they cured by procedures that render the
physics non-unique. This might not be a desirable property for a system that is
supposed to capture key features of quantum black holes. Presented here is a
model with identical perturbative physics at high energy that instead has a
stable and unambiguous non-perturbative completion of the physics at low
energy. An explicit examination of the full spectral density function shows how
this is achieved. The new model, which is based on complex matrix models, also
allows for the straightforward inclusion of spacetime features analogous to
Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that
connects this non-perturbative formulation of JT gravity to one which, at low
energy, has features of a super JT gravity. | Consistently melting crystals: Recently Ooguri and Yamazaki proposed a statistical model of melting crystals
to count BPS bound states of certain D-brane configurations on toric
Calabi--Yau manifolds [arXiv:0811.2801]. This construction relied on a set of
consistency conditions on the corresponding brane tiling, and in this note I
show that these conditions are satisfied for any physical brane tiling; they
follow from the conformality of the low energy field theory on the D-branes. As
a byproduct I also provide a simple direct proof that any physical brane tiling
has a perfect matching. |
Ultrarelativistic charged and magnetized objects in non-local ghost-free
electrodynamics: We study a non-local ghost-free Lorentz invariant modification of the Maxwell
equations in four- and higher-dimensional flat spacetimes. We construct
solutions of these equations for stationary charged and magnetized objects and
use them to find the field created by such objects moving with the speed of
light. | Large-N_c meson theory: We derive an effective Lagrangian for meson fields. This is done in the
light-cone gauge for two-dimensional large-N_c QCD by using the bilocal
auxiliary field method. The auxiliary fields are bilocal on light-cone space
and their Fourier transformation determines the parton momentum distribution.
As the first test of our method, the 't Hooft equation is derived from the
effective Lagrangian. |
Quantum Uncertainties in the Schmidt Basis Given by Decoherence: A common misconception is that decoherence gives the eigenstates that we
observe to be fairly definite about a subsystem (e.g., approximate eigenstates
of position) as the elements of the Schmidt basis in which the density matrix
of the subsystem is diagonal. Here I show that in simple examples of linear
systems with gaussian states, the Schmidt basis states have as much mean
uncertainty about position as the full density matrix with its combination of
different possibilities. | On the Renormalizability of Horava-Lifshitz-type Gravities: In this note, we discuss the renormalizability of Horava-Lifshitz-type
gravity theories. Using the fact that Horava-Lifshitz gravity is very closely
related to the stochastic quantization of topologically massive gravity, we
show that the renormalizability of HL gravity only depends on the
renormalizability of topologically massive gravity. This is a consequence of
the BRST and time-reversal symmetries pertinent to theories satisfying the
detailed balance condition. |
Black holes may not constrain varying constants: New and rather controversial observations hint that the fine structure
constant \alpha may have been smaller in the early universe, suggesting that
some of the fundamental ``constants'' of physics may be dynamical. In a recent
paper, Davies, Davis, and Lineweaver have argued that black hole thermodynamics
favors theories in which the speed of light c decreases with time, and
disfavors those in which the fundamental electric charge e increases. We show
that when one considers the full thermal environment of a black hole, no such
conclusion can be drawn: thermodynamics is consistent with an increase in
\alpha whether it comes from a decrease in c, an increase in e, or a
combination of the two. | Topological Field Theory and Rational Curves: We analyze the superstring propagating on a Calabi-Yau threefold. This theory
naturally leads to the consideration of Witten's topological non-linear
sigma-model and the structure of rational curves on the Calabi-Yau manifold. We
study in detail the case of the world-sheet of the string being mapped to a
multiple cover of an isolated rational curve and we show that a natural
compactification of the moduli space of such a multiple cover leads to a
formula in agreement with a conjecture by Candelas, de la Ossa, Green and
Parkes. |
D-brane couplings and Generalised Geometry: The goal of this paper is to re-examine D-brane Ramond-Ramond field couplings
in the presence of a B-field. We will argue that the generalised geometry
induced on the world volume by the B-field results in an important but subtle
change on the coupling. In order to explain this, we use the language of
differential K-theory. The expression determining the coupling is then seen to
be a consequence of the Riemann-Roch theorem. Our key assertion is that the
appropriate Riemann-Roch theorem changes in the presence of the B-field. In
particular, the A-hat forms appearing in the theorem are now constructed using
the torsionful Levi-Civita connection associated to the generalised geometry.
As we shall see, the resulting expression not only agrees with recently
discovered local couplings on the D-brane worldvolume involving RR fields and
derivatives of the B-field, but also makes the coupling manifestly T-duality
invariant. | Off-shell M5 Brane, Perturbed Seiberg-Witten Theory, and Metastable
Vacua: We demonstrate that, in an appropriate limit, the off-shell M5-brane
worldvolume action effectively captures the scalar potential of Seiberg-Witten
theory perturbed by a small superpotential and, consequently, any
nonsupersymmetric vacua that it describes. This happens in a similar manner to
the emergence from M5's of the scalar potential describing certain type IIB
flux configurations [arXiv:0705.0983]. We then construct exact nonholomorphic
M5 configurations in the special case of SU(2) Seiberg-Witten theory deformed
by a degree six superpotential which correspond to the recently discovered
metastable vacua of Ooguri, Ookouchi, Park [arXiv:0704.3613], and Pastras
[arXiv:0705.0505]. These solutions take the approximate form of a holomorphic
Seiberg-Witten geometry with harmonic embedding along a transverse direction
and allow us to obtain geometric intuition for local stability of the gauge
theory vacua. As usual, dynamical processes in the gauge theory, such as the
decay of nonsupersymmetric vacua, take on a different character in the M5
description which, due to issues of boundary conditions, typically involves
runaway behavior in MQCD. |
Asymptotic Structure of Higher Dimensional Yang-Mills Theory: Using the covariant phase space formalism, we construct the phase space for
non-Abelian gauge theories in $(d+2)$-dimensional Minkowski spacetime for any
$d \geq 2$, including the edge modes that symplectically pair to the low energy
degrees of freedom of the gauge field. Despite the fact that the symplectic
form in odd and even-dimensional spacetimes appear ostensibly different, we
demonstrate that both cases can be treated in a unified manner by utilizing the
shadow transform. Upon quantization, we recover the algebra of the vacuum
sector of the Hilbert space and derive a Ward identity that implies the leading
soft gluon theorem in $(d+2)$-dimensional spacetime. | The octic E8 invariant: We give an explicit expression for the primitive E8-invariant tensor with
eight symmetric indices. The result is presented in a manifestly
Spin(16)/Z2-covariant notation. |
Quantum entanglement measures from Hyperscaling violating geometries
with finite radial cut off at general d, $θ$ from the emergent global
symmetry: The quantum entanglement measures for $T{\overline{T}}$ deformed field theory
on boundary, deformation coefficient $\mu$, with dual bulk geometry with finite
radial cutoff $\rho_c$, for entangling region is single or disjoint intervals
on the boundary, of length l is expected to give global description of these
measures over the complete parameter-regime of $(l, \mu)$ or on 2D $(l,\rho_c)$
plane, because it is solvable irrelevant deformation. Here, to find
quantum-measures through RT prescription, from Hyperscaling violating bulk
geometry with finite radial cut off, we found mathematically it is impossible,
to obtain such global form, since the turning point $\rho_0 (l,\rho_c)$,
neither in its exact or in any perturbative form, is solvable globally, can
describe these quantum measures at most locally over some specific regime in 2D
$(l,\rho_c)$ plane! However, to find such global form, we found, on application
of RT formalism, a global symmetry structure, from the considered geometry
emerges, over 2D parameter-space, irrespective of d, $\theta$, which alongwith
global b.c and other consistency conditions, fix $\rho_0(l,\rho_c)$ globally,
exactly in $l >> \rho_c $ and $\rho_c >> l$ regime and as some interpolating
expressions, very close to the exact one in other regime. Some of the quantum
entanglement measures with this $\rho_0 (l,\rho_c)$, with our intuitively
predicted behaviour for them in the deformed theory, derived and shown,
behaving accordingly. The impact of this emergent symmetry on these
quantum-measures is discussed, the possible space time origin of this symmetry
is explored, although the later aspect is subjected to a proper and detailed
study. | Novel vortices and the role of complex chemical potential in a rotating
holographic superfluid: In this work, we have analytically devised novel vortex solutions in a
rotating holographic superfluid. To achieve this result, we have considered a
static disc at the AdS boundary and let the superfluid rotate relative to it.
This idea has been numerically exploited in [1] where formation of vortices in
such a setting was reported. We have found that these vortex solutions are
eigenfunctions of angular momentum. We have also shown that vortices with
higher winding numbers are associated with higher quantized rotation of the
superfluid. We have, then, analysed the equation of motion along bulk AdS
direction using St\"urm-Liouville eigenvalue approach. A surprising outcome of
our study is that the chemical potential must be purely imaginary. We have then
observed that the winding number of the vortices decreases with the increase in
the imaginary chemical potential. We conclude from this that imaginary chemical
potential leads to less dissipation in such holographic superfluids. |
Heterotic Strings on Generalized Calabi-Yau Manifolds and Kaehler Moduli
Stabilization: Compactifications of heterotic string theory on Generalized Calabi-Yau
manifolds have been expected to give the same type of flexibility that type IIB
compactifications on Calabi-Yau orientifolds have. In this note we generalize
the work done on half-flat manifolds by other authors, to show how flux
quantization occurs in the general case, by starting with a basis of harmonic
forms and then extending it. However it turns out that only the axions
associated with the non-harmonic directions in the space of Kaehler moduli, can
be stabilized by the geometric (torsion) terms. Also we argue that there are no
supersymmetric extrema of the potential when the second (and fourth) cohomology
groups on the manifold are non-trivial. We suggest that threshold corrections
to the classical gauge coupling function could solve these problems. | Spinning Skyrmions and the Skyrme Parameters: The traditional approach to fixing the parameters of the Skyrme model
requires the energy of a spinning Skyrmion to reproduce the nucleon and delta
masses. The standard Skyrme parameters, which are used almost exclusively, fix
the pion mass to its experimental value and fit the two remaining Skyrme
parameters by approximating the spinning Skyrmion as a rigid body. In this
paper we remove the rigid body approximation and perform numerical calculations
which allow the spinning Skyrmion to deform and break spherical symmetry. The
results show that if the pion mass is set to its experimental value then the
nucleon and delta masses can not be reproduced for any values of the Skyrme
parameters; the commonly used Skyrme parameters are simply an artifact of the
rigid body approximation. However, if the pion mass is taken to be
substantially larger than its experimental value then the nucleon and delta
masses can be reproduced. This result has a significant effect on the structure
of multi-Skyrmions. |
Type IIA Orientifolds on General Supersymmetric Z_N Orbifolds: We construct Type IIA orientifolds for general supersymmetric Z_N orbifolds.
In particular, we provide the methods to deal with the non-factorisable
six-dimensional tori for the cases Z7, Z8, Z8', Z12 and Z12'. As an application
of these methods we explicitly construct many new orientifold models. | Deriving the Simplest Gauge-String Duality -- I: Open-Closed-Open
Triality: We lay out an approach to derive the closed string dual to the simplest
possible gauge theory, a single hermitian matrix integral, in the conventional
't Hooft large $N$ limit. In this first installment of three papers, we propose
and verify an explicit correspondence with a (mirror) pair of closed
topological string theories. On the A-model side, this is a supersymmetric
$SL(2, \mathbb{R})_1/U(1)$ Kazama-Suzuki coset (with background momentum modes
turned on). The mirror B-model description is in terms of a Landau-Ginzburg
theory with superpotential $W(Z)=\frac{1}{Z}+t_2Z$ and its deformations. We
arrive at these duals through an "open-closed-open triality". This is the
notion that two open string descriptions ought to exist for the same closed
string theory depending on how closed strings manifest themselves from open
string modes. Applying this idea to the hermitian matrix model gives an exact
mapping to the Imbimbo-Mukhi matrix model. The latter model is known to capture
the physical correlators of the $c=1$ string theory at self-dual radius, which,
in turn, has the equivalent topological string descriptions given above. This
enables us to establish the equality of correlators, to all genus, between
single trace operators in our original matrix model and those of the dual
closed strings. Finally, we comment on how this simplest of dualities might be
fruitfully viewed in terms of an embedding into the full AdS/CFT
correspondence. |
Hawking Radiation due to Photon and Gravitino Tunneling: Applying the Hamilton--Jacobi method we investigate the tunneling of photon
across the event horizon of a static spherically symmetric black hole. The
necessity of the gauge condition on the photon field, to derive the
semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of
photon and gravitino beyond this semiclassical approximation are presented
separately. Quantum corrections of the action for both cases are found to be
proportional to the semiclassical contribution. Modifications to the Hawking
temperature and Bekenstein-Hawking area law are thereby obtained. Using this
corrected temperature and Hawking's periodicity argument, the modified metric
for the Schwarzschild black hole is given. This corrected version of the
metric, upto $\hbar$ order is equivalent to the metric obtained by including
one loop back reaction effect. Finally, the coefficient of the leading order
correction of entropy is shown to be related to the trace anomaly. | Goldstone Superfield Actions in AdS5 backgrounds: Nonlinear realizations superfield techniques, pertinent to the description of
partial breaking of global N=2 supersymmetry in a flat d=4 super Minkowski
background, are generalized to the case of partially broken N=1 AdS5
supersymmetry SU(2,2|1). We present, in an explicit form, off-shell manifestly
N=1, d=4 supersymmetric minimal Goldstone superfield actions for two patterns
of partial breaking of SU(2,2|1) supersymmetry. They correspond to two
different nonlinear realizations of the latter, in the supercosets with the
AdS5 and AdS5\times S1 bosonic parts. The relevant worldvolume Goldstone
supermultiplets are accommodated, respectively, by improved tensor and chiral
N=1, d=4 superfields. The second action is obtained from the first one by
dualizing the improved tensor Goldstone multiplet into a chiral Goldstone one.
In the bosonic sectors, the first and second actions yield static-gauge
Nambu-Goto actions for a L3-brane on AdS5 and a scalar 3-brane on AdS5\times
S1. |
Geometrically confined thermal field theory: Finite size corrections and
phase transitions: Motivated by the recent shocking results from RHIC and LHC that show
quark-gluon plasma signatures in small systems, we study a simple model of a
massless, noninteracting scalar field confined with Dirichlet boundary
conditions. We use this system to investigate the finite size corrections to
thermal field theoretically derived quantities compared to the usual
Stefan-Boltzmann limit of an ideal gas not confined in any direction. Two
equivalent expressions with different numerical convergence properties are
found for the free energy in $D$ rectilinear spacetime dimensions with $c\le
D-1$ spatial dimensions of finite extent. We find that the First Law of
Thermodynamics generalizes such that the pressure depends on direction but that
the Third Law is respected. For systems with finite dimension(s) but infinite
volumes, such as a field constrained between two parallel plates or a
rectangular tube, the relative fluctuations in energy are zero, and hence the
canonical and microcanonical ensembles are equivalent. We present precise
numerical results for the free energy, total internal energy, pressure,
entropy, and heat capacity of our field between parallel plates, in a tube, and
in finite volume boxes of various sizes in 4 spacetime dimensions. For
temperatures and system sizes relevant for heavy ion phenomenology, we find
large deviations from the Stefan-Boltzmann limit for these quantities,
especially for the pressure. Further investigation of an isolated system of
fields constrained between parallel plates reveals a divergent isoenergetic
compressibility at a critical length $L_c\sim1/T$. We have thus discovered a
new second order phase transition via a first principles calculation, a
transition that is driven by the size of the system. | Gromov-Witten invariants and localization: We give a pedagogical review of the computation of Gromov-Witten invariants
via localization in 2D gauged linear sigma models. We explain the relationship
between the two-sphere partition function of the theory and the Kahler
potential on the conformal manifold. We show how the Kahler potential can be
assembled from classical, perturbative, and non-perturbative contributions, and
explain how the non-perturbative contributions are related to the Gromov-Witten
invariants of the corresponding Calabi-Yau manifold. We then explain how
localization enables efficient calculation of the two-sphere partition function
and, ultimately, the Gromov-Witten invariants themselves. |
Two-dimensional conformal field theories with matrix-valued level: We introduce a new class of two dimensional conformal field theories by
extending Wess-Zumino-Witten (WZW) models to chiral algebras with matrix-valued
levels. The new CFTs are based on holomorphic currents with an operator product
expansion characterized by a positive integer-valued matrix $K_{AB}$. We use
the Sugawara construction to compute the energy-momentum tensor, the central
charge, and the spectrum of conformal dimensions of the CFTs based on this
algebra. We also construct a set of genus-$1$ characters and show that they
fulfil a representation of the modular group $\text{SL}(2,\mathbb{Z})$ up to a
modular anomaly. | Unifying fractons, gravitons and photons from a gauge theoretical
approach: We revisit the first principles gauge theoretical construction of
relativistic gapless fracton theory recently developed by A. Blasi and N.
Maggiore. The difference is that, instead of considering a symmetric tensor
field, we consider a vector field with a gauge group index, (i.e.) the usual
Einstein-Cartan variable used in the first order formalism of gravity. After
discussing the most general quadratic action for this field, we explore the
physical sectors contained in the model. Particularly, we show that the model
contains not only linear gravity and fractons, but also ordinary Maxwell
equations, suggesting an apparent electrically charged phase of, for instance,
spin liquids and glassy dynamical systems. Moreover, by a suitable change of
field variables, we recover the Blasi-Maggiore gauge model of fractons and
linear gravity. |
Exact eigenfunctions and the open topological string: Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to
trace class operators on the real line. The eigenvalues of these operators are
encoded in the BPS invariants of the underlying threefold, but much less is
known about their eigenfunctions. In this paper we first develop methods in
spectral theory to compute these eigenfunctions. We also provide a matrix
integral representation which allows to study them in a 't Hooft limit, where
they are described by standard topological open string amplitudes. Based on
these results, we propose a conjecture for the exact eigenfunctions which
involves both the WKB wavefunction and the standard topological string
wavefunction. This conjecture can be made completely explicit in the maximally
supersymmetric, or self-dual case, which we work out in detail for local P1xP1.
In this case, our conjectural eigenfunctions turn out to be closely related to
Baker-Akhiezer functions on the mirror curve, and they are in full agreement
with first-principle calculations in spectral theory. | On dynamical supergravity interacting with super-p-brane sources: We review recent progress in a fully dynamical Lagrangian description of the
supergravity-superbrane interaction. It suggests that the interacting
superfield action, when it exists, is gauge equivalent to the component action
of dynamical supergravity interacting with the bosonic limit of the superbrane. |
Inequivalent Goldstone Hierarchies for Spontaneously Broken Spacetime
Symmetries: The coset construction is a powerful tool for building theories that
non-linearly realize symmetries. We show that when the symmetry group is not
semisimple and includes spacetime symmetries, different parametrizations of the
coset space can prefer different Goldstones as essential or inessential, due to
the group's Levi decomposition. This leads to inequivalent physics. In
particular, we construct a theory of a scalar and vector Goldstones living in
de Sitter spacetime and non-linearly realizing the Poincar\'e group. Either
Goldstone can be seen as inessential and removed in favor of the other, but the
theory is only healthy when both are kept dynamical. The corresponding coset
space is the same, up to reparametrization, as that of a Minkowski brane
embedded in a Minkowski bulk, but the two theories are inequivalent. | Off-shell amplitudes for nonoriented closed strings: In the context of the bosonic closed string theory, by using the operatorial
formalism, we give a simple expression of the off-shell amplitude with an
arbitrary number of external massless states inserted on the Klein bottle. |
Gamma matrices, Majorana fermions, and discrete symmetries in Minkowski
and Euclidean signature: I describe the interplay between Minkowski and Euclidean signature gamma
matrices, Majorana fermions, and discrete and continuous symmetries in all
spacetime dimensions. | Dirac-Born-Infeld action, Seiberg-Witten map, and Wilson Lines: We write the recently conjectured action for transformation of the ordinary
Born-Infeld action under the Seiberg-Witten map with one open Wilson contour in
a manifestly non-commutative gauge invariant form. This action contains the
non-constant closed string fields, higher order derivatives of the
non-commutative gauge fields through the $*_N$-product, and a Wilson operator.
We extend this non-commutative $D_9$-brane action to the action for $D_p$-brane
by transforming it under T-duality. Using this non-commutative $D_p$-brane
action we then evaluate the linear couplings of the graviton and dilaton to the
brane for arbitrary non-commutative parameters. By taking the Seiberg-Witten
limit we show that they reduce exactly to the known results of the
energy-momentum tensor of the non-commutative super Yang-Mills theory. We take
this as an evidence that the non-commutative action in the Seiberg-Witten limit
includes properly all derivative correction terms. |
A self-tuning mechanism in 6d string theory: This paper has been withdrawn by the authors due to an incorrect analysis. | Holographic Non-local Rotating Observables and their Renormalization: We analyse non-local rotating observables in holography corresponding to
spinning bound states. To renormalize their energies and momenta we suggest and
discuss different holographic renormalization schemes motivated by the static
non-local observables. Namely the holographic renormalization and the rotating
color singlet mass subtraction scheme. In the holographic renormalization we
identify the infinite boundary terms and subtract them. In the mass subtraction
scheme we evaluate the energy of a spinning trailing string corresponding to
the color charged singlet which experiences dragging phenomena and we subtract
it from the energy of the bound state to obtain the renormalized finite energy.
Then we apply our generic framework to certain strongly coupled thermal
theories with broken rotational symmetry. We find numerical solutions
corresponding to spinning bound states with a fixed size while varying their
angular frequency. By applying numerically the renormalization schemes, we find
that there is a critical frequency where the bound state ceases to exist or
dissociates. We also note that bound states require lower angular frequencies
to dissociate when the theory has less symmetry. |
Global gravitational anomaly cancellation for five-branes: We show that the global mixed gauge-gravitational anomaly of the worldvolume
theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken
into account. This result extends to the type IIA and heterotic $E_8 \times
E_8$ five-branes. As a by-product, we provide a definition of the chiral
fermionic fields for generic non-spin M5-brane worldvolume and determine the
coupling between the self-dual field and the M-theory C-field. | The 2+2-Signature and the 1+1-Matrix-Brane: We discuss different aspects of the 2+2-signature from the point of view of
the quatl theory. In particular, we compare two alternative approaches to such
a spacetime signature, namely the 1+1-matrix-brane and the 2+2-target spacetime
of a string. This analysis also reveals hidden discrete symmetries of the
2+2-brane action associated with the 2+2-dimensional sector of a
2+10-dimensional target background. |
Calogero Model(s) and Deformed Oscillators: We briefly review some recent results concerning algebraical (oscillator)
aspects of the $N$-body single-species and multispecies Calogero models in one
dimension. We show how these models emerge from the matrix generalization of
the harmonic oscillator Hamiltonian. We make some comments on the solvability
of these models. | The KZB equations on Riemann surfaces: In this paper, based on the author's lectures at the 1995 les Houches Summer
school, explicit expressions for the Friedan--Shenker connection on the vector
bundle of WZW conformal blocks on the moduli space of curves with tangent
vectors at $n$ marked points are given. The covariant derivatives are expressed
in terms of ``dynamical $r$-matrices'', a notion borrowed from integrable
systems. The case of marked points moving on a fixed Riemann surface is studied
more closely. We prove a universal form of the (projective) flatness of the
connection: the covariant derivatives commute as differential operators with
coefficients in the universal enveloping algebra -- not just when acting on
conformal blocks. |
Exactly Marginal Operators and Running Coupling Constants in 2D Gravity: The Liouville action for two--dimensional quantum gravity coupled to
interacting matter contains terms that have not been considered previously.
They are crucial for understanding the renormalization group flow and can be
observed in recent matrix model results for the phase diagram of the
Sine--Gordon model coupled to gravity. These terms insure, order by order in
the coupling constant, that the dressed interaction is exactly marginal. They
are discussed up to second order. | Marginal Deformations of WZNW and Coset Models from O(d,d)
Transformation: We show that O(2,2) transformation of SU(2) WZNW model gives rise to marginal
deformation of this model by the operator $\int d^2 z J(z)\bar J(\bar z)$ where
$J$, $\bar J$ are U(1) currents in the Cartan subalgebra. Generalization of
this result to other WZNW theories is discussed. We also consider O(3,3)
transformation of the product of an SU(2) WZNW model and a gauged SU(2) WZNW
model. The three parameter set of models obtained after the transformation is
shown to be the result of first deforming the product of two SU(2) WZNW
theories by marginal operators of the form $\sum_{i,j=1}^2 C_{ij} J_i \bar
J_j$, and then gauging an appropriate U(1) subgroup of the theory. Our analysis
leads to a general conjecture that O(d,d) transformation of any WZNW model
corresponds to marginal deformation of the WZNW theory by combination of
appropriate left and right moving currents belonging to the Cartan subalgebra;
and O(d,d) transformation of a gauged WZNW model can be identified to the
gauged version of such marginally deformed WZNW models. |
Holographic Reconstruction of 3D Flat Space-Time: We study asymptotically flat space-times in 3 dimensions for Einstein gravity
near future null infinity and show that the boundary is described by Carrollian
geometry. This is used to add sources to the BMS gauge corresponding to a
non-trivial boundary metric in the sense of Carrollian geometry. We then solve
the Einstein equations in a derivative expansion and derive a general set of
equations that take the form of Ward identities. Next, it is shown that there
is a well-posed variational problem at future null infinity without the need to
add any boundary term. By varying the on-shell action with respect to the
metric data of the boundary Carrollian geometry we are able to define a
boundary energy-momentum tensor at future null infinity. We show that its
diffeomorphism Ward identity is compatible with Einstein's equations. There is
another Ward identity that states that the energy flux vanishes. It is this
fact that is responsible for the enhancement of global symmetries to the full
BMS$_3$ algebra when we are dealing with constant boundary sources. Using a
notion of generalized conformal boundary Killing vector we can construct all
conserved BMS$_3$ currents from the boundary energy-momentum tensor. | Dynamical supersymmetry breaking from unoriented D-brane instantons: We study the non-perturbative dynamics of an unoriented Z_5-quiver theory of
GUT kind with gauge group U(5) and chiral matter. At strong coupling the
non-perturbative dynamics is described in terms of set of baryon/meson
variables satisfying a quantum deformed constraint. We compute the effective
superpotential of the theory and show that it admits a line of supersymmetric
vacua and a phase where supersymmetry is dynamically broken via gaugino
condensation. |
Friedel oscillations and horizon charge in 1D holographic liquids: In many-body fermionic systems at finite density correlation functions of the
density operator exhibit Friedel oscillations at a wavevector that is twice the
Fermi momentum. We demonstrate the existence of such Friedel oscillations in a
3d gravity dual to a compressible finite-density state in a (1+1) dimensional
field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and
all the charge is behind a bulk horizon. The bulk gauge theory is compact and
so there exist magnetic monopole tunneling events. We compute the effect of
these monopoles on holographic density-density correlation functions and
demonstrate that they cause Friedel oscillations at a wavevector that directly
counts the charge behind the bulk horizon. If the magnetic monopoles are taken
to saturate the bulk Dirac quantization condition then the observed Fermi
momentum exactly agrees with that predicted by Luttinger's theorem, suggesting
some Fermi surface structure associated with the charged horizon. The mechanism
is generic and will apply to any charged horizon in three dimensions. Along the
way we clarify some aspects of the holographic interpretation of Maxwell
electromagnetism in three bulk dimensions and show that perturbations about the
charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature. | Gravitational Interaction of Higher Spin Massive Fields and String
Theory: We discuss the problem of consistent description of higher spin massive
fields coupled to external gravity. As an example we consider massive field of
spin 2 in arbitrary gravitational field. Consistency requires the theory to
have the same number of degrees of freedom as in flat spacetime and to describe
causal propagation. By careful analysis of lagrangian structure of the theory
and its constraints we show that there exist at least two possibilities of
achieving consistency. The first possibility is provided by a lagrangian on
specific manifolds such as static or Einstein spacetimes. The second
possibility is realized in arbitrary curved spacetime by a lagrangian
representing an infinite series in curvature. In the framework of string theory
we derive equations of motion for background massive spin 2 field coupled to
gravity from the requirement of quantum Weyl invariance. These equations appear
to be a particular case of the general consistent equations obtained from the
field theory point of view. |
The classical origin of quantum affine algebra in squashed sigma models: We consider a quantum affine algebra realized in two-dimensional non-linear
sigma models with target space three-dimensional squashed sphere. Its affine
generators are explicitly constructed and the Poisson brackets are computed.
The defining relations of quantum affine algebra in the sense of the Drinfeld
first realization are satisfied at classical level. The relation to the
Drinfeld second realization is also discussed including higher conserved
charges. Finally we comment on a semiclassical limit of quantum affine algebra
at quantum level. | Exact solution of higher-derivative conformal theory and minimal models: I investigate the two-dimensional four-derivative conformal theory that
emerges from the Nambu-Goto string after the path-integration over all fields
but the metric tensor. Using the method of singular products which accounts for
tremendous cancellations in perturbation theory, I show the (intelligent)
one-loop approximation to give an exact solution. It is conveniently described
through the minimal models where the central charge $c$ in the Kac spectrum
depends on the parameters of the four-derivative action. The relation is
nonlinear so the domain of physical parameters is mapped onto $c<1$ thus
bypassing the KPZ barrier of the Liouville action. |
Supersymmetric Wilson loops in two dimensions and duality: We classify bosonic $\mathcal{N}=(2,2)$ supersymmetric Wilson loops on
arbitrary backgrounds with vector-like R-symmetry. These can be defined on any
smooth contour and come in two forms which are universal across all
backgrounds. We show that these Wilson loops, thanks to their cohomological
properties, are all invariant under smooth deformations of their contour. At
genus zero they can always be mapped to local operators and computed exactly
with supersymmetric localisation. Finally, we find the precise map, under
two-dimensional Seiberg-like dualities, of correlators of supersymmetric Wilson
loops. | Bethe Ansatz solutions for highest states in ${\cal N}=4$ SYM and
AdS/CFT duality: We consider the operators with highest anomalous dimension $\Delta$ in the
compact rank-one sectors $\mathfrak{su}(1|1)$ and $\mathfrak{su}(2)$ of ${\cal
N}=4$ super Yang-Mills. We study the flow of $\Delta$ from weak to strong 't
Hooft coupling $\lambda$ by solving (i) the all-loop gauge Bethe Ansatz, (ii)
the quantum string Bethe Ansatz. The two calculations are carefully compared in
the strong coupling limit and exhibit different exponents $\nu$ in the leading
order expansion $\Delta\sim \lambda^{\nu}$. We find $\nu = 1/2$ and $\nu = 1/4$
for the gauge or string solution. This strong coupling discrepancy is not
unexpected, and it provides an explicit example where the gauge Bethe Ansatz
solution cannot be trusted at large $\lambda$. Instead, the string solution
perfectly reproduces the Gubser-Klebanov-Polyakov law $\Delta = 2\sqrt{n}
\lambda^{1/4}$. In particular, we provide an analytic expression for the
integer level $n$ as a function of the U(1) charge in both sectors. |
Quantum hair and the string-black hole correspondence: We consider a thought experiment in which an energetic massless string probes
a "stringhole" (a heavy string lying on the correspondence curve between
strings and black holes) at large enough impact parameter for the regime to be
under theoretical control. The corresponding, explicitly unitary, $S$-matrix
turns out to be perturbatively sensitive to the microstate of the stringhole:
in particular, at leading order in $l_s/b$, it depends on a projection of the
stringhole's Lorentz-contracted quadrupole moment. The string-black hole
correspondence is therefore violated if one assumes quantum hair to be
exponentially suppressed as a function of black-hole entropy. Implications for
the information paradox are briefly discussed. | Detecting quantum chaos via pseudo-entropy and negativity: Quantum informatic quantities such as entanglement entropy are useful in
detecting quantum phase transitions. Recently, a new entanglement measure
called pseudo-entropy was proposed which is a generalization of the more
well-known entanglement entropy. It has many nice properties and is useful in
the study of post-selection measurements. In this paper, one of our goals is to
explore the properties of pseudo-entropy and study the effectiveness of it as a
quantum chaos diagnostic, i.e. as a tool to distinguish between chaotic and
integrable systems. Using various variants of the SYK model, we study the
signal of quantum chaos captured in the pseudo-entropy and relate it to the
spectral form factor (SFF) and local operator entanglement (LOE). We also
explore another quantity called the negativity of entanglement which is a
useful entanglement measure for a mixed state. We generalized it to accommodate
the transition matrix and called it pseudo-negativity in analogy to
pseudo-entropy. We found that it also nicely captures the spectral properties
of a chaotic system and hence also plays a role as a tool of quantum chaos
diagnostic. |
Cubic interactions of massless bosonic fields in three dimensions: Parity-even cubic vertices of massless bosons of arbitrary spins in three
dimensional Minkowski space are classified in the metric-like formulation. As
opposed to higher dimensions, there is at most one vertex for any given triple
$s_1,s_2,s_3$ in three dimensions. All the vertices with more than three
derivatives are of the type $(s,0,0)$, $(s,1,1)$ and $(s,1,0)$ involving scalar
and/or Maxwell fields. All other vertices contain two (three) derivatives, when
the sum of the spins is even (odd). Minimal coupling to gravity, $(s,s,2)$, has
two derivatives and is universal for all spins (equivalence principle holds).
Minimal coupling to Maxwell field, $(s,s,1)$, distinguishes spins $s\leq 1$ and
$s\geq 2$ as it involves one derivative in the former case and three
derivatives in the latter case. Some consequences of this classification are
discussed. | Quantum field theory on quantum graphs and application to their
conductance: We construct a bosonic quantum field on a general quantum graph. Consistency
of the construction leads to the calculation of the total scattering matrix of
the graph. This matrix is equivalent to the one already proposed using
generalized star product approach. We give several examples and show how they
generalize some of the scattering matrices computed in the mathematical or
condensed matter physics litterature.
Then, we apply the construction for the calculation of the conductance of
graphs, within a small distance approximation. The consistency of the
approximation is proved by direct comparison with the exact calculation for the
`tadpole' graph. |
Entanglement entropy and vacuum states in Schwarzschild geometry: Recently, it was proposed that there must be either large violation of the
additivity conjecture or a set of disentangled states of the black hole in the
AdS/CFT correspondence. In this paper, we study the additivity conjecture for
quantum states of fields around the Schwarzschild black hole. In the eternal
Schwarzschild spacetime, the entanglement entropy of the Hawking radiation is
calculated assuming that the vacuum state is the Hartle-Hawking vacuum. In the
additivity conjecture, we need to consider the state which gives minimal output
entropy of a quantum channel. The Hartle-Hawking vacuum state does not give the
minimal output entropy which is consistent with the additivity conjecture. We
study the entanglement entropy in other static vacua and show that it is
consistent with the additivity conjecture. | Hierarchies of RG flows in 6d $(1,0)$ massive E-strings: We extend the analysis of arXiv:2208.11703 to the 6d $(1,0)$ SCFTs known as
massive E-string theories, which can be engineered in massive Type IIA with
$8-n_0<8$ D8-branes close to an O8$^-$ (or O8$^*$ if $n_0=8,9$). For each
choice of $n_0=1,\ldots,9$ the massive $E_{1+(8-n_0)}$-strings (including the
more exotic $\tilde{E}_1$ and $E_0$) are classified by constrained $E_8$ Kac
labels, i.e. a subset of $\text{Hom}(\mathbb{Z}_k,E_8)$, from which one can
read off the flavor subalgebra of $E_{1+(8-n_0)}$ of each SCFT. We construct
hierarchies for two types of Higgs branch RG flows: flows between massive
theories defined by the same $n_0$ but different labels; flows between massive
theories with different $n_0$. These latter flows are triggered by T-brane
vev's for the right $\mathrm{SU}$ factor of the SCFT global symmetry, whose
rank is a function of both $k$ and $n_0$, a situation which has so far remained
vastly unexplored. |
Semiclassical framed BPS states: We provide a semiclassical description of framed BPS states in
four-dimensional N = 2 super Yang-Mills theories probed by 't Hooft defects, in
terms of a supersymmetric quantum mechanics on the moduli space of singular
monopoles. Framed BPS states, like their ordinary counterparts in the theory
without defects, are associated with the L^2 kernel of certain Dirac operators
on moduli space, or equivalently with the L^2 cohomology of related Dolbeault
operators. The Dirac/Dolbeault operators depend on two Cartan-valued Higgs
vevs. We conjecture a map between these vevs and the Seiberg-Witten special
coordinates, consistent with a one-loop analysis and checked in examples. The
map incorporates all perturbative and nonperturbative corrections that are
relevant for the semiclassical construction of BPS states, over a suitably
defined weak coupling regime of the Coulomb branch. We use this map to
translate wall crossing formulae and the no-exotics theorem to statements about
the Dirac/Dolbeault operators. The no-exotics theorem, concerning the absence
of nontrivial SU(2)_R representations in the BPS spectrum, implies that the
kernel of the Dirac operator is chiral, and further translates into a statement
that all L^2 cohomology of the Dolbeault operator is concentrated in the middle
degree. Wall crossing formulae lead to detailed predictions for where the Dirac
operators fail to be Fredholm and how their kernels jump. We explore these
predictions in nontrivial examples. This paper explains the background and
arguments behind the results announced in a short accompanying note. | Charged scalar quasi-normal modes for linearly charged dilaton-Lifshitz
solutions: Most available studies of quasi-normal modes for Lifshitz black solutions are
limited to the neutral scalar perturbations. In this paper, we investigate the
wave dynamics of massive charged scalar perturbation in the background of
$(3+1)$-dimensional charged dilaton Lifshitz black branes/holes. We disclose
the dependence of the quasi-normal modes on the model parameters, such as the
Lifshitz exponent $z$, the mass and charge of the scalar perturbation field and
the charge of the Lifshitz configuration. In contrast with neutral
perturbations, we observe the possibility to destroy the original Lifshitz
background near the extreme value of charge where the temperature is low. We
find out that when the Lifshitz exponent deviates more from unity, it is more
difficult to break the stability of the configuration. We also study the
behavior of the real part of the quasi-normal frequencies. Unlike the neutral
scalar perturbation around uncharged black branes where an overdamping was
observed to start at $z=2$ and independent of the value of scalar mass, our
observation discloses that the overdamping starting point is no longer at $z=2$
and depends on the mass of scalar field for charged Lifshitz black branes. For
charged scalar perturbations, fixing $m_s$, the asymptotic value of $\omega_R$
for high $z$ is more away from zero when the charge of scalar perturbation
$q_s$ increases. There does not appear the overdamping. |
Modular flow in JT gravity and entanglement wedge reconstruction: It has been shown in recent works that JT gravity with matter with two
boundaries has a type II$_\infty$ algebra on each side. As the bulk spacetime
between the two boundaries fluctuates in quantum nature, we can only define the
entanglement wedge for each side in a pure algebraic sense. As we take the
semiclassical limit, we will have a fixed long wormhole spacetime for a generic
partially entangled thermal state (PETS), which is prepared by inserting heavy
operators on the Euclidean path integral. Under this limit, with appropriate
assumptions of the matter theory, geometric notions of the causal wedge and
entanglement wedge emerge in this background. In particular, the causal wedge
is manifestly nested in the entanglement wedge. Different PETS are orthogonal
to each other, and thus the Hilbert space has a direct sum structure over
sub-Hilbert spaces labeled by different Euclidean geometries. The full algebra
for both sides is decomposed accordingly. From the algebra viewpoint, the
causal wedge is dual to an emergent type III$_1$ subalgebra, which is generated
by boundary light operators. To reconstruct the entanglement wedge, we consider
the modular flow in a generic PETS for each boundary. We show that the modular
flow acts locally and is the boost transformation around the global RT surface
in the semiclassical limit. It follows that we can extend the causal wedge
algebra to a larger type III$_1$ algebra corresponding to the entanglement
wedge. Within each sub-Hilbert space, the original type II$_\infty$ reduces to
type III$_1$. | Quantum Description of Anyons: Role of Contact Terms: We make an all-order analysis to establish the precise correspondence between
nonrelativistic Chern-Simons quantum field theory and an appropriate
first-quantized description. Physical role of the field-theoretic contact term
in the context of renormalized perturbation theory is clarifed through their
connection to self-adjoint extension of the Hamiltonian in the first-quantized
approach. Our analysis provides a firm theoretical foundation on quantum field
theories of nonrelativistic anyons. |
A Family of M-theory Flows with Four Supersymmetries: We use the techniques of "algebraic Killing spinors" to obtain a family of
holographic flow solutions with four supersymmetries in M-theory. The family of
supersymmetric backgrounds constructed here includes the non-trivial flow to
the (2+1)-dimensional analog of the Leigh-Strassler fixed point as well as
generalizations that involve the M2-branes spreading in a radially symmetric
fashion on the Coulomb branch of this non-trivial fixed point theory. In
spreading out, these M2-branes also appear to undergo dielectric polarization
into M5-branes. Our results naturally extend the earlier applications of the
"algebraic Killing spinor" method and also generalize the harmonic Ansatz in
that our entire family of new supersymmetric backgrounds is characterized by
the solutions of a single, second-order, non-linear PDE. We also show that our
solution is a natural hybrid of special holonomy and the "dielectric
deformation" of the canonical supersymmetry projector on the M2-branes. | Construction Formulae for Singular Vectors of the Topological N=2
Superconformal Algebra: The Topological N=2 Superconformal algebra has 29 different types of singular
vectors (in complete Verma modules) distinguished by the relative U(1) charge
and the BRST-invariance properties of the vector and of the primary on which it
is built. Whereas one of these types only exists at level zero, the remaining
28 types exist for general levels and can be constructed already at level 1. In
this paper we write down one-to-one mappings between 16 of these types of
topological singular vectors and the singular vectors of the Antiperiodic NS
algebra. As a result one obtains construction formulae for these 16 types of
topological singular vectors using the construction formulae for the NS
singular vectors due to Doerrzapf. |
D3/D7 Branes at Singularities: Constraints from Global Embedding and
Moduli Stabilisation: In the framework of type IIB string compactifications on Calabi-Yau
orientifolds we describe how to construct consistent global embeddings of
models with fractional D3-branes and connected `flavour' D7-branes at del Pezzo
singularities with moduli stabilisation. Our results are applied to build an
explicit compact example with a left-right symmetric model at a dP_0
singularity which features three families of chiral matter and gauge coupling
unification at the intermediate scale. We show how to stabilise the moduli
obtaining a controlled de Sitter minimum and spontaneous supersymmetry
breaking. We find an interesting non-trivial dynamical relation between the
requirement of TeV-scale soft terms and the correct phenomenological values of
the unified gauge coupling and unification scale. | Localization of a supersymmetric gauge theory in the presence of a
surface defect: We use supersymmetric localization to compute the partition function of N=2
super-Yang-Mills on S^4 in the presence of a gauged linear sigma model surface
defect on a S^2 subspace. The result takes the form of a standard partition
function on S^4, with a modified instanton partition function and an additional
insertion corresponding to a shifted version of the gauged linear sigma model
partition function. |
Entanglement Degradation in the presence of $(4+n)$-dimensional
Schwarzschild Black Hole: In this short paper we compute the various bipartite quantum correlations in
the presence of the $(4+n)$-dimensional Schwarzschild black hole. In
particular, we focus on the $n$-dependence of various bosonic bipartite
entanglements. For the case between Alice and Rob, where the former is free
falling observer and the latter is at the near-horizon region, the quantum
correlation is degraded compared to the case in the absence of the black hole.
The degradation rate increases with decreasing $n$. We also compute the
physically inaccessible correlations. It is found that there is no creation of
quantum correlation between Alice and AntiRob. For the case between Rob and
AntiRob the quantum entanglement is created although they are separated in the
causally disconnected regions. It is found that contrary to the physically
accessible correlation the entanglement between Rob and AntiRob decreases with
decreasing $n$. | Kappa-deformed Dirac oscillator in an external magnetic field: We study the solutions of the (2+1)-dimensional kappa-deformed Dirac
oscillator in the presence of a constant transverse magnetic field. We
demonstrate how the deformation parameter affects the energy eigenvalues of the
system and the corresponding eigenfunctions. Our findings suggest that this
system could be used to detect experimentally the effect of the deformation. We
also show that the hidden supersymmetry of the non-deformed system reduces to a
hidden pseudo-supersymmetry having the same algebraic structure as a result of
the k-deformation. |
On the robustness of solitons crystals in the Skyrme model: In this work we analize how the inclusion of extra mesonic degrees of freedom
affect the finite density solitons crystals of the Skyrme model. In particular,
the first analytic examples of hadronic crystals at finite baryon density in
both the Skyrme $\omega$-mesons model as well as for the Skyrme $\rho$-mesons
theory are constructed. These configurations have arbitrary topological charge
and describe crystals of baryonic tubes surrounded by a cloud of vector-mesons.
In the $\omega$-mesons case, it is possible to reduce consistently the complete
set of seven coupled non-linear field equations to just two integrable
differential equations; one ODE for the Skyrmion profile and one PDE for the
$\omega$-mesons field. This analytical construction allows to show explicitly
how the inclusion of $\omega$-mesons in the Skyrme model reduces the repulsive
interaction energy between baryons. In the Skyrme $\rho$-mesons case, it is
possible to construct analytical solutions using a meron-type ansatz and fixing
one of the couplings of the $\rho$-mesons action in terms of the others. We
show that, quite remarkably, the values obtained for the coupling constants by
requiring the consistency of our ansatz are very close to the values used in
the literature to reduce nuclei binding energies of the Skyrme model without
vector-mesons. Moreover, our analytical results are in qualitative agreement
with the available results on the nuclear spaghetti phase. | On a $\mathbb{Z}_2^n$-Graded Version of Supersymmetry: We extend the notion of super-Minkowski space-time to include
$\mathbb{Z}_2^n$-graded (Majorana) spinor coordinates. Our choice of the
grading leads to spinor coordinates that are nilpotent but commute amongst
themselves. The mathematical framework we employ is the recently developed
category of $\mathbb{Z}_2^n$-manifolds understood as locally ringed spaces. The
formalism we present resembles $\mathcal{N}$-extended superspace (in the
presence of central charges), but with some subtle differences due to the
exotic nature of the grading employed. |
Breaking GUT Groups in F-Theory: We consider the possibility of breaking the GUT group to the Standard Model
gauge group in F-theory compactifications by turning on certain U(1) fluxes. We
show that the requirement of massless hypercharge is equivalent to a
topological constraint on the UV completion of the local model. The possibility
of this mechanism is intrinsic to F-theory. We address some of the
phenomenological signatures of this scenario. We show that our models predict
monopoles as in conventional GUT models. We discuss in detail the leading
threshold corrections to the gauge kinetic terms and their effect on
unification. They turn out to be related to Ray-Singer torsion. We also discuss
the issue of proton decay in F-theory models and explain how to engineer models
which satisfy current experimental bounds. | Tachyonic Instability and Darboux Transformation: Using Darboux transformation one can construct infinite family of potentials
which lead to the flat spectrum of scalar field fluctuations with arbitrary
multiple precision, and, at the same time, with "essentially blue" spectrum of
perturbations of metric. Besides, we describe reconstruction problem: find
classical potential V(phi) starting from the known "one-loop potential" u(t) =
d^2V(phi(t))/d phi(t)^2. |
Scalar field quasinormal modes on asymptotically locally flat rotating
black holes in three dimensions: The pure quadratic term of New Massive Gravity in three dimensions admits
asymptotically locally flat, rotating black holes. These black holes are
characterized by their mass and angular momentum, as well as by a hair of
gravitational origin. As in the Myers-Perry solution in dimensions greater than
five, there is no upper bound on the angular momentum. We show that,
remarkably, the equation for a massless scalar field on this background can be
solved in an analytic manner and that the quasinormal frequencies can be found
in a closed form. The spectrum is obtained requiring ingoing boundary
conditions at the horizon and an asymptotic behavior at spatial infinity that
provides a well-defined action principle for the scalar probe. As the angular
momentum of the black hole approaches zero, the imaginary part of the
quasinormal frequencies tends to minus infinity, migrating to the north pole of
the Riemann Sphere and providing infinitely damped modes of high frequency. We
show that this is consistent with the fact that the static black hole within
this family does not admit quasinormal modes for a massless scalar probe. | Thermodynamics of hairy black holes in Lovelock gravity: We perform a thorough study of the thermodynamic properties of a class of
Lovelock black holes with conformal scalar hair arising from coupling of a real
scalar field to the dimensionally extended Euler densities. We study the
linearized equations of motion of the theory and describe constraints under
which the theory is free from ghosts/tachyons. We then consider, within the
context of black hole chemistry, the thermodynamics of the hairy black holes in
the Gauss-Bonnet and cubic Lovelock theories. We clarify the connection between
isolated critical points and thermodynamic singularities, finding a one
parameter family of these critical points which occur for well-defined
thermodynamic parameters. We also report on a number of novel results,
including `virtual triple points' and the first example of a
`$\lambda$-line'---a line of second order phase transitions---in black hole
thermodynamics. |
General Form of Dilaton Gravity and Nonlinear Gauge Theory: We construct a gauge theory based on general nonlinear Lie algebras. The
generic form of `dilaton' gravity is derived from nonlinear Poincar{\' e}
algebra, which exhibits a gauge-theoretical origin of the non-geometric scalar
field in two-dimensional gravitation theory. | Fermions from Half-BPS Supergravity: We discuss collective coordinate quantization of the half-BPS geometries of
Lin, Lunin and Maldacena (hep-th/0409174). The LLM geometries are parameterized
by a single function $u$ on a plane. We treat this function as a collective
coordinate. We arrive at the collective coordinate action as well as path
integral measure by considering D3 branes in an arbitrary LLM geometry. The
resulting functional integral is shown, using known methods (hep-th/9309028),
to be the classical limit of a functional integral for free fermions in a
harmonic oscillator. The function $u$ gets identified with the classical limit
of the Wigner phase space distribution of the fermion theory which satisfies u
* u = u. The calculation shows how configuration space of supergravity becomes
a phase space (hence noncommutative) in the half-BPS sector. Our method sheds
new light on counting supersymmetric configurations in supergravity. |
On 6d N=(2,0) theory compactified on a Riemann surface with finite area: We study 6d N=(2,0) theory of type SU(N) compactified on Riemann surfaces
with finite area, including spheres with fewer than three punctures. The Higgs
branch, whose metric is inversely proportional to the total area of the Riemann
surface, is discussed in detail. We show that the zero-area limit, which gives
us a genuine 4d theory, can involve a Wigner-Inonu contraction of global
symmetries of the six-dimensional theory. We show how this explains why
subgroups of SU(N) can appear as the gauge group in the 4d limit. As a
by-product we suggest that half-BPS codimension-two defects in the
six-dimensional (2,0) theory have an operator product expansion whose operator
product coefficients are four-dimensional field theories. | W Symmetry and Integrability of Higher spin black holes: We obtain the asymptotic symmetry algebra of sl(3,R) x sl(3,R) Chern-Simons
theory with Dirichlet boundary conditions for fixed chemical potential. These
boundary conditions are obeyed by higher spin black holes. For each embedding
of sl(2,R) into sl(3,R), we show that the asymptotic symmetry group is
independent of the chemical potential. On the one hand, starting from AdS3 in
the principal embedding, we show that the W3 x W3 symmetry is preserved upon
turning on perturbatively spin 3 chemical potentials. On the other hand,
starting from AdS3 in the diagonal embedding, we show that the W3^(2) x W3^(2)
symmetry is preserved upon turning on finite spin 3/2 chemical potentials. We
also make connections between the canonical Lagrangian formalism and
integrability methods based on the third KdV (Boussinesq) hierarchy. |
Fluctuations, correlations and finite volume effects in heavy ion
collision: Finite volume corrections to higher moments are important observable
quantities. They make possible to differentiate between different statistical
ensembles even in the thermodynamic limit. It is shown that this property is a
universal one. The classical grand canonical distribution is compared to the
canonical distribution in the rigorous procedure of approaching the
thermodynamic limit. | On the two-loop divergences of the 2-point hypermultiplet supergraphs
for $6D$, ${\cal N} = (1,1)$ SYM theory: We consider $6D$, ${\cal N}=(1,1)$ supersymmetric Yang-Mills theory
formulated in ${\cal N}=(1,0)$ harmonic superspace and analyze the structure of
the two-loop divergences in the hypermultiplet sector. Using the ${\cal
N}=(1,0)$ superfield background field method we study the two-point supergraphs
with the hypermultiplet legs and prove that their total contribution to the
divergent part of effective action vanishes off shell. |
Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact
S-Matrices: Integrable deformation of SU(2) sigma and lambda models are considered at the
classical and quantum levels. These are the Yang-Baxter and XXZ-type
anisotropic deformations. The XXZ type deformations are UV safe in one regime,
while in another regime, like the Yang-Baxter deformations, they exhibit cyclic
RG behaviour. The associated affine quantum group symmetry, realized
classically at the Poisson bracket level, has q a complex phase in the UV safe
regime and q real in the cyclic RG regime, where q is an RG invariant. Based on
the symmetries and RG flow we propose exact factorizable S-matrices to describe
the scattering of states in the lambda models, from which the sigma models
follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes,
the S-matrices are periodic functions of rapidity, at large rapidity, and in
the Yang-Baxter case violate parity. | Z_2-Graded Cocycles in Higher Dimensions: Current superalgebras and corresponding Schwinger terms in 1 and 3 space
dimensions are studied. This is done by generalizing the quantization of chiral
fermions in an external Yang-Mills potential to the case of a Z_2-graded
potential coupled to bosons and fermions. |
E-Strings and N=4 Topological Yang-Mills Theories: We study certain properties of six-dimensional tensionless E-strings (arising
from zero size $E_8$ instantons). In particular we show that $n$ E-strings form
a bound string which carries an $E_8$ level $n$ current algebra as well as a
left-over conformal system with $c=12n-4-{248n \over n+30}$, whose characters
can be computed. Moreover we show that the characters of the $n$-string bound
state are captured by N=4 U(n) topological Yang-Mills theory on $\half K3$.
This relation not only illuminates certain aspects of E-strings but can also be
used to shed light on the properties of N=4 topological Yang-Mills theories on
manifolds with $b_2^+=1$. In particular the E-string partition functions, which
can be computed using local mirror symmetry on a Calabi-Yau three-fold, give
the Euler characteristics of the Yang-Mills instanton moduli space on $\half
K3$. Moreover, the partition functions are determined by a gap condition
combined with a simple recurrence relation which has its origins in a
holomorphic anomaly that has been conjectured to exist for N=4 topological
Yang-Mills on manifolds with $b_2^+=1$ and is also related to the holomorphic
anomaly for higher genus topological strings on Calabi-Yau threefolds. | Amplification of Vacuum Fluctuations in String Cosmology Backgrounds: Inflationary string cosmology backgrounds can amplify perturbations in a more
efficient way than conventional inflationary backgrounds, because the
perturbation amplitude may grow - instead of being constant - outside the
horizon. If not gauged away, the growing mode can limit the range of validity
of a linearized description of perturbations. Even in the restricted linear
range, however, this enhanced amplification may lead to phenomenological
consequences unexpected in the context of the standard inflationary scenario.
In particular, the production of a relic graviton background strong enough to
be detected in future by LIGO, and/or the generation of a stochastic
electromagnetic background strong enough to seed the cosmic magnetic fields and
to be responsible for the observed large scale anisotropy. |
Manifestly Finite Perturbation Theory for the Short-Distance Expansion
of Correlation Functions in the Two Dimensional Ising Model: In the spirit of classic works of Wilson on the renormalization group and
operator product expansion, a new framework for the study of the theory space
of euclidean quantum field theories has been introduced. This formalism is
particularly useful for elucidating the structure of the short-distance
expansions of the $n$-point functions of a renormalizable quantum field theory
near a non-trivial fixed point. We review and apply this formalism in the study
of the scaling limit of the two dimensional massive Ising model.
Renormalization group analysis and operator product expansions determine all
the non-analytic mass dependence of the short-distance expansion of the
correlation functions. An extension of the first order variational formula to
higher orders provides a manifestly finite scheme for the perturbative
calculation of the operator product coefficients to any order in parameters. A
perturbative expansion of the correlation functions follows. We implement this
scheme for a systematic study of correlation functions involving two spin
operators. We show how the necessary non-trivial integrals can be calculated.
As two concrete examples we explicitly calculate the short-distance expansion
of the spin-spin correlation function to third order and the spin-spin-energy
density correlation function to first order in the mass. We also discuss the
applicability of our results to perturbations near other non-trivial fixed
points corresponding to other unitary minimal models. | The Compatibility between the Higher Dimensions Self Duality and the
Yang-Mills Equation of Motion: We study the compatiblity between the higher dimension dualities and the
Yang-Mills equation of motion. Taking a 't Hooft solution as a starting point,
we come to the conclusion that for only 4 dimensions the self duality implies
the equation of motion for generic instanton size. Whereas in higher
dimensions, the self duality is compatable with the equation of motion,
approximately, for small instanton size i.e. the zero curvature condition. At
the mathematical level, the self duality is still useful since it transforms a
second order into a first order differential equation. |
Multibrane Solutions in Open String Field Theory: We study properties of a class of solutions of open string field theory which
depend on a single holomorphic function F(z). We show that the energy of these
solutions is well defined and is given by integer multiples of a single D-brane
tension. Potential anomalies are discussed in detail. Some of them can be
avoided by imposing suitable regularity conditions on F(z), while the anomaly
in the equation of motion seems to require an introduction of the so called
phantom term. | A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on
$S^4$: We consider a non-supersymmetric domain-wall version of $\mathcal{N} = 4$ SYM
theory where five out of the six scalar fields have non-zero classical values
on one side of a wall of codimension one. The classical fields have commutators
which constitute an irreducible representation of the Lie algebra
$\mathfrak{so}(5)$ leading to a highly non-trivial mixing between color and
flavor components of the quantum fields. Making use of fuzzy spherical
harmonics on $S^4$, we explicitly solve the mixing problem and derive not only
the spectrum of excitations at the quantum level but also the propagators of
the original fields needed for perturbative quantum computations. As an
application, we derive the one-loop one-point function of a chiral primary and
find complete agreement with a supergravity prediction of the same quantity in
a double-scaling limit which involves a limit of large instanton number in the
dual D3-D7 probe-brane setup. |
Classical self-energy and anomaly: We study the problem of self-energy of pointlike charges in higher
dimensional static spacetimes. Their energy, as a functional of the spacetime
metric, is invariant under a specific continuous transformation of the metric.
We show that the procedure of regularization of this formally divergent
functional breaks this symmetry and results in an anomalous contribution to the
finite renormalized self-energy. We proposed a method of calculation of this
anomaly and presented an explicit expressions for it in the case of a scalar
charge in four and five-dimensional static spacetimes. This anomalous
correction proves to be zero in even dimensions, but it does not vanish in
odd-dimensional spacetimes. | Black Hole Time Scales: Thermalization, Infall and Complexity: We argue that the infall time to the singularity in the interior of a black
hole, is always related to a classical thermalization time. This indicates that
singularities are related to the equilibration of infalling objects with the
microstates of the black hole, but only in the sense of classical
equilibration. When the singularity is reached, the quantum state of the black
hole, initially a tensor product of the state of the infalling object and that
of the black hole, is not yet a "generic" state in the enlarged Hilbert space,
so its complexity is not maximal. We relate these observations to the
phenomenon of mirages in the membrane paradigm description of the black hole
horizon and to the shrinking of the area of causal diamonds inside the black
hole. The observations are universal and we argue that they give a clue to the
nature of the underlying quantum theory of black holes in all types of
asymptotic space-times. |
Aspects of Type 0 String Theory: A construction of compact tachyon-free orientifolds of the non-supersymmetric
Type 0B string theory is presented. Moreover, we study effective
non-supersymmetric gauge theories arising on self-dual D3-branes in Type 0B
orbifolds and orientifolds. | Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical
system: In this article we provide three new twist-deformed Newtonian
Schwarzschild-(Anti-)de Sitter models. They are defined on the
Lie-algebraically as well as on the canonically noncommutative space-times
respectively. Particularly we find the corresponding Hamiltonian functions and
the proper equations of motion. The relations between the models are discussed
as well. |
Higgs mechanism in a light front formulation: We give a simple derivation of the Higgs mechanism in an abelian light front
field theory. It is based on a finite volume quantization with antiperiodic
scalar fields and a periodic gauge field. An infinite set of degenerate vacua
in the form of coherent states of the scalar field that minimize the light
front energy, is constructed. The corresponding effective Hamiltonian descibes
a massive vector field whose third component is generated by the would-be
Goldstone boson. This mechanism, understood here quantum mechanically in the
form analogous to the space-like quantization, is derived without gauge fixing
as well as in the unitary and the light cone gauge. | The double copy: Bremsstrahlung and accelerating black holes: Advances in our understanding of perturbation theory suggest the existence of
a correspondence between classical general relativity and Yang-Mills theory. A
concrete example of this correspondence, which is known as the double copy, was
recently introduced for the case of stationary Kerr-Schild spacetimes. Building
on this foundation, we examine the simple time-dependent case of an
accelerating, radiating point source. The gravitational solution, which
generalises the Schwarzschild solution, includes a non-trivial stress-energy
tensor. This stress-energy tensor corresponds to a gauge theoretic current in
the double copy. We interpret both of these sources as representing the
radiative part of the field. Furthermore, in the simple example of
Bremsstrahlung, we determine a scattering amplitude describing the radiation,
maintaining the double copy throughout. Our results provide the strongest
evidence yet that the classical double copy is directly related to the BCJ
double copy for scattering amplitudes. |
Kibble-Zurek Scaling in Holographic Quantum Quench : Backreaction: We study gauge and gravity backreaction in a holographic model of quantum
quench across a superfluid critical transition. The model involves a complex
scalar field coupled to a gauge and gravity field in the bulk. In earlier work
(arXiv:1211.1776) the scalar field had a strong self-coupling, in which case
the backreaction on both the metric and the gauge field can be ignored. In this
approximation, it was shown that when a time dependent source for the order
parameter drives the system across the critical point at a rate slow compared
to the initial gap, the dynamics in the critical region is dominated by a zero
mode of the bulk scalar, leading to a Kibble-Zurek type scaling function. We
show that this mechanism for emergence of scaling behavior continues to hold
without any self-coupling in the presence of backreaction of gauge field and
gravity. Even though there are no zero modes for the metric and the gauge
field, the scalar dynamics induces adiabaticity breakdown leading to scaling.
This yields scaling behavior for the time dependence of the charge density and
energy momentum tensor. | Open String Creation by S-Branes: An sp-brane can be viewed as the creation and decay of an unstable
D(p+1)-brane. It is argued that the decaying half of an sp-brane can be
described by a variant of boundary Liouville theory. The pair creation of open
strings by a decaying s-brane is studied in the minisuperspace approximation to
the Liouville theory. In this approximation a Hagedorn-like divergence is found
in the pair creation rate, suggesting the s-brane energy is rapidly transferred
into closed string radiation. |
Recurrent Nightmares?: Measurement Theory in de Sitter Space: The idea that asymptotic de Sitter space can be described by a finite Hilbert
Space implies that any quantum measurement has an irreducible innacuracy. We
argue that this prevents any measurement from verifying the existence of the
Poincare recurrences that occur in the mathematical formulation of quantum de
Sitter (dS) space. It also implies that the mathematical quantum theory of dS
space is not unique. There will be many different Hamiltonians, which give the
same results, within the uncertainty in all possible measurements. | Multi-Superthreads and Supersheets: We obtain new BPS solutions of six-dimensional, N = 1 supergravity coupled to
a tensor multiplet. These solutions are sourced by multiple "superthreads"
carrying D1-D5-P charges and two magnetic dipole charges. These new solutions
are sourced by multiple threads with independent and arbitrary shapes and
include new shape-shape interaction terms. Because the individual superthreads
can be given independent profiles, the new solutions can be smeared together
into continuous "supersheets," described by arbitrary functions of two
variables. The supersheet solutions have singularities like those of the
three-charge, two dipole-charge generalized supertube in five dimensions and we
show how such five-dimensional solutions emerge from a very simple choice of
profiles. The new solutions obtained here also represent an important step in
finding superstrata, which are expected to play a role in the description of
black-hole microstates, due to their ability to store a large amount of entropy
in their two-dimensional profile. |
The finite-temperature chiral transition in QCD with adjoint fermions: We study the nature of the finite-temperature chiral transition in QCD with
N_f light quarks in the adjoint representation (aQCD). Renormalization-group
arguments show that the transition can be continuous if a stable fixed point
exists in the renormalization-group flow of the corresponding three-dimensional
Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and
symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by
exploiting two three-dimensional perturbative approaches, the massless
minimal-subtraction scheme without epsilon expansion and a massive scheme in
which correlation functions are renormalized at zero momentum. We compute the
renormalization-group functions in the two schemes to five and six loops
respectively, and determine their large-order behavior.
The analyses of the series show the presence of a stable three-dimensional
fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This
fixed point does not appear in an epsilon-expansion analysis and therefore does
not exist close to four dimensions. The finite-temperature chiral transition in
two-flavor aQCD can therefore be continuous; in this case its critical behavior
is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may
show a more complex phase diagram with two phase transitions. One of them, if
continuous, should belong to the O(3) vector universality class. | Island in Charged Black Holes: We study the information paradox for the eternal black hole with charges on a
doubly-holographic model in general dimensions, where the charged black hole on
a Planck brane is coupled to the baths on the conformal boundaries. In the case
of weak tension, the brane can be treated as a probe such that its backreaction
to the bulk is negligible. We analytically calculate the entanglement entropy
of the radiation and obtain the Page curve with the presence of an island on
the brane. For the near-extremal black holes, the growth rate is linear in the
temperature. Taking both Dvali-Gabadadze-Porrati term and nonzero tension into
account, we obtain the numerical solution with backreaction in four-dimensional
spacetime and find the quantum extremal surface at $t=0$. To guarantee that a
Page curve can be obtained in general cases, we propose two strategies to
impose enough degrees of freedom on the brane such that the black hole
information paradox can be properly described by the doubly-holographic setup. |
No Firewalls in Holographic Space-Time or Matrix Theory: We use the formalisms of Holographic Space-time (HST) and Matrix Theory[11]
to investigate the claim of [1] that old black holes contain a firewall, i.e.
an in-falling detector encounters highly excited states at a time much shorter
than the light crossing time of the Schwarzschild radius. In both formalisms
there is no dramatic change in particle physics inside the horizon until a time
of order the Schwarzschild radius. The Matrix Theory formalism has been shown
to give rise to an S-matrix, which coincides with effective supergravity for an
infinite number of low energy amplitudes. We conclude that the firewall results
from an inappropriate use of quantum effective field theory to describe fine
details of localized events near a black hole horizon. In both HST and Matrix
Theory, the real quantum gravity Hilbert space in a localized region contains
many low energy degrees of freedom that are not captured in QU(antum)
E(ffective) F(ield) T(heory) and omits many of the high energy DOF in QUEFT. | Perturbative quantum gauge fields on the noncommutative torus: Using standard field theoretical techniques, we survey pure Yang-Mills theory
on the noncommutative torus, including Feynman rules and BRS symmetry. Although
in general free of any infrared singularity, the theory is ultraviolet
divergent. Because of an invariant regularization scheme, this theory turns out
to be renormalizable and the detailed computation of the one loop counterterms
is given, leading to an asymptoticaly free theory. Besides, it turns out that
non planar diagrams are overall convergent when $\theta$ is irrational. |
Kahler quantization of H*(T2,R) and modular forms: Kahler quantization of H1(T2,R) is studied. It is shown that this theory
corresponds to a fermionic sigma-model targeting a noncommutative space. By
solving the complex-structure moduli independence conditions, the quantum
background independent wave function is obtained. We study the transformation
of the wave function under modular transformation. It is shown that the
transformation rule is characteristic to the operator ordering. Similar results
are obtained for Kahler quantization of H2(T,R). | Soliton pair creation in classical wave scattering: We study classical production of soliton-antisoliton pairs from colliding
wave packets in (1+1)-dimensional scalar field model. Wave packets represent
multiparticle states in quantum theory; we characterize them by energy E and
particle number N. Sampling stochastically over the forms of wave packets, we
find the entire region in (E,N) plane which corresponds to classical creation
of soliton pairs. Particle number is parametrically large within this region
meaning that the probability of soliton-antisoliton pair production in
few-particle collisions is exponentially suppressed. |
Softly Broken N=2 QCD with Massive Quark Hypermultiplets, II: We analyze the vacuum structure of N=2, SU(2) QCD with massive quark
hypermultiplets, once supersymmetry is softly broken down to N=0 with dilaton
and mass spurions. We give general expressions for the low energy couplings of
the effective potential in terms of elliptic functions to have a complete
numerical control of the model. We study in detail the possible phases of the
theories with Nf = 1, 2 flavors for different values of the bare quark masses
and the supersymmetry breaking parameters and we find a rich structure of first
order phase transitions. The chiral symmetry breaking pattern of the Nf = 2
theory is considered, and we obtain the pion Lagrangian for this model up to
two derivatives. Exact expressions are given for the pion masses and the pion
decay constant in terms of the magnetic monopole description of chiral symmetry
breaking. | The Large N Limit of ${\cal N} =2,1 $ Field Theories from Threebranes in
F-theory: We consider field theories arising from a large number of D3-branes near
singularities in F-theory. We study the theories at various conformal points,
and compute, using their conjectured string theory duals, their large $N$
spectrum of chiral primary operators. This includes, as expected, operators of
fractional conformal dimensions for the theory at Argyres-Douglas points.
Additional operators, which are charged under the (sometimes exceptional)
global symmetries of these theories, come from the 7-branes. In the case of a
$D_4$ singularity we compare our results with field theory and find agreement
for large $N$. Finally, we consider deformations away from the conformal
points, which involve finding new supergravity solutions for the geometry
produced by the 3-branes in the 7-brane background. We also discuss 3-branes in
a general background. |
Nonlocal and quasi-local field theories: We investigate nonlocal field theories, a subject that has attracted some
renewed interest in connection with nonlocal gravity models. We study, in
particular, scalar theories of interacting delocalized fields, the
delocalization being specified by nonlocal integral kernels. We distinguish
between strictly nonlocal and quasi-local (compact support) kernels and impose
conditions on them to insure UV finiteness and unitarity of amplitudes. We
study the classical initial value problem for the partial integro-differential
equations of motion in detail. We give rigorous proofs of the existence but
accompanying loss of uniqueness of solutions due to the presence of future, as
well as past, "delays," a manifestation of acausality. In the quantum theory we
derive a generalization of the Bogoliubov causality condition equation for
amplitudes, which explicitly exhibits the corrections due to nonlocality. One
finds that, remarkably, for quasi-local kernels all acausal effects are
confined within the compact support regions. We briefly discuss the extension
to other types of fields and prospects of such theories. | Seiberg-Witten map for the 4D noncommutative BF theory: We describe the Seiberg-Witten map for the 4D noncommutative BF theory
(NCBF). We establish the existence of a map taking the abelian NCBF into its
commutative version, in agreement with the hypothesis that such maps are
available for any noncommutative theory with Schwarz type topological sectors. |
The massless string spectrum on AdS_3 x S^3 from the supergroup: String theory on AdS_3 x S^3 is studied in the hybrid formulation. We give a
detailed description of the PSL(2|2) supergroup WZW model that underlies the
background with pure NS-NS flux, and determine the BRST-cohomology
corresponding to the massless string states. The resulting spectrum is shown to
match exactly with the expected supergravity answer, including the sectors with
small KK momentum on the sphere. | Cosmological perturbations in $F(R)$ gravity: The quasi-static solutions of the matter density perturbation in $F(R)$
gravity models have been investigated in numerous papers. However, the
oscillating solutions in $F(R)$ gravity models have not been investigated
enough so far. In this paper, the oscillating solutions are also examined by
using appropriate approximations. And the behaviors of the matter density
perturbation in F(R) gravity models with singular evolutions of the physical
parameters are shortly investigated as applications of the approximated
calculations. |
Characters and relations among SW(3/2,2) algebras: The SW(3/2,2) current algebras come in two discrete series indexed by central
charge, with the chiral algebra of a supersymmetric sigma model on a Spin}(7)
manifold as a special case. The unitary representations of these algebras were
classified by Gepner and Noyvert, and we use their results to perform an
analysis of null descendants and compute the characters for every
representation. We obtain threshold relations between the characters of
discrete representations and those with continuous conformal weights. Modular
transformations are discussed, and we show that the continuous characters can
be written as bilinear combinations of characters for consecutive minimal
models. | The determinant representation for quantum correlation functions of the
sinh-Gordon model: We consider the quantum sinh-Gordon model in this paper. Using known formulae
for form factors we sum up all their contributions and obtain a closed
expression for a correlation function. This expression is a determinant of an
integral operator. Similar determinant representations were proven to be useful
not only in the theory of correlation functions, but also in the matrix models. |
Semi-classical spectrum of the Homogeneous sine-Gordon theories: The semi-classical spectrum of the Homogeneous sine-Gordon theories
associated with an arbitrary compact simple Lie group G is obtained and shown
to be entirely given by solitons. These theories describe quantum integrable
massive perturbations of Gepner's G-parafermions whose classical
equations-of-motion are non-abelian affine Toda equations. One-soliton
solutions are constructed by embeddings of the SU(2) complex sine-Gordon
soliton in the regular SU(2) subgroups of G. The resulting spectrum exhibits
both stable and unstable particles, which is a peculiar feature shared with the
spectrum of monopoles and dyons in N=2 and N=4 supersymmetric gauge theories. | Can a wormhole be interpreted as an EPR pair?: Recently, Maldacena and Susskind arXiv:1306.0533 and Jensen and Karch
arXiv:1307.1132 argued that a wormhole can be interpreted as an EPR pair. We
point out that a convincing justification of such an interpretation would
require a quantitative evidence that correlations between two ends of the
wormhole are equal to those between the members of the EPR pair. As long as the
existing results do not contain such evidence, the interpretation of wormhole
as an EPR pair does not seem justified. |
Integrability of the Gauged Linear Sigma Model for AdS_5xS^5: Recently, a gauged linear sigma model was proposed by Berkovits and Vafa
which can be used to describe the AdS_5xS^5 superstring at finite and zero
radius. In this paper we show that the model is classically integrable by
constructing its first non-local conserved charge and a superspace Lax
"quartet". Quantum conservation of the non-local charge follows easily from
superspace rules. | Entanglement Entropy from TFD Entropy Operator: In this work, a canonical method to compute entanglement entropy is proposed.
We show that for two-dimensional conformal theories defined in a torus, a
choice of moduli space allows the typical entropy operator of the TFD to
provide the entanglement entropy of the degrees of freedom defined in a segment
and their complement. In this procedure, it is not necessary to make an
analytic continuation from the R\'enyi entropy and the von Neumann entanglement
entropy is calculated directly from the expected value of an entanglement
entropy operator. We also propose a model for the evolution of the entanglement
entropy and show that it grows linearly with time. |
The geodesic rule for higher codimensional global defects: We generalize the geodesic rule to the case of formation of higher
codimensional global defects. Relying on energetic arguments, we argue that,
for such defects, the geometric structures of interest are the totally geodesic
submanifolds. On the other hand, stochastic arguments lead to a diffusion
equation approach, from which the geodesic rule is deduced. It turns out that
the most appropriate geometric structure that one should consider is the convex
hull of the values of the order parameter on the causal volumes whose collision
gives rise to the defect. We explain why these two approaches lead to similar
results when calculating the density of global defects by using a theorem of
Cheeger and Gromoll. We present a computation of the probability of formation
of strings/vortices in the case of a system, such as nematic liquid crystals,
whose vacuum is $\mathbb{R}P^2$. | Solutions to the Massive HLW IIA Supergravity: We find new supersymmetric solutions of the massive supergravity theory which
can be constructed by generalized Scherk-Schwarz dimensional reduction of
eleven dimensional supergravity, using the scaling symmetry of the equations of
motion. Firstly, we construct field configurations which solve the ten
dimensional equations of motion by reducing on the radial direction of
Ricci-flat cones. Secondly, we will extend this result to the supersymmetric
case by performing a dimensional reduction along the flow of a homothetic
Killing vector which is the Euler vector of the cone plus a boost. |
General classical solutions in the noncommutative CP^(N-1) model: We give an explicit construction of general classical solutions for the
noncommutative CP^(N-1) model in two dimensions, showing that they correspond
to integer values for the action and topological charge. We also give explicit
solutions for the Dirac equation in the background of these general solutions
and show that the index theorem is satisfied. | Entropy Balance Equation of Spacetime Thermodynamics in f(R) Gravity: We study spacetime thermodynamics for non-equilibrium processes. We first
generalize the formulation of spacetime thermodynamics by using an observer
outside the horizon. Then we construct the entropy balance equation of
spacetime thermodynamics for non-equilibrium processes in f(R) gravity. The
coefficients of the expansion and shear terms are equal to the viscosities of
the black hole membrane paradigm, and a new entropy production term appears. |
Half-BPS Solutions locally asymptotic to AdS_3 x S^3 and interface
conformal field theories: Type IIB superstring theory has AdS_3 x S^3 x M_4 (where the manifold M_4 is
either K_3 or T^4) solutions which preserve sixteen supersymmetries. In this
paper we consider half-BPS solutions which are locally asymptotic to AdS_3 x
S^3 x M_4 and preserve eight of the sixteen supersymmetries. We reduce the BPS
equations and the Bianchi identity for the self-dual five-form field to a set
of four differential equations. The complete local solution can be
parameterized in terms of two harmonic and two holomorphic functions and all
bosonic fields have explicit expressions in terms of these functions.
We analyze the conditions for global regularity and construct new half-BPS
Janus-solutions which have two asymptotic AdS_3 regions. In addition, our
analysis proves the global regularity of a class of solutions with more than
two asymptotic AdS_3 regions. Finally, we discuss the dual interpretation as a
supersymmetric interface theory for the half-BPS Janus solutions carrying only
Ramond-Ramond three-form charge. | General Solution of the non-abelian Gauss law and non-abelian analogs of
the Hodge decomposition: General solution of the non-abelian Gauss law in terms of covariant curls and
gradients is presented. Also two non-abelian analogs of the Hodge decomposition
in three dimensions are addressed. i) Decomposition of an isotriplet vector
field $V_{i}^{a}(x)$ as sum of covariant curl and gradient with respect to an
arbitrary background Yang-Mills potential is obtained. ii) A decomposition of
the form $V_{i}^{a}=B_{i}^{a}(C)+D_{i}(C) \phi^{a} $ which involves non-abelian
magnetic field of a new Yang-Mills potential C is also presented. These results
are relevant for duality transformation for non-abelian gauge fields. |
Donaldson-Witten theory and indefinite theta functions: We consider partition functions with insertions of surface operators of
topologically twisted N=2, SU(2) supersymmetric Yang-Mills theory, or
Donaldson-Witten theory for short, on a four-manifold. If the metric of the
compact four-manifold has positive scalar curvature, Moore and Witten have
shown that the partition function is completely determined by the integral over
the Coulomb branch parameter $a$, while more generally the Coulomb branch
integral captures the wall-crossing behavior of both Donaldson polynomials and
Seiberg-Witten invariants. We show that after addition of a Q-exact surface
operator to the Moore-Witten integrand, the integrand can be written as a total
derivative to the anti-holomorphic coordinate $\bar a$ using Zwegers'
indefinite theta functions. In this way, we reproduce G\"ottsche's expressions
for Donaldson invariants of rational surfaces in terms of indefinite theta
functions for any choice of metric. | A note on large gauge transformations in double field theory: We give a detailed proof of the conjecture by Hohm and Zwiebach in double
field theory. This result implies that their proposal for large gauge
transformations in terms of the Jacobian matrix for coordinate transformations
is, as required, equivalent to the standard exponential map associated with the
generalized Lie derivative along a suitable parameter. |
Casimir and Vacuum Energy of 5D Warped System and Sphere Lattice
Regularization: We examine the Casimir energy of 5D electro-magnetism in the recent
standpoint. Z$_2$ symmetry is taken into account. After confirming the
consistency with the past result, we do new things based on a new
regularization. The regularization is based on the minimal area principle and
the regularized configuration is the {\it sphere lattice}. We do it not in the
Kaluza-Klein expanded form but in the closed form. The formalism is based on
the heat-kernel approach using the position/momentum propagator. A useful
expression of the Casimir energy, in terms of the P/M propagator, is obtained.
Renormalization flow is realized as the change along the extra-axis. | Non-perturbative corrections in N=2 strings: We investigate the non-perturbative equivalence of some heterotic/type IIA
dual pairs with N=2 supersymmetry. We compute R2-like corrections, both on the
type IIA and on the heterotic side. The coincidence of their perturbative part
provides a test of duality. The type IIA result is then used to predict the
full, non-perturbative correction to the heterotic effective action. We
determine the instanton numbers and the Olive-Montonen duality groups. |
D=7 selfdual string in the 5-brane: Unlike the Schwarzschild black string in the Randall-Sundrum scenario which
is known to have the geodesics reaching the AdS-horizon terminating there, the
D=7 extremal BPS selfdual string of N=2 gauged supergravity potentially differs
from this result. I give a complete proof that timelike radial trajectories of
the selfdual string solution that escapes to r=\infty do not see a curvature
singularity on the horizon at z=\infty. | Canonical quantisation of thermal gauge theories: Canonical quantisation gives a new and convenient finite-temperature
perturbation theory in covariant gauges, and solves the problem of the
zero-frequency mode in the temporal gauge. [Talk at Workshop on Thermal Field
Theories and their Applications, Banff, August 1993] |
Off-shell hydrodynamics from holography: We outline a program for obtaining an action principle for dissipative fluid
dynamics by considering the holographic Wilsonian renormalization group applied
to systems with a gravity dual. As a first step, in this paper we restrict to
systems with a non-dissipative horizon. By integrating out gapped degrees of
freedom in the bulk gravitational system between an asymptotic boundary and a
horizon, we are led to a formulation of hydrodynamics where the dynamical
variables are not standard velocity and temperature fields, but the relative
embedding of the boundary and horizon hypersurfaces. At zeroth order, this
action reduces to that proposed by Dubovsky et al. as an off-shell formulation
of ideal fluid dynamics. | Holographic Stripes: We construct inhomogeneous asymptotically AdS black hole solutions
corresponding to the spontaneous breaking of translational invariance and the
formation of striped order in the boundary field theory. We find that the
system undergoes a second order phase transition in both the fixed density and
fixed chemical potential ensembles, for sufficiently large values of the axion
coupling. We investigate the phase structure as function of the temperature,
axion coupling and the stripe width. The bulk solutions have striking
geometrical features related to a magnetoelectric effect associated with the
existence of a near horizon topological insulator. At low temperatures the
horizon becomes highly inhomogeneous and tends to pinch off.} |
Quaternionic Electroweak Theory and CKM Matrix: We find in our quaternionic version of the electroweak theory an apparently
hopeless problem: In going from complex to quaternions, the calculation of the
real-valued parameters of the CKM matrix drastically changes. We aim to explain
this quaternionic puzzle. | Lorentz Invariant Renormalization in Causal Perturbation Theory: In the framework of causal perturbation theory renormalization consists of
the extension of distributions. We give the explicit form of a Lorentz
invariant extension of a scalar distribution, depending on one difference of
space time coordinates. |
Algebraic geometry informs perturbative quantum field theory: Single-scale Feynman diagrams yield integrals that are periods, namely
projective integrals of rational functions of Schwinger parameters. Algebraic
geometry may therefore inform us of the types of number to which these
integrals evaluate. We give examples at 3, 4 and 6 loops of massive Feynman
diagrams that evaluate to Dirichlet $L$-series of modular forms and examples at
6, 7 and 8 loops of counterterms that evaluate to multiple zeta values or
polylogarithms of the sixth root of unity. At 8 loops and beyond, algebraic
geometry informs us that polylogs are insufficient for the evaluation of terms
in the beta-function of $\phi^4$ theory. Here, modular forms appear as
obstructions to polylogarithmic evaluation. | Higgs-Chern-Simons gravity models in 2n+1 dimensions: We consider a family of new Higgs-Chern-Simons (HCS) gravity models in 2n+1
dimensions (n=1,2,3). This provides a generalization of the (usual)
gravitational Chern-Simons (CS) gravitaties resulting from non- Abelian CS
densities in all odd dimensions, which feature vector and scalar fields in
addition to the metric. The derivation of the new HCS gravitational (HCSG)
actions follows the same method as in the usual-CSG case resulting from the
usual CS densities. The HCSG result from the HCS densities, which result
through a one-step descent of the Higgs-Chern-Pontryagin (HCP), the latter
being descended from Chern-Pontryagin (CP) densities in some even dimension. A
preliminary study of the solutions of these models is considered, with exact
solutions being reported for spacetime dimensions d = 3, 5. |
3D Gravity, Point Particles and Liouville Theory: This paper elaborates on the bulk/boundary relation between negative
cosmological constant 3D gravity and Liouville field theory (LFT). We develop
an interpretation of LFT non-normalizable states in terms of particles moving
in the bulk. This interpretation is suggested by the fact that ``heavy'' vertex
operators of LFT create conical singularities and thus should correspond to
point particles moving inside AdS. We confirm this expectation by comparing the
(semi-classical approximation to the) LFT two-point function with the
(appropriately regularized) gravity action evaluated on the corresponding
metric. | Conifolds and Tunneling in the String Landscape: We investigate flux vacua on a variety of one-parameter Calabi-Yau
compactifications, and find many examples that are connected through continuous
monodromy transformations. For these, we undertake a detailed analysis of the
tunneling dynamics and find that tunneling trajectories typically graze the
conifold point---particular 3-cycles are forced to contract during such vacuum
transitions. Physically, these transitions arise from the competing effects of
minimizing the energy for brane nucleation (facilitating a change in flux),
versus the energy cost associated with dynamical changes in the periods of
certain Calabi-Yau 3-cycles. We find that tunneling only occurs when warping
due to back-reaction from the flux through the shrinking cycle is properly
taken into account. |
A model of persistent breaking of discrete symmetry: We show there exist UV-complete field-theoretic models in general dimension,
including $2+1$, with the spontaneous breaking of a global symmetry, which
persists to the arbitrarily high temperatures. Our example is a conformal
vector model with the $O(N)\times \mathbb{Z}_2$ symmetry at zero temperature.
Using conformal perturbation theory we establish $\mathbb{Z}_2$ symmetry is
broken at finite temperature for $N>10$. Similar to recent constructions, in
the infinite $N$ limit our model has a non-trivial conformal manifold, a moduli
space of vacua, which gets deformed at finite temperature. Furthermore, in this
regime the model admits a persistent breaking of $O(N)$ in $2+1$ dimensions,
therefore providing another example where the Coleman-Hohenberg-Mermin-Wagner
theorem can be bypassed. | A Classical String in Lifshitz-Vaidya Geometry: We study the time evolution of the expectation value of a rectangular Wilson
loop in strongly anisotropic time-dependent plasma using gauge-gravity duality.
The corresponding gravity theory is given by describing time evolution of a
classical string in the Lifshitz-Vaidya background. We show that the
expectation value of the Wilson loop oscillates about the value of the static
potential with the same parameters after the energy injection is over. We
discuss how the amplitude and frequency of the oscillation depend on the
parameters of the theory. In particular, by raising the anisotropy parameter,
we observe that the amplitude and frequency of the oscillation increase. |
Black Holes Coupled to a Massive Dilaton: We investigate charged black holes coupled to a massive dilaton. It is shown
that black holes which are large compared to the Compton wavelength of the
dilaton resemble the Reissner-Nordstr\"om solution, while those which are
smaller than this scale resemble the massless dilaton solutions. Black holes of
order the Compton wavelength of the dilaton can have wormholes outside the
event horizon in the string metric. Unlike all previous black hole solutions,
nearly extremal and extremal black holes (of any size) repel each other. We
argue that extremal black holes are quantum mechanically unstable to decay into
several widely separated black holes. We present analytic arguments and
extensive numerical results to support these conclusions. | Coupling M2-branes to background fields: We discuss some of the issues arising in trying to extend the ABJM action to
include couplings to background fields. This is analogous to the
Myers-Chern-Simons terms of the multiple Dp-brane action. We review and extend
previous results to include terms which are quadratic in the background fields.
These are fixed by requiring that we recover the correct Myers-type terms upon
using the novel Higgs mechanism to reduce to the multiple D2-brane action. |
Light-Cone Quantisation of Matrix Models at c>1: The technique of (discretised) light-cone quantisation, as applied to matrix
models of relativistic strings, is reviewed. The case of the c=2 non-critical
bosonic string is discussed in some detail to clarify the nature of the
continuum limit. Futher applications for the technique are then outlined. (To
appear in proceedings of the NATO Advanced Workshop on Recent Developments in
Strings, Conformal Models, and Topological Field Theory, Cargese 12-21 May
1993.) | Perturbative Couplings and Modular Forms in N=2 String Models with a
Wilson Line: We consider a class of four parameter D=4, N=2 string models, namely
heterotic strings compactified on K3 times T2 together with their dual type II
partners on Calabi-Yau three-folds. With the help of generalized modular forms
(such as Siegel and Jacobi forms), we compute the perturbative prepotential and
the perturbative Wilsonian gravitational coupling F1 for each of the models in
this class. We check heterotic/type II duality for one of the models by
relating the modular forms in the heterotic description to the known instanton
numbers in the type II description. We comment on the relation of our results
to recent proposals for closely related models. |
On S-duality in (2+1)-Chern-Simons Supergravity: Strong/weak coupling duality in Chern-Simons supergravity is studied. It is
argued that this duality can be regarded as an example of superduality. The use
of supergroup techniques for the description of Chern-Simons supergravity
greatly facilitates the analysis. | Renormalization properties of a Galilean Wess-Zumino model: We consider a Galilean N=2 supersymmetric theory in 2+1 dimensions with
F-term couplings, obtained by null reduction of a relativistic Wess-Zumino
model. We compute quantum corrections and we check that, as for the
relativistic parent theory, the F-term does not receive quantum corrections.
Even more, we find evidence that the causal structure of the non-relativistic
dynamics together with particle number conservation constrain the theory to be
one-loop exact. |
Unravelling T-Duality: Magnetic Quivers in Rank-zero Little String
Theories: An intriguing class of 6d supersymmetric theories are known as little strings
theories, which exhibit a rich network of T-dualities. A robust feature of
these theories are their Higgs branches. Focusing on the little string theories
that are realised on a single curve of zero self-intersection, we utilise brane
systems to derive the magnetic quivers. Using a variety of techniques
(including branching rules, brane dynamics, F-theory geometry, quiver
subtraction, and the decay and fission algorithm), we detail the Higgs branch
Hasse diagram and determine the transverse slices for every elementary Higgs
branch RG-flow. Building on these insights, we pursue two directions: firstly,
we used the established connection between the change of the 2-Group structure
constants along Higgs branch RG-flows and the transition-type in the Hasse
diagram to infer putative T-dual models. Secondly, we conjecture an algorithm
that predicts the non-Abelian flavour symmetry of the compactified little
string theory by inspecting the magnetic quivers of all T-dual frames. | The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory: We consider different large ${\cal N}$ limits of the one-dimensional
Chern-Simons action $i\int dt~ \Tr (\del_0 +A_0)$ where $A_0$ is an ${\cal
N}\times{\cal N}$ antihermitian matrix. The Hilbert space on which $A_0$ acts
as a linear transformation is taken as the quantization of a $2k$-dimensional
phase space ${\cal M}$ with different gauge field backgrounds. For slowly
varying fields, the large ${\cal N}$ limit of the one-dimensional CS action is
equal to the $(2k+1)$-dimensional CS theory on ${\cal M}\times {\bf R}$.
Different large ${\cal N}$ limits are parametrized by the gauge fields and the
dimension $2k$. The result is related to the bulk action for quantum Hall
droplets in higher dimensions. Since the isometries of ${\cal M}$ are gauged,
this has implications for gravity on fuzzy spaces. This is also briefly
discussed. |
Correlators of supersymmetric Wilson-loops, protected operators and
matrix models in N=4 SYM: We study the correlators of a recently discovered family of BPS Wilson loops
in ${\cal N}=4$ supersymmetric U(N) Yang-Mills theory. When the contours lie on
a two-sphere in the space-time, we propose a closed expression that is valid
for all values of the coupling constant $g$ and for any rank $N$, by exploiting
the suspected relation with two-dimensional gauge theories. We check this
formula perturbatively at order ${\cal O}(g^4)$ for two latitude Wilson loops
and we show that, in the limit where one of the loops shrinks to a point,
logarithmic corrections in the shrinking radius are absent at ${\cal O}(g^6)$.
This last result strongly supports the validity of our general expression and
suggests the existence of a peculiar protected local operator arising in the
OPE of the Wilson loop. At strong coupling we compare our result to the string
dual of the ${\cal N}=4$ SYM correlator in the limit of large separation,
presenting some preliminary evidence for the agreement. | Two-dimensional SCFTs from D3-branes: We find a large class of two-dimensional $\mathcal{N}=(0,2)$ SCFTs obtained
by compactifying four-dimensional $\mathcal{N}=1$ quiver gauge theories on a
Riemann surface. We study these theories using anomalies and $c$-extremization.
The gravitational duals to these fixed points are new AdS$_3$ solutions of IIB
supergravity which we exhibit explicitly. Along the way we uncover a universal
relation between the conformal anomaly coefficients of four-dimensional and
two-dimensional SCFTs connected by an RG flow across dimensions. We also
observe an interesting novel phenomenon in which the superconformal R-symmetry
mixes with baryonic symmetries along the RG flow. |
Is Alice burning or fuzzing?: Recently, Almheiri, Marolf, Polchinski and Sully (AMPS) have suggested a
Gedankenexperiment to test black hole complementarity. They claim that the
postulates of black hole complementarity are mutually inconsistent and choose
to give up the "absence of drama" for an infalling observer. According to them
the black hole is shielded by a firewall no later than Page time. This has
generated some controversy. We find that an interesting picture emerges when we
take into account objections from the advocates of fuzzballs. We reformulate
AMPS' Gedankenexperiment in the decoherence picture of quantum mechanics and
find that low energy wave packets interact with the radiation quanta rather
violently while high energy wave packets do not. This is consistent with
Mathur's recent proposal of fuzzball complementarity for high energy quanta
falling into fuzzballs. | Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$
dualities: Inspired by the gauge/YBE correspondence this paper derives some
star-triangle type relations from dualities in $2d$ $\mathcal{N}=(0,2)$
$USp(2N)$ supersymmetric quiver gauge theories. To be precise, we study two
cases. The first case is the Intriligator-Pouliot duality in $2d$
$\mathcal{N}=(0,2)$ $USp(2N)$ theories. The description is performed explicitly
for $N=1,2,3,4,5$ and also for $N=3k+2$, which generalizes the situation in
$N=2,5$. For $N=1$ a triangle identity is obtained. For $N=2,5$ it is found
that the realization of duality implies slight variations of a star-triangle
relation type (STR type). The values $N=3,4$ are associated to a similar
version of the asymmetric STR. The second case is a new duality for $2d$
$\mathcal{N}=(0,2)$ $USp(2N)$ theories with matter in the antisymmetric tensor
representation that arises from dimensional reduction of $4d$ $\mathcal{N}=1$
$USp(2N)$ Cs\'aki-Skiba-Schmaltz duality. It is shown that this duality is
associated to a triangle type identity for any value of $N$. In all cases
Boltzmann weights as well as interaction and normalization factors are
completely determined. Finally, our relations are compared with those
previously reported in the literature. |
Non-Hermitian Interactions Between Harmonic Oscillators, with
Applications to Stable, Lorentz-Violating QED: We examine a new application of the Holstein-Primakoff realization of the
simple harmonic oscillator Hamiltonian. This involves the use of
infinite-dimensional representations of the Lie algebra $su(2)$. The
representations contain nonstandard raising and lowering operators, which are
nonlinearly related to the standard $a^{\dag}$ and $a$. The new operators also
give rise to a natural family of two-oscillator couplings. These nonlinear
couplings are not generally self-adjoint, but their low-energy limits are
self-adjoint, exactly solvable, and stable. We discuss the structure of a
theory involving these couplings. Such a theory might have as its
ultra-low-energy limit a Lorentz-violating Abelian gauge theory, and we discuss
the extremely strong astrophysical constraints on such a model. | On Torsion and Nieh-Yan Form: Using the well-known Chern-Weil formula and its generalization, we
systematically construct the Chern-Simons forms and their generalization
induced by torsion as well as the Nieh-Yan (N-Y) forms. We also give an
argument on the vanishing of integration of N-Y form on any compact manifold
without boundary. A systematic construction of N-Y forms in D=4n dimension is
also given. |
The current density in quantum electrodynamics in external potentials: We review different definitions of the current density for quantized fermions
in the presence of an external electromagnetic field. Several deficiencies in
the popular prescription due to Schwinger and the mode sum formula for static
external potentials are pointed out. We argue that Dirac's method, which is the
analog of the Hadamard point-splitting employed in quantum field theory in
curved space-times, is conceptually the most satisfactory. As a concrete
example, we discuss vacuum polarization and the stress-energy tensor for
massless fermions in 1+1 dimension. Also a general formula for the vacuum
polarization in static external potentials in 3+1 dimensions is derived. | Characterizing the solutions to scattering equations that support
tree-level $\text{N}^{k}\text{MHV}$ gauge/gravity amplitudes: In this paper we define, independent of theories, two discriminant matrices
involving a solution to the scattering equations in four dimensions, the ranks
of which are used to divide the solution set into a disjoint union of subsets.
We further demonstrate, {entirely within the Cachazo-He-Yuan formalism,} that
each subset of solutions gives nonzero contribution to tree-level
$\text{N}^{k}\text{MHV}$ gauge/gravity amplitudes only for a specific value of
$k$. Thus the solutions can be characterized by the rank of their discriminant
matrices, which in turn determines the value of $k$ of the $\text{N}^{k}
\text{MHV}$ amplitudes a solution can support. As another application of the
technique developed, we show analytically that in Einstein-Yang-Mills theory,
if all gluons have the same helicity, the tree-level single-trace amplitudes
must vanish. |
Picard-Fuchs equations and mirror maps for hypersurfaces: We describe a strategy for computing Yukawa couplings and the mirror map,
based on the Picard-Fuchs equation. (Our strategy is a variant of the method
used by Candelas, de la Ossa, Green, and Parkes in the case of quintic
hypersurfaces.) We then explain a technique of Griffiths which can be used to
compute the Picard-Fuchs equations of hypersurfaces. Finally, we carry out the
computation for four specific examples (including quintic hypersurfaces,
previously done by Candelas et al.). This yields predictions for the number of
rational curves of various degrees on certain hypersurfaces in weighted
projective spaces. Some of these predictions have been confirmed by classical
techniques in algebraic geometry. | Hamiltonian truncation in Anti-de Sitter spacetime: Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often
strongly coupled when the radius of AdS is large, and few methods are available
to study them. In this work, we develop a Hamiltonian truncation method to
compute the energy spectrum of QFTs in two-dimensional AdS. The infinite volume
of constant timeslices of AdS leads to divergences in the energy levels. We
propose a simple prescription to obtain finite physical energies and test it
with numerical diagonalization in several models: the free massive scalar
field, $\phi^4$ theory, Lee-Yang and Ising field theory. Along the way, we
discuss spontaneous symmetry breaking in AdS and derive a compact formula for
perturbation theory in quantum mechanics at arbitrary order. Our results
suggest that all conformal boundary conditions for a given theory are connected
via bulk renormalization group flows in AdS. |
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