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Spin vortices in the Abelian-Higgs model with cholesteric vacuum
structure: We continue the study of $U(1)$ vortices with cholesteric vacuum structure. A
new class of solutions is found which represent global vortices of the internal
spin field. These spin vortices are characterized by a non-vanishing angular
dependence at spatial infinity, or winding. We show that despite the
topological $\mathbb{Z}_2$ behavior of $SO(3)$ windings, the topological charge
of the spin vortices is of the $\mathbb{Z}$ type in the cholesteric. We find
these solutions numerically and discuss the properties derived from their low
energy effective field theory in $1+1$ dimensions. | Vortex Solutions of Nonrelativistic Fermion and Scalar Field Theories
Coupled to Maxwell-Chern-Simons theories: We have constructed nonrelativistic fermion and scalar field theories coupled
to a Maxwell-Chern-Simons gauge field which admit static multi-vortex
solutions. This is achieved by introducing a magnetic coupling term in addition
to the usual minimal coupling. |
Comment on Path Integral Derivation of Schrödinger Equation in Spaces
with Curvature and Torsion: We present a derivation of the Schr\"odinger equation for a path integral of
a point particle in a space with curvature and torsion which is considerably
shorter and more elegant than what is commonly found in the literature. | Janus and Hades in M-theory: Multi-parametric and analytic families of four-dimensional
$\,\textrm{AdS}_{3} \times \mathbb{R}\,$ (Janus) and $\,\textrm{AdS}_{3}
\,\times\, \mathbb{R}^{+}$ (Hades) solutions are constructed in the SO(8)
gauged supergravity that arises from the consistent reduction of
eleven-dimensional supergravity on $\,\textrm{S}^7\,$. The solutions are
generically non-supersymmetric, involve non-trivial running scalars and
preserve a $\,\textrm{U}(1)^4\,$ symmetry. Different patterns of (super)
symmetry enhancement occur upon suitable adjustment of the free parameters
which further control the boundary conditions of the running scalars. We
concentrate on the non-supersymmetric Janus and Hades solutions with
$\,\textrm{SU}(3) \times \textrm{U}(1)^2\,$ symmetry and provide their
higher-dimensional description in terms of M-theory fluxes and membranes.
Special attention is paid to a class of such Hades solutions dubbed ''ridge
flows'' which resemble dielectric rotations of Coulomb branch flows previously
investigated in the literature. |
Holographic Wilsonian Renormalization and Chiral Phase Transitions: We explore the role of a holographic Wilsonian cut-off in simple probe brane
models with chiral symmetry breaking/restoration phase transitions. The
Wilsonian cut-off allows us to define supergravity solutions for off-shell
configurations and hence to define a potential for the chiral condensate. We
pay particular attention to the need for configurations whose action we are
comparing to have the same IR and UV boundary conditions. We exhibit new first
and second order phase transitions with changing cut-off. We derive the
effective potential for the condensate including mean field and BKT type
continuous transitions. | BIons in topological string theory: When many fundamental strings are stacked together, they puff up into
D-branes. BIons and giant gravitons are the examples of such D-brane
configurations that arise from coincident strings. We propose and demonstrate
analogous transitions in topological string theory. Such transitions can also
be understood in terms of the Fourier transform of D-brane amplitudes. |
On the Microscopic Perspective of Black Branes Thermodynamic Geometry: In this article we study correspondence between the microscopic spectrum and
macroscopic properties of a class of extremal and non-extremal black branes and
outline an origin of the interactions among various microstates of a given
black brane configuration from the perspective of an intrinsic Riemannian
geometry arising from the coarse graining entropy over a large number of
microstates. We have analyzed the state-space geometry in the case of various
extremal and non-extremal black branes arising from the string theories,
multi-centered black brane configurations, small black holes with fractional
branes, fuzzy rings in the set up of Mathur's fuzzballs and subensemble theory,
as well as that the black brane foams from the considerations of bubbling black
brane solutions in the M-theory. We have further shown that there exists a
clear mechanism on the black brane side that describes the notion of associated
interactions in the state-space or vice-versa. We thus find that in all such
cases there are no singularities in the state-space manifold of these black
brane configurations. This observation is in turn consistent with the existing
picture of corresponding microscopic CFT data. | Quantum (anti)de Sitter algebras and generalizations of the
kappa-Minkowski space: We present two different quantum deformations for the (anti)de Sitter
algebras and groups. The former is a non-standard (triangular) deformation of
SO(4,2) realized as the conformal group of the (3+1)D Minkowskian spacetime,
while the latter is a standard (quasitriangular) deformation of both SO(2,2)
and SO(3,1) expressed as the kinematical groups of the (2+1)D anti-de Sitter
and de Sitter spacetimes, respectively. The Hopf structure of the quantum
algebra and a study of the dual quantum group are presented for each
deformation. These results enable us to propose new non-commutative spacetimes
that can be interpreted as generalizations of the kappa-Minkowski space, either
by considering a variable deformation parameter (depending on the boost
coordinates) in the conformal deformation, or by introducing an explicit
curvature/cosmological constant in the kinematical one; kappa-Minkowski turns
out to be the common first-order structure for all of these quantum spaces.
Some properties provided by these deformations, such as dimensions of the
deformation parameter (related with the Planck length), space isotropy,
deformed boost transformations, etc., are also commented. |
Kazakov-Migdal model on the Graph and Ihara Zeta Function: We propose the Kazakov-Migdal model on graphs and show that, when the
parameters of this model are appropriately tuned, the partition function is
represented by the unitary matrix integral of an extended Ihara zeta function,
which has a series expansion by all non-collapsing Wilson loops with their
lengths as weights. The partition function of the model is expressed in two
different ways according to the order of integration. A specific unitary matrix
integral can be performed at any finite $N$ thanks to this duality. We exactly
evaluate the partition function of the parameter-tuned Kazakov-Migdal model on
an arbitrary graph in the large $N$ limit and show that it is expressed by the
infinite product of the Ihara zeta functions of the graph. | Chiral gauge theory in four dimensions: A formulation of abelian and non-abelian chiral gauge theories is presented
together with arguments for the unitarity and renormalisability in four
dimensions. IASSNS-HEP-94/70, UM-P-94/96, and RCHEP-94/26. |
Scalar Field Theory in the AdS/CFT Correspondence Revisited: We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$
correspondence for the scalar field theory. Also a careful analysis of some
limiting cases is presented. We study three possible types of boundary
conditions, Dirichlet, Neumann and mixed. We compute the two-point functions of
the conformal operators on the boundary for each type of boundary condition. We
show how particular choices of the mass require different treatments. In the
Dirichlet case we find that there is no double zero in the two-point function
of the operator with conformal dimension $\frac{d}{2}$. The Neumann case leads
to new normalizations for the boundary two-point functions. In the massless
case we show that the conformal dimension of the boundary conformal operator is
precisely the unitarity bound for scalar operators. We find a one-parameter
family of boundary conditions in the mixed case. There are again new
normalizations for the boundary two-point functions. For a particular choice of
the mixed boundary condition and with the mass squared in the range
$-d^2/4<m^2<-d^2/4+1$ the boundary operator has conformal dimension comprised
in the interval $[\frac{d-2}{2}, \frac{d}{2}]$. For mass squared $m^2>-d^2/4+1$
the same choice of mixed boundary condition leads to a boundary operator whose
conformal dimension is the unitarity bound. | Asymptotic Freedom: I discuss how the basic phenomenon of asymptotic freedom in QCD can be
understood in elementary physical terms. Similarly, I discuss how the
long-predicted phenomenon of ``gluonization of the proton'' -- recently
spectacularly confirmed at HERA -- is a rather direct manifestation of the
physics of asymptotic freedom. I review the broader significance of asymptotic
freedom in QCD in fundamental physics: how on the one hand it guides the
interpretation and now even the design of experiments, and how on the other it
makes possible a rational, quantitative theoretical approach to problems of
unification and early universe cosmology. |
Stringy Instantons and Cascading Quivers: D-brane instantons can perturb the quantum field theories on space-time
filling D-branes by interesting operators. In some cases, these D-brane
instantons are novel "stringy" effects (not interpretable directly as instanton
effects in the low-energy quantum field theory), while in others the D-brane
instantons can be directly interpreted as field theory effects. In this note,
we describe a situation where both perspectives are available, by studying
stringy instantons in quivers which arise at simple Calabi-Yau singularities.
We show that a stringy instanton which wraps an unoccupied node of the quiver,
and gives rise to a non-perturbative mass in the space-time field theory, can
be reinterpreted as a conventional gauge theory effect by going up in an
appropriate renormalization group cascade. Interestingly, in the cascade, the
contribution of the stringy instanton does not come from gauge theory
instantons but from strong coupling dynamics. | Meanders: A Direct Enumeration Approach: We study the statistics of semi-meanders, i.e. configurations of a set of
roads crossing a river through n bridges, and possibly winding around its
source, as a toy model for compact folding of polymers. By analyzing the
results of a direct enumeration up to n=29, we perform on the one hand a large
n extrapolation and on the other hand we reformulate the available data into a
large q expansion, where q is a weight attached to each road. We predict a
transition at q=2 between a low-q regime with irrelevant winding, and a large-q
regime with relevant winding. |
Iterated amplitudes in the high-energy limit: We consider the high-energy limits of the colour ordered four-, five- and
six-gluon MHV amplitudes of the maximally supersymmetric QCD in the multi-Regge
kinematics where all the gluons are strongly ordered in rapidity. We show that
various building blocks occurring in the Regge factorisation (the Regge
trajectory, the coefficient functions and the Lipatov vertex) satisfy an
iterative structure very similar to the Bern-Dixon-Smirnov (BDS) ansatz. This
iterative structure, combined with the universality of the building blocks,
enables us to show that in the Euclidean region any two- and three-loop
amplitude in multi-Regge kinematics is guaranteed to satisfy the BDS ansatz. We
also consider slightly more general kinematics where the strong rapidity
ordering applies to all the gluons except the two with either the largest or
smallest rapidities, and we derive the iterative formula for the associated
coefficient function. We show that in this kinematic limit the BDS ansatz is
also satisfied. Finally, we argue that only for more general kinematics - e.g.
with three gluons having similar rapidities, or where the two central gluons
have similar rapidities - can a disagreement with the BDS ansatz arise. | Scattering of fermionic isodoublets on the sine-Gordon kink: The scattering of Dirac fermions on the sine-Gordon kink is studied both
analytically and numerically. To achieve invariance with respect to a discrete
symmetry, the sine-Gordon model is treated as a nonlinear $\sigma$-model with a
circular target space that interacts with fermionic isodublets through the
Yukawa interaction. It is shown that the diagonal and antidiagonal parts of the
fermionic wave function interact independently with the external field of the
sine-Gordon kink. The wave functions of the fermionic scattering states are
expressed in terms of the Heun functions. General expressions for the
transmission and reflection coefficients are derived, and their dependences on
the fermion momentum and mass are studied numerically. The existence condition
is found for two fermionic zero modes, and their analytical expressions are
obtained. It is shown that the zero modes do not lead to fragmentation of the
fermionic charge, but can lead to polarization of the fermionic vacuum. The
scattering of the diagonal and antidiagonal fermionic states is found to be
significantly different; this difference is shown to be due to the different
dependences of the energy levels of these bound states on the fermion mass, and
is in accordance with Levinson's theorem. |
Nonabelian interactions from Hamiltonian BRST cohomology: Consistent Hamiltonian couplings between a set of vector fields and a system
of matter fields are derived by means of BRST cohomological techniques. | Convex programs for minimal-area problems: The closed string field theory minimal-area problem asks for the conformal
metric of least area on a Riemann surface with the condition that all
non-contractible closed curves have length at least 2\pi. This is an extremal
length problem in conformal geometry as well as a problem in systolic geometry.
We consider the analogous minimal-area problem for homology classes of curves
and, with the aid of calibrations and the max flow-min cut theorem, formulate
it as a local convex program. We derive an equivalent dual program involving
maximization of a concave functional. These two programs give new insights into
the form of the minimal-area metric and are amenable to numerical solution. We
explain how the homology problem can be modified to provide the solution to the
original homotopy problem. |
A strange relationship between 2d CFT and 4d gauge theory: A relationship between 4d gauge theory and 2d CFT will be reviewed from the
very basics. We will first cover the introductory material on the 2d CFT and on
the instantons of 4d gauge theory. Next we will explicitly calculate and check
the agreement of the norm of a coherent state on the 2d side and the instanton
partition function on the 4d side. We will then see how this agreement can be
understood from the perspective of string and M theory. | Phases of unstable conifolds: We explore the phase structure induced by closed string tachyon condensation
of toric nonsupersymmetric conifold-like singularities described by an integral
charge matrix $Q=(n_1 n_2 -n_3 -n_4), n_i>0, \sum_i Q_i\neq 0$, initiated in
hep-th/0510104. Using gauged linear sigma model renormalization group flows and
toric geometry techniques, we see a cascade-like phase structure containing
decays to lower order conifold-like singularities, including in particular the
supersymmetric conifold and the $Y^{pq}$ spaces. This structure is consistent
with the Type II GSO projection obtained previously for these singularities.
Transitions between the various phases of these geometries include flips and
flops. |
A Covariant Master Theory for Novel Galilean Invariant Models and
Massive Gravity: Coupling the galileons to a curved background has been a tradeoff between
maintaining second order equations of motion, maintaining the galilean shift
symmetries, and allowing the background metric to be dynamical. We propose a
construction which can achieve all three for a novel class of galilean
invariant models, by coupling a scalar with the galilean symmetry to a massive
graviton. This generalizes the brane construction for galileons, by adding to
the brane a dynamical metric, (non-universally) interacting with the galileon
field. Alternatively, it can be thought of as an extension of the ghost-free
massive gravity, or as a massive graviton-galileon scalar-tensor theory. In the
decoupling limit of these theories, new kinds of galileon invariant
interactions arise between the scalar and the longitudinal mode of the
graviton. These have higher order equations of motion and infinite powers of
the field, yet are ghost-free. | Superradiance from a Charged Dilaton Black Hole: We study the behavior of the wave function of charged Klein-Gordon field
around a charge dilaton black hole. The rate of spontaneous charge loss is
estimated for large black hole case. |
Subleading Soft Graviton Theorem for Loop Amplitudes: Superstring field theory gives expressions for heterotic and type II string
loop amplitudes that are free from ultraviolet and infrared divergences when
the number of non-compact space-time dimensions is five or more. We prove the
subleading soft graviton theorem in these theories to all orders in
perturbation theory for S-matrix elements of arbitrary number of finite energy
external states but only one external soft graviton. We also prove the leading
soft graviton theorem for arbitrary number of finite energy external states and
arbitrary number of soft gravitons. Since our analysis is based on general
properties of one particle irreducible effective action, the results are valid
in any theory of quantum gravity that gives finite result for the S-matrix
order by order in perturbation theory without violating general coordinate
invariance. | Threshold corrections in orbifold models and superstring unification of
gauge interactions: The string one loop renormalization of the gauge coupling constants is
examined in abelian orbifold models. The contributions to string threshold
corrections independent of the compactification moduli fields are evaluated
numerically for several representative examples of orbifold models. We consider
cases with standard and non-standard embeddings as well as cases with discrete
Wilson lines background fields which match reasonably well with low energy
phenomenology. We examine one loop gauge coupling constants unification in a
description incorporating the combined effects of moduli dependent and
independent threshold corrections, an adjustable Kac-Moody level for the
hypercharge group factor and a large mass threshold associated with an
anomalous $U(1)$ mechanism. |
Thermodynamics on Fuzzy Spacetime: We investigate the thermodynamics of non-relativistic and relativistic ideal
gases on the spacetime with noncommutative fuzzy geometry. We first find that
the heat capacities of the non-relativistic ideal boson and fermion on the
fuzzy two-sphere have different values, contrast to that on the commutative
geometry. We calculate the "statistical interparticle potential" therein and
interprete this property as a result that the non-commutativity of the fuzzy
sphere has an inclination to enhance the statistical "attraction (repulsion)
interparticle potential" between boson (fermion). We also see that at high
temperature the heat capacity approaches to zero. We next evaluate the heat
capacities of the non-relativistic ideal boson and fermion on the product of
the 1+D (with D=2,3) Minkowski spacetime by a fuzzy two-sphere and see that the
fermion capacity could be a decreasing function of temperature in
high-temperature limit, contrast to that always being an increasing function on
the commutative geometry. Also, the boson and fermion heat capacities both
approach to that on the 1+D Minkowski spacetime in high-temperature limit. We
discuss these results and mention that the properties may be traced to the
mechanism of "thermal reduction of the fuzzy space". We also investigate the
same problems in the relativistic system with free Klein-Gordon field and Dirac
field and find the similar properties. | Non-Abelian U-duality for membrane: T-duality of string theory can be extended to the Poisson-Lie T-duality when
the target space has a generalized isometry group given by a Drinfel'd double.
In M-theory, T-duality is understood as a subgroup of U-duality, but the
non-Abelian extension of U-duality is still a mystery. In this paper, we study
membrane theory on a curved background with a generalized isometry group given
by the $\mathcal{E}_n$ algebra. This provides a natural setup to study
non-Abelian U-duality because the $\mathcal{E}_n$ algebra has been proposed as
a U-duality extension of the Drinfel'd double. We show that the standard
treatment of Abelian U-duality can be extended to the non-Abelian setup.
However, a famous issue in Abelian U-duality still exists in the non-Abelian
extension. |
Maximally Supersymmetric RG Flows and AdS Duality: We discuss four dimensional renormalization group flows which preserve
sixteen supersymmetries. In the infra-red, these can be viewed as deformations
of the N=4 superconformal fixed points by special, irrelevant operators. It is
argued that the gauge coupling beta function continues to vanish identically,
for all coupling constants and energy scales, for such RG flows. In addition,
the dimensions of all operators in short supersymmetry representations are
constant along such flows. It is conjectured that there is a generalization of
the AdS/CFT holography correspondence which describes such flows, e.g. the D3
brane vacuum before taking the near-horizon limit, at all energy scales. RG
flows in three and six dimensions, preserving 16 supersymmetries, are also
briefly discussed, including a conjectured generalized AdS/CFT duality for the
M2 and M5 brane cases. Finally, we discuss maximally supersymmetric RG flows
associated with non-commutative geometry. | T-duality of Non-Relativistic String in Torsional Newton-Cartan
Background: In this short note we analyse T-duality properties of non-relativistic String
in Torsional Newton-Cartan Background. We also determine condition that ensures
that non-relativistic string maps to non-relativistic string under T-duality. |
D-brane in R-R Field Background: The purpose of this paper is to understand the low energy effective theory of
a Dp-brane in the background of a large constant R-R (p-1)-form field. We start
with the M5-brane theory in large C-field background. The C-field background
defines a 3-dimensional volume form on an M5-brane, and it is known that the
low energy M5-brane theory can be described as a Nambu-Poisson gauge theory
with the volume-preserving diffeomorphism symmetry (VPD). Via a double
dimensional reduction we obtain a D4-brane in R-R 3-form field background. This
theory has both the usual U(1) gauge symmetry and the new symmetry of VPD. We
find that the gauge potential for VPD is electric-magnetic dual to the U(1)
gauge potential, sharing the same physical degrees of freedom. The result can
be generalized to Dp-branes. | High-energy effective theory for matter on close Randall Sundrum branes: Extending the analysis of hep-th/0504128, we obtain a formal expression for
the coupling between brane matter and the radion in a Randall-Sundrum
braneworld. This effective theory is correct to all orders in derivatives of
the radion in the limit of small brane separation, and, in particular, contains
no higher than second derivatives. In the case of cosmological symmetry the
theory can be obtained in closed form and reproduces the five-dimensional
behaviour. Perturbations in the tensor and scalar sectors are then studied.
When the branes are moving, the effective Newtonian constant on the brane is
shown to depend both on the distance between the branes and on their velocity.
In the small distance limit, we compute the exact dependence between the
four-dimensional and the five-dimensional Newtonian constants. |
Schwarzschild de Sitter and extremal surfaces: We study extremal surfaces in the Schwarzschild de Sitter spacetime with real
mass parameter. We find codim-2 timelike extremal surfaces stretching between
the future and past boundaries that pass through the vicinity of the
cosmological horizon in a certain limit. These are analogous to the surfaces in
arXiv:1711.01107 [hep-th]. We also find spacelike surfaces that never reach the
future/past boundaries but stretch indefinitely through the extended Penrose
diagram, passing through the vicinity of the cosmological and Schwarzschild
horizons in a certain limit. Further, these exhibit interesting structure for
de Sitter space (zero mass) as well as in the extremal, or Nariai, limit. | Fermions on spontaneously generated spherical extra dimensions: We include fermions to the model proposed in hep-th/0606021, and obtain a
renormalizable 4-dimensional SU(N) gauge theory which spontaneously generates
fuzzy extra dimensions and behaves like Yang-Mills theory on M^4 \times S^2. We
find a truncated tower of fermionic Kaluza-Klein states transforming under the
low-energy gauge group, which is found to be either SU(n), or SU(n_1) x SU(n_2)
x U(1). The latter case implies a nontrivial U(1) flux on S^2, leading to
would-be zero modes for the bifundamental fermions. In the non-chiral case they
may pair up to acquire a mass, and the emerging picture is that of mirror
fermions. We discuss the possible implementation of a chirality constraint in 6
dimensions, which is nontrivial at the quantum level due to the fuzzy nature of
the extra dimensions. |
Quantizations of D=3 Lorentz symmetry: Using the isomorphism
$\mathfrak{o}(3;\mathbb{C})\simeq\mathfrak{sl}(2;\mathbb{C})$ we develop a new
simple algebraic technique for complete classification of quantum deformations
(the classical $r$-matrices) for real forms $\mathfrak{o}(3)$ and
$\mathfrak{o}(2,1)$ of the complex Lie algebra $\mathfrak{o}(3;\mathbb{C})$ in
terms of real forms of $\mathfrak{sl}(2;\mathbb{C})$: $\mathfrak{su}(2)$,
$\mathfrak{su}(1,1)$ and $\mathfrak{sl}(2;\mathbb{R})$. We prove that the $D=3$
Lorentz symmetry
$\mathfrak{o}(2,1)\simeq\mathfrak{su}(1,1)\simeq\mathfrak{sl}(2;\mathbb{R})$
has three different Hopf-algebraic quantum deformations which are expressed in
the simplest way by two standard $\mathfrak{su}(1,1)$ and
$\mathfrak{sl}(2;\mathbb{R})$ $q$-analogs and by simple Jordanian
$\mathfrak{sl}(2;\mathbb{R})$ twist deformations. These quantizations are
presented in terms of the quantum Cartan-Weyl generators for the quantized
algebras $\mathfrak{su}(1,1)$ and $\mathfrak{sl}(2;\mathbb{R})$ as well as in
terms of quantum Cartesian generators for the quantized algebra
$\mathfrak{o}(2,1)$. Finaly, some applications of the deformed $D=3$ Lorentz
symmetry are mentioned. | Holographic RG Flows for Kondo-like Impurities: Boundary, defect, and interface RG flows, as exemplified by the famous Kondo
model, play a significant role in the theory of quantum fields. We study in
detail the holographic dual of a non-conformal supersymmetric impurity in the
D1/D5 CFT. Its RG flow bears similarities to the Kondo model, although unlike
the Kondo model the CFT is strongly coupled in the holographic regime. The
interface we study preserves $d = 1$ $\mathcal{N} = 4$ supersymmetry and flows
to conformal fixed points in both the UV and IR. The interface's UV fixed point
is described by $d = 1$ fermionic degrees of freedom, coupled to a gauge
connection on the CFT target space that is induced by the ADHM construction. We
briefly discuss its field-theoretic properties before shifting our focus to its
holographic dual. We analyze the supergravity dual of this interface RG flow,
first in the probe limit and then including gravitational backreaction. In the
probe limit, the flow is realized by the puffing up of probe branes on an
internal $\mathsf{S}^3$ via the Myers effect. We further identify the
backreacted supergravity configurations dual to the interface fixed points.
These supergravity solutions provide a geometric realization of critical
screening of the defect degrees of freedom. This critical screening arises in a
way similar to the original Kondo model. We compute the $g$-factor both in the
probe brane approximation and using backreacted supergravity solutions, and
show that it decreases from the UV to the IR as required by the $g$-theorem. |
Turbulent Two Dimensional Magnetohydrodynamics and Conformal Field
Theory.: We show that an infinite number of non-unitary minimal models may describe
two dimensional turbulent magnetohydrodynamics (MHD), both in the presence and
absence of the Alf'ven effect.
We argue that the existence of a critical dynamical index results in the
Alf'ven effect or equivelently the equipartition of energy. We show that there
are an infinite number of conserved quantities in $2D-MHD$ turbulent systems
both in the limit of vanishing the viscocities and in force free case. In the
force free case, using the non-unitary minimal model $ M_{2,7} $ we derive the
correlation functions for the velocity stream function and magnetic flux
function. Generalising this simple model we find the exponents of the energy
spectrum in the inertial range for a class of conformal field theories. | Functional Renormalisation Group Approach for Tensorial Group Field
Theory: a Rank-3 Model: We set up the Functional Renormalisation Group formalism for Tensorial Group
Field Theory in full generality. We then apply it to a rank-3 model over U(1) x
U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The
system of FRG equations turns out to be non-autonomous in the RG flow
parameter. This feature is explained by the existence of a hidden scale, the
radius of the group manifold. We investigate in detail the opposite regimes of
large cut-off (UV) and small cut-off (IR) of the FRG equations, where the
system becomes autonomous, and we find, in both case, Gaussian and non-Gaussian
fixed points. We derive and interpret the critical exponents and flow diagrams
associated with these fixed points, and discuss how the UV and IR regimes are
matched at finite N. Finally, we discuss the evidence for a phase transition
from a symmetric phase to a broken or condensed phase, from an RG perspective,
finding that this seems to exist only in the approximate regime of very large
radius of the group manifold, as to be expected for systems on compact
manifolds. |
Higher spin holography for SYM in d dimensions: We derive the spectrum of gauge invariant operators for maximally
supersymmetric Yang-Mills theories in d dimensions. After subtracting the tower
of BPS multiplets, states are shown to fall into long multiplets of a hidden
SO(10,2) symmetry dressed by thirty-two supercharges. Their primaries organize
into a universal, i.e. d-independent pattern. The results are in perfect
agreement with those following from (naive) KK reduction of type II strings on
the warped AdS x S near-horizon geometry of Dp-branes. | Parametric holomorphy? Triviality versus Duality in Sinh-Gordon: Suppose a regularised functional integral depends holomorphically on a
parameter that receives only a finite renormalization. Can one expect the
correlation functions to retain the analyticity in the parameter after removal
of the cutoff(s)? We examine the issue in the Sinh-Gordon theory by computing
the intrinsic 4-point coupling as a function of the Lagrangian coupling \beta.
Drawing on the conjectured triviality of the model in its functional integral
formulation for \beta^2 > 8\pi, and the weak-strong coupling duality in the
bootstrap formulation on the other hand, we conclude that the operations:
``Removal of the cutoff(s)'' and ``analytic continuation in \beta'' do not
commute. |
Covariant procedures for perturbative non-linear deformation of
duality-invariant theories: We analyze a recent conjecture regarding the perturbative construction of
non-linear deformations of all classically duality invariant theories,
including N=8 supergravity. Starting with an initial quartic deformation, we
engineer a procedure that generates a particular non-linear deformation
(Born-Infeld) of the Maxwell theory. This procedure requires the introduction
of an infinite number of modifications to a constraint which eliminates degrees
of freedom consistent with the duality and field content of the system. We
discuss the extension of this procedure to N=1 and N=2 supersymmetric theories,
and comment on its potential to either construct new supergravity theories with
non-linear Born-Infeld type duality, or to constrain the finiteness of N=8
supergravity. | Higher Derivative Couplings and Heterotic-Type I Duality in Eight
Dimensions: We calculate F^4 and R^4T^(4g-4) couplings in d=8 heterotic and type I string
vacua (with gauge and graviphoton field strengths F,T, and Riemann curvature
R). The holomorphic piece F_g of the heterotic one-loop coupling R^4T^(4g-4) is
given by a polylogarithm of index 5-4g and encodes the counting of genus g
curves with g nodes on the K3 of the dual F-theory side. We present closed
expressions for world-sheet tau-integrals with an arbitrary number of lattice
vector insertions. Furthermore we verify that the corresponding heterotic
one-loop couplings sum up perturbative open string and non-perturbative
D-string contributions on the type I side. Finally we discuss a type I one-loop
correction to the R^2 term. |
Algebraic Aspects of Orbifold Models: : Algebraic properties of orbifold models on arbitrary Riemann surfaces are
investigated. The action of mapping class group transformations and of standard
geometric operations is given explicitly. An infinite dimensional extension of
the quantum group is presented. | $(n+1)$-Dimensional Lorentzian Wormholes in an Expanding Cosmological
Background: We discuss $(n+1)$-dimensional dynamical wormholes in an evolving
cosmological background with a throat expanding with time. These solutions are
examined in the general relativity framework. A linear relation between
diagonal elements of an anisotropic energy-momentum tensor is used to obtain
the solutions. The energy-momentum tensor elements approach the vacuum case
when we are far from the central object for one class of solutions. Finally, we
discuss the energy-momentum tensor which supports this geometry, taking into
account the energy conditions . |
Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model: We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere
from a three dimensional matrix model by expanding the model around a classical
solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to
make the fuzzy sphere as a classical solution of the model. Majorana mass term
is also added to make it supersymmetric. We consider two large $N$ limits, one
corresponding to a gauge theory on a commutative sphere and the other to that
on a noncommutative plane. We also investigate stability of the fuzzy sphere by
calculating one-loop effective action around classical solutions. In the final
part of this paper, we consider another matrix model which gives a
supersymmetric gauge theory on the fuzzy sphere. In this matrix model, only
Chern-Simons term is added and supersymmetry transformation is modified. | Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface: By applying the conformal SO(2,4) transformations to the elementary one-cusp
Wilson loop surface we construct various two-cusp and four-cusp Wilson loop
surface configurations in AdS_5 and demonstrate that they solve the string
equations of the Nambu-Goto string action. The conformal boosts of the basic
four-cusp Wilson loop surface with a square-form projection generate various
four-cusp Wilson loop surfaces with projections of the rescaled square, the
rhombus and the trapezium, on which surfaces the classical Euclidean Nambu-Goto
string actions in the IR dimensional regularization are evaluated. |
Off-shell Closed String Amplitudes: Towards a Computation of the Tachyon
Potential: We derive an explicit formula for the evaluation of the classical closed
string action for any off-shell string field, and for the calculation of
arbitrary off-shell amplitudes. The formulae require a parametrization, in
terms of some moduli space coordinates, of the family of local coordinates
needed to insert the off-shell states on Riemann surfaces. We discuss in detail
the evaluation of the tachyon potential as a power series in the tachyon field.
The expansion coefficients in this series are shown to be geometrical
invariants of Strebel quadratic differentials whose variational properties
imply that closed string polyhedra, among all possible choices of string
vertices, yield a tachyon potential which is as small as possible order by
order in the string coupling constant. Our discussion emphasizes the
geometrical meaning of off-shell amplitudes. | The Solution of the d-Dimensional Twisted Group Lattices: The general d-dimensional twisted group lattice is solved. The irreducible
representations of the corresponding group are constructed by an explicit
procedure. It is proven that they are complete. All matrix representation
solutions to the quantum hyperplane equations are obtained. |
Fischler-Susskind holographic cosmology revisited: When Fischler and Susskind proposed a holographic prescription based on the
Particle Horizon, they found that spatially closed cosmological models do not
verify it due to the apparently unavoidable recontraction of the Particle
Horizon area. In this article, after a short review of their original work, we
expose graphically and analytically that spatially closed cosmological models
can avoid this problem if they expand fast enough. It has been also shown that
the Holographic Principle is saturated for a codimension one brane dominated
Universe. The Fischler-Susskind prescription is used to obtain the maximum
number of degrees of freedom per Planck volume at the Planck era compatible
with the Holographic Principle. | Localization of Vortex Partition Functions in $\mathcal{N}=(2,2) $ Super
Yang-Mills theory: In this article, we study the localizaiton of the partition function of BPS
vortices in $\mathcal{N}=(2,2)$ $U(N)$ super Yang-Mills theory with $N$-flavor
on $\R^2$. The vortex partition function for $\mathcal{N}=(2,2)$ super
Yang-Mills theory is obtained from the one in $\mathcal{N}=(4,4)$ super
Yang-Mills theory by mass deformation. We show that the partition function can
be written as $Q$-exact form and integration in the partition functions is
localized to the fixed points which are related to $N$-tuple one dimensional
partitions of positive integers. |
Graded Quivers, Generalized Dimer Models and Toric Geometry: The open string sector of the topological B-model model on CY $(m+2)$-folds
is described by $m$-graded quivers with superpotentials. This correspondence
extends to general $m$ the well known connection between CY $(m+2)$-folds and
gauge theories on the worldvolume of D$(5-2m)$-branes for $m=0,\ldots, 3$. We
introduce $m$-dimers, which fully encode the $m$-graded quivers and their
superpotentials, in the case in which the CY $(m+2)$-folds are toric.
Generalizing the well known $m=1,2$ cases, $m$-dimers significantly simplify
the connection between geometry and $m$-graded quivers. A key result of this
paper is the generalization of the concept of perfect matching, which plays a
central role in this map, to arbitrary $m$. We also introduce a simplified
algorithm for the computation of perfect matchings, which generalizes the
Kasteleyn matrix approach to any $m$. We illustrate these new tools with a few
infinite families of CY singularities. | Bosonization in the path integral formulation: We establish the direct $d=2$ on-shell bosonization
$\psi_{L}(x_{+})=e^{i\xi(x_{+})}$ and
$\psi_{R}^{\dagger}(x_{-})=e^{i\xi(x_{-})}$ in path integral formulation by
deriving the off-shell relations
$\psi_{L}(x)\psi_{R}^{\dagger}(x)=\exp[i\xi(x)]$ and
$\psi_{R}(x)\psi_{L}^{\dagger}(x)=\exp[-i\xi(x)]$. Similarly, the on-shell
bosonization of the bosonic commuting spinor,
$\phi_{L}(x_{+})=ie^{-i\xi(x_{+})}\partial^{+}e^{-i\chi(x_{+})}$,
$\phi^{\dagger}_{R}(x_{-})=e^{-i\xi(x_{-})-i\chi(x_{-})}$ and
$\phi_{R}(x_{-})=ie^{i\xi(x_{-})}\partial^{-}e^{+i\chi(x_{-})}$,
$\phi^{\dagger}_{L}(x_{+})=e^{i\xi(x_{+})+i\chi(x_{+})}$, is established in
path integral formulation by deriving the off-shell relations
$\phi_{L}(x)\phi^{\dagger}_{R}(x)=ie^{-i\xi(x)}\partial^{+}e^{-i\chi(x)}$ and
$\phi_{R}(x)\phi^{\dagger}_{L}(x)=ie^{i\xi(x)}\partial^{-}e^{i\chi(x)}$. |
Tachyon Hair for Two-Dimensional Black Holes: Using a combination of analytical and numerical methods, we obtain a
two-dimensional spacetime describing a black hole with tachyon hair. The
physical ADM mass of the black hole is finite. The presence of tachyon hair
increases the Hawking temperature. | Resolved gravity duals of ${\cal N}=4$ quiver field theories in 2+1
dimensions: We generalize the construction by Aharony, Hashimoto, Hirano, and Ouyang of
${\cal N}=4$ quiver gauge theory with gauge group $U(N+M) \times U(N)$, $k$
fundamentals charged under $U(N)$ and bi-fundamentals, to the case with gauge
group $\prod_{i=1}^{\hat k} U(N_i)$ with $k_i$ fundamentals charged under
$U(N_i)$. This construction is facilitated by considering the resolved
$ALE_{\hat k} \times TN_{k}$ background in M-theory including non-trivial
fluxes through the resolved 4-cycles in the geometry. We also describe the
M-theory lift of the IIA Page charge quantization condition. Finally, we
clarify the role of string corrections in various regimes of parameter space. |
Semiclassical Unimodular Gravity: Classically, unimodular gravity is known to be equivalent to General
Relativity (GR), except for the fact that the effective cosmological constant
$\Lambda$ has the status of an integration constant. Here, we explore various
formulations of unimodular gravity beyond the classical limit. We first
consider the non-generally covariant action formulation in which the
determinant of the metric is held fixed to unity. We argue that the
corresponding quantum theory is also equivalent to General Relativity for
localized perturbative processes which take place in generic backgrounds of
infinite volume (such as asymptotically flat spacetimes). Next, using the same
action, we calculate semiclassical non-perturbative quantities, which we expect
will be dominated by Euclidean instanton solutions. We derive the entropy/area
ratio for cosmological and black hole horizons, finding agreement with GR for
solutions in backgrounds of infinite volume, but disagreement for backgrounds
with finite volume. In deriving the above results, the path integral is taken
over histories with fixed 4-volume. We point out that the results are different
if we allow the 4-volume of the different histories to vary over a continuum
range. In this "generalized" version of unimodular gravity, one recovers the
full set of Einstein's equations in the classical limit, including the trace,
so $\Lambda$ is no longer an integration constant. Finally, we consider the
generally covariant theory due to Henneaux and Teitelboim, which is classically
equivalent to unimodular gravity. In this case, the standard semiclassical GR
results are recovered provided that the boundary term in the Euclidean action
is chosen appropriately. | Path integral representations in noncommutative quantum mechanics and
noncommutative version of Berezin-Marinov action: It is known that actions of field theories on a noncommutative space-time can
be written as some modified (we call them $\theta$-modified) classical actions
already on the commutative space-time (introducing a star product). Then the
quantization of such modified actions reproduces both space-time
noncommutativity and usual quantum mechanical features of the corresponding
field theory. The $\theta$-modification for arbitrary finite-dimensional
nonrelativistic system was proposed by Deriglazov (2003). In the present
article, we discuss the problem of constructing $\theta$-modified actions for
relativistic QM. We construct such actions for relativistic spinless and
spinning particles. The key idea is to extract $\theta$-modified actions of the
relativistic particles from path integral representations of the corresponding
noncommtative field theory propagators. We consider Klein-Gordon and Dirac
equations for the causal propagators in such theories. Then we construct for
the propagators path-integral representations. Effective actions in such
representations we treat as $\theta$-modified actions of the relativistic
particles. To confirm the interpretation, we quantize canonically these
actions. Thus, we obtain the Klein-Gordon and Dirac equations in the
noncommutative field theories. The $\theta$-modified action of the relativistic
spinning particle is just a generalization of the Berezin-Marinov
pseudoclassical action for the noncommutative case. |
Jordan C*-Algebras and Supergravity: It is known that black hole charge vectors of N=8 and magic N=2 supergravity
in four and five dimensions can be represented as elements of Jordan algebras
of degree three over the octonions and split-octonions and their Freudenthal
triple systems. We show both such Jordan algebras are contained in the
exceptional Jordan C*-algebra and construct its corresponding Freudenthal
triple system and single variable extension. The transformation groups for
these structures give rise to the complex forms of the U-duality groups for N=8
and magic N=2 supergravities in three, four and five dimensions. | Rotating NS5-brane solution and its exact string theoretical description: We construct the most general solution in type-II string theory that
represents N coincident non-extremal rotating NS5-branes and determine the
relevant thermodynamic quantities. We show that in the field theory limit, it
has an exact description. In particular, it can be obtained by an O(3,3)
duality transformation on the exact string background for the coset model
SL(2,R)_{-N}/U(1) \times SU(2)_N. In the extreme supersymmetric limit we
recover the multicenter solution, with a ring singularity structure, that has
been discussed recently. |
Open strings, Born--Infeld action and the heat kernel: In the derivation of the Born-Infeld action for the case with a nontrivial
boundary of the string world sheet the appearance of a new term changes the
conformal anomaly. This may have many consequences, especially also in the
study of generalized interacting brane systems. | Background Independent Algebraic Structures in Closed String Field
Theory: We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann
surfaces. This algebra is background independent in that it makes no reference
to a state space of a conformal field theory. Conformal theories define a
homomorphism of this algebra to the BV algebra of string functionals. The
construction begins with a graded-commutative free associative algebra $\C$
built from the vector space whose elements are orientable subspaces of moduli
spaces of punctured Riemann surfaces. The typical element here is a surface
with several connected components. The operation $\Delta$ of sewing two
punctures with a full twist is shown to be an odd, second order derivation that
squares to zero. It follows that $(\C, \Delta)$ is a Batalin-Vilkovisky
algebra. We introduce the odd operator $\delta = \partial + \hbar\Delta$, where
$\partial$ is the boundary operator. It is seen that $\delta^2=0$, and that
consistent closed string vertices define a cohomology class of $\delta$. This
cohomology class is used to construct a Lie algebra on a quotient space of
$\C$. This Lie algebra gives a manifestly background independent description of
a subalgebra of the closed string gauge algebra. |
The Power of M Theory: A proposed duality between type IIB superstring theory on R^9 X S^1 and a
conjectured 11D fundamental theory (``M theory'') on R^9 X T^2 is investigated.
Simple heuristic reasoning leads to a consistent picture relating the various
p-branes and their tensions in each theory. Identifying the M theory on R^{10}
X S^1 with type IIA superstring theory on R^{10}, in a similar fashion, leads
to various relations among the p-branes of the IIA theory. | Anisotropic Four-Dimensional NS-NS String Cosmology: An anisotropic (Bianchi type I) cosmology is considered in the
four-dimensional NS-NS sector of low-energy effective string theory coupled to
a dilaton and an axion-like $H$-field within a de Sitter-Einstein frame
background. The time evolution of this Universe is discussed in both the
Einstein and string frames. |
Axial-Current Anomaly in Euler Fluid: We argue that a close analog of the axial-current anomaly of quantum field
theories with fermions occurs in the classical Euler fluid. The conservation of
the axial current (closely related to the helicity of inviscid barotropic flow)
is anomalously broken by the external electromagnetic field as $\partial_\mu
j_{A}^\mu = 2\,\bf E\!\cdot\! \bf B$ similar to that of the axial current of a
quantum field theory with Dirac fermions such as QED. | Non-supersymmetric heterotic strings and chiral CFTs: Non-supersymmetric heterotic strings share various properties with their
supersymmetric counterparts. Torus compactifications of the latter live in a
component of the moduli space of string vacua with 16 supercharges, and various
asymmetric orbifolds thereof realize vacua in other components, exhibiting
qualitative differences such as rank reduction. We set out to study the
analogous problem for non-supersymmetric heterotic strings, framing it in
relation to chiral fermionic CFTs with central charge 24, which were classified
recently. We find that for the case analogous to the so-called CHL string,
which has gauge group rank reduced by 8, there are in total four
non-supersymmetric versions. These include the well known $E_8$ string and
three other constructions a la CHL, which can be distinguished qualitatively by
how tachyons appear in their classical moduli spaces. We also discuss the
classification problem for lower rank theories and the relationship between
MSDS models and Scherk-Schwarz reductions. |
Effective field theory approach to quasi-single field inflation and
effects of heavy fields: We apply the effective field theory approach to quasi-single field inflation,
which contains an additional scalar field with Hubble scale mass other than
inflaton. Based on the time-dependent spatial diffeomorphism, which is not
broken by the time-dependent background evolution, the most generic action of
quasi-single field inflation is constructed up to third order fluctuations.
Using the obtained action, the effects of the additional massive scalar field
on the primordial curvature perturbations are discussed. In particular, we
calculate the power spectrum and discuss the momentum-dependence of three point
functions in the squeezed limit for general settings of quasi-single field
inflation. Our framework can be also applied to inflation models with heavy
particles. We make a qualitative discussion on the effects of heavy particles
during inflation and that of sudden turning trajectory in our framework. | A geometrical approach to degenerate scalar-tensor theories: Degenerate scalar-tensor theories are recently proposed covariant theories of
gravity coupled with a scalar field. Despite being characterised by higher
order equations of motion, they do not propagate more than three degrees of
freedom, thanks to the existence of constraints. We discuss a geometrical
approach to degenerate scalar-tensor systems, and analyse its consequences. We
show that some of these theories emerge as a certain limit of DBI Galileons. In
absence of dynamical gravity, these systems correspond to scalar theories
enjoying a symmetry which is different from Galileon invariance. The scalar
theories have however problems concerning the propagation of fluctuations
around a time dependent background. These issues can be tamed by breaking the
symmetry by hand, or by minimally coupling the scalar with dynamical gravity in
a way that leads to degenerate scalar-tensor systems. We show that distinct
theories can be connected by a relation which generalizes Galileon duality, in
certain cases also when gravity is dynamical. We discuss some implications of
our results in concrete examples. Our findings can be helpful for assessing
stability properties and understanding the non-perturbative structure of
systems based on degenerate scalar-tensor systems. |
Emergent Global Symmetry from IR N-ality: We present a new family of IR dualities in three space-time dimensions with
eight supercharges. In contrast to 3d mirror symmetry, these dualities map
Coulomb branches to Coulomb branches and Higgs branches to Higgs branches in
the deep IR. For a large class of quiver gauge theories with an emergent
Coulomb branch global symmetry, one can construct a sequence of such dualities
by step-wise implementing a set of quiver mutations. The duality sequence leads
to a set of quiver gauge theories which flow to the same IR superconformal
field theory -- a phenomenon we refer to as IR N-ality. We show that this set
of N-al quivers always contains a theory for which the rank of the IR Coulomb
branch symmetry is manifest in the UV. For a special subclass of theories, the
emergent symmetry algebra itself can be read off from the quiver description of
the aforementioned theory. | Generalized Coherent State Approach to Star Products and Applications to
the Fuzzy Sphere: We construct a star product associated with an arbitrary two dimensional
Poisson structure using generalized coherent states on the complex plane. From
our approach one easily recovers the star product for the fuzzy torus, and also
one for the fuzzy sphere. For the latter we need to define the `fuzzy'
stereographic projection to the plane and the fuzzy sphere integration measure,
which in the commutative limit reduce to the usual formulae for the sphere. |
Holographic non-relativistic fermionic fixed point by the charged
dilatonic black hole: Driven by the landscape of garden-variety condensed matter systems, we have
investigated how the dual spectral function behaves at the non-relativistic as
well as relativistic fermionic fixed point by considering the probe Dirac
fermion in an extremal charged dilatonic black hole with zero entropy. Although
the pattern for both of the appearance of flat band and emergence of Fermi
surface is qualitatively similar to that given by the probe fermion in the
extremal Reissner-Nordstrom AdS black hole, we find a distinctly different low
energy behavior around the Fermi surface, which can be traced back to the
different near horizon geometry. In particular, with the peculiar near horizon
geometry of our extremal charged dilatonic black hole, the low energy behavior
exhibits the universal linear dispersion relation and scaling property, where
the former indicates that the dual liquid is a Fermi one while the latter
implies that the dual liquid is not exactly of Landau Fermi type. | Non-Standard neutral kaons dynamics from D-brane statistics: The neutral kaon system can be effectively described by non-unitary,
dissipative, completely positive dynamics that extend the usual treatment. In
the framework of open quantum systems, we show how the origin of these
non-standard time evolutions can be traced to the interaction of the kaon
system with a large environment. We find that D-branes, effectively described
by a heat-bath of quanta obeying infinite statistics, could constitute a
realistic example of such an environment. |
Graph complexes and Feynman rules: We investigate Feynman graphs and their Feynman rules from the viewpoint of
graph complexes. We focus on graph homology and on the appearance of cubical
complexes when either reducing internal edges or when removing them by putting
them on the massshell. | Maximal super Yang-Mills theories on curved background with off-shell
supercharges: We construct d<=7 dimensional maximally supersymmetric Yang-Mills theories on
a class of curved backgrounds with off-shell supercharges. The off-shell
supersymmetry is mainly a generalization of on-shell supersymmetry constructed
previously by Blau. We present several examples of backgrounds and discuss the
number of the preserved supersymmetries on these backgrounds. We also construct
another maximally supersymmetric Yang-Mills theories on S^3 by dimensional
reducing along the R-direction of N=4 super Yang-Mills theory on RxS^3. |
BMS charges in polyhomogeneous spacetimes: We classify the asymptotic charges of a class of polyhomogeneous
asymptotically-flat spacetimes with finite shear, generalising recent results
on smooth asymptotically-flat spacetimes. Polyhomogenous spacetimes are a
formally consistent class of spacetimes that do not satisfy the well-known
peeling property. As such, they constitute a more physical class of
asymptotically-flat spacetimes compared to the smooth class. In particular, we
establish that the generalised conserved non-linear Newman-Penrose charges that
are known to exist for such spacetimes are a subset of asymptotic BMS charges. | Phase transitions and light scalars in bottom-up holography: Within the bottom-up approach to holography, we construct a class of
six-dimensional gravity models, and discuss solutions that can be interpreted,
asymptotically in the far UV, in terms of dual five-dimensional conformal field
theories deformed by a single scalar operator. We treat the scaling dimension
of such operator, related to the mass of the one scalar field in the gravity
theory, as a free parameter. One dimension in the regular geometry is
compactified on a shrinking circle, hence mimicking confinement in the
resulting dual four-dimensional theories.
We study the mass spectrum of bosonic states. The lightest state in this
spectrum is a scalar particle. Along the regular (confining) branch of
solutions, we find the presence of a tachyonic instability in part of the
parameter space, reached by a smooth deformation of the mass spectrum, as a
function of the boundary value of the background scalar field in the gravity
theory. In a region of parameter space nearby the tachyonic one, the lightest
scalar particle can be interpreted as an approximate dilaton, sourced by the
trace of the stress-energy tensor, and its mass is parametrically suppressed.
We also compute the free energy, along several branches of gravity solutions.
We find that both the dilatonic and tachyonic regions of parameter space,
identified along the branch of confining solutions, are hidden behind a
first-order phase transition, so that they are not realised as stable
solutions, irrespectively of the scaling dimension of the deforming
field-theory operator. The (approximate) dilaton, in particular, appears in
metastable solutions. Yet, the mass of the lightest state, computed close to
the phase transition, is (mildly) suppressed. This feature is amplified when
the (free) parameter controlling the scaling dimension of the deformation is
5/2, half the dimension of space-time in the field theory. |
A Solution of the Relativistic Schrödinger Equation for the
$δ$-Function Potential in 1-dimensiona with Cutoff Regularization: We study the solution of the relativistic Schr\"odinger equation for a point
particle in 1-d under $\delta$-function potential by using cutoff
regularization. We show that the problem is renormalizable, and the results are
exactly the same as the ones obtained using dimensional regularization. | Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory: The purpose of this paper is to present our study on the restoration of the
Lorentz symmetry for a Lifshitz-type scalar theory in the infrared region by
using nonperturbative methods. We apply the Wegner-Houghton equation, which is
one of the exact renormalization group equations, to the Lifshitz-type theory.
Analyzing the equation for a z=2, d=3+1 Lifshitz-type scalar model, and using
some variable transformations, we found that broken symmetry terms vanish in
the infrared region. This shows that the Lifshitz-type scalar model dynamically
restores the Lorentz symmetry at low energy. Our result provides a definition
of ultraviolet complete renormalizable scalar field theories. These theories
can have nontrivial interaction terms of \phi^{n} (n=4, 6, 8, 10) even when the
Lorentz symmetry is restored at low energy. |
Instability of Chern-Simons Theory with Fermions at Large N: We study the (in)stability around the dynamical gap solution of the $U(N)$
Chern-Simons gauge theory with fundamental fermions (massless or massive)
coupled in $D=3$ at large $N$. Explicit analyses on both the Auxiliary-Field
(AF) and the Cornwall-Jackiw-Tomboulis (CJT) effective potentials are given. In
both approaches we manage to analytically identify the saddle-point instability
around the gap solution. We also give a comparison with the QCD-like theories.
This study can help understanding the scale symmetry breaking picture of this
theory. | Environmentally Friendly Renormalization: We analyze the renormalization of systems whose effective degrees of freedom
are described in terms of fluctuations which are ``environment'' dependent.
Relevant environmental parameters considered are: temperature, system size,
boundary conditions, and external fields. The points in the space of \lq\lq
coupling constants'' at which such systems exhibit scale invariance coincide
only with the fixed points of a global renormalization group which is
necessarily environment dependent. Using such a renormalization group we give
formal expressions to two loops for effective critical exponents for a generic
crossover induced by a relevant mass scale $g$. These effective exponents are
seen to obey scaling laws across the entire crossover, including hyperscaling,
but in terms of an effective dimensionality, $d\ef=4-\gl$, which represents the
effects of the leading irrelevant operator. We analyze the crossover of an
$O(N)$ model on a $d$ dimensional layered geometry with periodic, antiperiodic
and Dirichlet boundary conditions. Explicit results to two loops for effective
exponents are obtained using a [2,1] Pad\'e resummed coupling, for: the
``Gaussian model'' ($N=-2$), spherical model ($N=\infty$), Ising Model ($N=1$),
polymers ($N=0$), XY-model ($N=2$) and Heisenberg ($N=3$) models in four
dimensions. We also give two loop Pad\'e resummed results for a three
dimensional Ising ferromagnet in a transverse magnetic field and corresponding
one loop results for the two dimensional model. One loop results are also
presented for a three dimensional layered Ising model with Dirichlet and
antiperiodic boundary conditions. Asymptotically the effective exponents are in
excellent agreement with known results. |
Generalized Chern-Simons Form and Descent Equation: We present the general method to introduce the generalized Chern-Simons form
and the descent equation which contain the scalar field in addition to the
gauge fields. It is based on the technique in a noncommutative differential
geometry (NCG) which extends the $N$-dimensional Minkowski space $M_N$ to the
discrete space such as $M_N\times Z_2$ with two point space $Z_2$. However, the
resultant equations do not depend on NCG but are justified by the algebraic
rules in the ordinary differential geometry. | 4d F(4) gauged supergravity and black holes of class $\mathcal{F}$: We perform a consistent reduction of 6d matter-coupled F(4) supergravity on a
compact Riemann surface $\Sigma_\mathfrak{g}$ of genus $\mathfrak{g}$, at the
level of the bosonic action. The result is an $\mathcal{N}=2$ gauged
supergravity coupled to two vector multiplets and a single hypermultiplet. The
four-dimensional model is holographically dual to the 3d superconformal field
theories of class $\mathcal{F}$, describing different brane systems in massive
type IIA and IIB wrapped on $\Sigma_\mathfrak{g}$. The naive reduction leads to
a non-standard 4d mixed duality frame with both electric and magnetic gauge
fields, as well as a massive tensor, that can be only described in the
embedding tensor formalism. Upon a chain of electromagnetic dualities, we are
able to determine the scalar manifolds and electric gaugings that uniquely
specify the model in the standard supergravity frame. We then use the result to
construct the first examples of static dyonic black holes in AdS$_6$ and
perform a microscopic counting of their entropy via the 5d topologically
twisted index. Finally, we show the existence of further subtruncations to the
massless sector of the 4d theory, such as the Fayet-Iliopoulos gauged $T^3$
model and minimal gauged supergravity. We are in turn able to find new
asymptotically AdS$_4$ solutions, providing predictions for the squashed $S^3$
partition functions and the superconformal and refined twisted indices of class
$\mathcal{F}$ theories. |
Topological and Universal Aspects of Bosonized Interacting Fermionic
Systems in (2+1)d: General results on the structure of the bosonization of fermionic systems in
$(2+1)$d are obtained. In particular, the universal character of the bosonized
topological current is established and applied to generic fermionic current
interactions. The final form of the bosonized action is shown to be given by
the sum of two terms. The first one corresponds to the bosonization of the free
fermionic action and turns out to be cast in the form of a pure Chern-Simons
term, up to a suitable nonlinear field redefinition. We show that the second
term, following from the bosonization of the interactions, can be obtained by
simply replacing the fermionic current by the corresponding bosonized
expression. | D1/D5 System with B-field, Noncommutative Geometry and the CFT of the
Higgs Branch: The D1/D5 system is considered in the presence of the NS B field. An explicit
supergravity solution in the asymptotically flat and near horizon limits is
presented. Explicit mass formulae are presented in both cases. This solution
has no D3 source branes and represents a true bound state of the D1/D5 system.
We study the motion of a separated D1-brane in the background geometry
described above and reproduce the Liouville potential that binds the D1 brane.
A gauge theory analysis is also presented in the presence of Fayet-Iliopoulos
(FI) parameters which can be identified with the self-dual part of the NS B
field. In the case of a single D5-brane and an arbitrary number of D1 branes we
can demonstrate the existence of a bound state in the Higgs branch. We also
point out the connection of the SCFT on the resolved Sym$_{Q_1Q_5}(\tilde T^4)$
with recent developments in non-commutative Yang-Mills theory. |
Induced Angular Momentum in (2+1)-Dimensional Spinor Electrodynamics in
Curved Space: Effects due to fermion-vacuum polarization by an external static magnetic
field are considered in a two-dimensional noncompact curved space with a
nontrivial topology. An expression for the vacuun angular momentum is obtained.
Like the vacuum fermion number, it proves to be dependent on the global
characteristics of the field and space. | The duality between $κ$-Poincaré algebra and $κ$-Poincaré
group: The full duality between the $\kappa$-Poincar\'e algebra and
$\kappa$-Poincar\'e group is proved. |
Bosonic Tensor Models at Large $N$ and Small $ε$: We study the spectrum of the large $N$ quantum field theory of bosonic
rank-$3$ tensors, whose quartic interactions are such that the perturbative
expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson
equations to determine the scaling dimensions of the bilinear operators of
arbitrary spin. Using the fact that the theory is renormalizable in $d=4$, we
compare some of these results with the $4-\epsilon$ expansion, finding perfect
agreement. This helps elucidate why the dimension of operator
$\phi^{abc}\phi^{abc}$ is complex for $d<4$: the large $N$ fixed point in
$d=4-\epsilon$ has complex values of the couplings for some of the $O(N)^3$
invariant operators. We show that a similar phenomenon holds in the $O(N)^2$
symmetric theory of a matrix field $\phi^{ab}$, where the double-trace operator
has a complex coupling in $4-\epsilon$ dimensions. We also study the spectra of
bosonic theories of rank $q-1$ tensors with $\phi^q$ interactions. In
dimensions $d>1.93$ there is a critical value of $q$, above which we have not
found any complex scaling dimensions. The critical value is a decreasing
function of $d$, and it becomes $6$ in $d\approx 2.97$. This raises a
possibility that the large $N$ theory of rank-$5$ tensors with sextic potential
has an IR fixed point which is free of perturbative instabilities for
$2.97<d<3$. This theory may be studied using renormalized perturbation theory
in $d=3-\epsilon$. | 2D Gravity and Random Matrices: We review recent progress in 2D gravity coupled to $d<1$ conformal matter,
based on a representation of discrete gravity in terms of random matrices. We
discuss the saddle point approximation for these models, including a class of
related $O(n)$ matrix models. For $d<1$ matter, the matrix problem can be
completely solved in many cases by the introduction of suitable orthogonal
polynomials. Alternatively, in the continuum limit the orthogonal polynomial
method can be shown to be equivalent to the construction of representations of
the canonical commutation relations in terms of differential operators. In the
case of pure gravity or discrete Ising--like matter, the sum over topologies is
reduced to the solution of non-linear differential equations (the Painlev\'e
equation in the pure gravity case) which can be shown to follow from an action
principle. In the case of pure gravity and more generally all unitary models,
the perturbation theory is not Borel summable and therefore alone does not
define a unique solution. In the non-Borel summable case, the matrix model does
not define the sum over topologies beyond perturbation theory. We also review
the computation of correlation functions directly in the continuum formulation
of matter coupled to 2D gravity, and compare with the matrix model results.
Finally, we review the relation between matrix models and topological gravity,
and as well the relation to intersection theory of the moduli space of
punctured Riemann surfaces. |
Interpolating between open and closed strings - a BSFT approach: We address the conjecture that at the tachyonic vacuum open strings get
transformed into closed strings. We show that it is possible in the context of
boundary string field theory to interpolate between the conventional open
string theory, characterized by having the D25 brane as the boundary state, and
an off-shell (open) string theory where the boundary state is identified with
the closed string vacuum, where holomorphic and antiholomorphic modes decouple
and where bulk vertex operator correlation functions are identical to those of
the closed string. | Spinorial Snyder and Yang Models From Superalgebras And Noncommutative
Quantum Superspaces: The relativistic Lorentz-covariant quantum space-times obtained by Snyder can
be described by the coset generators of (anti) de-Sitter algebras. Similarly,
the Lorentz-covariant quantum phase spaces introduced by Yang, which contain
additionally quantum curved fourmomenta and quantum-deformed relativistic
Heisenberg algebra, can be defined by suitably chosen coset generators of
conformal algebras. We extend such algebraic construction to the respective
superalgebras, which provide quantum Lorentz-covariant superspaces (SUSY Snyder
model) and indicate also how to obtain the quantum relativistic phase
superspaces (SUSY Yang model). In last Section we recall briefly other ways of
deriving quantum phase (super)spaces and we compare the spinorial Snyder type
models defining bosonic or fermionic quantum-deformed spinors. |
A Universal Lower Bound on the Specific Temperatures of
AdS-Reissner-Nordstrom Black Holes with Flat Event Horizons: We show that, in a gravitational theory [in any number of dimensions greater
than 3] which admits BPS branes and AdS-Reissner-Nordstrom black holes with
flat event horizons, the specific [dimensionless] temperature of such a black
hole is bounded below by approximately 0.156875. This confirms the recent
suggestion by Hartnoll and Tavanfar, to the effect that no such black hole can
be arbitrarily cold, since from the AdS/CFT dual point of view the
low-temperature degrees of freedom should not be concealed by the equivalent of
an event horizon. | Weak-strong duality of the non-commutative Landau problem induced by a
two-vortex permutation, and conformal bridge transformation: A correspondence is established between the dynamics of the two-vortex system
and the non-commutative Landau problem (NCLP) in its sub- (non-chiral), super-
(chiral) and critical phases. As a result, a trivial permutation symmetry of
the point vortices induces a weak-strong coupling duality in the NCLP. We show
that quantum two-vortex systems with non-zero total vorticity can be generated
by applying conformal bridge transformation to a two-dimensional quantum free
particle or to a quantum vortex-antivortex system of zero total vorticity. The
sub- and super-critical phases of the quantum NCLP are generated in a similar
way from the 2D quantum free particle in a commutative or non-commutative
plane. The composition of the inverse and direct transformations of the
conformal bridge also makes it possible to link the non-chiral and chiral
phases in each of these two systems. |
Non-Equilibrium Field Dynamics of an Honest Holographic Superconductor: Most holographic models of superconducting systems neglect the effects of
dynamical boundary gauge fields during the process of spontaneous
symmetry-breaking. Usually a global symmetry gets broken. This yields a
superfluid, which then is gauged "weakly" afterwards. In this work we build
(and probe the dynamics of) a holographic model in which a local boundary
symmetry is spontaneously broken instead. We compute two-point functions of
dynamical non-Abelian gauge fields in the normal and in the broken phase, and
find non-trivial gapless modes. Our AdS3 gravity dual realizes a p-wave
superconductor in (1+1) dimensions. The ground state of this model also breaks
(1+1)-dimensional parity spontaneously, while the Hamiltonian is
parity-invariant. We discuss possible implications of our results for a wider
class of holographic liquids. | Cosmological Perturbations in Non-Commutative Inflation: We compute the spectrum of cosmological perturbations in a scenario in which
inflation is driven by radiation in a non-commutative space-time. In this
scenario, the non-commutativity of space and time leads to a modified
dispersion relation for radiation with two branches, which allows for
inflation. The initial conditions for the cosmological fluctuations are
thermal. This is to be contrasted with the situation in models of inflation in
which the accelerated expansion of space is driven by the potential energy of a
scalar field, and in which the fluctuations are of quantum vacuum type. We find
that, in the limit that the expansion of space is almost exponential, the
spectrum of fluctuations is scale-invariant with a slight red tilt. The
magnitude of the tilt is different from what is obtained in a usual
inflationary model with the same expansion rate during the period of inflation.
The amplitude also differs, and can easily be adjusted to agree with
observations. |
Brane-bulk energy exchange and cosmological acceleration: The consequences for the brane cosmological evolution of energy exchange
between the brane and the bulk are analyzed. A rich variety of brane
cosmologies is obtained, depending on the precise mechanism of energy transfer,
the equation of state of brane-matter and the spatial topology. An accelerating
era is generically a feature of the solutions.
(Prepared for 36th International Symposium Ahrenshoop on the Theory of
Elementary Particles: Recent Developments in String M Theory and Field Theory,
Wernsdorf, Germany, 26-30 Aug 2003.) | Inflation in string theory: a graceful exit to the real world: The most important criteria for a successful inflation are to explain the
observed temperature anisotropy in the cosmic microwave background radiation,
and exiting inflation in a vacuum where it can excite the Standard Model quarks
and leptons required for the success of Big Bang Nucleosynthesis. In this paper
we provide the first ever closed string model of inflation where the inflaton
couplings to hidden sector, moduli sector, and visible sector fields can be
computed, showing that inflation can lead to reheating the Standard Model
degrees of freedom before the electro-weak scale. |
Strong Coupling Phase of Chiral Gross Neveu Model: We perform the numerical simulation of the two dimensional chiral Gross Neveu
model using the Kogut-Susskind(KS) fermion. In the case of SU(4), the
Kosterlitz-Thouless phase transition happens at some critical value of the
coupling constant. In the case of one flavour, there exists the strong coupling
phase in which the correlation functions vanish and the general covariance is
realized in the quantum field thoery through the dynamical process. | Construction of irregular conformal/W block and flavor mass relations of
$\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model: A sequence of massive scaling limits of the $\beta$-deformed $A_{n-1}$ quiver
matrix model that keeps the size of the matrices finite and that corresponds to
the $N_{f} =2n \rightarrow 2n-1, 2n-2$ limits on the number of flavors at 4d
$su(n)$ ${\cal N} = 2$ SUSY gauge theory side is carried out to provide us with
the integral representation of $su(n)$ irregular conformal/W block. The
original paths are naturally deformed into those in the complex plane,
permitting us to convert into an $su(n)$ extension of the unitary matrix model
of GWW type with a set of log potentials for all species of eigenvalues.
Looking at the region in the parameter space that enjoys the maximal symmetry
of the model, we derive a set of relations among the mass parameters which may
serve as evidence for the existence of the Argyres-Douglas critical
hypersurface. |
Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM
theory: We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory.
The proof uses a shift acting on all external momenta, and we show that every
N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this
shift. The MHV vertex expansion allows us to derive compact and efficient
generating functions for all N^kMHV tree amplitudes of the theory. We also
derive an improved form of the anti-NMHV generating function. The proof leads
to a curious set of sum rules for the diagrams of the MHV vertex expansion. | D-brane Superpotentials and Geometric Invariants in Complete
Intersection Calabi-Yau Manifolds: By blowing up the ambient space along the curve wrapped by B-branes, we study
the brane superpotentials and Ooguri-Vafa invariants on complete intersections
Calabi-Yau threefolds. On the topological B-model side, B-brane superpotentials
are expressed in terms of the period integral of the blow-up manifolds. By
mirror maps, the superpotentials are generating functions of Ooguri-Vafa
invariants counting holomorphic disks on the topological A-model side. |
Duality, gauging and superHiggs effect in string and M-theory: We consider no-scale extended supergravity models as they arise from string
and M-theory compactifications in presence of fluxes. The special role of
gauging axion symmetries for the Higgs and superHiggs mechanism is outlined. | Percolation and the existence of a soft phase in the classical
Heisenberg model: We present the results of a numerical investigation of percolation properties
in a version of the classical Heisenberg model. In particular we study the
percolation properties of the subsets of the lattice corresponding to
equatorial strips of the target manifold ${\cal S}^2$. As shown by us several
years ago, this is relevant for the existence of a massless phase of the model.
Our investigation yields strong evidence that such a massless phase does indeed
exist. It is further shown that this result implies lack of asymptotic freedom
in the massive continuum limit. A heuristic estimate of the transition
temperature is given which is consistent with the numerical data. |
Extremal Branes as Elementary Particles: The supersymmetric p-branes of Type II string theory can be interpreted after
compactification as extremal black holes with zero entropy and infinite
temperature. We show how the p-branes avoid this apparent, catastrophic
instability by developing an infinite mass gap. Equivalently, these black holes
behave like elementary particles: they are dressed by effective potentials that
prevent absorption of impinging particles. In contrast, configurations with 2,
3, and 4 intersecting branes and their nonextremal extensions, behave
increasingly like conventional black holes. These results extend and clarify
earlier work by Holzhey and Wilczek in the context of four dimensional dilaton
gravity. | Path-Integral for Quantum Tunneling: Path-integral for theories with degenerate vacua is investigated. The origin
of the non Borel-summability of the perturbation theory is studied. A new
prescription to deal with small coupling is proposed. It leads to a series,
which at low orders and small coupling differs from the ordinary perturbative
series by nonperturbative amount, but is Borel-summable. |
Conformal renormalization of scalar-tensor theories: We study a conformally coupled scalar-tensor theory with a quartic potential
possessing local conformal symmetry up to a boundary term. We show that
requiring the restoration of the full local conformal symmetry fixes the
counterterms that render the on-shell action finite. The building block of the
resulting action is a conformally covariant tensor which is constructed out of
the metric and the scalar field and it has the same conformal weight as the
Weyl tensor. This allows us to obtain the counterterms for the scalar-tensor
sector in a closed form. The finiteness of the conformally complete version of
the action is suggestive on the validity of the Conformal Renormalization
prescription. We extend this theory by adding the Conformal Gravity action and
also the Einstein-AdS action written in McDowell-Mansouri form. Even though the
latter breaks the conformal symmetry, we find that the action is still
renormalized provided a suitable falloff of the scalar field when considering
asymptotically locally anti-de Sitter solutions. Black hole solutions in these
theories are studied, for which the Hawking temperature and the partition
function to first order in the saddle-point approximation are calculated,
providing a concrete example of this renormalization scheme. | On q-Electroweak: The q-electroweak theory obtained by replacing SU(2) by $SU_q(2)$ in the
Weinberg-Salam model is experimentally not distinguishable from the standard
model at the level of the doublet representation. However, differences between
the two theories should be observable when higher dimensional representations
are taken into account. In addition the possibility of probing non-local
structure may be offered by the q-theory. |
Quantum Holonomies based on the Lorentz-violating tensor background: We study geometric quantum phases corresponding to analogues of the Anandan
quantum phase [J. Anandan, Phys. Lett. A {\bf138}, 347 (1989)] based on a
possible scenario of the Lorentz symmetry violation background in a tensor
background. We also show that quantum holonomies associated with the analogue
of the Anandan quantum phase can be determined, and discuss a way of performing
one-qubit quantum gates by analogy with the holonomic quantum computation [P.
Zanardi and M. Rasetti, Phys. Lett. A {\bf264}, 94 (1999)]. | Generalized supersymmetric cosmological term in N=1 Supergravity: An alternative way of introducing the supersymmetric cosmological term in a
supergravity theory is presented. We show that the $AdS$-Lorentz superalgebra
allows to construct a geometrical formulation of supergravity containing a
generalized supersymmetric cosmological constant. The $N=1$, $D=4$ supergravity
action is built only from the curvatures of the $AdS$-Lorentz superalgebra and
corresponds to a MacDowell-Mansouri like action. The extension to a generalized
$AdS$-Lorentz superalgebra is also analyzed. |
The Schwarzschild Black Hole from Perturbation Theory to all Orders: Applying the quantum field theoretic perturbiner approach to Einstein
gravity, we compute the metric of a Schwarzschild black hole order by order in
perturbation theory. Using recursion, this calculation can be carried out in de
Donder gauge to all orders in Newton's constant. The result is a geometric
series which is convergent outside a disk of finite radius, and it agrees
within its region of convergence with the known de Donder gauge metric of a
Schwarzschild black hole. It thus provides a first all-order perturbative
computation in Einstein gravity with a matter source, and this series converges
to the known non-perturbative expression in the expected range of convergence. | Membranes on an Orbifold: We harvest clues to aid with the interpretation of the recently discovered
N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is
argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and
k=2, the classical moduli space M coincides with the infra-red moduli space of
SO(4) and SO(5) super Yang-Mills theory respectively. For higher Chern-Simons
level, the moduli space is a quotient of M. At a generic point in the moduli
space, the massive spectrum is proportional to the area of the triangle formed
by the two membranes and the orbifold fixed point. |
Higher spin currents in the critical $O(N)$ vector model at $1/N^2$: We calculate the anomalous dimensions of higher spin singlet currents in the
critical $O(N)$ vector model at order $1/N^2$. The results are shown to be in
agreement with the four-loop perturbative computation in $\phi^4$ theory in
$4-2\epsilon$ dimensions. It is known that the order $1/N$ anomalous dimensions
of higher-spin currents happen to be the same in the Gross-Neveu and the
critical vector model. On the contrary, the order $1/N^2$ corrections are
different. The results can also be interpreted as a prediction for the two-loop
computation in the dual higher-spin gravity. | Casimir force between surfaces close to each other: Casimir interactions (due to the massless scalar field fluctuations) of two
surfaces which are close to each other are studied.
After a brief general presentation, explicit calculations for co-axial
cylinders, co-centric spheres and co-axial cones are performed. |
String correlators on $\text{AdS}_3$: Three-point functions: We revisit the computation of string worldsheet correlators on Euclidean
$\text{AdS}_3$ with pure NS-NS background. We compute correlation functions
with insertions of spectrally flowed operators. We explicitly solve all the
known constraints of the model and for the first time conjecture a closed
formula for three-point functions with arbitrary amount of spectral flow. We
explain the relation of our results with previous computations in the
literature and derive the fusion rules of the model. This paper is the first in
a series with several installments. | Non-relativistic Nambu-Goldstone modes associated with spontaneously
broken space-time and internal symmetries: We show that a momentum operator of a translational symmetry may not commute
with an internal symmetry operator in the presence of a topological soliton in
non-relativistic theories. As a striking consequence, there appears a coupled
Nambu-Goldstone mode with a quadratic dispersion consisting of translational
and internal zero modes in the vicinity of a domain wall in an O(3) sigma
model, a magnetic domain wall in ferromagnets with an easy axis. |
Non-renormalization of the $V\bar cc$-vertices in ${\cal N}=1$
supersymmetric theories: Using the Slavnov--Taylor identities we prove that the three-point ghost
vertices with a single line of the quantum gauge superfield are not
renormalized in all loops in ${\cal N}=1$ supersymmetric gauge theories. This
statement is verified by the explicit one-loop calculation made by the help of
the BRST invariant version of the higher covariant derivative regularization.
Using the restrictions to the renormalization constants which are imposed by
the non-renormalization of the considered vertices we express the exact NSVZ
$\beta$-function in terms of the anomalous dimensions of the Faddeev--Popov
ghosts and of the quantum gauge superfield. In the expression for the NSVZ
$\beta$-function obtained in this way the contributions of the Faddeev--Popov
ghosts and of the matter superfields have the same structure. | Cosmological solutions with massive gravitons in the bigravity theory: We present solutions describing homogeneous and isotropic cosmologies in the
massive gravity theory with two dynamical metrics recently proposed in
arXiv:1109.3515 and claimed to be ghost free. These solutions can be spatially
open, closed, or flat, and at early times they are sourced by the perfect
fluid, while the graviton mass typically manifests itself at late times by
giving rise to a cosmological term. In addition, there are also exotic
solutions, for which already at early times, when the matter density is high,
the contribution of the graviton mass to the energy density is negative and
large enough to screen that of the matter contribution. The total energy can
then be negative, which may result in removing the initial singularity. For
special parameter values there are also solutions for which the two metrics
effectively decouple and evolve independently of each other. In the limit where
one of the gravitational coupling constant vanishes, such special solutions
reduce to those found in arXiv:1107.5504 within the theory where one of the
metrics is flat. |
New N=1 AdS$_4$ solutions of type IIB supergravity: We construct analytically a new family of supersymmetric AdS$_4$ solutions of
IIB supergravity, with the internal space provided by a deformed $S^5\times
S^1$. The solutions preserve N=1 supersymmetry and an SO(3) subgroup of
isometries of $S^5$, which is broken to U(1) along a flat direction. They are
further parametrised by a winding number and a choice of SL(2) duality twist
along the circle in an elliptic conjugacy class, thus including both globally
geometric and S-fold configurations. We identify these solutions by first
constructing a new family of vacua of D=4, $U(4)\ltimes\mathbb{R}^{12}$ gauged
maximal supergravity and use exceptional field theory to perform the uplift to
ten dimensions. We discuss the relevance of D=5 Wilson loops associated to
preserved and broken gauge symmetries in the construction of these classes of
solutions. | Second Quantization of the Wilson Loop: Treating the QCD Wilson loop as amplitude for the propagation of the first
quantized particle we develop the second quantization of the same propagation.
The operator of the particle position $\hat{\cal X}_{\mu}$ (the endpoint of the
"open string") is introduced as a limit of the large $N$ Hermitean matrix. We
then derive the set of equations for the expectation values of the vertex
operators $\VEV{ V(k_1)\dots V(k_n)} $. The remarkable property of these
equations is that they can be expanded at small momenta (less than the QCD mass
scale), and solved for expansion coefficients. This provides the relations for
multiple commutators of position operator, which can be used to construct this
operator. We employ the noncommutative probability theory and find the
expansion of the operator $\hat{\cal X}_\mu $ in terms of products of creation
operators $ a_\mu^{\dagger}$. In general, there are some free parameters left
in this expansion. In two dimensions we fix parameters uniquely from the
symplectic invariance. The Fock space of our theory is much smaller than that
of perturbative QCD, where the creation and annihilation operators were
labelled by continuous momenta. In our case this is a space generated by $d =
4$ creation operators. The corresponding states are given by all sentences made
of the four letter words. We discuss the implication of this construction for
the mass spectra of mesons and glueballs. |
Functional Schroedinger and BRST Quantization of (1+1)--Dimensional
Gravity: We discuss the quantization of pure string--inspired dilaton--gravity in
$(1+1)$--dimensions, and of the same theory coupled to scalar matter. We
perform the quantization using the functional Schroedinger and BRST formalisms.
We find, both for pure gravity and the matter--coupled theory, that the two
quantization procedures give inequivalent ``physical'' results. | Null Strings in Schwarzschild Spacetime: The null string equations of motion and constraints in the Schwarzschild
spacetime are given. The solutions are those of the null geodesics of General
Relativity appended by a null string constraint in which the "constants of
motion" depend on the world-sheet spatial coordinate. Because of the extended
nature of a string, the physical interpretation of the solutions is completely
different from the point particle case. In particular, a null string is
generally not propagating in a plane through the origin, although each of its
individual points is. Some special solutions are obtained and their physical
interpretation is given. Especially, the solution for a null string with a
constant radial coordinate $r$ moving vertically from the south pole to the
north pole around the photon sphere, is presented. A general discussion of
classical null/tensile strings as compared to massless/massive particles is
given. For instance, tensile circular solutions with a constant radial
coordinate $r$ do not exist at all. The results are discussed in relation to
the previous literature on the subject. |
Relative Topological Integrals and Relative Cheeger-Simons Differential
Characters: Topological integrals appear frequently in Lagrangian field theories. On
manifolds without boundary, they can be treated in the framework of (absolute)
(co)homology using the formalism of Cheeger--Simons differential characters.
String and D--brane theory involve field theoretic models on worldvolumes with
boundary. On manifolds with boundary, the proper treatment of topological
integrals requires a generalization of the usual differential topological set
up and leads naturally to relative (co)homology and relative Cheeger--Simons
differential characters. In this paper, we present a construction of relative
Cheeger--Simons differential characters which is computable in principle and
which contains the ordinary Cheeger--Simons differential characters as a
particular case. | Localised Gravity and Resolved Braneworlds: Deriving an effective massless field theory for fluctuations about a
braneworld spacetime requires analysis of the transverse-space-wavefunction's
second-order differential equation. There can be two strikingly different types
of effective theory. For a supersymmetric braneworld, one involves a
technically consistent embedding of a supergravity theory on the worldvolume;
the other can produce, in certain situations, a genuine localisation of gravity
near the worldvolume but not via a technically consistent embedding. So, in the
latter situation, the theory's dynamics remains higher-dimensional but there
can still be a lower-dimensional effective-theory interpretation of the
dynamics at low worldvolume momenta / large worldvolume distances.
This paper examines the conditions for such a gravity localisation to be
possible. Localising gravity about braneworld spacetimes requires finding
solutions to transverse-space self-adjoint Sturm-Liouville problems admitting a
normalisable zero mode in the noncompact transverse space. This in turn
requires analysis of Sturm-Liouville problems with radial singular endpoints
following a formalism originating in the work of Hermann Weyl. Examples of such
gravity-localising braneworld systems are found and analysed in this formalism
with underlying "skeleton" braneworlds of Salam-Sezgin, resolved D3-brane and
Randall-Sundrum II types. |
N=2 Supersymmetry and U(1)-Duality: Understanding the consequences of the E_{7(7)} duality on the UV properties
of N=8 supergravity requires unravelling when and how duality-covariant actions
can be constructed so as to accommodate duality-invariant counter-terms. For
non-supersymmetric abelian gauge theories exhibiting U(1)-duality, with and
without derivative couplings, it was shown that such a covariant construction
is always possible. In this paper we describe a similar procedure for the
construction of covariant non-linear deformations of U(1)-duality invariant
theories in the presence of rigid N=2 supersymmetry. This is a concrete step
towards studying the interplay of duality and extended supersymmetry. | Sp-brane accelerating cosmologies: We investigate time dependent solutions (S-brane solutions) for product
manifolds consisting of factor spaces where only one of them is non-Ricci-flat.
Our model contains minimally coupled free scalar field as a matter source. We
discuss a possibility of generating late time acceleration of the Universe. The
analysis is performed in conformally related Brans-Dicke and Einstein frames.
Dynamical behavior of our Universe is described by its scale factor. Since the
scale factors of our Universe are described by different variables in both
frames, they can have different dynamics.
Indeed, we show that with our S-brane ansatz in the Brans-Dicke frame the
stages of accelerating expansion exist for all types of the external space
(flat, spherical and hyperbolic). However, applying the same ansatz for the
metric in the Einstein frame, we find that a model with flat external space and
hyperbolic compactification of the internal space is the only one with the
stage of the accelerating expansion. Scalar field can prevent this
acceleration. It is shown that the case of hyperbolic external space in
Brans-Dicke frame is the only model which can satisfy experimental bounds for
the fine structure constant variations. We obtain a class of models where a
pare of dynamical internal spaces have fixed total volume. It results in fixed
fine structure constant. However, these models are unstable and external space
is non-accelerating. |
Effective Stringy Description of Schwarzschild Black Holes: We start by pointing out that certain Riemann surfaces appear rather
naturally in the context of wave equations in the black hole background. For a
given black hole there are two closely related surfaces. One is the Riemann
surface of complexified ``tortoise'' coordinate. The other Riemann surface
appears when the radial wave equation is interpreted as the Fuchsian
differential equation. We study these surfaces in detail for the BTZ and
Schwarzschild black holes in four and higher dimensions. Topologically, in all
cases both surfaces are a sphere with a set of marked points; for BTZ and 4D
Schwarzschild black holes there is 3 marked points. In certain limits the
surfaces can be characterized very explicitly. We then show how properties of
the wave equation (quasi-normal modes) in such limits are encoded in the
geometry of the corresponding surfaces. In particular, for the Schwarzschild
black hole in the high damping limit we describe the Riemann surface in
question and use this to derive the quasi-normal mode frequencies with the
log(3) as the real part. We then argue that the surfaces one finds this way
signal an appearance of an effective string. We propose that a description of
this effective string propagating in the black hole background can be given in
terms of the Liouville theory living on the corresponding Riemann surface. We
give such a stringy description for the Schwarzschild black hole in the limit
of high damping and show that the quasi-normal modes emerge naturally as the
poles in 3-point correlation function in the effective conformal theory. | Hard thermal effective action in QCD through the thermal operator: Through the application of the thermal operator to the zero temperature
retarded Green's functions, we derive in a simple way the well known hard
thermal effective action in QCD. By relating these functions to forward
scattering amplitudes for on-shell particles, this derivation also clarifies
the origin of important properties of the hard thermal effective action, such
as the manifest Lorentz and gauge invariance of its integrand. |
Covariant Hamiltonian formalisms for particles and antiparticles: The hyperplane and proper time formalisms are discussed mainly for the
spin-half particles in the quantum case. A connection between these covariant
Hamiltonian formalisms is established. It is showed that choosing the
space-like hyperplanes instantaneously orthogonal to the direction of motion of
the particle the proper time formalism is retrieved on the mass shell. As a
consequence, the relation between the St\"uckelberg-Feynman picture and the
standard canonical picture of quantum field theory is clarified. | Heterotic supersymmetric backgrounds with compact holonomy revisited: We simplify the classification of supersymmetric solutions with compact
holonomy of the Killing spinor equations of heterotic supergravity using the
field equations and the additional assumption that the 3-form flux is closed.
We determine all the fractions of supersymmetry that the solutions preserve and
find that there is a restriction on the number of supersymmetries which depends
on the isometry group of the background. We examine the geometry of spacetime
in all cases. We find that the supersymmetric solutions of heterotic
supergravity are associated with a large number of geometric structures which
include 7-dimensional manifolds with $G_2$ structure,
6-dimensional complex and almost complex manifolds, and 4-dimensional
hyper-K\"ahler, K\"ahler and anti-self-dual Weyl manifolds. |
Supersymmetric K field theories and defect structures: We construct supersymmetric K field theories (i.e., theories with a
non-standard kinetic term) in 1+1 and 2+1 dimensions such that the bosonic
sector just consists of a nonstandard kinetic term plus a potential. Further,
we study the possibility of topological defect formation in these
supersymmetric models. Finally, we consider more general supersymmetric K field
theories where, again, topological defects exist in some cases. | Deep Inelastic Scattering on an Extremal RN-AdS Black Hole II:
Holographic Fermi Surface: We consider deep inelastic scattering (DIS) on a dense nucleus described as
an extremal RN-AdS black hole with holographic quantum fermions in the bulk. We
evaluate the 1-loop fermion contribution to the R-current on the charged black
hole, and map it on scattering off a Fermi surface of a dense and large nucleus
with fixed atomic number. Near the black hole horizon, the geometry is that of
AdS$_2\times $R$^3$ where the fermions develop an emergent Fermi surface with
anomalous dimensions. DIS scattering off these fermions yields to anomalous
partonic distributions mostly at large-x, as well as modified hard scattering
rules. The pertinent R-ratio for the black hole is discussed. For comparison,
the structure functions and the R-ratio in the probe or dilute limit with no
back-reaction on the geometry, are also derived. We formulate a hybrid
holographic model for DIS scattering on heavy and light nuclei, which compares
favorably to the existing data for Pb, Au, Fe, C and He over a wide range of
parton-x. |
(2,0) Superconformal OPEs in D=6, Selection Rules and
Non-renormalization Theorems: We analyse the OPE of any two 1/2 BPS operators of (2,0) SCFT$_6$ by
constructing all possible three-point functions that they can form with
another, in general long operator. Such three-point functions are uniquely
determined by superconformal symmetry. Selection rules are derived, which allow
us to infer ``non-renormalization theorems'' for an abstract superconformal
field theory. The latter is supposedly related to the strong-coupling dynamics
of $N_c$ coincident M5 branes, dual, in the large-$N_c$ limit, to the bulk
M-theory compactified on AdS$_7 \times$S$_4$. An interpretation of extremal and
next-to-extremal correlators in terms of exchange of operators with protected
conformal dimension is given. | Superluminal Propagation and Acausality of Nonlinear Massive Gravity: Massive gravity is an old idea: trading geometry for mass. Much effort has
been expended on establishing a healthy model, culminating in the current
ghost-free version. We summarize here our recent findings -- that it is still
untenable -- because it is locally acausal: CTC solutions can be constructed in
a small neighborhood of any event. |
Two Moving-Angled 1-Branes with Electric Fields in a Partially Compact
Spacetime: In this article we consider two $m1$-branes at angle in the presence of the
background electric fields, in a partially compact spacetime. The branes have
motions along a common direction that is perpendicular to both of them. Using
the boundary state formalism, we calculate their interaction amplitude. Some
special cases of this interaction will be studied in detail. | Bound states in N=2 Liouville theory with boundary and Deep throat
D-branes: We exhibit bound states in the spectrum of non-compact D-branes in N=2
Liouville conformal field theory. We interpret these states in the study of
D-branes in the near-horizon limit of Neveu-Schwarz five-branes spread on a
topologically trivial circle. We match semi-classical di-electric and repulsion
effects with exact conformal field theory results and describe the fate of
D-branes hitting NS5-branes. We also show that the bound states can give rise
to massless vector and hyper multiplets in a low-energy gauge theory on
D-branes deep inside the throat. |
Motion of a Rigid Body in Body-Fixed Coordinate System -- for
Autoparrallel Trajectories in Spaces with Torsion: We use a recently developed action principle in spaces with curvature and
torsion to derive the Euler equations of motion for a rigid body within the
body-fixed coordinate system. This serves as an example that the particle
trajectories in a space with curvature and torsion follow the straightest paths
(autoparallels), not the shortest paths (geodesics), as commonly believed. | Refined Black Hole Ensembles and Topological Strings: We formulate a refined version of the Ooguri-Strominger-Vafa (OSV)
conjecture. The OSV conjecture that Z_{BH} = |Z_{top}|^2 relates the BPS black
hole partition function to the topological string partition function Z_{top}.
In the refined conjecture, Z_{BH} is the partition function of BPS black holes
counted with spin, or more precisely the protected spin character. Z_{top}
becomes the partition function of the refined topological string, which is
itself an index. Both the original and the refined conjecture are examples of
large N duality in the 't Hooft sense. The refined conjecture applies to
non-compact Calabi-Yau manifolds only, so the black holes are really BPS
particles with large entropy, of order N^2. The refined OSV conjecture states
that the refined BPS partition function has a large N dual which is captured by
the refined topological string. We provide evidence that the conjecture holds
by studying local Calabi-Yau threefolds consisting of line bundles over a genus
g Riemann surface. We show that the refined topological string partition
function on these geometries is computed by a two-dimensional TQFT. We also
study the refined black hole partition function arising from N D4 branes on the
Calabi-Yau, and argue that it reduces to a (q,t)-deformed version of
two-dimensional SU(N) Yang-Mills. Finally, we show that in the large N limit
this theory factorizes to the square of the refined topological string in
accordance with the refined OSV conjecture. |
$d>2$ Stress-Tensor OPE near a Line: We study the $TT$ OPE in $d>2$ CFTs whose bulk dual is Einstein gravity.
Directly from the $TT$ OPE, we obtain, in a certain null-like limit, an
algebraic structure consistent with the Jacobi identity: $[{\cal L}_m, {\cal
L}_n]= (m-n) {\cal L}_{m+n}+ C m (m^2-1) \delta_{m+n,0}$. The dimensionless
constant $C$ is proportional to the central charge $C_T$. Transverse integrals
in the definition of ${\cal L}_m$ play a crucial role. We comment on the
corresponding limiting procedure and point out a curiosity related to the
central term. A connection between the $d>2$ near-lightcone stress-tensor
conformal block and the $d=2$ $\cal W$-algebra is observed. This note is
motivated by the search for a field-theoretic derivation of $d>2$ correlators
in strong coupling critical phenomena. | Torus HOMFLY as the Hall-Littlewood Polynomials: We show that the HOMFLY polynomials for torus knots T[m,n] in all fundamental
representations are equal to the Hall-Littlewood polynomials in representation
which depends on m, and with quantum parameter, which depends on n. This makes
the long-anticipated interpretation of Wilson averages in 3d Chern-Simons
theory as characters precise, at least for the torus knots, and calls for
further studies in this direction. This fact is deeply related to
Hall-Littlewood-MacDonald duality of character expansion of superpolynomials
found in arXiv:1201.3339. In fact, the relation continues to hold for extended
polynomials, but the symmetry between m and n is broken, then m is the number
of strands in the braid. Besides the HOMFLY case with q=t, the torus
superpolynomials are reduced to the single Hall-Littlewood characters in the
two other distinguished cases: q=0 and t=0. |
The Non-BPS Black Hole Attractor Equation: We study the attractor mechanism for extremal non-BPS black holes with an
infinite throat near horizon geometry, developing, as we do so, a physical
argument as to why such a mechanism does not exist in non-extremal cases. We
present a detailed derivation of the non-supersymmetric attractor equation.
This equation defines the stabilization of moduli near the black hole horizon:
the fixed moduli take values specified by electric and magnetic charges
corresponding to the fluxes in a Calabi Yau compactification of string theory.
They also define the so-called double-extremal solutions. In some examples,
studied previously by Tripathy and Trivedi, we solve the equation and show that
the moduli are fixed at values which may also be derived from the critical
points of the black hole potential. | Hagedorn Behavior of Little String Theories: We examine the Hagedorn behavior of little string theory using its
conjectured duality with near-horizon NS5-branes. In particular, by studying
the string-corrected NS5-brane supergravity solution, it is shown that
tree-level corrections to the temperature vanish, while the leading one-loop
string correction generates the correct temperature dependence of the entropy
near the Hagedorn temperature. Finally, the Hagedorn behavior of ODp-brane
theories, which are deformed versions of little string theory, is considered
via their supergravity duals. |
Correction terms to Newton law due to induced gravity in AdS background: We calculate small correction terms to gravitational potential on
Randall-Sundrum brane with an induced Einstein term. The behaviors of the
correction terms depend on the magnitudes of $AdS$ radius $k^{-1}$ and a
characteristic length scale $\l$ of model. We represent the gravitational
potential for arbitrary $k$ and $\l$ at all distances. | Semirelativistic stability of N-boson systems bound by 1/r pair
potentials: We analyze a system of self-gravitating identical bosons by means of a
semirelativistic Hamiltonian comprising the relativistic kinetic energies of
the involved particles and added (instantaneous) Newtonian gravitational pair
potentials. With the help of an improved lower bound to the bottom of the
spectrum of this Hamiltonian, we are able to enlarge the known region for
relativistic stability for such boson systems against gravitational collapse
and to sharpen the predictions for their maximum stable mass. |
Renyi entropy for monodromy defects of higher derivative free fields on
even-dimensional spheres: Explicit polynomial forms for R\'enyi and entanglement entropies are given on
even --dimensional spheres which possess a codimension--2 U(1) monodromy
defect. Free scalar and Dirac fields are treated and higher-derivative
propagation operators employed. The central charge, $C_T$, is also calculated.
Comparison with existing results is made and it is shown how these can be
obtained from the values here. | Emerging AdS from Extremally Rotating NS5-branes: We investigate the near-horizon limit of extremally rotating NS5-branes. The
resulting geometry has SL(2,R) \times U(1)^2 isometry. The asymptotic symmetry
group contains a chiral Virasoro algebra, and we obtain two different
realizations depending on the boundary conditions we impose. When one of the
two angular momenta vanishes, the symmetry is enhanced to AdS_3. The entropy of
the boundary theory can be estimated from the Cardy formula and it agrees with
the Bekenstein-Hawking entropy of the bulk theory. We can embed the extremally
rotating NS5-brane geometry in an exactly solvable string background, which may
yield microscopic understanding of this duality, especially about the
mysterious enhancement of the symmetry from AdS_2 to AdS_3. The construction
suggests emerging Virasoro symmetries in the extreme corner of the (1+5)
dimensional little string theory. |
M-theory Potential from the $G_2$ Hitchin Functional in Superspace: We embed the component fields of eleven-dimensional supergravity into a
superspace of the form $X\times Y$ where $X$ is the standard 4D, $N=1$
superspace and $Y$ is a smooth 7-manifold. The eleven-dimensional 3-form gives
rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of $Y$.
It contains a natural candidate for a $G_2$ structure on $Y$, and being a
complex of superforms, defines a superspace Chern-Simons invariant. Adding to
this a natural generalization of the Riemannian volume on $X\times Y$ and
freezing the (superspin-$\frac32$ and 1) supergravity fields on $X$, we obtain
an approximation to the eleven-dimensional supergravity action that suffices to
compute the scalar potential. In this approximation the action is the sum of
the superspace Chern-Simons term and a superspace generalization of the Hitchin
functional for $Y$ as a $G_2$-structure manifold. Integrating out auxiliary
fields, we obtain the conditions for unbroken supersymmetry and the scalar
potential. The latter reproduces the Einstein-Hilbert term on $Y$ in a form due
to Bryant. | Degenerate noncommutativity: We study a renormalizable four dimensional model with two deformed quantized
space directions. A one-loop renormalization is performed explicitly. The
Euclidean model is connected to the Minkowski version via an analytic
continuation. At a special value of the parameters a nontrivial fixed point of
the renormalization group occurs. |
Penrose limits and Green-Schwarz strings: We discuss the Green-Schwarz action for type IIB strings in general
plane-wave backgrounds obtained as Penrose limits from any IIB supergravity
solutions with vanishing background fermions. Using the normal-coordinate
expansion in superspace, we prove that the light-cone action is necessarily
quadratic in the fermionic coordinates. This proof is valid for more general
pp-wave backgrounds under certain conditions. We also write down the complete
quadratic action for general bosonic on-shell backgrounds in a form in which
its geometrical meaning is manifest both in the Einstein and string frames.
When the dilaton and 1-form field strength are vanishing, and the other field
strengths are constant, our string-frame action reduces, up to conventions, to
the one which has been written down using the supercovariant derivative. | Binary AdS black holes coupled to a bath in Type IIB: We construct Type IIB string theory setups which, via double holography,
realize two gravitational systems in separate AdS spaces which interact with
each other and with a non-gravitational bath. We employ top-down string theory
solutions with concrete field theory duals in the form of 4d $\mathcal N=4$ SYM
BCFTs and a first-principles notion of double holography. The setups are used
to realize pairs of `near' and `far' black holes from the perspective of the
bath, which exchange Hawking radiation with each other and radiate into the
bath. We identify three phases for the entropy in the bath characterized as no
island, partial island and full island, and discuss the entropy curves. The
setups differ from the black hole binaries observed in gravitational wave
experiments but may capture certain aspects. |
A Positive Energy Theorem for AdS Solitons: The uncharged AdS$_4$ soliton has been recently shown to be continuously
connected to a magnetic, supersymmetric AdS$_4$ soliton within $\mathcal{N}=8$
gauged supergravity. By constructing the asymptotic superalgebra, we establish
a positive energy theorem for the magnetic AdS$_4$ solitons admitting
well-defined asymptotic Killing spinors, antiperiodic on a contractible $S^1$.
We show that there exists only one discrete solution endowed with these
boundary conditions satisfying the bound, the latter being saturated by the
null energy supersymmetric configuration. Despite having negative energy, the
uncharged AdS$_4$ soliton does not contradict the positive energy theorem, as
it does not admit well-defined asymptotic Killing spinors. | Decomposition of $\mathcal{N}=1$ superconformal minimal models and their
fractional quantum Hall wavefunctions: $\mathcal{N}=1$ superconformal minimal models are the first series of unitary
conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset
constructions, we characterize CFTs in $\mathcal{N}=1$ superconformal minimal
models using combinations of a parafermion theory, an Ising theory and a free
boson theory. Supercurrent operators in the original theory also becomes sums
of operators from each constituent theory. If we take our $\mathcal{N}=1$
superconformal theories as the neutral part of the edge theory of a fractional
quantum Hall state, we present a systematic way of calculating its ground state
wavefunction using free field methods. Each ground state wavefunction is known
previously as a sum of polynomials with distinct clustering behaviours. Based
on our decomposition, we find explicit expressions for each summand polynomial.
A brief generalization to $S_3$ minimal models using coset construction is also
included. |
Logarithmic supertranslations and supertranslation-invariant Lorentz
charges: We extend the BMS(4) group by adding logarithmic supertranslations. This is
done by relaxing the boundary conditions on the metric and its conjugate
momentum at spatial infinity in order to allow logarithmic terms of carefully
designed form in the asymptotic expansion, while still preserving finiteness of
the action. Standard theorems of the Hamiltonian formalism are used to derive
the (finite) generators of the logarithmic supertranslations. As the ordinary
supertranslations, these depend on a function of the angles. Ordinary and
logarithmic supertranslations are then shown to form an abelian subalgebra with
non-vanishing central extension. Because of this central term, one can make
nonlinear redefinitions of the generators of the algebra so that the pure
supertranslations ($\ell >1$ in a spherical harmonic expansion) and the
logarithmic supertranslations have vanishing brackets with all the Poincar\'e
generators, and, in particular, transform in the trivial representation of the
Lorentz group. The symmetry algebra is then the direct sum of the Poincar\'e
algebra and the infinite-dimensional abelian algebra formed by the pure
supertranslations and the logarithmic supertranslations (with central
extension). The pure supertranslations are thus completely decoupled from the
standard Poincar\'e algebra in the asymptotic symmetry algebra. This implies in
particular that one can provide a definition of the angular momentum which is
manifestly free from supertranslation ambiguities. An intermediate redefinition
providing a partial decoupling of the pure and logarithmic supertranslations is
also given. | General N = 1 Supersymmetric Flux Vacua of (Massive) Type IIA String
Theory: We derive conditions for the existence of four-dimensional \N=1
supersymmetric flux vacua of massive type IIA string theory with general
supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show
that such flux vacua exist only when the internal geometry is nearly-K\"ahler.
The geometry is not warped, all the allowed fluxes are proportional to the mass
parameter and the dilaton is fixed by a ratio of (quantized) fluxes. The
four-dimensional cosmological constant, while negative, becomes small in the
vacuum with the weak string coupling. |
String tension and string susceptibility in two-dimensional generalized
Weingarten model: We study the two-dimensional generalized Weingarten model reduced to a point,
which interpolates reduced Weingarten model and the large-N gauge theory. We
calculate the expectation value of the Wilson loop using Monte-Carlo method and
determine the string tension and string susceptibility. The numerical result
suggests that the string susceptibility approaches to -2 in a certain
parametric region, which implies that the branched-polymer configurations are
suppressed. | All Global One- and Two-Dimensional Higher-Point Conformal Blocks: We introduce a full set of rules to directly express all $M$-point conformal
blocks in one- and two-dimensional conformal field theories, irrespective of
the topology. The $M$-point conformal blocks are power series expansion in some
carefully-chosen conformal cross-ratios. We then prove the rules for any
topology constructively with the help of the known position space operator
product expansion. To this end, we first compute the action of the position
space operator product expansion on the most general function of position space
coordinates relevant to conformal field theory. These results provide the
complete knowledge of all $M$-point conformal blocks with arbitrary external
and internal quasi-primary operators (including arbitrary spins in two
dimensions) in any topology. |
Perturbations of W(infinity) CFTs: The holographic duals of higher spin theories on AdS_3 are described by the
large N limit of a family of minimal model CFTs, whose symmetry algebra is
equivalent to W(infinity)[lambda]. We study perturbations of these limit
theories, and show that they possess a marginal symmetry-preserving
perturbation that describes switching on the 1/N corrections. We also test our
general results for the specific cases of lambda=0,1, where free field
realisations are available. | Fermions, boundaries and conformal and chiral anomalies in $d=3,\ 4$ and
$5$ dimensions: In the presence of boundaries, the quantum anomalies acquire additional
boundary terms. In odd dimensions the integrated conformal anomaly, for which
the bulk contribution is known to be absent, is non-trivial due to the boundary
terms. These terms became a subject of active study in the recent years. In the
present paper we continue our previous study [1], [2] and compute explicitly
the anomaly for fermions in dimensions $d=3, \ 4 \ $ and $5$. The calculation
in dimension $5$ is new. It contains both contributions of the gravitational
field and the gauge fields to the anomaly. In dimensions $d=3$ and $4$ we
reproduce and clarify the derivation of the results available in the
literature. Imposing the conformal invariant mixed boundary conditions for
fermions in odd dimension $d$ we particularly pay attention to the necessity of
choosing the doubling representation for gamma matrices. In this representation
there exists a possibility to define chirality and thus address the question of
the chiral anomaly. The anomaly is entirely due to terms defined on the
boundary. They are calculated in the present paper in dimensions $d=3$ and $5$
due to both gravitational and gauge fields. To complete the picture we
re-evaluate the chiral anomaly in $d=4$ dimensions and find a new boundary term
that is supplementary to the well-known Pontryagin term. |
Continuity and Resurgence: towards a continuum definition of the CP(N-1)
model: We introduce a non-perturbative continuum framework to study the dynamics of
quantum field theory (QFT), applied here to the CP(N-1) model, using Ecalle's
theory of resurgent trans-series, combined with the physical principle of
continuity, in which spatial compactification and a Born-Oppenheimer
approximation reduce QFT to quantum mechanics, while preventing all intervening
rapid cross-overs or phase transitions. The reduced quantum mechanics contains
the germ of all non-perturbative data, e.g., mass gap, of the QFT, all of which
are calculable. For CP(N-1), the results obtained at arbitrary N are consistent
with lattice and large-N results. These theories are perturbatively non-Borel
summable and possess the elusive IR-renormalon singularities. The trans-series
expansion, in which perturbative and non-perturbative effects are intertwined,
encapsulates the multi-length-scale nature of the theory, and eliminates all
perturbative and non-perturbative ambiguities under consistent analytic
continuation of the coupling. We demonstrate the cancellation of the leading
non-perturbative ambiguity in perturbation theory against the ambiguity in
neutral bion amplitudes. This provides a weak-coupling interpretation of the
IR-renormalon, and a theorem by Pham et al implies that the mass gap is a
resurgent function, for which resummation of the semi-classical expansion
yields finite exact results. | Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at
Large N: We study all three-point functions of normalized chiral operators in D=4,
$\mathcal{N}=4$, U(N) supersymmetric Yang-Mills theory in the large $N$ limit.
We compute them for small 't Hooft coupling $\lambda=g_{YM}^2N<<1$ using free
field theory and at strong coupling $\lambda=g_{YM}^2>>1$ using the $AdS$/CFT
correspondence. Surprisingly, we find the same answers in the two limits. We
conjecture that at least for large $N$ the exact answers are independent of
$\lambda $ . |
Wilson loop and dS/CFT correspondence: We calculate Wilson loop (quark anti-quark potential) in dS/CFT
correspondence. The brane-world model is considered where bulk is two 5d
Euclidean de Sitter spaces and boundary (brane) is 4d de Sitter one. Starting
from the Nambu-Goto action, the calculation of the effective tension (average
energy) is presented. Unlike to the case of supergravity calculation of Wilson
loop in AdS/CFT set-up, there is no need to regularize the Nambu-Goto action
(the volume of de Sitter space is finite). It turns out that at sufficiently
small curvature of 5d background the energy (potential) is positive and linear
on the distance between quark and anti-quark what indicates to the possibility
of confinement. | Black Holes with Flavors of Quantum Hair?: We show that black holes can posses a long-range quantum hair of
super-massive tensor fields, which can be detected by Aharonov-Bohm tabletop
interference experiments, in which a quantum-hairy black hole, or a remnant
particle, passes through the loop of a magnetic solenoid. The long distance
effect does not decouple for an arbitrarily high mass of the hair-providing
field. Because Kaluza-Klein and String theories contain infinite number of
massive tensor fields, we study black holes with quantum Kaluza-Klein hair. We
show that in five dimensions such a black hole can be interpreted as a string
of `combed' generalized magnetic monopoles, with their fluxes confined along
it. For the compactification on a translation-invariant circle, this
substructure uncovers hidden flux conservation and quantization of the monopole
charges, which constrain the quantum hair of the resulting four-dimensional
black hole. For the spin-2 quantum hair this result is somewhat unexpected,
since the constituent `magnetic' charges have no `electric' counterparts.
Nevertheless, the information about their quantization is encoded in
singularity. |
Primordial Black Holes from non-Gaussian tails: We develop a primordial black hole (PBH) production mechanism, deriving
non-Gaussian tails from interacting quantum fields during early universe
inflation. The multi-field potential landscape may contain relatively flat
directions, as a result of energetically favorable adjustments of fields
coupled to the inflaton. Such additional fields do not contribute to CMB
fluctuations given a sufficient large-scale decay, related to a gap in the
critical exponents computed using stochastic methods. Along such directions
transverse to the inflaton, the field makes rare jumps to large values. Mixing
with the inflaton leads to a substantial tail in the resulting probability
distribution for the primordial perturbations. Incorporating a large number of
flavors of fields ensures theoretical control of radiative corrections and a
substantial abundance. This generates significant PBH production for a
reasonable window of parameters, with the mass range determined by the time
period of mixing and the inflationary Hubble scale. We analyze a particular
model in detail, and then comment on a broader family of models in this class
which suggests a mechanism for primordial seeds for early super-massive black
holes in the universe. Along the way, we encounter an analytically tractable
example of stochastic dynamics and provide some representative calculations of
its correlations and probability distributions. | Holographic renormalization group flows in two-dimensional gravity and
$AdS$ black holes: We look into the $AdS$ black holes from two-dimensional gravity perspective.
In this work, we extend the previous results of holographic renormalization
group flows to dimensions two. By introducing a superpotential, we derive the
flow equations in two-dimensional dilaton gravity. We find a quantity which
monotonically decreases along flows and give some comments on holographic
$c$-theorem. As examples, we show that recently studied supersymmetric $AdS$
black hole solutions generically dimensionally reduce to two-dimensional
dilaton gravity, and obtain the flow equations for black hole solutions. |
Topological field theories, string backgrounds and homotopy algebras: String backgrounds are described as purely geometric objects related to
moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a
conformal field theory. Relations with conformal field theory, topological
field theory and topological gravity are studied. For each field theory, an
algebraic counterpart, the (homotopy) algebra satisfied by the tree level
correlators, is constructed. | Holographic Screens and Transport Coefficients in the Fluid/Gravity
Correspondence: We consider in the framework of the fluid/gravity correspondence the dynamics
of hypersurfaces located in the holographic radial direction at r = r_0. We
prove that these hypersurfaces evolve, to all orders in the derivative
expansion and including all higher curvature corrections, according to the same
hydrodynamics equations with identical transport coefficients. The analysis is
carried out for normal fluids as well as for superfluids. Consequently, this
proves the exactness of the bulk viscosity formula derived in arXiv:1103.1657
via the null horizon dynamics. |
Stairway to equilibrium entropy: We compute the time evolution of the non-equilibrium entropy in the
homogeneous isotropization dynamics of the 1RCBH model, corresponding to a
top-down holographic construction describing a strongly coupled $\mathcal{N}=4$
Supersymmetric Yang-Mills fluid charged under an Abelian $U(1)$ subgroup of the
global $SU(4)$ R-symmetry. The model has a critical point in its conformal
phase diagram and for the analyzed set of initial data we also evaluate the
time evolution of the pressure anisotropy and the scalar condensate of the
medium. As found previously for the Bjorken flow of the same model, we observe
that for some initial data satisfying all the energy conditions, dynamical
transient violations of the dominant and the weak energy conditions take place
when the fluid is still far from equilibrium. However, a more complex structure
than in Bjorken flow is observed in the formation of transient plateaus during
the time evolution of the entropy density in the homogeneous isotropization
dynamics. In fact, a new feature disclosed in this work is the formation of a
periodic sequence of several close plateaus in the form of a stairway for the
entropy density near thermodynamic equilibrium, which is observed for all the
initial data analyzed. | Exact Green's Function and Fermi Surfaces from Conformal Gravity: We study the Dirac equation of a charged massless spinor on the general
charged AdS black hole of conformal gravity. The equation can be solved exactly
in terms of Heun's functions. We obtain the exact Green's function in the phase
space (\omega,k). This allows us to obtain Fermi surfaces for both Fermi and
non-Fermi liquids. Our analytic results provide a more elegant approach of
studying some strongly interacting fermionic systems not only at zero
temperature, but also at any finite temperature. At zero temperature, we
analyse the motion of the poles in the complex \omega plane and obtain the
leading order terms of the dispersion relation, expressed as the Laurent
expansion of \omega in terms of k. We illustrate new distinguishing features
arising at the finite temperature. The Green's function with vanishing \omega
at finite temperature has a fascinating rich structure of spiked maxima in the
plane of k and the fermion charge q. |
Aspects of Effective Theory for Multiple M5-Branes Compactified On
Circle: A supersymmetric non-Abelian self-dual gauge theory with the explicit
introduction of Kaluza-Klein modes is proposed to give a classical description
of multiple M5-branes on $R^5 \times S^1$. The gauge symmetry is parametrized
by Lie-algebra valued 1-forms with the redundancy of a 0-form, and the
supersymmetry transformations without gauge-fixing are given. We study BPS
configurations involving KK modes, including M-waves and M2-branes with
non-trivial distributions around the circle. Finally, this supersymmetric gauge
theory of two-forms can be equipped with more general non-Abelian gerbes in
five dimensions. | On the algebraic approach to cubic lattice Potts models: We consider Diagram algebras, $\Dg(G)$ (generalized Temperley-Lieb algebras)
defined for a large class of graphs $G$, including those of relevance for cubic
lattice Potts models, and study their structure for generic $Q$. We find that
these algebras are too large to play the precisely analogous role in three
dimensions to that played by the Temperley-Lieb algebras for generic $Q$ in the
planar case. We outline measures to extract the quotient algebra that would
illuminate the physics of three dimensional Potts models. |
Perturbative zero-point energy for a cylinder of elliptical section: We examine the Casimir effect for a perfectly conducting cylinder of
elliptical section, taking as reference the known case of circular section. The
zero-point energy of this system is evaluated by the mode summation method,
using the ellipticity as a perturbation parameter. Mathieu function techniques
are applied. | Reflection algebra, Yangian symmetry and bound-states in AdS/CFT: We present the `Heisenberg picture' of the reflection algebra by explicitly
constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends
on a boundary with non-trivial degrees of freedom and which preserves the full
bulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary
states and some automorphisms of the underlying algebras. |
Flopping and Slicing: SO(4) and Spin(4)-models: We study the geometric engineering of gauge theories with gauge group Spin(4)
and SO(4) using crepant resolutions of Weierstrass models. The corresponding
elliptic fibrations realize a collision of singularities corresponding to two
fibers with dual graph the affine $A_1$ Dynkin diagram. There are eight
different ways to engineer such collisions using decorated Kodaira fibers. The
Mordell-Weil group of the elliptic fibration is required to be trivial for
Spin(4) and Z/2Z for SO(4).
Each of these models have two possible crepant resolutions connected by a
flop. We also compute a generating function for the Euler characteristic of
such elliptic fibrations over a base of arbitrary dimensions. In the case of a
threefold, we also compute the triple intersection numbers of the fibral
divisors. In the case of Calabi-Yau threefolds, we also compute their Hodge
numbers, and check the cancellations of anomalies in a six-dimensional
supergravity theory. | Covariant Closed String Bits -- Classical Theory: We study lattice wouldsheet theory with continuous time describing free
motion of a system of bound string bits. We use a non-local lattice derivative
that allows us to preserve all the symmetries of the continuum including the
worldsheet local symmetries. There exists a ``local correspondence'' between
the continuum and lattice theories in the sense that every local dynamical or
constraint equation in the continuum also holds true on the lattice, site-wise.
We perform a detailed symmetry analysis for the bits and establish conservation
laws. In particular, for a bosonic non-linear sigma model with arbitrary target
space, we demonstrate both the global symmetry algebra and classical Virasoro
algebra (in position space) on the lattice. Our construction is generalizable
to higher dimensions for any generally covariant theory that can be studied by
expanding around a globally hyperbolic spacetime with conformally flat Cauchy
slices. |
Gravity and instantons: Conventional non-Abelian SO(4) gauge theory is able to describe gravity
provided the gauge field possesses a specific polarized vacuum state in which
the instantons have a preferred orientation. Their orientation plays the role
of the order parameter for the polarized phase of the gauge field. The
interaction of a weak and smooth gauge field with the polarized vacuum is
described by an effective long-range action which is identical to the Hilbert
action of general relativity. In the classical limit this action results in the
Einstein equations of general relativity. Gravitons appear as the mode
describing propagation of the gauge field which strongly interacts with the
oriented instantons. The Newton gravitational constant describes the density of
the considered phase of the gauge field. The radius of the instantons under
consideration is comparable with the Planck radius. | String theory in target space: It is argued that the complete S-matrix of string theory at tree level in a
flat background can be obtained from a small set of target space properties,
without recourse to the worldsheet description. The main non-standard inputs
are (generalised) Britto-Cachazo-Feng-Witten shifts, as well as the monodromy
relations for open string theory and the Kawai-Lewellen-Tye relations for
closed string theory. The roots of the scattering amplitudes and especially
their appearance in the residues at the kinematic poles are central to the
story. These residues determine the amplitudes through on-shell recursion
relations. Several checks of the formalism are presented, including a
computation of the Koba-Nielsen amplitude in the bosonic string. Furthermore
the question of target space unitarity is (re-)investigated. For the Veneziano
amplitude this question is reduced by Poincare invariance, unitarity and
locality to that of positivity of a particular numerical sum. Interestingly,
this analysis produces the main conditions of the no-ghost theorem on dimension
and intercept from the first three poles of this amplitude. |
`Stringy' Newton-Cartan Gravity: We construct a "stringy" version of Newton-Cartan gravity in which the
concept of a Galilean observer plays a central role. We present both the
geodesic equations of motion for a fundamental string and the bulk equations of
motion in terms of a gravitational potential which is a symmetric tensor with
respect to the longitudinal directions of the string. The extension to include
a non-zero cosmological constant is given. We stress the symmetries and
(partial) gaugings underlying our construction. Our results provide a
convenient starting point to investigate applications of the AdS/CFT
correspondence based on the non-relativistic "stringy" Galilei algebra. | On Soliton Content of Self Dual Yang-Mills Equations: Exploiting the formulation of the Self Dual Yang-Mills equations as a
Riemann-Hilbert factorization problem, we present a theory of pulling back
soliton hierarchies to the Self Dual Yang-Mills equations. We show that for
each map $ \C^4 \to \C^{\infty } $ satisfying a simple system of linear
equations formulated below one can pull back the (generalized) Drinfeld-Sokolov
hierarchies to the Self Dual Yang-Mills equations. This indicates that there is
a class of solutions to the Self Dual Yang-Mills equations which can be
constructed using the soliton techniques like the $\tau$ function method. In
particular this class contains the solutions obtained via the symmetry
reductions of the Self Dual Yang-Mills equations. It also contains genuine 4
dimensional solutions . The method can be used to study the symmetry reductions
and as an example of that we get an equation exibiting breaking solitons,
formulated by O. Bogoyavlenskii, as one of the $2 + 1 $ dimensional reductions
of the Self Dual Yang-Mills equations. |
Linear response of entanglement entropy from holography: For time-independent excited states in conformal field theories, the
entanglement entropy of small subsystems satisfies a `first law'-like relation,
in which the change in entanglement is proportional to the energy within the
entangling region. Such a law holds for time-dependent scenarios as long as the
state is perturbatively close to the vacuum, but is not expected otherwise. In
this paper we use holography to investigate the spread of entanglement entropy
for unitary evolutions of special physical interest, the so-called global
quenches. We model these using AdS-Vaidya geometries. We find that the first
law of entanglement is replaced by a linear response relation, in which the
energy density takes the role of the source and is integrated against a
time-dependent kernel with compact support. For adiabatic quenches the standard
first law is recovered, while for rapid quenches the linear response includes
an extra term that encodes the process of thermalization. This extra term has
properties that resemble a time-dependent `relative entropy'. We propose that
this quantity serves as a useful order parameter to characterize
far-from-equilibrium excited states. We illustrate our findings with concrete
examples, including generic power-law and periodically driven quenches. | Stationary black holes: Large $D$ analysis: We consider the effective theory of the large D stationary black hole. By
solving Einstein equation with a cosmological constant using the 1/D expansion
in near zone of a black hole we obtain the effective equation for the
stationary black hole. The effective equation describes the Myers-Perry black
hole, bumpy black holes and, possibly, the black ring solution as its
solutions. In this effective theory the black hole is represented as the
embedded membrane in the background, i.e., Minkowski or Anti-de Sitter
spacetime and its mean curvature is given by the redshifted surface gravity by
the background geometry and the local Lorentz boost. The local Lorentz boost
property of the effective equation is observed also in the metric. In fact we
show that the leading order metric of the Einstein equation in the 1/D
expansion is generically regarded as the Lorentz boosted Schwarzschild black
hole. We apply this Lorentz boost property of the stationary black hole
solution to solve the perturbation equation. As a result we obtain the analytic
formula for the quasinormal mode of the singly rotating Myers-Perry black hole
in the 1/D expansion. |
Renormalization group study of the higher derivative conformal scalar
model: The second alternative conformal limit of the recently proposed general
higher derivative dilaton quantum theory in curved spacetime is explored. In
this version of the theory the dilaton is transformed, along with the metric,
to provide the conformal invariance of the classical action. We find the
corresponding quantum theory to be renormalizable at one loop, and the
renormalization constants for the dimensionless parameters are explicitly shown
to be universal for an arbitrary parametrization of the quantum field. The
renormalization group equations indicate an asymptotic freedom in the IR limit.
In this respect the theory is similar to the well-known model based on the
anomaly-induced effective action. | Dark Energy, Inflation and Extra Dimensions: We consider how accelerated expansion, whether due to inflation or dark
energy, imposes strong constraints on fundamental theories obtained by
compactification from higher dimensions. For theories that obey the null energy
condition (NEC), we find that inflationary cosmology is impossible for a wide
range of compactifications; and a dark energy phase consistent with
observations is only possible if both Newton's gravitational constant and the
dark energy equation-of-state vary with time. If the theory violates the NEC,
inflation and dark energy are only possible if the NEC-violating elements are
inhomogeneously distributed in thecompact dimensions and vary with time in
precise synchrony with the matter and energy density in the non-compact
dimensions. Although our proofs are derived assuming general relativity applies
in both four and higher dimensions and certain forms of metrics, we argue that
similar constraints must apply for more general compactifications. |
Equivalence of Geometric Engineering and Hanany-Witten via Fractional
Branes: We present an explicit relation between the Hanany-Witten and Geometric
Engineering approaches of realising gauge theories in string theory. The last
piece in the puzzle is a T-duality relating arbitrary Hanany-Witten setups and
fractional branes. | On infinite symmetry algebras in Yang-Mills theory: Similar to gravity, an infinite tower of symmetries generated by higher-spin
charges has been identified in Yang-Mills theory by studying collinear limits
or celestial operator products of gluons. This work aims to recover this loop
symmetry in terms of charge aspects constructed on the gluonic Fock space. We
propose an explicit construction for these higher spin charge aspects as
operators which are polynomial in the gluonic annihilation and creation
operators. The core of the paper consists of a proof that the charges we
propose form a closed loop algebra to quadratic order. This closure involves
using the commutator of the cubic order expansion of the charges with the
linear (soft) charge. Quite remarkably, this shows that this
infinite-dimensional symmetry constrains the non-linear structure of Yang-Mills
theory. We provide a similar all spin proof in gravity for the so-called global
quadratic (hard) charges which form the loop wedge subalgebra of
$w_{1+\infty}$. |
Gauged supergravities and non-geometric Q/R-fluxes from asymmetric
orbifold CFT's: We investigate the orbifold limits of string theory compactifications with
geometric and non-geometric fluxes. Exploiting the connection between internal
fluxes and structure constants of the gaugings in the reduced supergravity
theory, we can identify the types of fluxes arising in certain classes of
freely-acting symmetric and asymmetric orbifolds. We give a general procedure
for deriving the gauge algebra of the effective gauged supergravity using the
exact CFT description at the orbifold point. We find that the asymmetry is, in
general, related to the presence of non-geometric Q- and R- fluxes. The action
of T-duality is studied explicitly on various orbifold models and the resulting
transformation of the fluxes is derived. Several explicit examples are
provided, including compactifications with geometric fluxes, Q-backgrounds
(T-folds) and R-backgrounds. In particular, we present an asymmetric Z4xZ2
orbifold in which all geometric and non-geometric fluxes {\omega}, H, Q, R are
turned on simultaneously. We also derive the corresponding flux backgrounds,
which are not in general T-dual to geometric ones, and may even simultaneously
depend non-trivially on both the coordinates and their winding T-duals. | A Non-minimally Coupled Quintom Dark Energy Model on the Warped DGP
Brane: We study dynamics of equation of state parameter for a non-minimally coupled
quintom dark energy component on the warped DGP brane. We investigate crossing
of the cosmological constant line in this scenario. This crossing occurs in
both DGP$^{\pm}$ branches of the model. |
The effect of Chern-Simons dynamics on the energy of electrically
charged and spinning vortices: We study the effect of a Chern-Simons term on the electrically charged and
spinning solitons of several $U(1)$ gauged models in $2+1$ dimensions. These
are vortices of complex scalar field theories, both with and without symmetry
breaking dynamics, and the $O(3)$ Skyrme model. In all cases the gauge
decoupling limits are also considered. It is well known that the effect of the
Chern-Simons dynamics is to endow vortices with electric charge $Q_e$ and spin
$J$, but our main aim here is to reveal a new feature: that the mass-energy $E$
of the electrically charged vortex can be lower than that of the electrically
neutral one, in contrast to the usual monotonic increase of $E$ with $Q_e$.
These effects of Chern-Simons dynamics were observed previously in $3+1$
dimensional systems, and the present results can be viewed as corroborating the
latter. Moreover, the usual energy-spin relationship is likewise altered. We
carry out a detailed quantitative analysis of azimuthally symmetric vortices
and describe their qualitative features by constructing the solutions
numerically. | Non linear realizations of isometry groups, conformal algebras and
geodesics in Anti-de Sitter like spaces: We present the explicit global realization of the isometries of anti-de
Sitter like spaces of signature $(d_-,d_+)$, and their algebras in the space of
functions on the pseudo-Riemannian symmetric space $SO(d_- +1,d_+) /
SO(d_-,d_+)$. The process of going to the invariant boundaries leads to the
realization of the corresponding conformal groups and algebras. We compute
systematically the geodesics in these spaces by considering the coset
representation of them. |
Matter Coupled F(4) Supergravity and the AdS_6/CFT_5 Correspondence: F(4) supergravity, the gauge theory of the exceptional six-dimensional
Anti-de Sitter superalgebra, is coupled to an arbitrary number of vector
multiplets whose scalar components parametrize the quaternionic manifold
$SO(4,n)/SO(4)\times SO(n)$. By gauging the compact subgroup $SU(2)_d \otimes
\cG$, where SU(2)_d is the diagonal subgroup of $SO(4)\simeq SU(2)_L\otimes
SU(2)_R$ (the R-symmetry group of six-dimensional Poincar\'e supergravity) and
$\cG$ is a compact group such that $dim\cG = n$, we compute the scalar
potential which, besides the gauge coupling constants, also depends in non
trivial way on the parameter m associated to a massive 2-form $B_{\mu\nu}$ of
the gravitational multiplet. The potential admits an AdS background for g=3m,
as the pure F(4)-supergravity. We compute the scalar squared masses (which are
all negative) and retrieve the results dictated by AdS_6/CFT_5 correspondence
from the conformal dimensions of boundary operators. The boundary F(4)
superconformal fields are realized in terms of a singleton superfield
(hypermultiplet) in harmonic superspace with flag manifold SU(2)/U(1)=S^2. We
analize the spectrum of short representations in terms of superconformal
primaries and predict general features of the K-K specrum of massive type IIA
supergravity compactified on warped $AdS_6\otimes S^4$. | Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$: We determine the $1/N_f^2$ and $1/N_f^3$ contributions to the QED beta
function stemming from the closed set of nested diagrams. At order $1/N_f^2$ we
discover a new logarithmic branch-cut closer to the origin when compared to the
$1/N_f$ results. The same singularity location appears at $1/N_f^3$, and these
correspond to a UV renormalon singularity in the finite part of the photon
two-point function. |
On the integrability of Einstein-Maxwell-(A)dS gravity in presence of
Killing vectors: We study some symmetry and integrability properties of four-dimensional
Einstein-Maxwell gravity with nonvanishing cosmological constant in the
presence of Killing vectors. First of all, we consider stationary spacetimes,
which lead, after a timelike Kaluza-Klein reduction followed by a dualization
of the two vector fields, to a three-dimensional nonlinear sigma model coupled
to gravity, whose target space is a noncompact version of
$\mathbb{C}\text{P}^2$ with SU(2,1) isometry group. It is shown that the
potential for the scalars, that arises from the cosmological constant in four
dimensions, breaks three of the eight SU(2,1) symmetries, corresponding to the
generalized Ehlers and the two Harrison transformations. This leaves a
semidirect product of a one-dimensional Heisenberg group and a translation
group $\mathbb{R}^2$ as residual symmetry. We show that, under the additional
assumptions that the three-dimensional manifold is conformal to a product space
$\mathbb{R}\times\Sigma$, and all fields depend only on the coordinate along
$\mathbb{R}$, the equations of motion are integrable. This generalizes the
results of Leigh et al. in arXiv:1403.6511 to the case where also
electromagnetic fields are present. In the second part of the paper we consider
the purely gravitational spacetime admitting a second Killing vector that
commutes with the timelike one. We write down the resulting two-dimensional
action and discuss its symmetries. If the fields depend only on one of the two
coordinates, the equations of motion are again integrable, and the solution
turns out to be one constructed by Krasinski many years ago. | Multi-centered black holes in gauged D=5 supergravity: One of the important consequences of the no-force condition for BPS states is
the existence of stable static multi-center solutions, at least in ungauged
supergravities. This observation has been at the heart of many developments in
brane physics, including the construction of intersecting branes and reduced
symmetry D-brane configurations corresponding to the Coulomb branch of the
gauge theory. However the search for multi-center solutions to gauged
supergravities has proven rather elusive. Because of the background curvature,
it appears such solutions cannot be static. Nevertheless even allowing for time
dependence, general multi-center solutions to gauged supergravity have yet to
be constructed. In this letter we investigate the construction of such
solutions for the case of D=5, N=2 gauged supergravity coupled to an arbitrary
number of vector multiplets. Formally, we find a family of time dependent
multi-center black hole solutions which are easily generalized to the case of
AdS supergravities in general dimensions. While these are not true solutions,
as they have a complex metric and gauge potential, they may be related to a
Wick rotated theory or to a theory where the coupling is taken to be imaginary.
These solutions thus provide a partial realization of true multi-center
black-holes in gauged supergravities. |
Ashtekar variables, self-dual metrics and w-infinity: The self-duality equations for the Riemann tensor are studied using the
Ashtekar Hamiltonian formulation for general relativity. These equations may be
written as dynamical equations for three divergence free vector fields on a
three dimensional surface in the spacetime. A simplified form of these
equations, describing metrics with a one Killing field symmetry are written
down, and it shown that a particular sector of these equations has a
Hamiltonian form where the Hamiltonian is an arbitrary function on a
two-surface. In particular, any element of the $w_\infty$ algebra may be chosen
as a the Hamiltonian. For a special choice of this Hamiltonian, an infinite set
of solutions of the self-duality equations are given. These solutions are
parametrized by elements of the $w_\infty$ algebra, which in turn leads to an
explicit form of four dimensional complex self-dual metrics that are in one to
one correspondence with elements of this algebra. | Equivalent Dual Theories for 3D N=2 Supergravity: N=2 three dimensional Supergravity with internal $R-$symmetry generators can
be understood as a two dimensional chiral Wess-Zumino-Witten model. In this
paper, we present the reduced phase space description of the theory, which
turns out to be flat limit of a generalised Liouville theory, up to zero modes.
The reduced phase space description can also be explained as a gauged chiral
Wess-Zumino-Witten model. We show that both these descriptions possess
identical gauge and global (quantum N=2 superBMS$_3$) symmetries. |
Spinning strings: $λ$-deformation and non-Abelian T-dual limit: The simplest example of the $\lambda$-deformation connects the SU(2)
Wess-Zumino-Witten model with the non-Abelian T-dual (NATD) of the SU(2)
principal chiral model. We analyze spinning strings with one spin propagating
through the $\lambda$-deformation of the target space of the interpolation. We
show that the situation apart from the NATD limit parallels the undeformed
case. We demonstrate that regular spinning strings are either folded or
circular, and that nearly degenerate spinning strings are either nearly
point-like, fast, or slow. The effects of the $\lambda$-deformation are both
the overall increment of the energy of spinning strings and the enlargement of
the gap between the energies of folded and circular strings. In the NATD limit,
we prove that circular strings disappear and that fast strings realize the
dispersion relation of Gubser-Klebanov-Polyakov strings. | Superintegrability of matrix Student's distribution: For ordinary matrix models, the eigenvalue probability density decays rapidly
as one goes to infinity, in other words, has "short tails". This ensures that
all the multiple trace correlators (multipoint moments) are convergent and
well-defined.
Still, many critical phenomena are associated with an enhanced probability of
seemingly rare effects, and one expects that they are better described by the
"long tail" models. In absence of the exponential fall-off, the integrals for
high moments diverge, and this could imply a loss of (super)integrability
properties pertinent to matrix and eigenvalue models and, presumably, to the
non-perturbative (exact) treatment of more general quantum systems. In this
paper, we explain that this danger to modern understanding could be
exaggerated. We consider a simple family of long-tail matrix models, which
preserve the crucial feature of superintegrability: exact factorized
expressions for a full set of basic averages. It turns out that
superintegrability can survive after an appropriate (natural and obvious)
analytical continuation even in the presence of divergencies, which opens new
perspectives for the study of the long-tail matrix models. |
Past incompleteness of a bouncing multiverse: According to classical GR, Anti-de Sitter (AdS) bubbles in the multiverse
terminate in big crunch singularities. It has been conjectured, however, that
the fundamental theory may resolve these singularities and replace them by
nonsingular bounces. This may have important implications for the beginning of
the multiverse. Geodesics in cosmological spacetimes are known to be
past-incomplete, as long as the average expansion rate along the geodesic is
positive, but it is not clear that the latter condition is satisfied if the
geodesic repeatedly passes through crunching AdS bubbles. We investigate this
issue in a simple multiverse model, where the spacetime consists of a patchwork
of FRW regions. The conclusion is that the spacetime is still past-incomplete,
even in the presence of AdS bounces. | Betti multiplets, flows across dimensions and c-extremization: We consider 4d N=1 SCFTs, topologically twisted on compact constant curvature
Riemann surfaces, giving rise to 2d N=(0,2) SCFTs. The exact R-current of these
2d SCFT extremizes the central charge c_{2d}, similarly to the 4d picture,
where the exact R-current maximizes the central charge a_{4d}. There are global
currents that do not mix with the R-current in 4d but their mixing becomes non
trivial in 2d. In this paper we study the holographic dual of this process by
analyzing a 5d N=2 truncation of T^{1,1} with one Betti vector multiplet, dual
to the baryonic current on the CFT side. The holographic realization of the
flow across dimensions connects AdS_5 to AdS_3 vacua in the supergravity
picture. We verify the existence of the flow to AdS_3 solutions and we retrieve
the field theory results for the mixing of the Betti vector with the
graviphoton. Moreover, we extract the central charge from the Brown-Henneaux
formula, matching with the results obtained in field theory. We develop a
general formalism to obtain the central charge of a 2d SCFT from 5d N=2 gauged
supergravity with a generic number of vector multiplets, showing that its
extremization corresponds to an attractor mechanism for the scalars in the
supergravity picture. |
Absorption of Fixed scalars and the D-brane Approach to Black Holes: We calculate the emission and absorption rates of fixed scalars by the
near-extremal five-dimensional black holes that have recently been modeled
using intersecting D-branes. We find agreement between the semi-classical and
D-brane computations. At low energies the fixed scalar absorption cross-section
is smaller than for ordinary scalars and depends on other properties of the
black hole than just the horizon area. In the D-brane description, fixed scalar
absorption is suppressed because these scalars must split into at least four,
rather than two, open strings running along the D-brane. Consequently, this
comparison provides a more sensitive test of the effective string picture of
the D-brane bound state than does the cross-section for ordinary scalars. In
particular, it allows us to read off the value of the effective string tension.
That value is precisely what is needed to reproduce the near-extremal 5-brane
entropy. | N=1 supersymmetric higher spin holography on AdS_3: We propose a duality between a higher spin N=1 supergravity on AdS_3 and a
large N limit of a family of N=(1,1) superconformal field theories. The gravity
theory is an N=1 truncation of the N=2 supergravity found by Prokushkin and
Vasiliev, and the dual conformal field theory is defined by a supersymmetric
coset model. We check this conjecture by comparing one loop partition functions
and find agreement. Moreover, we study the symmetry of the dual coset model and
in particular compute fields of the coset algebra of dimension 3/2, 2, 2 and
5/2 explicitely. |
Correlation functions of the open XXZ chain I: We consider the XXZ spin chain with diagonal boundary conditions in the
framework of algebraic Bethe Ansatz. Using the explicit computation of the
scalar products of Bethe states and a revisited version of the bulk inverse
problem, we calculate the elementary building blocks for the correlation
functions. In the limit of half-infinite chain, they are obtained as multiple
integrals of usual functions, similar to the case of periodic boundary
conditions. | Asymptotic safety of gravity and the Higgs boson mass: There are indications that gravity is asymptotically safe. The Standard Model
(SM) plus gravity could be valid up to arbitrarily high energies. Supposing
that this is indeed the case and assuming that there are no intermediate energy
scales between the Fermi and Planck scales we address the question of whether
the mass of the Higgs boson $m_H$ can be predicted. For a positive gravity
induced anomalous dimension $A_\lambda>0$ the running of the quartic scalar
self interaction $\lambda$ at scales beyond the Planck mass is determined by a
fixed point at zero. This results in $m_H=m_{\rm min}=126$ GeV, with only a few
GeV uncertainty. This prediction is independent of the details of the short
distance running and holds for a wide class of extensions of the SM as well.
For $A_\lambda <0$ one finds $m_H$ in the interval $m_{\rm min}< m_H < m_{\rm
max}\simeq 174$ GeV, now sensitive to $A_\lambda$ and other properties of the
short distance running. The case $A_\lambda>0$ is favored by explicit
computations existing in the literature. |
Singularities, Gauge Dynamics, and Nonperturbative Superpotentials in
String Theory: We describe a class of 4d N=1 compactifications of the $SO(32)$
heterotic/type I string theory which are destabilized by nonperturbatively
generated superpotentials. In the type I description, the destabilizing
superpotential is generated by a one instanton effect or gaugino condensation
in a nonperturbative $SU(2)$ gauge group. The dual, heterotic description
involves destabilization due to worldsheet instanton or $\it half$ worldsheet
instanton effects in the two cases. A genericity argument suggests that a
(global) supersymmetry-breaking model of Intriligator and Thomas might be
typical in a class of string theory models. Our analysis also suggests that the
tensionless strings which arise in the $E_8 \times E_8$ theory in six
dimensions when an instanton shrinks to zero size should, in some cases, have
supersymmetry breaking dynamics upon further compactification to four
dimensions. We provide explicit examples, constructed using F-theory, of the
two cases of dynamically generated superpotentials. | A Note on Quantum Geometric Langlands Duality, Gauge Theory, and
Quantization of the Moduli Space of Flat Connections: Montonen-Olive duality implies that the categories of A-branes on the moduli
spaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dual
groups are equivalent. We reformulate this as a statement about categories of
B-branes on the quantized moduli spaces of flat connections for these groups.
We show that it implies the statement of the Quantum Geometric Langlands
duality with a purely imaginary ``quantum parameter'' which is proportional to
the inverse of the Planck constant of the gauge theory. The ramified version of
the story is also considered. |
Quantum Group Symmetric Bargmann Fock Construction: Usually in quantum mechanics the Heisenberg algebra is generated by operators
of position and momentum. The algebra is then represented on an Hilbert space
of square integrable functions. Alternatively one generates the Heisenberg
algebra by the raising and lowering operators. It is then natural to represent
it on the Bargmann Fock space of holomorphic functions. In the following I show
that the Bargmann Fock construction can also be done in the quantum group
symmetric case. This leads to a 'q- deformed quantum mechanics' in which the
basic concepts, Hilbert space of states and unitarity of time evolution, are
preserved. | Studies of low-energy effective actions in supersymmetric field theories: This thesis examines low-energy effective actions of supersymmetric quantum
field theories. These actions contain information about the low-energy field
content and dynamics of quantum field theories and are essential for
understanding their phenomenological and theoretical properties.
In chapters 2 to 5, the covariant background field method is used to
investigate quantum corrections to sectors of a variety of supersymmetric field
theories at 1 and 2 loops. We start by looking at the background field
quantisation of a general N=1 super-Yang-Mills theory, rederiving the
well-known 1 loop finiteness conditions. This is followed by a reexamination of
the effective potential of the Wess-Zumino model, focusing on a derivation of
the full auxiliary fields' potential. Next, the 2 loop Euler-Heisenberg
effective action is constructed for N=1 supersymmetric quantum electrodynamics;
its renormalisation properties and self-dual limit are studied. The final
action studied is the 2 loop Kahler potential for beta-deformed N=4
super-Yang-Mills. This sector is purely a product of the deformation and its
finiteness is demonstrated in a general background before examining two special
cases.
Chapter 6 studies spontaneously broken supersymmetry and the pure Goldstino
action. A general approach to constructing explicit field redefinitions is used
to relate all known models of the Goldstino and to study their nonlinear
supersymmetries. This approach is also used to construct the most general pure
Goldstino action and to examine its supersymmetry transformations. Finally, a
new embedding of the Goldstino into a complex linear superfield is presented.
Its interactions to matter and gravity are examined and compared to existing
Goldstino superfield constructions. |
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