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Nonlinear (Super)Symmetries and Amplitudes: There is an increasing interest in nonlinear supersymmetries in cosmological
model building. Independently, elegant expressions for the all-tree amplitudes
in models with nonlinear symmetries, like D3 brane
Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the
generalized background field method we show how, in general, nonlinear
symmetries of the action, bosonic and fermionic, constrain amplitudes beyond
soft limits. The same identities control, for example, bosonic E_{7(7)} scalar
sector symmetries as well as the fermionic goldstino symmetries.
We present a universal derivation of the vanishing amplitudes in the single
(bosonic or fermionic) soft limit. We explain why, universally, the double-soft
limit probes the coset space algebra. We also provide identities describing the
multiple-soft limit. We discuss loop corrections to N\geq 5 supergravity, to
the D3 brane, and the UV completion of constrained multiplets in string theory. | Formation of Black Holes in Topologically Massive Gravity: We present an exact solution in 3-dimensional topologically massive gravity
with negative cosmological constant which dynamically interpolates between a
past horizon and a chiral AdS pp-wave. Similarly, upon time reversal, one
obtains an AdS pp-wave with a future event horizon |
On holographic entanglement entropy of Horndeski black holes: We study entanglement entropy in a particular tensor-scalar theory: Horndeski
gravity. Our goal is two-fold: investigate the Lewkowycz-Maldacena proposal for
entanglement entropy in the presence of a tensor-scalar coupling and address a
puzzle existing in the literature regarding the thermal entropy of
asymptotically AdS Horndeski black holes. Using the squashed cone method, i.e.
turning on a conical singularity in the bulk, we derive the functional for
entanglement entropy in Horndeski gravity. We analyze the divergence structure
of the bulk equation of motion. Demanding that the leading divergence of the
transverse component of the equation of motion vanishes we identify the surface
where to evaluate the entanglement functional. We show that the surface
obtained is precisely the one that minimizes said functional. By evaluating the
entanglement entropy functional on the horizon we obtain the thermal entropy
for Horndeski black holes; this result clarifies discrepancies in the
literature. As an application of the functional derived we find the minimal
surfaces numerically and study the entanglement plateaux. | Polylogarithm identities, cluster algebras and the N=4 supersymmetric
theory: Scattering amplitudes in N = 4 super-Yang Mills theory can be computed to
higher perturbative orders than in any other four-dimensional quantum field
theory. The results are interesting transcendental functions. By a hidden
symmetry (dual conformal symmetry) the arguments of these functions have a
geometric interpretation in terms of configurations of points in CP^3 and they
turn out to be cluster coordinates. We briefly introduce cluster algebras and
discuss their Poisson structure and the Sklyanin bracket. Finally, we present a
40-term trilogarithm identity which was discovered by accident while studying
the physical results. |
Static supersymmetric black holes in AdS_4 with spherical symmetry: We elaborate further on the static supersymmetric AdS_4 black holes found in
arXiv:0911.4926, investigating thoroughly the BPS constraints for spherical
symmetry in N = 2 gauged supergravity in the presence of Fayet-Iliopoulos
terms. We find Killing spinors that preserve two of the original eight
supercharges and investigate the conditions for genuine black holes free of
naked singularities. The existence of a horizon is intimately related with the
requirement that the scalars are not constant, but given in terms of harmonic
functions in analogy to the attractor flow in ungauged supergravity. The black
hole charges depend on the choice of the electromagnetic gauging, with only
magnetic charges for purely electric gaugings. Finally we show how these black
holes can be embedded in N = 8 supergravity and thus in M-theory. | Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant
Differential (TED) K-theory: We demonstrate that twisted equivariant differential K-theory of transverse
complex curves accommodates exotic charges of the form expected of
codimension=2 defect branes, such as of D7-branes in IIB/F-theory on A-type
orbifold singularities, but also of their dual 3-brane defects of class-S
theories on M5-branes. These branes have been argued, within F-theory and the
AGT correspondence, to carry special SL(2)-monodromy charges not seen for other
branes, but none of these had previously been identified in the expected brane
charge quantization law given by K-theory.
Here we observe that it is the subtle (and previously somewhat neglected)
twisting of equivariant K-theory by flat complex line bundles appearing inside
orbi-singularities ("inner local systems") that makes the secondary Chern
character on a punctured plane inside an A-type singularity evaluate to the
twisted holomorphic de Rham cohomology which Feigin, Schechtman & Varchenko
showed realizes sl(2,C)-conformal blocks, here in degree 1 -- in fact it gives
the direct sum of these over all admissible fractional levels. The remaining
higher-degree conformal blocks appear similarly if we assume our previously
discussed "Hypothesis H" about brane charge quantization in M-theory. Since
conformal blocks -- and hence these twisted equivariant secondary Chern
characters -- solve the Knizhnik-Zamolodchikov equation and thus constitute
representations of the braid group of motions of defect branes inside their
transverse space, this provides a concrete first-principles realization of
anyon statistics of -- and hence of topological quantum computation on --
defect branes in string/M-theory. |
Heat-Kernel Asymptotics of Locally Symmetric Spaces of Rank One and
Chern-Simons Invariants: The asymptotic expansion of the heat kernel associated with Laplace operators
is considered for general irreducible rank one locally symmetric spaces.
Invariants of the Chern-Simons theory of irreducible U(n)- flat connections on
real compact hyperbolic 3-manifolds are derived | Lorentzian AdS, Wormholes and Holography: We investigate the structure of two point functions for the QFT dual to an
asymptotically Lorentzian AdS-wormhole. The bulk geometry is a solution of
5-dimensional second order Einstein Gauss Bonnet gravity and causally connects
two asymptotically AdS space times. We revisit the GKPW prescription for
computing two-point correlation functions for dual QFT operators O in
Lorentzian signature and we propose to express the bulk fields in terms of the
independent boundary values phi_0^\pm at each of the two asymptotic AdS
regions, along the way we exhibit how the ambiguity of normalizable modes in
the bulk, related to initial and final states, show up in the computations. The
independent boundary values are interpreted as sources for dual operators O^\pm
and we argue that, apart from the possibility of entanglement, there exists a
coupling between the degrees of freedom leaving at each boundary. The AdS_(1+1)
geometry is also discussed in view of its similar boundary structure. Based on
the analysis, we propose a very simple geometric criterium to distinguish
coupling from entanglement effects among the two set of degrees of freedom
associated to each of the disconnected parts of the boundary. |
Entropy and topology for manifolds with boundaries: In this work a deep relation between topology and thermodynamical features of
manifolds with boundaries is shown. The expression for the Euler
characteristic, through the Gauss- Bonnet integral, and the one for the entropy
of gravitational instantons are proposed in a form which makes the relation
between them self-evident. A generalization of Bekenstein-Hawking formula, in
which entropy and Euler characteristic are related in the form $S=\chi A/8$, is
obtained. This formula reproduces the correct result for extreme black hole,
where the Bekenstein-Hawking one fails ($S=0$ but $A \neq 0$). In such a way it
recovers a unified picture for the black hole entropy law. Moreover, it is
proved that such a relation can be generalized to a wide class of manifolds
with boundaries which are described by spherically symmetric metrics (e.g.
Schwarzschild, Reissner-Nordstr\"{o}m, static de Sitter). | Reheating after relaxation of large cosmological constant: We present a cosmological model of an early-time scenario that incorporates a
relaxation process of the would-be large vacuum energy, followed by a reheating
era connecting to the standard hot big bang universe. Avoiding fine-tuning the
cosmological constant is achieved by the dynamics of a scalar field whose
kinetic term is modulated by an inverse power of spacetime curvature. While it
is at work against radiative corrections to the dark energy, this mechanism
alone would wipe out not only the vacuum energy but also all other matter
contents. Our present work aims to complete the scenario by exploiting a
null-energy-condition violating sector whose energy is eventually transferred
to a reheating sector. We provide an explicit example of this process and thus
a concrete scenario of the cosmic onset that realizes the thermal history of
the Universe with a negligible cosmological constant. |
Stable causality of Black Saturns: We prove that the Black Saturns are stably causal on the closure of the
domain of outer communications. | Flux corrections to anomaly cancellation in M-theory on a manifold with
boundary: We show how the coupling of gravitinos and gauginos to fluxes modifies
anomaly cancellation in M-theory on a manifold with boundary. Anomaly
cancellation continues to hold, after a shift of the definition of the gauge
currents by a local gauge invariant expression in the curvatures and E8
fieldstrengths. We compute the first nontrivial correction of this kind.
Warning: Ian Moss has called into question several of the numerical
coefficients in the extended Dirac operators in this paper. We have not
confirmed this but the reader is warned not to trust the precise coefficients
in the formulae for the Dirac operators and heat kernel expansions. We believe
these possible errors do not change our qualitative conclusions. One of us
intends to return to the issue and recheck the formulae. We thank Ian Moss for
pointing out these problems. |
Firewalls in General Relativity: We present spherically symmetric solutions to Einstein's equations which are
equivalent to canonical Schwarzschild and Reissner-Nordstrom black holes on the
exterior, but with singular (Planck-density) shells at their respective event
and inner horizons. The locally measured mass of the shell and the singularity
are much larger than the asymptotic ADM mass. The area of the shell is equal to
that of the corresponding canonical black hole, but the physical distance from
the shell to the singularity is a Planck length, suggesting a natural
explanation for the scaling of the black hole entropy with area. The existence
of such singular shells enables solutions to the black hole information problem
of Schwarzschild black holes and the Cauchy horizon problem of
Reissner-Nordstrom black holes. While we cannot rigorously address the
formation of these solutions, we suggest plausibility arguments for how normal
black hole solutions may evolve into such states. We also comment on the
possibility of negative mass Schwarzschild solutions that could be constructed
using our methods. Requirements for the non-existence of negative-mass
solutions may put restrictions on the types of singularities allowed in an
ultraviolet theory of gravity. | Correlation measures and distillable entanglement in AdS/CFT: Recent developments have exposed close connections between quantum
information and holography. In this paper, we explore the geometrical
interpretations of the recently introduced $Q$-correlation and $R$-correlation,
$E_Q$ and $E_R$. We find that $E_Q$ admits a natural geometric interpretation
via the surface-state correspondence: it is a minimal mutual information
between a surface region $A$ and a cross-section of $A$'s entanglement wedge
with $B$. We note a strict trade-off between this minimal mutual information
and the symmetric side-channel assisted distillable entanglement from the
environment $E$ to $A$, $I^{ss}(E\rangle A)$. We also show that the
$R$-correlation, $E_R$, coincides holographically with the entanglement wedge
cross-section. This further elucidates the intricate relationship between
entanglement, correlations, and geometry in holographic field theories. |
How to superize Liouville equation: So far, there are described in the literature two ways to superize the
Liouville equation: for a scalar field (for $N\leq 4$) and for a vector-valued
field (analogs of the Leznov--Saveliev equations) for N=1. Both superizations
are performed with the help of Neveu--Schwarz superalgebra. We consider another
version of these superLiouville equations based on the Ramond superalgebra,
their explicit solutions are given by Ivanov--Krivonos' scheme. Open problems
are offered. | Lifshitz/Schrödinger D-p-branes and dynamical exponents: We extend our earlier study of special double limits of `boosted' $AdS_5$
black hole solutions to include all black D$p$-branes of type II strings. We
find that Lifshitz solutions can be obtained in generality, with varied
dynamical exponents, by employing these limits. We then study such double
limits for `boosted' D$p$-brane bubble solutions and find that the resulting
non-relativistic solutions instead describe Schr\"odinger like spacetimes,
having varied dynamical exponents. We get a simple map between these Lifshitz &
Schr\"odinger solutions and a relationship between two types of dynamical
exponents. We also discuss about the singularities of the Lifshitz solutions
and an intriguing thermodynamic duality. |
Metric Flows with Neural Networks: We develop a theory of flows in the space of Riemannian metrics induced by
neural network gradient descent. This is motivated in part by recent advances
in approximating Calabi-Yau metrics with neural networks and is enabled by
recent advances in understanding flows in the space of neural networks. We
derive the corresponding metric flow equations, which are governed by a metric
neural tangent kernel, a complicated, non-local object that evolves in time.
However, many architectures admit an infinite-width limit in which the kernel
becomes fixed and the dynamics simplify. Additional assumptions can induce
locality in the flow, which allows for the realization of Perelman's
formulation of Ricci flow that was used to resolve the 3d Poincar\'e
conjecture. We apply these ideas to numerical Calabi-Yau metrics, including a
discussion on the importance of feature learning. | Black Holes and Massive Remnants: This paper revisits the conundrum faced when one attempts to understand the
dynamics of black hole formation and evaporation without abandoning unitary
evolution. Previous efforts to resolve this puzzle assume that information
escapes in corrections to the Hawking process, that an arbitrarily large amount
of information is transmitted by a planckian energy or contained in a
Planck-sized remnant, or that the information is lost to another universe. Each
of these possibilities has serious difficulties. This paper considers another
alternative: remnants that carry large amounts of information and whose size
and mass depend on their information content. The existence of such objects is
suggested by attempts to incorporate a Planck scale cutoff into physics. They
would greatly alter the late stages of the evaporation process. The main
drawback of this scenario is apparent acausal behavior behind the horizon. |
Non-abelian black strings: Non-abelian black strings in a 5-dimensional Einstein-Yang-Mills model are
considered. The solutions are spherically symmetric non-abelian black holes in
4 dimensions extended into an extra dimension and thus possess horizon topology
S^2 x R. We find that several branches of solutions exist. In addition, we
determine the domain of existence of the non-abelian black strings. | IR properties of one loop corrections to brane-to-brane propagators in
models with localized vector bosons: We discuss the one loop effects of massless fermion fields on the low energy
vector brane-to-brane propagators in the framework of two QED brane-world
scenarios. We show that one loop photon brane-to-brane propagator has a power
law pathologic IR divergences in the 5D QED brane-world model with gap between
the vector zero mode and continuous states. We also find that bulk fermions do
not give rise to IR divergences in a photon brane-to-brane Green's function at
least at the one loop level in the framework of 6D QED brane model with gapless
mass spectrum between vector zero mode and higher states. |
The Theory of Stochastic Space-Time. 1. Gravitation as a Quantum
Diffusion: The Nelson stochastic mechanics of inhomogeneous quantum diffusion in flat
spacetime with a tensor of diffusion can be described as a homogeneous one in a
Riemannian manifold where this tensor of diffusion plays the role of a metric
tensor. It is shown that the such diffusion accelerates both a sample particle
and a local frame such that their mean accelerations do not depend on their
masses. This fact, explaining the principle of equivalence, allows one to
represent the curvature and gravitation as consequences of the quantum
fluctuations. In this diffusional treatment of gravitation it can be naturally
explained the fact that the energy density of the instantaneous Newtonian
interaction is negative defined. | Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential
Problems with Integrability: The super Yang-Mills duals of open strings attached to maximal giant
gravitons are studied in perturbation theory. It is shown that non-BPS baryonic
excitations of the gauge theory can be studied within the paradigm of open
quantum spin chains even beyond the leading order in perturbation theory. The
open spin chain describing the two loop mixing of non-BPS giant gravitons
charged under an su(2) of the so(6) R symmetry group is explicitly constructed.
It is also shown that although the corresponding open spin chain is integrable
at the one loop order, there is a potential breakdown of integrability at two
and higher loops. The study of integrability is performed using coordinate
Bethe ansatz techniques. |
Fivebranes and 4-manifolds: We describe rules for building 2d theories labeled by 4-manifolds. Using the
proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2)
theories, we obtain a number of results, which include new 3d N=2 theories
T[M_3] associated with rational homology spheres and new results for
Vafa-Witten partition functions on 4-manifolds. In particular, we point out
that the gluing measure for the latter is precisely the superconformal index of
2d (0,2) vector multiplet and relate the basic building blocks with coset
branching functions. We also offer a new look at the fusion of defect lines /
walls, and a physical interpretation of the 4d and 3d Kirby calculus as
dualities of 2d N=(0,2) theories and 3d N=2 theories, respectively | Derivation of spontaneously broken gauge symmetry from the consistency
of effective field theory I: Massive vector bosons coupled to a scalar field: We revisit the problem of deriving local gauge invariance with spontaneous
symmetry breaking in the context of an effective field theory. Previous
derivations were based on the condition of tree-order unitarity. However, the
modern point of view considers the Standard Model as the leading order
approximation to an effective field theory. As tree-order unitarity is in any
case violated by higher-order terms in an effective field theory, it is
instructive to investigate a formalism which can be also applied to analyze
higher-order interactions. In the current work we consider an effective field
theory of massive vector bosons interacting with a massive scalar field. We
impose the conditions of generating the right number of constraints for systems
with spin-one particles and perturbative renormalizability as well as the
separation of scales at one-loop order. We find that the above conditions
impose severe restrictions on the coupling constants of the interaction terms.
Except for the strengths of the self-interactions of the scalar field, that can
not be determined at this order from the analysis of three- and four-point
functions, we recover the gauge-invariant Lagrangian with spontaneous symmetry
breaking taken in the unitary gauge as the leading order approximation to an
effective field theory. We also outline the additional work that is required to
finish this program. |
Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations: We describe how the geometry of the Higgs branch of 5d superconformal field
theories is transformed under movement along the extended Coulomb branch.
Working directly with the (unitary) magnetic quiver, we demonstrate a
correspondence between Fayet-Iliopoulos deformations in 3d and 5d mass
deformations. When the Higgs branch has multiple cones, characterised by a
collection of magnetic quivers, the mirror map is not globally well-defined,
however we are able to utilize the correspondence to establish a local version
of mirror symmetry. We give several detailed examples of deformations,
including decouplings and weak-coupling limits, in $(D_n,D_n)$ conformal matter
theories, $T_N$ theory and its parent $P_N$, for which we find new Lagrangian
descriptions given by quiver gauge theories with fundamental and anti-symmetric
matter. | Some Remarks on Anthropic Approaches to the Strong CP Problem: The peculiar value of $\theta$ is a challenge to the notion of an anthropic
landscape. We briefly review the possibility that a suitable axion might arise
from an anthropic requirement of dark matter. We then consider an alternative
suggestion of Kaloper and Terning that $\theta$ might be correlated with the
cosmological constant. We note that in a landscape one expects that $\theta$ is
determined by the expectation value of one or more axions. We discuss how a
discretuum of values of $\theta$ might arise with an energy distribution
dominated by QCD, and find the requirements to be quite stringent. Given such a
discretuum, we find limited circumstances where small $\theta$ might be
selected by anthropic requirements on the cosmological constant. |
Dynamical systems of eternal inflation: A possible solution to the
problems of entropy, measure, observables and initial conditions: There are two main approaches to non-equlibrium statistical mechanics: one
using stochastic processes and the other using dynamical systems. To model the
dynamics during inflation one usually adopts a stochastic description, which is
known to suffer from serious conceptual problems. To overcome the problems
and/or to gain more insight, we develop a dynamical systems approach. A key
assumption that goes into analysis is the chaotic hypothesis, which is a
natural generalization of the ergodic hypothesis to non-Hamiltonian systems.
The unfamiliar feature for gravitational systems is that the local phase space
trajectories can either reproduce or escape due to the presence of cosmological
and black hole horizons. We argue that the effect of horizons can be studied
using dynamical systems and apply the so-called thermodynamic formalism to
derive the equilibrium (or Sinai-Ruelle-Bowen) measure given by a variational
principle. We show that the only physical measure is not the Liouville measure
(i.e. no entropy problem), but the equilibrium measure (i.e. no measure
problem) defined over local trajectories (i.e. no problem of observables) and
supported on only infinite trajectories (i.e. no problem of initial
conditions). Phenomenological aspects of the fluctuation theorem are discussed. | Inflation with a stringy minimal length, reworked: In this paper we revisit the formulation of scalar field theories on de
Sitter backgrounds subject to the generalized uncertainty principle (GUP). The
GUP arises in several contexts in string theory, but is most readily thought of
as resulting from using strings as effective probes of geometry, which suggests
an uncertainty relation incorporating the string scale $l_s$. After reviewing
the string theoretic case for the GUP, which implies a minimum length scale
$l_s$, we follow in the footsteps of Kempf and concern ourselves with how one
might write down field theories which respect the GUP. We uncover a new
representation of the GUP, which unlike previous studies, readily permits exact
analytical solutions for the mode functions of a scalar field on de Sitter
backgrounds. We find that scalar fields cannot be quantized on inflationary
backgrounds with a Hubble radius $H^{-1}$ smaller than the string scale,
implying a sensibly stringy (as opposed to Planckian) cutoff on the scale of
inflation resulting from the GUP. We also compute $(H l_s)^2$ corrections to
the two point correlation function analytically and comment on the future
prospects of observing such corrections in the fortunate circumstance our
universe is described by a very weakly coupled string theory. |
Observer-dependent black hole interior from operator collision: We present concrete construction of interior operators for a black hole which
is perturbed by an infalling observer. The construction is independent from the
initial states of the black hole while dependent only on the quantum state of
the infalling observer. The construction has a natural interpretation from the
perspective of the boundary operator's growth, resulting from the collision
between operators accounting for the infalling and outgoing modes. The interior
partner modes are created once the infalling observer measures the outgoing
mode, suggesting that the black hole interior is observer-dependent.
Implications of our results on various conceptual puzzles, including the
firewall puzzle and the information problem, are also discussed. | The Holographic Landscape of Symmetric Product Orbifolds: We investigate the growth of coefficients in the elliptic genus of symmetric
product orbifolds at large central charge. We find that this landscape
decomposes into two regions. In one region, the growth of the low energy states
is Hagedorn, which indicates a stringy dual. In the other, the growth is much
slower, and compatible with the spectrum of a supergravity theory on AdS$_3$.
We provide a simple diagnostic which places any symmetric product orbifold in
either region. We construct a class of elliptic genera with such
supergravity-like growth, indicating the possible existence of new realizations
of AdS$_3$/CFT$_2$ where the bulk is a semi-classical supergravity theory. In
such cases, we give exact expressions for the BPS degeneracies, which could be
matched with the spectrum of perturbative states in a dual supergravity
description. |
Eschenburg space as gravity dual of flavored N=4 Chern-Simons-matter
theory: We find 3D flavored N=4 Chern-Simons-matter theory, a kind of N=3 SCFT, has a
gravity dual AdS4xM7(t1,t2,t3) where three coprime parameters can be read off
according to the number and charge of 5-branes in Type IIB setup. Because
M7(t1,t2,t3) has been known in literatures as Eschenburg space, we exploit some
of its properties to examine the correspondence between two sides. | Two-loop kite master integral for a correlator of two composite vertices: We consider the most general two-loop massless correlator
$I(n_1,n_2,n_3,n_4,n_5; x,y;D)$ of two composite vertices with the Bjorken
fractions $x$ and $y$ for arbitrary indices $\{n_i\}$ and space-time dimension
$D$; this correlator is represented by a "kite" diagram. The correlator
$I(\{n_i\};x,y;D)$ is the generating function for any scalar Feynman integrals
related to this kind of diagrams. We calculate $I(\{n_i\};x,y;D)$ and its
Mellin moments in a direct way by evaluating hypergeometric integrals in the
$\alpha$ representation. The result for $I(\{n_i\};x,y;D)$ is given in terms of
a double hypergeometric series -- the Kamp\'{e} de F\'{e}rriet function. In
some particular but still quite general cases it reduces to a sum of
generalized hypergeometric functions $_3F_2$. The Mellin moments can be
expressed through generalized Lauricella functions, which reduce to the
Kamp\'{e} de F\'{e}rriet functions in several physically interesting
situations. A number of Feynman integrals involved and relations for them are
obtained. |
More Curiosities at Effective c = 1: The moduli space of all rational conformal quantum field theories with
effective central charge c_eff = 1 is considered. Whereas the space of unitary
theories essentially forms a manifold, the non unitary ones form a fractal
which lies dense in the parameter plane. Moreover, the points of this set are
shown to be in one-to-one correspondence with the elements of the modular group
for which an action on this set is defined. | Effects of quantum deformation on the integer quantum Hall effect: In this work an application of the $\kappa$--deformed algebra in condensed
matter physics is presented. Starting by the $\kappa$--deformed Dirac equation
we study the relativistic generalization of the $\kappa$--deformed Landau
levels as well as the consequences of the deformation on the Hall conductivity.
By comparing the $\kappa$--deformed Landau levels in the nonrelativistic regime
with the energy levels of a two-dimensional electron gas (2DEG) in the presence
of a normal magnetic field, upper bounds for the deformation parameter in
different materials are established. An expression for the $\kappa$--deformed
Hall conductivity of a 2DEG is obtained as well. The expression recovers the
well-known result for the usual Hall conductivity in the limit
$\varepsilon=\kappa^{-1}\to 0$. The deformation parameter breaks the Landau
levels degeneracy and due to this, it is observed that deformation gives rise
to new plateaus of conductivity in a such way that the plateaus widths of the
$\kappa$--deformed Hall conductivity are less than the usual one. By studying
the temperature dependence of the $\kappa$--deformed Hall conductivity, we show
that an increase of the temperature causes the smearing of the plateaus and a
diminution of the effect of the deformation, whilst an increase in the magnetic
field enhances the effect of the deformation. |
Holographic Complexity Of Cold Hyperbolic Black Holes: AdS black holes with hyperbolic horizons provide strong-coupling descriptions
of thermal CFT states on hyperboloids. The low-temperature limit of these
systems is peculiar. In this note we show that, in addition to a large ground
state degeneracy, these states also have an anomalously large holographic
complexity, scaling logarithmically with the temperature. We speculate on
whether this fact generalizes to other systems whose extreme infrared regime is
formally controlled by Conformal Quantum Mechanics, such as various instances
of near-extremal charged black holes. | Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum
Aspects: We study complexified Harmonic Oscillator models in two and three dimensions.
Our work is a generalization of the work of Smilga \cite{sm} who initiated the
study of these Crypto-gauge invariant models that can be related to
$PT$-symmetric models. We show that rotational symmetry in higher spatial
dimensions naturally introduces more constraints, (in contrast to \cite{sm}
where one deals with a single constraint), with a much richer constraint
structure. Some common as well as distinct features in the study of the same
Crypto-oscillator in different dimensions are revealed. We also quantize the
two dimensional Crypto-oscillator. |
Unique Nilpotent Symmetry Transformations For Matter Fields In QED:
Augmented Superfield Formalism: We derive the local, covariant, continuous, anticommuting and off-shell
nilpotent (anti-)BRST symmetry transformations for the interacting U(1) gauge
theory of quantum electrodynamics (QED) in the framework of augmented
superfield approach to BRST formalism. In addition to the horizontality
condition, we invoke another gauge invariant condition on the six (4,
2)-dimensional supermanifold to obtain the exact and unique nilpotent symmetry
transformations for all the basic fields, present in the (anti-)BRST invariant
Lagrangian density of the physical four (3 + 1)-dimensional QED. The above
supermanifold is parametrized by four even spacetime variables x^\mu (with \mu
= 0, 1, 2, 3) and a couple of odd variables (\theta and \bar\theta) of the
Grassmann algebra. The new gauge invariant condition on the supermanifold owes
its origin to the (super) covariant derivatives and leads to the derivation of
unique nilpotent symmetry transformations for the matter fields. The
geometrical interpretations for all the above off-shell nilpotent
transformations are discussed, too. | Chiral dynamics in QED and QCD in a magnetic background and nonlocal
noncommutative field theories: We study the connection of the chiral dynamics in QED and QCD in a strong
magnetic field with noncommutative field theories (NCFT). It is shown that
these dynamics determine complicated nonlocal NCFT. In particular, although the
interaction vertices for electrically neutral composites in these gauge models
can be represented in the space with noncommutative spatial coordinates, there
is no field transformation that could put the vertices in the conventional form
considered in the literature. It is unlike the Nambu-Jona-Lasinio (NJL) model
in a magnetic field where such a field transformation can be found, with a cost
of introducing an exponentially damping form factor in field propagators. The
crucial distinction between these two types of models is in the characters of
their interactions, being short-range in the NJL-like models and long-range in
gauge theories. The relevance of the NCFT connected with the gauge models for
the description of the quantum Hall effect in condensed matter systems with
long-range interactions is briefly discussed. |
A Gauge Theory that mixes Bosonic and Fermionic Gauge Fields: Using a gauge symmetry derived by applying the Dirac constraint formalism to
supergravity with cosmological term in 2+1 dimensions, we construct a gauge
theory with many characteristics of Yang-Mills theory. The gauge transformation
mixes two Bosonic fields and one Fermionic field. | Berezinskii-Kosterlitz-Thouless transition and criticality of an
elliptic deformation of the sine-Gordon model: We introduce and study the properties of a periodic model interpolating
between the sine-- and the sinh--Gordon theories in $1+1$ dimensions. This
model shows the peculiarities, due to the preservation of the functional form
of their potential across RG flows, of the two limiting cases: the sine-Gordon,
not having conventional order/magnetization at finite temperature, but
exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the
sinh-Gordon, not having a phase transition, but being integrable. The
considered interpolation, which we term as {\em sn-Gordon} model, is performed
with potentials written in terms of Jacobi functions. The critical properties
of the sn-Gordon theory are discussed by a renormalization-group approach. The
critical points, except the sinh-Gordon one, are found to be of BKT type.
Explicit expressions for the critical coupling as a function of the elliptic
modulus are given. |
Critical exponents and amplitude ratios of scalar nonextensive $q$-field
theories: We compute the radiative quantum corrections to the critical exponents and
amplitude ratios for O($N$) $\lambda\phi^{4}$ scalar high energy nonextensive
$q$-field theories. We employ the field theoretic renormalization group
approach through six methods for evaluating the high energy nonextensive
critical exponents up to next-to-leading order while the high energy
nonextensive amplitude ratios are computed up to leading level by applying
three methods. Later we generalize these high energy nonextensive finite loop
order results for any loop level. We find that the high energy nonextensive
critical exponents are the same when obtained through all the methods employed.
The same fact occurs for the high energy nonextensive amplitude ratios.
Furthermore, we show that these high energy nonextensive universal quantities
are equal to their low energy extensive counterparts, thus showing that the
nonextensivity is broken down at high energies. | The emergence of Special and Doubly Special Relativity: Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this
paper how a Brownian motion on a short scale can originate a relativistic
motion on scales that are larger than particle's Compton wavelength. This can
be described in terms of polycrystalline vacuum. Viewed in this way, special
relativity is not a primitive concept, but rather it statistically emerges when
a coarse graining average over distances of order, or longer than the Compton
wavelength is taken. By analyzing the robustness of such a special relativity
under small variations in the polycrystalline grain-size distribution we
naturally arrive at the notion of doubly-special relativistic dynamics. In this
way, a previously unsuspected, common statistical origin of the two frameworks
is brought to light. Salient issues such as the role of gauge fixing in
emergent relativity, generalized commutation relations, Hausdorff dimensions of
representative path-integral trajectories and a connection with Feynman
chessboard model are also discussed. |
Horizon Strings and Interior States of a Black Hole: We provide an explicit construction of classical strings that have endpoints
on the horizons of the 2D Lorentzian black hole. We argue that this is a dual
description of geodesics that are localized around the horizon which are the
Lorentzian counterparts of the winding strings of the Euclidean black hole (the
cigar geometry). Identifying these with the states of the black hole, we can
expect that issues of black hole information loss can be posed sharply in terms
of a fully quantizable string theory. | The Quantum Darboux Theorem,: The problem of computing quantum mechanical propagators can be recast as a
computation of a Wilson line operator for parallel transport by a flat
connection acting on a vector bundle of wavefunctions. In this picture the base
manifold is an odd dimensional symplectic geometry, or quite generically a
contact manifold that can be viewed as a "phase-spacetime", while the fibers
are Hilbert spaces. This approach enjoys a "quantum Darboux theorem" that
parallels the Darboux theorem on contact manifolds which turns local classical
dynamics into straight lines. We detail how the quantum Darboux theorem works
for anharmonic quantum potentials. In particular, we develop a novel
diagrammatic approach for computing the asymptotics of a gauge transformation
that locally makes complicated quantum dynamics trivial. |
Quantum Energies of Strings in a 2+1 Dimensional Gauge Theory: We study classically unstable string type configurations and compute the
renormalized vacuum polarization energies that arise from fermion fluctuations
in a 2+1 dimensional analog of the standard model. We then search for a minimum
of the total energy (classical plus vacuum polarization energies) by varying
the profile functions that characterize the string. We find that typical string
configurations bind numerous fermions and that populating these levels is
beneficial to further decrease the total energy. Ultimately our goal is to
explore the stabilization of string type configurations in the standard model
through quantum effects.
We compute the vacuum polarization energy within the phase shift formalism
which identifies terms in the Born series for scattering data and Feynman
diagrams. This approach allows us to implement standard renormalization
conditions of perturbation theory and thus yields the unambiguous result for
this non--perturbative contribution to the total energy. | Multiloop String Amplitudes with B-Field and Noncommutative QFT: The multiloop amplitudes for the bosonic string in presence of a constant
B-field are built by using the basic commutation relations for the open string
zero modes and oscillators. The open string Green function on the annulus is
obtained from the one loop scattering amplitude among N tachyons. For higher
loops, it is necessary to use the so called three Reggeon vertex, which
describes the emission from the open string of another string and not simply of
a tachyon. We find that the modifications to the three (and multi) Reggeon
vertex due to the B-field only affect the zero modes and can be written in a
simple and elegant way. Therefore we can easily sew these vertices together and
write the general expression for the multiloop N-Reggeon vertex, which contains
any loop string amplitude, in presence of the B-field. The field theory limit
is also considered in some examples at two loops and reproduces exactly the
results of a noncommutative scalar field theory. |
Near horizon data and physical charges of extremal AdS black holes: We compute the physical charges and discuss the properties of a large class
of five-dimensional extremal AdS black holes by using the near horizon data.
Our examples include baryonic and electromagnetic black branes, as well as
supersymmetric spinning black holes. In the presence of the gauge Chern-Simons
term, the five-dimensional physical charges are the Page charges. We carry out
the near horizon analysis and compute the four-dimensional charges of the
corresponding black holes by using the entropy function formalism and show that
they match the Page charges. | Scalar Quartic Effective Action on $AdS_5$: We review the recent results concerning the computation of cubic and quartic
couplings of scalar fields in type IIB supergravity on AdS_5\times S^5
background that are dual to (extended) chiral primary operators in N=4 SYM_4.
We discuss the vanishing of certain cubic and quartic couplings and
non-renormalization property of corresponding correlators in the conformal
field theory |
Topological Open/Closed String Dualities: Matrix Models and Wave
Functions: We sharpen the duality between open and closed topological string partition
functions for topological gravity coupled to matter. The closed string
partition function is a generalised Kontsevich matrix model in the large
dimension limit. We integrate out off-diagonal degrees of freedom associated to
one source eigenvalue, and find an open/closed topological string partition
function, thus proving open/closed duality. We match the resulting open
partition function to the generating function of intersection numbers on moduli
spaces of Riemann surfaces with boundaries and boundary insertions. Moreover,
we connect our work to the literature on a wave function of the KP integrable
hierarchy and clarify the role of the extended Virasoro generators that include
all time variables as well as the coupling to the open string observable. | Dynamical sectors for a spinning particle in AdS_3: We consider the dynamics of the motion of a particle of mass M and spin J in
AdS_3. The study reveals the presence of different dynamical sectors depending
on the relative values of M, J and the AdS_3 radius R. For the subcritical M^2
R^2-J^2 >0 and supercritical M^2 R^2-J^2<0 cases, it is seen that the equations
of motion give the geodesics of AdS_3. For the critical case M^2R^2=J^2 there
exist extra gauge transformations which further reduce the physical degrees of
freedom, and the motion corresponds to the geodesics of AdS_2. This result
should be useful in the holographic interpretation of the entanglement entropy
for 2d conformal field theories with gravitational anomalies. |
Single impurity operators at critical wrapping order in the
beta-deformed N=4 SYM: We study the spectrum of one single magnon in the superconformal
beta-deformed N=4 SYM theory in the planar limit. We compute the anomalous
dimensions of one-impurity operators O_{1,L}= tr(phi Z^{L-1}), including
wrapping contributions at their critical order L. | Baby Skyrme model and fermionic zero modes: In this work we investigate some features of the fermionic sector of the
supersymmetric version of the baby Skyrme model. We find that, in the
background of BPS compact Skyrmions, fermionic zero modes are confined to the
defect core. Further, we show that, while three SUSY generators are broken in
the defect core, SUSY is completely restored outside. We study also the effect
of a D-term deformation of the model. Such a deformation allows for the
existence of fermionic zero modes and broken SUSY outside the compact defect. |
Tadpole versus anomaly cancellation in D=4,6 compact IIB orientifolds: It is often stated in the literature concerning D=4,6 compact Type IIB
orientifolds that tadpole cancellation conditions i) uniquely fix the gauge
group (up to Wilson lines and/or moving of branes) and ii) are equivalent to
gauge anomaly cancellation. We study the relationship between tadpole and
anomaly cancellation conditions and qualify both statements. In general the
tadpole cancellation conditions imply gauge anomaly cancellation but are
stronger than the latter conditions in D=4, N=1 orientifolds. We also find that
tadpole cancellation conditions in Z_N D=4,6 compact orientifolds do not
completely fix the gauge group and we provide new solutions different from
those previously reported in the literature. | USp(2k) Matrix Model: Nonperturbative Approach to Orientifolds: We discuss theoretical implications of the large k USp(2k) matrix model in
zero dimension. The model appears as the matrix model of type IIB superstrings
on a large $T^{6}/Z^{2}$ orientifold via the matrix twist operation. In the
small volume limit, the model behaves four dimensional and its T dual is
six-dimensional worldvolume theory of type I superstrings in ten spacetime
dimensions. Several theoretical considerations including the analysis on planar
diagrams, the commutativity of the projectors with supersymmetries and the
cancellation of gauge anomalies are given, providing us with the rationales for
the choice of the Lie algebra and the field content. A few classical solutions
are constructed which correspond to Dirichlet p-branes and some fluctuations
are evaluated. The particular scaling limit with matrix T duality
transformation is discussed which derives the F theory compactification on an
elliptic fibered K3. |
Quiver Tails and N=1 SCFTs from M5-branes: We study a class of four-dimensional N=1 superconformal field theories
obtained by wrapping M5-branes on a Riemann surface with punctures. We identify
UV descriptions of four-dimensional SCFTs corresponding to curves with a class
of punctures. The quiver tails appearing in these UV descriptions differ
significantly from their N=2 counterpart. We find a new type of object that we
call the `Fan'. We show how to construct new N=1 superconformal theories using
the Fan. Various dual descriptions for these SCFTs can be identified with
different colored pair-of-pants decompositions. For example, we find an N=1
analog of Argyres-Seiberg duality for the SU(N) SQCD with 2N flavors. We also
compute anomaly coefficients and superconformal indices for these theories and
show that they are invariant under dualities. | Quantisation of Klein-Gordon field in $κ$ space-time: deformed
oscillators and Unruh effect: In this paper we study the quantisation of scalar field theory in
$\kappa$-deformed space-time. Using a quantisation scheme that use only field
equations, we derive the quantisation rules for deformed scalar theory,
starting from the $\kappa$-deformed equations of motion. This scheme allows two
choices; (i)a deformed commutation relation between the field and its conjugate
which leads to usual oscillator algebra, (ii) an undeformed commutation
relation between field and its conjugate leading to a deformed oscillator
algebra. This deformed oscillator algebra is used to derive modification to
Unruh effect in the $\kappa$-space-time. |
The Standard Model of Particles and Forces in the Framework of
2T-physics: In this paper it will be shown that the Standard Model in 3+1 dimensions is a
gauge fixed version of a 2T-physics field theory in 4+2 dimensions, thus
establishing that 2T-physics provides a correct description of Nature from the
point of view of 4+2 dimensions. The 2T formulation leads to phenomenological
consequences of considerable significance. In particular, the higher structure
in 4+2 dimensions prevents the problematic F*F term in QCD. This resolves the
strong CP problem without a need for the Peccei-Quinn symmetry or the
corresponding elusive axion. Mass generation with the Higgs mechanism is less
straightforward in the new formulation of the Standard Model, but its
resolution leads to an appealing deeper physical basis for mass, coupled with
phenomena that could be measurable. In addition, there are some brand new
mechanisms of mass generation related to the higher dimensions that deserve
further study. The technical progress is based on the construction of a new
field theoretic version of 2T-physics including interactions in an action
formalism in d+2 dimensions. The action is invariant under a new type of gauge
symmetry which we call 2Tgauge-symmetry in field theory. This opens the way for
investigations of the Standard Model directly in 4+2 dimensions, or from the
point of view of various embeddings of 3+1 dimensions, by using the duality,
holography, symmetry and unifying features of 2T-physics. | Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field
Theory: The metric algebroid proposed by Vaisman (the Vaisman algebroid) governs the
gauge symmetry algebra generated by the C-bracket in double field theory (DFT).
We show that the Vaisman algebroid is obtained by an analogue of the Drinfel'd
double of Lie algebroids. Based on a geometric realization of doubled
space-time as a para-Hermitian manifold, we examine exterior algebras and a
para-Dolbeault cohomology on DFT and discuss the structure of the Drinfel'd
double behind the DFT gauge symmetry. Similar to the Courant algebroid in the
generalized geometry, Lagrangian subbundles $(L,\tilde{L})$ in a para-Hermitian
manifold play Dirac-like structures in the Vaisman algebroid. We find that an
algebraic origin of the strong constraint in DFT is traced back to the
compatibility condition needed for $(L,\tilde{L})$ be a Lie bialgebroid. The
analysis provides a foundation toward the "coquecigrue problem" for the gauge
symmetry in DFT. |
Yang-Mills and Supersymmetry Covariance Must Coexist: Supersymmetry and Yang-Mills type gauge invariance are two of the essential
properties of most, and possibly the most important models in fundamental
physics. Supersymmetry is nearly trivial to prove in the (traditionally
gauge-noncovariant) superfield formalism, whereas the gauge-covariant formalism
makes gauge invariance manifest. In 3+1-dimensions, the transformation from one
into the other is elementary and essentially unique. By contrast, this
transformation turns out to be impossible in the most general 1+1-dimensional
case. In fact, only the (manifestly) gauge- and supersymmetry-covariant
formalism guarantees both universal gauge-invariance and supersymmetry. | Non-minimal Higgs content in standard-like models from D-branes at a Z_N
singularity: We show that attempts to construct the standard model, or the MSSM, by
placing D3-branes and D7-branes at a Z_N orbifold or orientifold singularity
all require that the electroweak Higgs content is non-minimal. For the orbifold
the lower bound on the number n(H) + n({\bar{H}}) of electroweak Higgs doublets
is the number n(q^c_L)=6 of quark singlets, and for the orientifold the lower
bound can be one less. As a consequence there is a generic flavour changing
neutral current problem in such models. |
Kähler potential of heterotic orbifolds with multiple Kähler moduli: Aiming at improving our knowledge of the low-energy limit of heterotic
orbifold compactifications, we determine at lowest order the Kahler potential
of matter fields in the case where more than three bulk Kahler moduli appear.
Interestingly, bulk matter fields couple to more than one Kahler modulus, a
subtle difference with models with only three Kahler moduli that may provide a
tool to address the question of moduli stabilization in these models. | $L_\infty$ algebras for extended geometry: Extended geometry provides a unified framework for double geometry,
exceptional geometry, etc., i.e., for the geometrisations of the string theory
and M-theory dualities. In this talk, we will explain the structure of gauge
transformations (generalised diffeomorphisms) in these models. They are
generically infinitely reducible, and arise as derived brackets from an
underlying Borcherds superalgebra or tensor hierarchy algebra. The infinite
reducibility gives rise to an $L_\infty$ structure, the brackets of which have
universal expressions in terms of the underlying superalgebra. |
New Exact Quantization Condition for Toric Calabi-Yau Geometries: We propose a new exact quantization condition for a class of quantum
mechanical systems derived from local toric Calabi-Yau three-folds. Our
proposal includes all contributions to the energy spectrum which are
non-perturbative in the Planck constant, and is much simpler than the available
quantization condition in the literature. We check that our proposal is
consistent with previous works and implies non-trivial relations among the
topological Gopakumar-Vafa invariants of the toric Calabi-Yau geometries.
Together with the recent developments, our proposal opens a new avenue in the
long investigations at the interface of geometry, topology and quantum
mechanics. | TASI lectures on black holes in string theory: This is a write-up of introductory lectures on black holes in string theory
given at TASI-99. Topics discussed include: Black holes, thermodynamics and the
Bekenstein-Hawking entropy, the information problem; supergravity actions,
conserved quantum numbers, supersymmetry and BPS states, units and duality,
dimensional reduction, solution-generating; extremal M-branes and D-branes,
smearing, probe actions, nonextremal branes, the Gregory-Laflamme instability;
breakdown of supergravity and the Correspondence Principle, limits in parameter
space, singularity resolution; making black holes with branes,
intersection-ology, explicit d=5,4 examples; string/brane computations of
extremal black hole entropy in d=5,4, rotation, fractionation; non-extremality
and entropy, the link to BTZ black holes, Hawking radiation and absorption
cross-sections in the string/brane and supergravity pictures. |
Freudenthal Duality and Generalized Special Geometry: Freudenthal duality, introduced in L. Borsten, D. Dahanayake, M. J. Duff and
W. Rubens, Phys.Rev. D80, 026003 (2009), and defined as an anti-involution on
the dyonic charge vector in d = 4 space-time dimensions for those dualities
admitting a quartic invariant, is proved to be a symmetry not only of the
classical Bekenstein-Hawking entropy but also of the critical points of the
black hole potential. Furthermore, Freudenthal duality is extended to any
generalized special geometry, thus encompassing all N > 2 supergravities, as
well as N = 2 generic special geometry, not necessarily having a coset space
structure. | Coherence revival and metrological advantage for moving Unruh-DeWitt
detector: In this paper, we investigate the quantum coherence extraction for two
accelerating Unruh-DeWitt detectors coupling to a scalar background in $3+1$
Minkowski spacetime. We find that quantum coherence as a sort of nonclassical
correlation can be generated through the Markovian evolution of the detectors
system just like quantum entanglement. However, with growing Unruh temperature,
in contrast to monotonous degrading entanglement, we find that quantum
coherence exhibits a striking revival phenomenon. That is, for certain choice
of detectors' initial state, coherence measure will reduce to zero firstly then
grow up to an asymptotic value. We verify such coherence revival by inspecting
its metrological advantage on enhancing the quantum Fisher information (QFI).
Since the maximal QFI bounding the accuracy of a quantum measurement, we
conclude that the extracted coherence can be utilized as a physical resource in
quantum metrology. |
Exact Half-BPS Flux Solutions in M-theory I, Local Solutions: The complete eleven-dimensional supergravity solutions with 16
supersymmetries on manifolds of the form $AdS_3 \times S^3 \times S^3 \times
\Sigma$, with isometry $SO(2,2) \times SO(4) \times SO(4)$, and with either
$AdS_4 \times S^7$ or $AdS_7 \times S^4$ boundary behavior, are obtained in
exact form. The two-dimensional parameter space $\Sigma$ is a Riemann surface
with boundary, over which the product space $AdS_3 \times S^3 \times S^3$ is
warped. By mapping the reduced BPS equations to an integrable system of the
sine-Gordon/Liouville type, and then mapping this integrable system onto a
linear equation, the general local solutions are constructed explicitly in
terms of one harmonic function on $\Sigma$, and an integral transform of two
further harmonic functions on $\Sigma$. The solutions to the BPS equations are
shown to automatically solve the Bianchi identities and field equations for the
4-form field, as well as Einstein's equations. The solutions we obtain have
non-vanishing 4-form field strength on each of the three factors of $AdS_3
\times S^3 \times S^3$, and include fully back-reacted M2-branes in $AdS_7
\times S^4$ and M5-branes in $AdS_4 \times S^7$. No interpolating solutions
exist with mixed $AdS_4 \times S^7$ and $AdS_7 \times S^4$ boundary behavior.
Global regularity of these local solutions, as well as the existence of further
solutions with neither $AdS_4 \times S^7$ nor $AdS_7 \times S^4$ boundary
behavior will be studied elsewhere. | Duality in Matrix Theory and Three Dimensional Mirror Symmetry: Certain limits of the duality between M-theory on ${T^5/Z_2}$ and IIB on K3
are analyzed in Matrix theory. The correspondence between M-theory five-branes
and ALE backgrounds is realized as three dimensional mirror symmetry.
Non-critical strings dual to open membranes are explicitly described as gauge
theory excitations. We also comment on Type IIA on K3 and the appearance of
gauge symmetry enhancement at special points in the moduli space. |
On integrability of geodesics in near-horizon extremal geometries: Case
of Myers-Perry black holes in arbitrary dimensions: We investigate dynamics of probe particles moving in the near-horizon limit
of extremal Myers-Perry black holes in arbitrary dimensions. Employing
ellipsoidal coordinates we show that this problem is integrable and separable,
extending the results of the odd dimensional case discussed in
arXiv:1703.00713. We find the general solution of the Hamilton-Jacobi equations
for these systems and present explicit expressions for the Liouville integrals,
discuss Killing tensors and the associated constants of motion. We analyze
special cases of the background near-horizon geometry were the system possesses
more constants of motion and is hence superintegrable. Finally, we consider
near-horizon extremal vanishing horizon case which happens for Myers-Perry
black holes in odd dimensions and show that geodesic equations on this geometry
are also separable and work out its integrals of motion. | Fractional Virasoro Algebras: We show that it is possible to construct a Virasoro algebra as a central
extension of the fractional Witt algebra generated by non-local operators of
the form, $L_n^a\equiv\left(\frac{\partial f}{\partial z}\right)^a$ where $a\in
{\mathbb R}$. The Virasoro algebra is explicitly of the form, \beq
[L^a_m,L_n^a]=A_{m,n}L^a_{m+n}+\delta_{m,n}h(n)cZ^a \eeq where $c$ is the
central charge (not necessarily a constant), $Z^a$ is in the center of the
algebra and $h(n)$ obeys a recursion relation related to the coefficients
$A_{m,n}$. In fact, we show that all central extensions which respect the
special structure developed here which we term a multimodule Lie-Algebra, are
of this form. This result provides a mathematical foundation for non-local
conformal field theories, in particular recent proposals in condensed matter in
which the current has an anomalous dimension. |
Classical and quantum gravitational scattering with Generalized Wilson
Lines: The all-order structure of scattering amplitudes is greatly simplified by the
use of Wilson line operators, describing eikonal emissions from straight lines
extending to infinity. A generalization at subleading powers in the eikonal
expansion, known as Generalized Wilson Line (GWL), has been proposed some time
ago, and has been applied both in QCD phenomenology and in the high energy
limits of gravitational amplitudes. In this paper we revisit the construction
of the scalar gravitational GWL starting from first principles in the worldline
formalism. We identify the correct Hamiltonian that leads to a simple
correspondence between the soft expansion and the weak field expansion. This
allows us to isolate the terms in the GWL that are relevant in the classical
limit. In doing so we devote special care to the regularization of UV
divergences that were not discussed in an earlier derivation. We also clarify
the relation with a parallel body of work that recently investigated the
classical limit of scattering amplitudes in gravity in the worldline formalism. | Two Ramond-Ramond corrections to type II supergravity via field-theory
amplitude: Motivated by the standard form of string-theory amplitude, we calculate the
field-theory amplitude to complete the higher-derivative terms in type II
supergravity theories in their conventional form. We derive explicitly the $
O(\alpha'^3) $ interactions for the RR (Ramond-Ramond) fields with graviton,
B-field and dilaton in the low-energy effective action of type II superstrings.
We check our results by comparison with previous works that have been done by
the other methods, and find an exact agreement. |
Modular anomaly equations and S-duality in N=2 conformal SQCD: We use localization techniques to study the non-perturbative properties of an
N=2 superconformal gauge theory with gauge group SU(3) and six fundamental
flavours. The instanton corrections to the prepotential, the dual periods and
the period matrix are calculated in a locus of special vacua possessing a Z_3
symmetry. In a semi-classical expansion, we show that these observables are
constrained by S-duality via a modular anomaly equation which takes the form of
a recursion relation. The solutions of the recursion relation are quasi-modular
functions of Gamma_1(3), which is a subgroup of the S-duality group and is also
a congruence subgroup of SL(2,Z). | BRST invariant approach to quantum mechanical tunneling: A new approach with BRST invariance is suggested to cure the degeneracy
problem of ill defined path integrals in the path-integral calculationof
quantum mechanical tunneling effects in which the problem arises due to the
occurrence of zero modes. The Faddeev-Popov procedure is avoided and the
integral over the zero mode is transformed in a systematic way into a well
defined integral over instanton positions. No special procedure has to be
adopted as in the Faddeev-Popov method in calculating the Jacobian of the
transformation. The quantum mechanical tunneling for the Sine-Gordon potential
is used as a test of the method and the width of the lowest energy band is
obtained in exact agreement with that of WKB calculations. |
Noncommutativity from the symplectic point of view: The great deal in noncommutative (NC) field theories started when it was
noted that NC spaces naturally arise in string theory with a constant
background magnetic field in the presence of $D$-branes. Besides their origin
in string theories and branes, NC field theories have been studied extensively
in many branches of physics. In this work we explore how NC geometry can be
introduced into a commutative field theory besides the usual introduction of
the Moyal product. We propose a systematic new way to introduce NC geometry
into commutative systems, based mainly on the symplectic approach. Further, as
example, this formalism describes precisely how to obtain a Lagrangian
description for the NC version of some systems reproducing well known theories. | Gauge Theories from Orientifolds and Large N Limit: Extending the recent work in hep-th/9803076, we consider string perturbative
expansion in the presence of D-branes and orientifold planes imbedded in
orbifolded space-time. In the $\alpha'\to 0$ limit the weak coupling string
perturbative expansion maps to `t Hooft's large N expansion. We focus on four
dimensional ${\cal N}=1,2,4$ supersymmetric theories, and also discuss possible
extensions to ${\cal N}=0$ cases. Utilizing the string theory perturbation
techniques we show that computation of any M-point correlation function in
these theories reduces to the corresponding computation in the parent ${\cal
N}=4$ theory. In particular, we discuss theories (which are rather constrained)
with vanishing beta-functions to all orders in perturbation theory in the large
N limit. We also point out that in theories with non-vanishing beta-functions
the gauge coupling running is suppressed in the large N limit. Introduction of
orientifold planes allows to construct certain gauge theories with SO, Sp and
SU gauge groups and various matter (only unitary gauge groups with
bi-fundamental/adjoint matter arise in theories without orientifold planes). |
Lagrangians with electric and magnetic charges of N=2 supersymmetric
gauge theories: General Lagrangians are constructed for N=2 supersymmetric gauge theories in
four space-time dimensions involving gauge groups with (non-abelian) electric
and magnetic charges. The charges induce a scalar potential, which, when the
charges are regarded as spurionic quantities, is invariant under
electric/magnetic duality. The resulting theories are especially relevant for
supergravity, but details of the extension to local supersymmetry will be
discussed elsewhere. The results include the coupling to hypermultiplets.
Without the latter, it is demonstrated how an off-shell representation can be
constructed based on vector and tensor supermultiplets. | Tree-level Correlators of scalar and vector fields in AdS/CFT: Extending earlier results by Paulos, we discuss further the use of the
embedding formalism and Mellin transform in the calculation of tree-level
correlators of scalar and vector fields in AdS/CFT. We present an iterative
procedure that builds amplitudes by sewing together lower-point off-shell
diagrams. Both scalar and vector correlators are shown to be given in terms of
Mellin amplitudes. We apply the procedure to the explicit calculation of
three-, four- and five-point correlators. |
Superconformal Index for $\mathcal{N}=3$ $\hat{ADE}$ Chern-Simons Quiver
Gauge Theories: We compute superconformal indices for $\mathcal{N} = 3$ $\hat{ADE}$
Chern-Simons quiver gauge theories with a product gauge group $\prod_i U(N)_i$,
using the method of supersymmetric localization. We also perform a large $N$
analysis of the index. This index includes contribution from non zero magnetic
flux sector. The fact that these theories have a weakly coupled UV completion
in terms of $\mathcal{N}= 3$ supersymmetric Chern-Simons Yang-Mills theories
enables us to apply the localization technique. Such theories have dual
M-theory description on $\mathrm{AdS}_4\times M_7$, where $M_7$ is a tri-Sasaki
Einstein manifold. | Orientifolds and duality cascades: confinement before the wall: We consider D-branes at orientifold singularities and discuss two properties
of the corresponding low energy four-dimensional effective theories which are
not shared, generically, by other Calabi-Yau singularities. The first property
is that duality cascades are finite and, unlike ordinary ones, do not require
an infinite number of degrees of freedom to be UV-completed. The second is that
orientifolds tend to stabilize runaway directions. These two properties can
have interesting implications and widen in an intriguing way the variety of
gauge theories one can describe using D-branes. |
Double Scaling Limits and Twisted Non-Critical Superstrings: We consider double-scaling limits of multicut solutions of certain one matrix
models that are related to Calabi-Yau singularities of type A and the
respective topological B model via the Dijkgraaf-Vafa correspondence. These
double-scaling limits naturally lead to a bosonic string with c $\leq$ 1. We
argue that this non-critical string is given by the topologically twisted
non-critical superstring background which provides the dual description of the
double-scaled little string theory at the Calabi-Yau singularity. The
algorithms developed recently to solve a generic multicut matrix model by means
of the loop equations allow to show that the scaling of the higher genus terms
in the matrix model free energy matches the expected behaviour in the
topological B-model. This result applies to a generic matrix model singularity
and the relative double-scaling limit. We use these techniques to explicitly
evaluate the free energy at genus one and genus two. | Boundary Reflection Matrix in Perturbative Quantum Field Theory: We study boundary reflection matrix for the quantum field theory defined on a
half line using Feynman's perturbation theory. The boundary reflection matrix
can be extracted directly from the two-point correlation function. This enables
us to determine the boundary reflection matrix for affine Toda field theory
with the Neumann boundary condition modulo `a mysterious factor half'. |
Superstring Dualities, Dirichlet Branes and the Small Scale Structure of
Space: We give a broad overview of superstring duality, Dirichlet branes, and some
implications of both for questions about the structure of space-time at short
distances. | Four-dimensional QCD and fiberwise duality: We transform, by means of a fiberwise duality, the partition function of QCD
on a product of two two-tori, into a four-dimensional sigma-model, whose target
space is the cotangent space of unitary connections on the fiber torus
fiberwise. |
A Spin-2 Conjecture on the Swampland: We consider effective theories with massive fields that have spins larger
than or equal to two. We conjecture a universal cutoff scale on any such theory
that depends on the lightest mass of such fields. This cutoff corresponds to
the mass scale of an infinite tower of states, signalling the breakdown of the
effective theory. The cutoff can be understood as the Weak Gravity Conjecture
applied to the St\"uckelberg gauge field in the mass term of the high spin
fields. A strong version of our conjecture applies even if the graviton itself
is massive, so to massive gravity. We provide further evidence for the
conjecture from string theory. | Holographic Friedmann Equation and $\cal{N}=$4 SYM theory: According to the AdS/CFT correspondence, the ${\cal N}=4$ supersymmetric
Yang-Mills (SYM) theory has been studied by solving the dual supergravity. In
solving the bulk Einstein equation, we find that it could be related to the 4D
Friedmann equation, which is solved by using the cosmological constant and the
energy density of the matters on the boundary, and they are dynamically
decoupled from the SYM theory. We call this combination of the bulk Einstein
equations and the 4D Friedmann equation as holographic Friedmann equations
(HFE). Solving the HFE, it is shown how the 4D decoupled matters and the
cosmological constant control the dynamical properties of the SYM theory, quark
confinement, chiral symmetry breaking, and baryon stability. From their effect
on the SYM, the matters are separated to two groups. Our results would give
important information in studying the cosmological development of our universe. |
Irreducible Hamiltonian BRST symmetry for reducible first-class systems: An irreducible Hamiltonian BRST quantization method for reducible first-class
systems is proposed. The general theory is illustrated on a two-stage reducible
model, the link with the standard reducible BRST treatment being also
emphasized. | Charged Magnetic Brane Correlators and Twisted Virasoro Algebras: Prior work using gauge/gravity duality has established the existence of a
quantum critical point in the phase diagram of 3+1-dimensional gauge theories
at finite charge density and background magnetic field. The critical theory,
obtained by tuning the dimensionless charge density to magnetic field ratio,
exhibits nontrivial scaling in its thermodynamic properties, and an associated
nontrivial dynamical critical exponent. In the present work, we analytically
compute low energy correlation functions in the background of the charged
magnetic brane solution to 4+1-dimensional Einstein-Maxwell-Chern-Simons
theory, which represents the bulk description of the critical point. Results
are obtained for neutral scalar operators, the stress tensor, and the
U(1)-current. The theory is found to exhibit a twisted Virasoro algebra,
constructed from a linear combination of the original stress tensor and chiral
U(1)-current. The effective speed of light in the IR is renormalized downward
for one chirality, but not the other, by finite density, a behavior that is
consistent with a Luttinger liquid description of fermions in the lowest Landau
level. The results obtained here do not directly shed light on the mechanism
driving the phase transition, and we comment on why this is so. |
Off-shell Invariant D=N=2 Twisted Super Yang-Mills Theory with a Gauged
Central Charge without Constraints: We formulate N=2 twisted super Yang-Mills theory with a gauged central charge
by superconnection formalism in two dimensions. We obtain off-shell invariant
supermultiplets and actions with and without constraints, which is in contrast
with the off-shell invariant D=N=4 super Yang-Mills formulation with
unavoidable constraints. | Runaway dilatonic domain walls: We explore the stability of domain wall and bubble solutions in theories with
compact extra dimensions. The energy density stored inside of the wall can
destabilize the volume modulus of a compactification, leading to solutions
containing either a timelike singularity or a region where space
decompactifies, depending on the metric ansatz. We determine the structure of
such solutions both analytically and using numerical simulations, and analyze
how they arise in compactifications of Einstein--Maxwell theory and Type IIB
string theory. The existence of instabilities has important implications for
the formation of networks of topological defects and the population of vacua
during eternal inflation. |
Hyperspherical Harmonics, Separation of Variables and the Bethe Ansatz: The relation between solutions to Helmholtz's equation on the sphere
$S^{n-1}$ and the $[{\gr sl}(2)]^n$ Gaudin spin chain is clarified. The joint
eigenfuctions of the Laplacian and a complete set of commuting second order
operators suggested by the $R$--matrix approach to integrable systems, based on
the loop algebra $\wt{sl}(2)_R$, are found in terms of homogeneous polynomials
in the ambient space. The relation of this method of determining a basis of
harmonic functions on $S^{n-1}$ to the Bethe ansatz approach to integrable
systems is explained. | Chiral Limit of 2d QCD Revisited with Lightcone Conformal Truncation: We study the chiral limit of 2d QCD with a single quark flavor at finite
$N_c$ using LCT. By modifying the LCT basis according to the quark mass in a
manner motivated by 't Hooft's analysis, we are able to restore convergence for
quark masses much smaller than the QCD strong coupling scale. For such small
quark masses, the IR of the theory is expected to be well described by the
Sine-Gordon model. We verify that LCT numerics are able to capture in detail
the spectrum and correlation functions of the Sine-Gordon model. This opens up
the possibility for studying deformations of various integrable CFTs using LCT
by considering the chiral limit of QCD like theories. |
Soft theorems for boosts and other time symmetries: We derive soft theorems for theories in which time symmetries -- symmetries
that involve the transformation of time, an example of which are Lorentz boosts
-- are spontaneously broken. The soft theorems involve unequal-time correlation
functions with the insertion of a soft Goldstone in the far past. Explicit
checks are provided for several examples, including the effective theory of a
relativistic superfluid and the effective field theory of inflation. We discuss
how in certain cases these unequal-time identities capture information at the
level of observables that cannot be seen purely in terms of equal-time
correlators of the field alone. We also discuss when it is possible to phrase
these soft theorems as identities involving equal-time correlators. | Gravitationally Dressed Conformal Field Theory and Emergence of
Logarithmic Operators: We study correlation functions in two-dimensional conformal field theory
coupled to induced gravity in the light-cone gauge. Focussing on the fermion
four-point function, we display an unexpected non-perturbative singularity
structure: coupling to gravity {\it qualitatively} changes the perturbative
$(x_1-x_2)^{-1}(x_3-x_4)^{-1}$ singularity into a logarithmic one plus a
non-singular piece. We argue that this is related to the appearence of new
logarithmic operators in the gravitationally dressed operator product
expansions. We also show some evidence that non-conformal but integrable models
may remain integrable when coupled to gravity. |
Boundary terms, branes and AdS/BCFT in first-order gravity: We provide an account of the issue of Gibbons-Hawking-York-like boundary
terms for a gravity theory defined on a Riemman-Cartan spacetime. We further
discuss different criteria for introducing boundary terms in some familiar
first-order gravity theories with both on-shell vanishing and non-vanishing
torsion, along with considerations regarding the thermodynamics of black holes
and profiles of the End-of-the-World branes. Our analysis confirms the expected
geodesic profile of the End-of-the-World brane in the BF formulation of
Jackiw-Teitelboim gravity. Finally, we present the first realisation of the
AdS/BCFT duality for spacetime with torsion. | Lifshitz Scale Anomalies: We analyse scale anomalies in Lifshitz field theories, formulated as the
relative cohomology of the scaling operator with respect to foliation
preserving diffeomorphisms. We construct a detailed framework that enables us
to calculate the anomalies for any number of spatial dimensions, and for any
value of the dynamical exponent. We derive selection rules, and establish the
anomaly structure in diverse universal sectors. We present the complete
cohomologies for various examples in one, two and three space dimensions for
several values of the dynamical exponent. Our calculations indicate that all
the Lifshitz scale anomalies are trivial descents, called B-type in the
terminology of conformal anomalies. However, not all the trivial descents are
cohomologically non-trivial. We compare the conformal anomalies to Lifshitz
scale anomalies with a dynamical exponent equal to one. |
Witten index for weak supersymmetric systems: invariance under
deformations: When a $4D$ supersymmetric theory is placed on $S^3 \times \mathbb{R}$, the
supersymmetric algebra is necessarily modified to $su(2|1)$ and we are dealing
with a weak supersymmetric system. For such systems, the excited states of the
Hamiltonian are not all paired. As a result, the Witten index Tr$\{(-1)^F
e^{-\beta H}\}$ is no longer an integer number, but a $\beta$-dependent
function.
However, this function stays invariant under deformations of the theory that
keep the supersymmetry algebra intact. Based on the Hilbert space analysis, we
give a simple general proof of this fact. We then show how this invariance
works for two simplest weak supersymmetric quantum mechanical systems involving
a real or a complex bosonic degree of freedom. | Calculable membrane theory: The key to membrane theory is to enlarge the diffeomorphism group until 4D
gravity becomes almost topological. Just one ghost survives and its central
charges can cancel against matter. A simple bosonic membrane emerges, but its
flat D = 28 target space is unstable. Adding supersymmetry ought to give
calculable (2,2) membranes in 12 target dimensions, but (2,1) membranes won't
work. |
A Quantum Integrable System with Two Colour-Components in Two Dimensions: The Davey-Stewartson 1(DS1) system[9] is an integrable model in two
dimensions. A quantum DS1 system with 2 colour-components in two dimensions has
been formulated. This two-dimensional problem has been reduced to two
one-dimensional many-body problems with 2 colour-components. The solutions of
the two-dimensional problem under consideration has been constructed from the
resulting problems in one dimensions. For latters with the $\delta $-function
interactions and being solved by the Bethe ansatz, we introduce symmetrical and
antisymmetrical Young operators of the permutation group and obtain the exact
solutions for the quantum DS1 system. The application of the solusions is
discussed. | Topological Excitation in Skyrme Theory: Based on the $\phi$-mapping topological current theory and the decomposition
of gauge potential theory, we investigate knotted vortex lines and monopoles in
Skyrme theory and simply discuss the branch processes (splitting, merging and
intersection) during the evolution of the monopoles. |
Kink Dynamics in a Topological Phi^4 Lattice: It was recently proposed a novel discretization for nonlinear Klein-Gordon
field theories in which the resulting lattice preserves the topological
(Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no
Peierls-Nabarro barrier even for large spatial discretizations (h~1.0). It was
then suggested that these ``topological discrete systems'' are a natural choice
for the numerical study of continuum kink dynamics. Giving particular emphasis
to the phi^4 theory, we numerically investigate kink-antikink scattering and
breather formation in these topological lattices. Our results indicate that,
even though these systems are quite accurate for studying free kinks in coarse
lattices, for legitimate dynamical kink problems the accuracy is rather
restricted to fine lattices (h~0.1). We suggest that this fact is related to
the breaking of the Bogomol'nyi bound during the kink-antikink interaction,
where the field profile loses its static property as required by the
Bogomol'nyi argument. We conclude, therefore, that these lattices are not
suitable for the study of more general kink dynamics, since a standard
discretization is simpler and has effectively the same accuracy for such
resolutions. | Is it possible to relate MOND with Horava Gravity?: In this work we present a scalar field theory invariant under space-time
anisotropic transformations with a dynamic exponet $z$. It is shown that this
theory possess symmetries similar to Horava gravity and that in the limit $z=0$
the equations of motion of the non-relativistic MOND theory are obtained. This
result allow us to conjecture the existence of a Horava type gravity that in
the limit $z=0$ is consistent with MOND. |
Preheating a bouncing universe: Preheating describes the stage of rapidly depositing the energy of
cosmological scalar field into excitations of other light fields. This stage is
characterized by exponential particle production due to the parametric
resonance. We study this process in the frame of matter bounce cosmology. Our
results show that the preheating process in bouncing cosmology is even more
efficient than that in inflationary cosmology. In the limit of weak coupling,
the period of preheating is doubled. For the case of normal coupling, the
back-reaction of light fields can lead to thermalization before the bouncing
point. The scenario of matter bounce curvaton could be tightly constrained due
to a large coupling coefficient if the curvaton field is expected to preheat
the universe directly. However, this concern can be greatly relaxed through the
process of geometric preheating. | Topological anomalies for Seifert 3-manifolds: We study globally supersymmetric 3d gauge theories on curved manifolds by
describing the coupling of 3d topological gauge theories, with both Yang-Mills
and Chern-Simons terms in the action, to background topological gravity. In our
approach the Seifert condition for manifolds supporting global supersymmetry is
elegantly deduced from the topological gravity BRST transformations. A
cohomological characterization of the geometrical moduli which affect the
partition function is obtained. In the Seifert context Chern-Simons topological
(framing) anomaly is BRST trivial. We compute explicitly the corresponding
local Wess-Zumino functional. As an application, we obtain the dependence on
the Seifert moduli of the partition function of 3d supersymmetric gauge theory
on the squashed sphere by solving the anomalous topological Ward identities, in
a regularization independent way and without the need of evaluating any
functional determinant. |
Simplifying one-loop amplitudes in superstring theory: We show that 4-point vector boson one-loop amplitudes, computed in ref.[1] in
the RNS formalism, around vacuum configurations with open unoriented strings,
preserving at least N=1 SUSY in D=4, satisfy the correct supersymmetry Ward
identities, in that they vanish for non MHV configurations (++++) and (-+++).
In the MHV case (--++) we drastically simplify their expressions. We then study
factorisation and the limiting IR and UV behaviour and find some unexpected
results. In particular no massless poles are exposed at generic values of the
modular parameter. Relying on the supersymmetric properties of our bosonic
amplitudes, we extend them to manifestly supersymmetric super-amplitudes and
compare our results with those obtained in the D=4 hybrid formalism, pointing
out difficulties in reconciling the two approaches for contributions from N=1,2
sectors. | Stationary equilibrium of test particles near charged black branes with
the hyperscaling violating factor: We explore the upper bound of the Lyapunov exponent for test particles that
maintain equilibrium in the radial direction near the charged black brane with
the hyperscaling violating factor. The influences of black brane parameters
(hyperscaling violation exponent $\theta$ and dynamical exponent $z$) are
investigated. We show that the equilibrium in the radial direction of test
particles can violate the chaos bound. The chaos bound is more easily violated
for the near-extremal charged black branes. When the null energy condition
($T_{\mu\nu}\xi^\mu\xi^\nu \geq 0$) is broken, the bound is also more likely to
be violated. These results indicate that the chaos bound of particle motion is
related to the temperature of the black hole and the null energy condition
(NEC). By considering the zero-temperature and $T_{\mu\nu}\xi^\mu\xi^\nu=0$
cases, we obtain the critical parameters $\theta_c$ and $z_c$ for the violation
of chaos bound. The chaos bound is always satisfied in the range $\theta >
\theta_c$ or $z>z_c$. |
Brane World Models And Darboux Transformations: We consider a 5-D gravity plus a bulk scalar field, and with a 3-brane. The
Darboux transformation is used to construct some exact solutions. To do this we
reduce the system of equations, which describes the 5-D gravity and bulk scalar
field to the Schr\"odinger equation. The jump conditions at the branes lead to
the jump potential in the Schr\"odinger equation. Using the Darboux
transformation with these jump conditions, we offer a new exact solution of the
brane equations, which represents a generalization of the Rundall-Sundrum
solution. For simplicity, the main attention is focused on the case when Hubble
root on the visible brane is zero. However, the argument is given that our
method is valid in more realistic models with cosmological expansion. | Tree Level Supergravity and the Matrix Model: It has recently been shown that the Matrix model and supergravity give the
same predictions for three graviton scattering. This contradicts an earlier
claim in the literature (hep-th/9710174). We explain the error in this earlier
work, and go on to show that certain terms in the $n$-graviton scattering
amplitude involving $v^{2n}$ are given correctly by the Matrix model. The
Matrix model also generates certain $v^6$ terms in four graviton scattering at
three loops, which do not seem to have any counterparts in supergravity. The
connection of these results with nonrenormalization theorems is discussed. |
Towards a Theory of the QCD String: We construct a new model of four-dimensional relativistic strings with
integrable dynamics on the worldsheet. In addition to translational modes this
model contains a single massless pseudoscalar worldsheet field - the worldsheet
axion. The axion couples to a topological density which counts the
self-intersection number of a string. The corresponding coupling is fixed by
integrability to $Q=\sqrt{7\over 16\pi}\approx 0.37$. We argue that this model
is a member of a larger family of relativistic non-critical integrable string
models. This family includes and extends conventional non-critical strings
described by the linear dilaton CFT. Intriguingly, recent lattice data in
$SU(3)$ and $SU(5)$ gluodynamics reveals the presence of a massive pseudoscalar
axion on the worldsheet of confining flux tubes. The value of the corresponding
coupling, as determined from the lattice data, is equal to
$Q_L\approx0.38\pm0.04$. | On Schwinger pair production between D3 branes: We study the open string pair production between two D3 branes, which will
give rise to similar effect as Schwinger pair production for observers on one
of the D3 branes. The D3 branes are placed parallel at a distance, and they are
carrying world-volume electromagnetic fluxes that takes general form. We derive
the pair production rate by computing the interaction amplitude between the D3
branes. We discussed how to maximize the pair production rate in this general
case. We also mentioned that the general result can be used to describe other
system such as D3-D1, where the pair production is ultra large compared to
original Schwinger pair production, making it hopeful to observe pair
production in experiments. |
Torsional response of relativistic fermions in $2+1$ dimensions: We consider the equilibrium partition function of an ideal gas of Dirac
fermions minimally coupled to torsion in $2+1$ dimensions. We show that the
energy-momentum tensor reproduces the Hall viscosity and other parity violating
terms of first order in the torsion. We also consider the modifications of the
constitutive relations, and classify the corresponding susceptibilities. An
entropy current consistent with zero production of entropy in equilibrium is
constructed. | Berry Connections for 2d $(2,2)$ Theories, Monopole Spectral Data &
(Generalised) Cohomology Theories: We study Berry connections for supersymmetric ground states of 2d
$\mathcal{N}=(2,2)$ GLSMs quantised on a circle, which are generalised periodic
monopoles, with the aim to provide a fruitful physical arena for mathematical
constructions related to the latter. These are difference modules encoding
monopole solutions due to Mochizuki, as well as an alternative algebraic
description of solutions in terms of vector bundles endowed with filtrations.
The simultaneous existence of these descriptions is an example of a
Riemann-Hilbert correspondence. We demonstrate how these constructions arise
naturally by studying the ground states as the cohomology of a one-parameter
family of supercharges. Through this, we show that the two sides of this
correspondence are related to two types of monopole spectral data that have a
direct interpretation in terms of the physics of the GLSM: the Cherkis-Kapustin
spectral variety (difference modules) as well as twistorial spectral data
(vector bundles with filtrations). By considering states generated by D-branes
and leveraging the difference modules, we derive novel difference equations for
brane amplitudes. We then show that in the conformal limit, these degenerate
into novel difference equations for hemisphere or vortex partition functions,
which are exactly calculable. Beautifully, when the GLSM flows to a nonlinear
sigma model with K\"ahler target $X$, we show that the difference modules are
related to deformations of the equivariant quantum cohomology of $X$, whereas
the vector bundles with filtrations are related to the equivariant K-theory. |
Horava-Lifshitz gravity and Godel Universe: We prove the consistency of the G\"{o}del metric with the Horava-Lifshitz
gravity whose action involves terms with z=1, z=2 and z=3. We show that, for
different relations between the parameters of the theory, this consistency is
achieved for different classes of matter, in particular, for the small
cosmological constant it is achieved only for the exotic matter, that is,
ghosts or phantom matter. | Black holes thermodynamics with CFT re-scaling: In this paper, we study the thermodynamic behavior of charged AdS black holes
in a conformal holographic extended thermodynamic. Our setup is constructed
using a new dictionary that relates AdS black hole quantities to the
corresponding dual conformal field theory (CFT) one, with the conformal factor
being treated as a variable thermodynamic. In this thermodynamic study, we
investigate the critical phenomena of charged AdS black holes and their
relationship to the central charge value, \(C\). Additionally, we examine the
phase transitions and black hole stability using the free energy and the heat
capacity, respectively. Furthermore, by examining the chemical potential, we
establish criteria that differentiate between quantum and classical black hole
behaviors. Our setup highlights one of the key findings, namely traditional
black hole thermodynamics acts as a boundary between quantum and classical
regimes. |
Correlation functions, null polygonal Wilson loops, and local operators: We consider the ratio of the correlation function of n+1 local operators over
the correlator of the first n of these operators in planar N=4 super-Yang-Mills
theory, and consider the limit where the first n operators become pairwise null
separated. By studying the problem in twistor space, we prove that this is
equivalent to the correlator of a n-cusp null polygonal Wilson loop with the
remaining operator in general position, normalized by the expectation value of
the Wilson loop itself, as recently conjectured by Alday, Buchbinder and
Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such
correlators. Finally, we study the natural extension where n operators become
pairwise null separated with k operators in general position. As an example, we
perform an analysis of the resulting correlator for k=2 and discuss some of the
difficulties associated to fixing the correlator completely in the strong
coupling regime. | Standard Model Vacua in Heterotic M-Theory: We present a class of N=1 supersymmetric ``standard'' models of particle
physics, derived directly from heterotic M-theory, that contain three families
of chiral quarks and leptons coupled to the gauge group SU(3)_C X SU(2)_L X
U(1)_Y. These models are a fundamental form of ``brane world'' theories, with
an observable and hidden sector each confined, after compactification on a
Calabi--Yau threefold, to a BPS three-brane separated by a higher dimensional
bulk space with size of the order of the intermediate scale. The requirement of
three families, coupled to the fundamental conditions of anomaly freedom and
supersymmetry, constrains these models to contain additional five-branes
located in the bulk space and wrapped around holomorphic curves in the
Calabi--Yau threefold. |
The holographic entropy zoo: We study the holographic dual of a two parameter family of quantities known
as the $\alpha$-$z$ divergences. Many familiar information theoretic quantities
occur within this family, including the relative entropy, fidelity, and
collision relative entropy. We find explicit bulk expressions for the boundary
divergences to second order in a state perturbation whenever $\alpha$ is an
integer and $z\geq0$, as well as when $z\in\{0,\infty\}$ and $\alpha\in
\mathbb{R}$. Our results apply for perturbations around an arbitrary background
state and in any dimension, under the assumption of the equality of bulk and
boundary modular flows. | Reverse geometric engineering of singularities: One can geometrically engineer supersymmetric field theories theories by
placing D-branes at or near singularities. The opposite process is described,
where one can reconstruct the singularities from quiver theories. The
description is in terms of a noncommutative quiver algebra which is constructed
from the quiver diagram and the superpotential. The center of this
noncommutative algebra is a commutative algebra, which is the ring of
holomorphic functions on a variety V. If certain algebraic conditions are met,
then the reverse geometric engineering produces V as the geometry that D-branes
probe. It is also argued that the identification of V is invariant under
Seiberg dualities. |
Toric Lego: A method for modular model building: Within the context of local type IIB models arising from branes at toric
Calabi-Yau singularities, we present a systematic way of joining any number of
desired sectors into a consistent theory. The different sectors interact via
massive messengers with masses controlled by tunable parameters. We apply this
method to a toy model of the minimal supersymmetric standard model (MSSM)
interacting via gauge mediation with a metastable supersymmetry breaking sector
and an interacting dark matter sector. We discuss how a mirror procedure can be
applied in the type IIA case, allowing us to join certain intersecting brane
configurations through massive mediators. | Classical Inflationary and Ekpyrotic Universes in the No-Boundary
Wavefunction: This paper investigates the manner in which classical universes are obtained
in the no-boundary quantum state. In this context, universes can be
characterised as classical (in a WKB sense) when the wavefunction is highly
oscillatory, i.e. when the ratio of the change in the amplitude of the
wavefunction becomes small compared to the change in the phase. In the presence
of a positive or negative exponential potential, the WKB condition is satisfied
in proportion to a factor $e^{-(\epsilon - 3)N/(\epsilon -1)},$ where
$\epsilon$ is the (constant) slow-roll/fast-roll parameter and $N$ designates
the number of e-folds. Thus classicality is reached exponentially fast in $N$,
but only when $\epsilon < 1$ (inflation) or $\epsilon > 3$ (ekpyrosis).
Furthermore, when the potential switches off and the ekpyrotic phase goes over
into a phase of kinetic domination, the level of classicality obtained up to
that point is preserved. Similar results are obtained in a cyclic potential,
where a dark energy plateau is added. Finally, for a potential of the form
$-\phi^n$ (with $n=4,6,8$), where the classical solution becomes increasingly
kinetic-dominated, there is an initial burst of classicalisation which then
quickly levels off. These results demonstrate that inflation and ekpyrosis,
which are the only dynamical mechanisms known for smoothing the universe, share
the perhaps even more fundamental property of rendering space and time
classical in the first place. |
Remarks on self-dual formulation of Born-Infeld-Chern-Simons theory: We study the self-duality of Born-Infeld-Chern-Simons theory which can be
interpreted as a massive D2 brane in IIA string theory and exhibit the
self-dual formulation in terms of the gauge invariant master Lagrangian. The
proposed master Lagrangian contains the nonlocal auxiliary field and approaches
self-dual formulation of Maxwell-Chern-Simons theory in a point-particle limit
with the weak string-coupling limit. The consistent canonical brackets of dual
system are derived. | Self-Dual Black Holes in Celestial Holography: We construct two-dimensional quantum states associated to four-dimensional
linearized rotating self-dual black holes in $(2,2)$ signature Klein space. The
states are comprised of global conformal primaries circulating on the celestial
torus, the Kleinian analog of the celestial sphere. By introducing a
generalized tower of Goldstone operators we identify the states as coherent
exponentiations carrying an infinite tower of ${\rm w}_{1+\infty}$ charges or
soft hair. We relate our results to recent approaches to black hole scattering,
including a connection to Wilson lines, $\mathcal{S}$-matrix results, and
celestial holography in curved backgrounds. |
Minimal and maximal lengths from position-dependent noncommutativity: Fring and al in their paper entitled "Strings from position-dependent
noncommutativity" have introduced a new set of noncommutative space commutation
relations in two space dimensions. It had been shown that any fundamental
objects introduced in this space-space non-commutativity are string-like.
Taking this result into account, we generalize the seminal work of Fring and al
to the case that there is also a maximal length from position-dependent
noncommutativity and minimal momentum arising from generalized versions of
Heisenberg's uncertainty relations. The existence of maximal length is related
to the presence of an extra, first order term in particle's length that
provides the basic difference of our analysis with theirs. This maximal length
breaks up the well known singularity problem of space time. We establish
different representations of this noncommutative space and finally we study
some basic and interesting quantum mechanical systems in these new variables. | Holographic Mutual and Tripartite Information in a Non-Conformal
Background: Holographic mutual and tripartite information have been studied in a
non-conformal background. We have investigated how these observables behave as
the energy scale and number of degrees of freedom vary. We have found out that
the effect of degrees of freedom and energy scale is opposite. Moreover, it has
been observed that the disentangling transition occurs at large distance
between sub-systems in non-conformal field theory independent of l. The mutual
information in a non-conformal background remains also monogamous. |
Self-dual solitons in a Born-Infeld baby Skyrme model: We show the existence of self-dual (topological) solitons in a gauged version
of the baby Skyrme model in which the Born-Infeld term governs the gauge field
dynamics. The successful implementation of the Bogomol'nyi-Prasad-Sommerfield
formalism provides a lower bound for the energy and the respective self-dual
equations whose solutions are the solitons saturating such a limit. The energy
lower bound (Bogomol'nyi bound) is proportional to the topological charge of
the Skyrme field and therefore quantized. In contrast, the total magnetic flux
is a nonquantized quantity. Furthermore, the model supports three types of
self-dual solitons profiles: the first describes compacton solitons, the second
follows a Gaussian decay law, and the third portrays a power-law decay.
Finally, we perform numerical solutions of the self-dual equations and depicted
the soliton profiles for different values of the parameters controlling the
nonlinearity of the model. | The nonrelativistic limit of the Magueijo-Smolin model of deformed
special relativity: We study the nonrelativistic limit of the motion of a classical particle in a
model of deformed special relativity and of the corresponding generalized
Klein-Gordon and Dirac equations, and show that they reproduce nonrelativistic
classical and quantum mechanics, respectively, although the rest mass of a
particle no longer coincides with its inertial mass. This fact clarifies the
meaning of the different definitions of velocity of a particle available in DSR
literature. Moreover, the rest mass of particles and antiparticles differ,
breaking the CPT invariance. This effect is close to observational limits and
future experiments may give indications on its effective existence. |
Towards the most general scalar-tensor theories of gravity: a unified
approach in the language of differential forms: We use a description based on differential forms to systematically explore
the space of scalar-tensor theories of gravity. Within this formalism, we
propose a basis for the scalar sector at the lowest order in derivatives of the
field and in any number of dimensions. This minimal basis is used to construct
a finite and closed set of Lagrangians describing general scalar-tensor
theories invariant under Local Lorentz Transformations in a pseudo-Riemannian
manifold, which contains ten physically distinct elements in four spacetime
dimensions. Subsequently, we compute their corresponding equations of motion
and find which combinations are at most second order in derivatives in four as
well as arbitrary number of dimensions. By studying the possible exact forms
(total derivatives) and algebraic relations between the basis components, we
discover that there are only four Lagrangian combinations producing second
order equations, which can be associated with Horndeski's theory. In this
process, we identify a new second order Lagrangian, named kinetic Gauss-Bonnet,
that was not previously considered in the literature. However, we show that its
dynamics is already contained in Horndeski's theory. Finally, we provide a full
classification of the relations between different second order theories. This
allows us to clarify, for instance, the connection between different
covariantizations of Galileons theory. In conclusion, our formulation affords
great computational simplicity with a systematic structure. As a first step we
focus on theories with second order equations of motion. However, this new
formalism aims to facilitate advances towards unveiling the most general
scalar-tensor theories. | Completing the solution for the $OSp(1|2)$ spin chain: The periodic $OSp(1|2)$ quantum spin chain has both a graded and a non-graded
version. Naively, the Bethe ansatz solution for the non-graded version does not
account for the complete spectrum of the transfer matrix, and we propose a
simple mechanism for achieving completeness. In contrast, for the graded
version, this issue does not arise. We also clarify the symmetries of both
versions of the model, and we show how these symmetries are manifested in the
degeneracies and multiplicities of the transfer-matrix spectrum. While the
graded version has $OSp(1|2)$ symmetry, the non-graded version has only $SU(2)$
symmetry. Moreover, we obtain conditions for selecting the physical singular
solutions of the Bethe equations. This analysis solves a lasting controversy
over signs in the Bethe equations. |
Theories with Two Times: General considerations on the unification of A-type and B-type
supersymmetries in the context of interacting p-branes strongly suggest that
the signature of spacetime includes two timelike dimensions. This leads to the
puzzle of how ordinary physics with a single timelike dimension emerges. In
this letter we suggest that the two timelike dimensions could be real, and
belong to two physical sectors of a single theory each containing its own
timelike dimension. Effectively there is a single time evolution parameter. We
substantiate this idea by constructing certain actions for interacting p-branes
with signature (n,2) that have gauge symmetries and constraints appropriate for
a physical interpretation with no ghosts. In combination with related ideas and
general constraints in S-theory, we are led to a cosmological scenario in
which, after a phase transition, the extra timelike dimension becomes part of
the compactified universe residing inside microscopic matter. The internal
space, whose geometry is expected to determine the flavor quantum numbers of
low energy matter, thus acquires a Minkowski signature. The formalism meshes
naturally with a new supersymmetry in the context of field theory that we
suggested in an earlier paper. The structure of this supersymmetry gives rise
to a new Kaluza-Klein type mechanism for determining the quantum numbers of low
energy families, thus suggesting that the extra timelike dimension would be
taken into account in understanding the Standard Model of particle physics. | Motion on moduli spaces with potentials: In the limit of small velocities, the dynamics of half-BPS Yang-Mills-Higgs
solitons can be described by the geodesic approximation. Recently, it has been
shown that quarter-BPS states require the addition of a potential term to this
approximation. We explain the logic behind this modification for a larger class
of models and then analyse in detail the dynamics of two five-dimensional
dyonic instantons, using both analytical and numerical techniques.
Nonzero-modes are shown to play a crucial role in the analysis of these
systems, and we explain how these modes lead to qualitatively new types of
dynamics. |
Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains: The master equation describing non-equilibrium one-dimensional problems like
diffusion limited reactions or critical dynamics of classical spin systems can
be written as a Schr\"odinger equation in which the wave function is the
probability distribution and the Hamiltonian is that of a quantum chain with
nearest neighbor interactions. Since many one-dimensional quantum chains are
integrable, this opens a new field of applications. At the same time physical
intuition and probabilistic methods bring new insight into the understanding of
the properties of quantum chains. A simple example is the asymmetric diffusion
of several species of particles which leads naturally to Hecke algebras and
$q$-deformed quantum groups. Many other examples are given. Several relevant
technical aspects like critical exponents, correlation functions and
finite-size scaling are also discussed in detail. | Edge Asymptotics of Planar Electron Densities: The $N\to\infty$ limit of the edges of finite planar electron densities is
discussed for higher Landau levels. For full filling, the particle number is
correlated with the magnetic flux, and hence with the boundary location, making
the $N\to\infty$ limit more subtle at the edges than in the bulk. In the
$n^{\rm th}$ Landau level, the density exhibits $n$ distinct steps at the edge,
in both circular and rectangular samples. The boundary characteristics for
individual Landau levels, and for successively filled Landau levels, are
computed in an asymptotic expansion. |
The Heat Kernel on AdS_3 and its Applications: We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean)
AdS_3 using a group theoretic approach. We use these results to also obtain the
heat kernel on certain quotients of these spaces. In particular, we give a
simple, explicit expression for the one loop determinant for a field of
arbitrary spin s in thermal AdS_3. We apply this to the calculation of the one
loop partition function of N=1 supergravity on AdS_3. We find that the answer
factorizes into left- and right-moving super Virasoro characters built on the
SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds. | D3-brane shells to black branes on the Coulomb branch: We use the AdS/CFT duality to study the special point on the Coulomb branch
of ${\cal N}=4$ SU(N) gauge theory which corresponds to a spherically symmetric
shell of D3-branes. This point is of interest both because the spacetime region
inside the shell is flat, and because this configuration gives a very simple
example of the transition between D-branes in the perturbative string regime
and the non-perturbative regime of black holes. We discuss how this geometry is
described in the dual gauge theory, through its effect on the two-point
functions and Wilson loops. In the calculation of the two-point function, we
stress the importance of absorption by the branes. |
Chern-Simons Theory in the Temporal Gauge and Knot Invariants through
the Universal Quantum R-Matrix: In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic
action and an ultralocal propagator. This directly implies a 2d R-matrix
representation for the correlators of Wilson lines (knot invariants), where
only the crossing points of the contours projection on the xy plane contribute.
Though the theory is quadratic, P-exponents remain non-trivial operators and
R-factors are easier to guess then derive. We show that the topological
invariants arise if additional flag structure (xy plane and an y line in it) is
introduced, R is the universal quantum R-matrix and turning points contribute
the "enhancement" factors q^{\rho}. | Tensionless branes and the null string critical dimension: BRST quantization is carried out for a model of p-branes with second class
constraints. After extension of the phase space the constraint algebra
coincides with the one of null string when p=1. It is shown that in this case
one can or can not obtain critical dimension for the null string, depending on
the choice of the operator ordering and corresponding vacuum states. When p>1,
operator orderings leading to critical dimension in the p=1 case are not
allowed. Admissable orderings give no restrictions on the dimension of the
embedding space-time. Finally, a generalization to supersymmetric null branes
is proposed. |
p-Wave holographic superconductors with Weyl corrections: We study the (3+1) dimensional p-wave holographic superconductors with Weyl
corrections both numerically and analytically. We describe numerically the
behavior of critical temperature $T_{c}$ with respect to charge density $\rho$
in a limited range of Weyl coupling parameter $\gamma$ and we find in general
the condensation becomes harder with the increase of parameter $\gamma$. In
strong coupling limit of Yang-Mills theory, we show that the minimum value of
$T_{c}$ obtained from analytical approach is in good agreement with the
numerical results, and finally show how we got remarkably a similar result in
the critical exponent 1/2 of the chemical potential $\mu$ and the order
parameter$<J^1_x>$ with the numerical curves of superconductors. | Non-perturbative Yukawa Couplings from String Instantons: Non-perturbative D-brane instantons can generate perturbatively absent though
phenomenologically relevant couplings for Type II orientifold compactifications
with D-branes. We discuss the generation of the perturbatively vanishing SU(5)
GUT Yukawa coupling of type 10 10 5_H. Moreover, for a simple globally
consistent intersecting D6-brane model, we discuss the generation of mass terms
for matter fields. This can serve as a mechanism for decoupling exotic matter. |
Singularity Resolution + Unitary Evolution + Horizon = Firewall ?: We assume that a quantum gravity theory exists where evolutions are unitary,
no information is lost, singularities are resolved, and horizons form. Thus a
massive star will collapse to a black hole having a horizon and an interior
singularity--resolved region. Based on unitarity and on a postulated relation,
we obtain an evolution equation for the size of this region. As the black hole
evolves by evaporation and accretions, this region grows, meets the horizon,
and becomes accessible to an outside observer. The required time is typically
of the order of black hole evaporation time. If the boundary of the
singularity--resolved region can be considered as the firewall of Almheiri et
al then this marks the appearance of a firewall. | Dynamical r-matrices and Separation of Variables: The Generalised
Calogero-Moser Model: A generalisation of the classical Calogero-Moser model obtained by coupling
it to the Gaudin model is considered. The recently found classical dynamical
r-matrix [E. Billey, J. Avan and O. Babelon, PAR LPTHE 93-55] for the
Euler-Calogero-Moser model is used to separate variables for this generalised
Calogero-Moser model in the case in which there are two Calogero-Moser
particles. The model is then canonically quantised and the same classical
r-matrix is employed to separate variables in the Schr\"odinger equations. |
On bounds and boundary conditions in the continuum Landau gauge: In this note, we consider the Landau gauge in the continuum formulation. Our
purposes are twofold. Firstly, we try to work out the consequences of the
recently derived Cucchieri-Mendes bounds on the inverse Faddeev-Popov operator
at the level of the path integral quantization. Secondly, we give an explicit
renormalizable prescription to implement the so-called Landau B-gauges as
introduced by Maas. | Instantons on Gravitons: Yang-Mills instantons on ALE gravitational instantons were constructed by
Kronheimer and Nakajima in terms of matrices satisfying algebraic equations.
These were conveniently organized into a quiver. We construct generic
Yang-Mills instantons on ALF gravitational instantons. Our data are formulated
in terms of matrix-valued functions of a single variable, that are in turn
organized into a bow. We introduce the general notion of a bow, its
representation, its associated data and moduli space of solutions. For a
judiciously chosen bow the Nahm transform maps any bow solution to an instanton
on an ALF space. We demonstrate that this map respects all complex structures
on the moduli spaces, so it is likely to be an isometry, and use this fact to
study the asymptotics of the moduli spaces of instantons on ALF spaces. |
Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model: We continue explorations of non-Abelian strings, focusing on the solution of
a heterotic deformation of the CP(N-1) model with an extra right-handed fermion
field and N=(0,2) supersymmetry. This model emerges as a low-energy theory on
the worldsheet of the BPS-saturated flux tubes (strings) in N=2 supersymmetric
QCD deformed by a superpotential of a special type breaking N=2 supersymmetry
down to N=1. Using large-N expansion we solve this model to the leading order
in 1/N. Our solution exhibits spontaneous supersymmetry breaking for all values
of the deformation parameter. We identify the Goldstino field. The discrete
Z_{2N} symmetry is shown to be spontaneously broken down to Z_2; therefore, the
worldsheet model has N strictly degenerate vacua (with nonvanishing vacuum
energy). Thus, the heterotic CP(N-1) model is in the deconfinement phase. We
can compare this dynamical pattern, on the one hand, with the N=(2,2) CP(N-1)
model which has N degenerate vacua with unbroken supersymmetry, and, on the
other hand, with nonsupersymmetric CP(N-1) model with split quasivacua and the
Coulomb/confining phase. We determine the mass spectrum of the heterotic
CP(N-1) model in the large-N limit. | Sequential Monte Carlo with Cross-validated Neural Networks for
Complexity of Hyperbolic Black Hole Solutions in 4D: This paper investigates the self-similar solutions of the
Einstein-axion-dilaton configuration from type IIB string theory and the global
SL(2,R) symmetry. We consider the Continuous Self Similarity (CSS), where the
scale transformation is controlled by an SL(2, R) boost or hyperbolic
translation. The solutions stay invariant under the combination of space-time
dilation with internal SL(2,R) transformations. We develop a new formalism
based on Sequential Monte Carlo (SMC) and artificial neural networks (NNs) to
estimate the self-similar solutions to the equations of motion in the
hyperbolic class in four dimensions. Due to the complex and highly nonlinear
patterns, researchers typically have to use various constraints and numerical
approximation methods to estimate the equations of motion; thus, they have to
overlook the measurement errors in parameter estimation. Through a Bayesian
framework, we incorporate measurement errors into our models to find the
solutions to the hyperbolic equations of motion. It is well known that the
hyperbolic class suffers from multiple solutions where the critical collapse
functions have overlap domains for these solutions. To deal with this
complexity, for the first time in literature on the axion-dilaton system, we
propose the SMC approach to obtain the multi-modal posterior distributions.
Through a probabilistic perspective, we confirm the deterministic $\alpha$ and
$\beta$ solutions available in the literature and determine all possible
solutions that may occur due to measurement errors. We finally proposed the
penalized Leave-One-Out Cross-validation (LOOCV) to combine the Bayesian
NN-based estimates optimally. The approach enables us to determine the optimum
weights while dealing with the co-linearity issue in the NN-based estimates and
better predict the critical functions corresponding to multiple solutions of
the equations of motion. |
Born-Infeld-Goldstone superfield actions for gauge-fixed D-5- and
D-3-branes in 6d: The supersymmetric Born-Infeld actions describing gauge-fixed D-5- and
D-3-branes in ambient six-dimensional (6d) spacetime are constructed in
superspace. A new 6d action is the (1,0) supersymmetric extension of the 6d
Born-Infeld action. It is related via dimensional reduction to another
remarkable 4d action describing the N=2 supersymmetric extension of the
Born-Infeld-Nambu-Goto action with two real scalars. Both actions are the
Goldstone actions associated with partial (1/2) spontaneous breaking of
extended supersymmetry having 16 supercharges down to 8 supercharges. Both
actions can be put into the `non-linear sigma-model' form by using certain
non-linear superfield constraints. The unbroken supersymmetry is always
linearly realised in our construction. | Nambu-like odd bracket on Grassmann algebra: The Grassmann-odd Nambu-like bracket corresponding to an arbitrary Lie
algebra and realized on the Grassmann algebra is proposed. |
D-Brane Propagation in Two-Dimensional Black Hole Geometries: We study propagation of D0-brane in two-dimensional Lorentzian black hole
backgrounds by the method of boundary conformal field theory of SL(2,R)/U(1)
supercoset at level k. Typically, such backgrounds arise as near-horizon
geometries of k coincident non-extremal NS5-branes, where 1/k measures
curvature of the backgrounds in string unit and hence size of string worldsheet
effects. At classical level, string worldsheet effects are suppressed and
D0-brane propagation in the Lorentzian black hole geometry is simply given by
the Wick rotation of D1-brane contour in the Euclidean black hole geometry.
Taking account of string worldsheet effects, boundary state of the Lorentzian
D0-brane is formally constructible via Wick rotation from that of the Euclidean
D1-brane. However, the construction is subject to ambiguities in boundary
conditions. We propose exact boundary states describing the D0-brane, and
clarify physical interpretations of various boundary states constructed from
different boundary conditions. As it falls into the black hole, the D0-brane
radiates off to the horizon and to the infinity. From the boundary states
constructed, we compute physical observables of such radiative process. We find
that part of the radiation to infinity is in effective thermal distribution at
the Hawking temperature. We also find that part of the radiation to horizon is
in the Hagedorn distribution, dominated by massive, highly non-relativistic
closed string states, much like the tachyon matter. Remarkably, such
distribution emerges only after string worldsheet effects are taken exactly
into account. From these results, we observe that nature of the radiation
distribution changes dramatically across the conifold geometry k=1 (k=3 for the
bosonic case), exposing the `string - black hole transition' therein. | Generalized Calabi-Yau structures and mirror symmetry: We use the differential geometrical framework of generalized (almost)
Calabi-Yau structures to reconsider the concept of mirror symmetry. It is shown
that not only the metric and B-field but also the algebraic structures are
uniquely mapped. As an example we use the six-torus as a trivial generalized
Calabi-Yau 6-fold and an appropriate B-field. |
Light-front Schwinger Model at Finite Temperature: We study the light-front Schwinger model at finite temperature following the
recent proposal in \cite{alves}. We show that the calculations are carried out
efficiently by working with the full propagator for the fermion, which also
avoids subtleties that arise with light-front regularizations. We demonstrate
this with the calculation of the zero temperature anomaly. We show that
temperature dependent corrections to the anomaly vanish, consistent with the
results from the calculations in the conventional quantization. The gauge
self-energy is seen to have the expected non-analytic behavior at finite
temperature, but does not quite coincide with the conventional results.
However, the two structures are exactly the same on-shell. We show that
temperature does not modify the bound state equations and that the fermion
condensate has the same behavior at finite temperature as that obtained in the
conventional quantization. | One-loop background calculations in the general field theory: We present master formulas for the divergent part of the one-loop effective
action for a minimal operator of any order in the 4-dimensional curved space
and for an arbitrary nonminimal operator in the flat space. |
Vortex Pair Creation on Brane-Antibrane Pair via Marginal Deformation: It has been conjectured that the vortex solution on a D-brane - anti-D-brane
system represents a D-brane of two lower dimension. We establish this result by
first identifying a series of marginal deformations which create the vortex -
antivortex pair on the brane - antibrane system, and then showing that under
this series of marginal deformations the original D-brane - anti-D-brane system
becomes a D-brane - anti-D-brane system with two lower dimensions.
Generalization of this construction to the case of solitons of higher
codimension is also discussed. | Quantum Black Hole Entropy, Localization and the Stringy Exclusion
Principle: Supersymmetric localization has lead to remarkable progress in computing
quantum corrections to BPS black hole entropy. The program has been successful
especially for computing perturbative corrections to the Bekenstein-Hawking
area formula. In this work, we consider non-perturbative corrections related to
polar states in the Rademacher expansion, which describes the entropy in the
microcanonical ensemble. We propose that these non-perturbative effects can be
identified with a new family of saddles in the localization of the quantum
entropy path integral. We argue that these saddles, which are euclidean
$AdS_2\times S^1\times S^2$ geometries, arise after turning on singular fluxes
in M-theory on a Calabi-Yau. They cease to exist after a certain amount of
flux, resulting in a finite number of geometries; the bound on that number is
in precise agreement with the stringy exclusion principle. Localization of
supergravity on these backgrounds gives rise to a finite tail of Bessel
functions in agreement with the Rademacher expansion. As a check of our
proposal, we test our results against well-known microscopic formulas for
one-eighth and one-quarter BPS black holes in $\mathcal{N}=8$ and
$\mathcal{N}=4$ string theory respectively, finding agreement. Our method
breaks down precisely when mock-modular effects are expected in the entropy of
one-quarter BPS dyons and we comment upon this. Furthermore, we mention
possible applications of these results, including an exact formula for the
entropy of four dimensional $\mathcal{N}=2$ black holes. |
Natural solution to the naturalness problem -- Universe does fine-tuning: We propose a new mechanism to solve the fine-tuning problem. We start from a
multi-local action $
S=\sum_{i}c_{i}S_{i}+\sum_{i,j}c_{i,j}S_{i}S_{j}+\sum_{i,j,k}c_{i,j,k}S_{i}S_{j}S_{k}+\cdots$,
where $S_{i}$'s are ordinary local actions. Then, the partition function of
this system is given by \begin{equation} Z=\int d\overrightarrow{\lambda}
f(\overrightarrow{\lambda})\langle
f|T\exp\left(-i\int_{0}^{+\infty}dt\hat{H}(\overrightarrow{\lambda};a_{cl}(t))\right)|i\rangle,\nonumber\end{equation}
where $\overrightarrow{\lambda}$ represents the parameters of the system whose
Hamiltonian is given by $\hat{H}(\overrightarrow{\lambda};a_{cl}(t))$,
$a_{cl}(t)$ is the radius of the universe determined by the Friedman equation,
and $f(\overrightarrow{\lambda})$, which is determined by $S$, is a smooth
function of $\overrightarrow{\lambda}$. If a value of
$\overrightarrow{\lambda}$, $\overrightarrow{\lambda}_{0}$, dominates in the
integral, we can interpret that the parameters are dynamically tuned to
$\overrightarrow{\lambda}_{0}$. We show that indeed it happens in some
realistic systems. In particular, we consider the strong CP problem, multiple
point criticality principle and cosmological constant problem. It is
interesting that these different phenomena can be explained by one mechanism. | String Theory, Unification and Quantum Gravity: An overview is given of the way in which the unification program of particle
physics has evolved into the proposal of superstring theory as a prime
candidate for unifying quantum gravity with the other forces and particles of
nature. A key concern with quantum gravity has been the problem of ultraviolet
divergences, which is naturally solved in string theory by replacing particles
with spatially extended states as the fundamental excitations. String theory
turns out, however, to contain many more extended-object states than just
strings. Combining all this into an integrated picture, called M-theory,
requires recognition of the r\^ole played by a web of nonperturbative duality
symmetries suggested by the nonlinear structures of the field-theoretic
supergravity limits of string theory. |
Logarithmic Corrections to Schwarzschild and Other Non-extremal Black
Hole Entropy in Different Dimensions: Euclidean gravity method has been successful in computing logarithmic
corrections to extremal black hole entropy in terms of low energy data, and
gives results in perfect agreement with the microscopic results in string
theory. Motivated by this success we apply Euclidean gravity to compute
logarithmic corrections to the entropy of various non-extremal black holes in
different dimensions, taking special care of integration over the zero modes
and keeping track of the ensemble in which the computation is done. These
results provide strong constraint on any ultraviolet completion of the theory
if the latter is able to give an independent computation of the entropy of
non-extremal black holes from microscopic description. For Schwarzschild black
holes in four space-time dimensions the macroscopic result seems to disagree
with the existing result in loop quantum gravity. | Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory: We analyze the gauge structure of a recently proposed superconformal field
theory in six dimensions. We find that this structure amounts to a weak
Courant-Dorfman algebra, which, in turn, can be interpreted as a strong
homotopy Lie algebra. This suggests that the superconformal field theory is
closely related to higher gauge theory, describing the parallel transport of
extended objects. Indeed we find that, under certain restrictions, the field
content and gauge transformations reduce to those of higher gauge theory. We
also present a number of interesting examples of admissible gauge structures
such as the structure Lie 2-algebra of an abelian gerbe, differential crossed
modules, the 3-algebras of M2-brane models and string Lie 2-algebras. |
Nonderivative Modified Gravity: a Classification: We analyze the theories of gravity modified by a generic nonderivative
potential built from the metric, under the minimal requirement of unbroken
spatial rotations. Using the canonical analysis, we classify the potentials $V$
according to the number of degrees of freedom (DoF) that propagate at the
nonperturbative level. We then compare the nonperturbative results with the
perturbative DoF propagating around Minkowski and FRW backgrounds. A generic
$V$ implies 6 propagating DoF at the non-perturbative level, with a ghost on
Minkowski background. There exist potentials which propagate 5 DoF, as already
studied in previous works. Here, no $V$ with unbroken rotational invariance
admitting 4 DoF is found. Theories with 3 DoF turn out to be strongly coupled
on Minkowski background. Finally, potentials with only the 2 DoF of a massive
graviton exist. Their effect on cosmology is simply equivalent to a
cosmological constant. Potentials with 2 or 5 DoF and explicit time dependence
appear to be a further viable possibility. | Small Volumes in Compactified String Theory: We discuss some of the classical and quantum geometry associated to the
degeneration of cycles within a Calabi-Yau compactification. In particular, we
focus on the definition and properties of quantum volume, especially as it
applies to identifying the physics associated to loci in moduli space where
nonperturbative effects become manifest. We discuss some unusual features of
quantum volume relative to its classical counterpart. |
Bit Strings from N=4 Gauge Theory: We present an improvement of the interacting string bit theory proposed in
hep-th/0206059, designed to reproduce the non-planar perturbative amplitudes
between BMN operators in N=4 gauge theory. Our formalism incorporates the
effect of operator mixing and all non-planar corrections to the inner product.
We use supersymmetry to construct the bosonic matrix elements of the light-cone
Hamiltonian to all orders in g_2, and make a detailed comparison with the
non-planar amplitudes obtained from gauge theory to order (g_2)^2. We find a
precise match. | Finiteness of N =4 super-Yang-Mills effective action in terms of dressed
N =1 superfields: We argue in favor of the independence on any scale, ultraviolet or infrared,
in kernels of the effective action expressed in terms of dressed ${\cal N} =1$
superfields for the case of ${\cal N} =4$ super-Yang--Mills theory. Under
``scale independence '' of the effective action of dressed mean superfields we
mean its `` finiteness in the off-shell limit of removing all the
regularizations.'' This off-shell limit is scale independent because no scale
remains inside these kernels after removing the regularizations. We use two
types of regularization: regularization by dimensional reduction and
regularization by higher derivatives in its supersymmetric form. Based on the
Slavnov-Taylor identity we show that dressed fields of matter and of vector
multiplets can be introduced to express the effective action in terms of them.
Kernels of the effective action expressed in terms of such dressed effective
fields do not depend on the ultraviolet scale. In the case of dimensional
reduction, by using the developed technique we show how the problem of
inconsistency of the dimensional reduction can be solved. Using Piguet and
Sibold formalism, we indicate that the dependence on the infrared scale
disappears off shell in both the regularizations. |
Q-Balls Meet Fuzzballs: Non-BPS Microstate Geometries: We construct a three-parameter family of non-extremal microstate geometries,
or "microstrata," that are dual to states and deformations of the D1-D5 CFT.
These families are non-extremal analogues of superstrata. We find these
microstrata by using a Q-ball-inspired Ansatz that reduces the equations of
motion to solving for eleven functions of one variable. We then solve this
system both perturbatively and numerically and the results match extremely
well. We find that the solutions have normal mode frequencies that depend upon
the amplitudes of the excitations. We also show that, at higher order in
perturbations, some of the solutions, having started with normalizable modes,
develop a "non-normalizable" part, suggesting that the microstrata represent
states in a perturbed form of the D1-D5 CFT. This paper is intended as a "Proof
of Concept" for the Q-ball-inspired approach, and we will describe how it opens
the way to many interesting follow-up calculations both in supergravity and in
the dual holographic field theory. | Noncommutative Harmonic Oscillator at Finite Temperature: A Path
Integral Approach: We use the path integral approach to a two-dimensional noncommutative
harmonic oscillator to derive the partition function of the system at finite
temperature. It is shown that the result based on the Lagrangian formulation of
the problem, coincides with the Hamiltonian derivation of the partition
function. |
Gravitational waves in dark bubble cosmology: In this paper we construct the 5D uplift of 4D gravitational waves in de
Sitter cosmology for the brane world scenario based on a nucleated bubble in
AdS5. This makes it possible to generalize the connection between the dark
bubbles and Vilenkin's quantum cosmology to include gravitational
perturbations. We also use the uplift to explain the interpretation of the
apparently negative energy contributions in the 4D Einstein equations, which
distinguish the dark bubble scenario from Randall-Sundrum. | The simplest massive S-matrix: from minimal coupling to Black Holes: In this paper, we explore the physics of electromagnetically and
gravitationally coupled massive higher spin states from the on-shell point of
view. Starting with the three-point amplitude, we focus on the simplest
amplitude which is characterized by matching to minimal coupling in the UV. In
the IR such amplitude leads to g = 2 for arbitrary charged spin states, and the
best high energy behavior for a given spin. We proceed to construct the
(gravitational) Compton amplitude for generic spins. We find that the leading
deformation away from minimal coupling, in the gravitation sector, will lead to
inconsistent factorizations and are thus forbidden. As the corresponding
deformation in the gauge sector encodes the anomalous magnetic dipole moment,
this leads to the prediction that for systems with gauge2 =gravity relations,
such as perturbative string theory, all charged states must have g = 2. It is
then natural to ask for generic spin, what is the theory that yields such
minimal coupling. By matching to the one body effective action, remarkably we
verify that for large spins, the answer is Kerr black holes. This
identification is then an on-shell avatar of the no hair theorem. Finally using
this identification as well as the newly constructed Compton amplitudes, we
proceed to compute the spin dependent pieces for the classical potential at 2PM
order up to degree four in spin operator of either black holes. |
Radiative Properties of the Stueckelberg Mechanism: We examine the mechanism for generating a mass for a U(1) vector field
introduced by Stueckelberg. First, it is shown that renormalization of the
vector mass is identical to the renormalization of the vector field on account
of gauge invariance. We then consider how the vector mass affects the effective
potential in scalar quantum electrodynamics at one-loop order. The possibility
of extending this mechanism to couple, in a gauge invariant way, a charged
vector field to the photon is discussed. | Holographic superconductors at zero density: We construct holographic superconductors at zero density. The model enjoys a
luxury property that the background geometry dual to the ground state is
analytically available. It has a hyperscaling-violating geometry in the IR and
is asymptotically AdS in the UV. Classification by IR geometries gives new
insights on supergravity solutions. We numerically construct the finite
temperature solution of hairy black holes and verify the phase transition by
tuning a double-trace deformation parameter. For a holographic superconductor
from M-theory, we obtain an analytic solution of the AC conductivity, which
explicitly shows a superconducting delta function and a hard gap. |
Quantum corrections for D-brane models with broken supersymmetry: Intersecting D-brane models and their T-dual magnetic compactifications yield
attractive models of particle physics where magnetic flux plays a twofold role,
being the source of fermion chirality as well as supersymmetry breaking. A
potential problem of these models is the appearance of tachyons which can only
be avoided in certain regions of moduli space and in the presence of Wilson
lines. We study the effective four-dimensional field theory for an orientifold
compactification of type IIA string theory and the corresponding toroidal
compactification of type I string theory. After determining the Kaluza-Klein
and Landau-level towers of massive states in different sectors of the model, we
evaluate their contributions to the one-loop effective potential, summing over
all massive states, and we relate the result to the corresponding string
partition functions. We find that the Wilson-line effective potential has only
saddle points, and the theory is therefore driven to the tachyonic regime.
There tachyon condensation takes place and chiral fermions acquire a mass of
the order of the compactification scale. We also find evidence for a tachyonic
behaviour of the volume moduli. More work on tachyon condensation is needed to
clarify the connection between supersymmetry breaking, a chiral fermion
spectrum and vacuum stability. | Five-Dimensional Gauge Theories and Unitary Matrix Models: The matrix model computations of effective superpotential terms in N=1
supersymmetric gauge theories in four dimensions have been proposed to apply
more generally to gauge theories in higher dimensions. We discuss aspects of
five-dimensional gauge theory compactified on a circle, which leads to a
unitary matrix model. |
Matrix Theory: This is an expanded version of talks given by the author at the Trieste
Spring School on Supergravity and Superstrings in April of 1997 and at the
accompanying workshop. The manuscript is intended to be a mini-review of Matrix
Theory. The motivations and some of the evidence for the theory are presented,
as well as a clear statement of the current puzzles about compactification to
low dimensions. | Second Class Constraints in a Higher-Order Lagrangian Formalism: We consider the description of second-class constraints in a Lagrangian path
integral associated with a higher-order $\Delta$-operator. Based on two
conjugate higher-order $\Delta$-operators, we also propose a Lagrangian path
integral with $Sp(2)$ symmetry, and describe the corresponding system in the
presence of second-class constraints. |
Renormalization Group Transformation for the Wave Function: The problem considered here is the determination of the hamiltonian of a
first quantized nonrelativistic particle by the help of some measurements of
the location with a finite resolution. The resulting hamiltonian depends on the
resolution of the measuring device. This dependence is reproduced by the help
of a blocking transformation on the wave function. The systems with quadratic
hamiltonian are studied in details. The representation of the renormalization
group in the space of observables is identified. | On higher derivative corrections of tachyon action: We have examined the momentum expansion of the disk level S-matrix element of
two tachyons and two gauge fields to find, up to on-shell ambiguity, the
couplings of these fields in the world volume theory of N coincident non-BPS
D-branes to all order of $\alpha'$. Using the proposal that the action of
D-brane-anti-D-brane is given by the projection of the action of two non-BPS
D-branes with $(-1)^{F_L}$, we find the corresponding couplings in the world
volume theory of the brane-anti-brane system. Using these infinite tower of
couplings, we then calculate the massless pole of the scattering amplitude of
one RR field, two tachyons and one gauge field in the brane-anti-brane theory.
We find that the massless pole of the field theory amplitude is exactly equal
to the massless pole of the disk level S-matrix element of one RR, two tachyons
and one gauge field to all order of $\alpha'$. |
Integer solutions to the anomaly equations for a class of chiral gauge
theories: We find all the integer charge solutions to the equations for the
cancellation of local gauge anomalies in a class of gauge theories which extend
the Standard Model (SM) by a gauge group of the form $G \times U(1)$, where $G$
is an arbitrary semisimple compact Lie group. The SM fermions are assumed to be
neutral under $G \times U(1)$ gauge interactions, while the new fermions
transform in non-trivial representations of both the new and the SM gauge
groups. Our analysis is valid also when the latter is embedded in an arbitrary
semisimple compact Lie group. Theories with this structure have been recently
studied as models of composite axions based on accidental symmetries and can
provide a field theory resolution to the axion quality problem. We apply our
results to cases of phenomenological interest and prove the existence of charge
assignments with Peccei-Quinn symmetry protected up to dimension 18. | Introduction to noncommutative field and gauge theory: These are lecture notes for an introductory course on noncommutative field
and gauge theory. We begin by reviewing quantum mechanics as the prototypical
noncommutative theory, as well as the geometrical language of standard gauge
theory. Then, we review a specific approach to noncommutative field and gauge
theory, which relies on the introduction of a derivations-based differential
calculus. We focus on the cases of constant and linear noncommutativity, e.g.,
the Moyal spacetime and the so-called $\mathbb{R}^3_\lambda$, respectively. In
particular, we review the $g\varphi^4$ scalar field theory and the $U(1)$ gauge
theory on such noncommutative spaces. Finally, we discuss noncommutative
spacetime symmetries from both the observer and particle point of view. In this
context, the twist approach is reviewed and the $\lambda$-Minkowski
$g\varphi^4$ model is discussed. |
Time evolution of the complexity in chaotic systems: concrete examples: We investigate the time evolution of the complexity of the operator by the
Sachdev-Ye-Kitaev (SYK) model with $N$ Majorana fermions. We follow Nielsen's
idea of complexity geometry and geodesics thereof. We show that it is possible
that the bi-invariant complexity geometry can exhibit the conjectured time
evolution of the complexity in chaotic systems: i) linear growth until $t\sim
e^{N}$, ii) saturation and small fluctuations after then. We also show that the
Lloyd's bound is realized in this model. Interestingly, these characteristic
features appear only if the complexity geometry is the most natural
"non-Riemannian" Finsler geometry. This serves as a concrete example showing
that the bi-invariant complexity may be a competitive candidate for the
complexity in quantum mechanics/field theory (QM/QFT). We provide another
argument showing a naturalness of bi-invariant complexity in QM/QFT. That is
that the bi-invariance naturally implies the equivalence of the right-invariant
complexity and left-invariant complexity, either of which may correspond to the
complexity of a given operator. Without bi-invariance, one needs to answer why
only right (left) invariant complexity corresponds to the "complexity", instead
of only left (right) invariant complexity. | Calogero-Moser models with noncommutative spin interactions: We construct integrable generalizations of the elliptic
Calogero-Sutherland-Moser model of particles with spin, involving
noncommutative spin interactions. The spin coupling potential is a modular
function and, generically, breaks the global spin symmetry of the model down to
a product of U(1) phase symmetries. Previously known models are recovered as
special cases. |
Complexity and Behind the Horizon Cut Off: Motivated by $T{\overline T}$ deformation of a conformal field theory we
compute holographic complexity for a black brane solution with a cut off using
"complexity=action" proposal. In order to have a late time behavior consistent
with Lloyd's bound one is forced to have a cut off behind the horizon whose
value is fixed by the boundary cut off. Using this result we compute
holographic complexity for two dimensional AdS solutions where we get expected
late times linear growth. It is in contrast with the naively computation which
is done without assuming the cut off where the complexity approaches a constant
at the late time. | Evaluation of conformal integrals: We present a comprehensive method for the evaluation of a vast class of
integrals representing 3-point functions of conformal field theories in
momentum space. The method leads to analytic, closed-form expressions for all
scalar and tensorial 3-point functions of operators with integer dimensions in
any spacetime dimension. In particular, this encompasses all 3-point functions
of the stress tensor, conserved currents and marginal scalar operators. |
More on complexity of operators in quantum field theory: Recently it has been shown that the complexity of SU($n$) operator is
determined by the geodesic length in a bi-invariant Finsler geometry, which is
constrained by some symmetries of quantum field theory. It is based on three
axioms and one assumption regarding the complexity in continuous systems. By
relaxing one axiom and an assumption, we find that the complexity formula is
naturally generalized to the Schatten $p$-norm type. We also clarify the
relation between our complexity and other works. First, we show that our
results in a bi-invariant geometry are consistent with the ones in a
right-invariant geometry such as $k$-local geometry. Here, a careful analysis
of the sectional curvature is crucial. Second, we show that our complexity can
concretely realize the conjectured pattern of the time-evolution of the
complexity: the linear growth up to saturation time. The saturation time can be
estimated by the relation between the topology and curvature of SU($n$) groups. | $α'$ corrections of Reissner-Nordström black holes: We study the first-order in $\alpha'$ corrections to non-extremal
4-dimensional dyonic Reissner-Nordstr\"om (RN) black holes with equal electric
and magnetic charges in the context of Heterotic Superstring effective field
theory (HST) compactified on a $T^{6}$. The particular embedding of the dyonic
RN black hole in HST considered here is not supersymmetric in the extremal
limit. We show that, at first order in $\alpha'$, consistency with the
equations of motion of the HST demands additional scalar and vector fields
become active, and we provide explicit expressions for all of them. We
determine analytically the position of the event horizon of the black hole, as
well as the corrections to the extremality bound, to the temperature and to the
entropy, checking that they are related by the first law of black-hole
thermodynamics, so that $\partial S/\partial M=1/T$. We discuss the
implications of our results in the context of the Weak Gravity Conjecture,
clarifying that entropy corrections for fixed mass and charge at extremality do
not necessarily imply corrections to the extremal charge-to-mass ratio. |
Kinks, extra dimensions, and gravitational waves: We investigate in detail the gravitational wave signal from kinks on cosmic
(super)strings, including the kinematical effects from the internal extra
dimensions. We find that the signal is suppressed, however, the effect is less
significant that that for cusps. Combined with the greater incidence of kinks
on (super)strings, it is likely that the kink signal offers the better chance
for detection of cosmic (super)strings. | Equivariant Topological Sigma Models: We identify and examine a generalization of topological sigma models suitable
for coupling to topological open strings. The targets are Kahler manifolds with
a real structure, i.e. with an involution acting as a complex conjugation,
compatible with the Kahler metric. These models satisfy axioms of what might be
called ``equivariant topological quantum field theory,'' generalizing the
axioms of topological field theory as given by Atiyah. Observables of the
equivariant topological sigma models correspond to cohomological classes in an
equivariant cohomology theory of the targets. Their correlation functions can
be computed, leading to intersection theory on instanton moduli spaces with a
natural real structure. An equivariant $CP^1\times CP^1$ model is discussed in
detail, and solved explicitly. Finally, we discuss the equivariant formulation
of topological gravity on surfaces of unoriented open and closed string theory,
and find a $Z_2$ anomaly explaining some problems with the formulation of
topological open string theory. |
The (1,0) tensor and hypermultiplets in loop space: We show that the (1,0) tensor and hypermultiplet superconformal symmetry
variations can be uplifted to loop space if we assume that two lightlike
conformal Killing vectors commute. Upon dimensional reduction we make contact
with five dimensional super-Yang-Mills and its nonabelian generalization that
we subsequently uplift back to loop space where we conjecture a nonabelian
generalization of the (1,0) superconformal symmetry variations and demonstrate
their on-shell closure. | Hairpin-Branes and Tachyon-Paperclips in Holographic Backgrounds: D-branes with a U-shaped geometry, like the D8 flavor branes in the
Sakai-Sugimoto model of QCD, are encountered frequently in holographic
backgrounds. We argue that the commonly used DBI action is inadequate as an
effective field theory description of these branes, because it misses a crucial
component of the low-energy dynamics: a light complex scalar mode. Following an
idea of Erkal, Kutasov and Lunin we elaborate on an effective description based
on the abelian tachyon-DBI action which incorporates naturally the non-local
physics of the complex scalar mode. We demonstrate its power in a context where
an explicit worldsheet description of the open string dynamics exists
--hairpin-branes in the background of NS5-branes. Our results are relevant for
the holographic description of chiral symmetry breaking and bare quark mass in
QCD and open string tachyon condensation in curved backgrounds. |
Free Quotients of Favorable Calabi-Yau Manifolds: Non-simply connected Calabi-Yau threefolds play a central role in the study
of string compactifications. Such manifolds are usually described by
quotienting a simply connected Calabi-Yau variety by a freely acting discrete
symmetry. For the Calabi-Yau threefolds described as complete intersections in
products of projective spaces, a classification of such symmetries descending
from linear actions on the ambient spaces of the varieties has been given in
the literature. However, which symmetries can be described in this manner
depends upon the description that is being used to represent the manifold. In
recent work new, favorable, descriptions were given of this data set of
Calabi-Yau threefolds. In this paper, we perform a classification of cyclic
symmetries that descend from linear actions on the ambient spaces of these new
favorable descriptions. We present a list of 129 symmetries/non-simply
connected Calabi-Yau threefolds. Of these, at least 33, and potentially many
more, are topologically new varieties. | A universal formula for the density of states in theories with
finite-group symmetry: In this paper we use Euclidean gravity to derive a simple formula for the
density of black hole microstates which transform in each irreducible
representation of any finite gauge group. Since each representation appears
with nonzero density, this gives a new proof of the completeness hypothesis for
finite gauge fields. Inspired by the generality of the argument we further
propose that the formula applies at high energy in any quantum field theory
with a finite-group global symmetry, and give some evidence for this
conjecture. |
String Network from M-theory: We study the three string junctions and string networks in Type IIB string
theory by explicity constructing the holomorphic embeddings of the M-theory
membrane that describe such configurations. The main feature of them such as
supersymmetry, charge conservation and balance of tensions are derived in a
more unified manner. We calculate the energy of the string junction and show
that there is no binding energy associated with the junction. | Effects of temperature on thick branes and the fermion
(quasi-)localization: Following Campos's work [Phys. Rev. Lett. 88, 141602 (2002)], we investigate
the effects of temperature on flat, de Sitter (dS), and anti-de Following
Campos's work [Phys. Rev. Lett. \textbf{88}, 141602 (2002)], we investigate the
effects of temperature on flat, de Sitter (dS), and anti-de Sitter (AdS) thick
branes in five-dimensional (5D) warped spacetime, and on the fermion
(quasi-)localization. First, in the case of flat brane, when the critical
temperature reaches, the solution of the background scalar field and the warp
factor is not unique. So the thickness of the flat thick brane is uncertain at
the critical value of the temperature parameter, which is found to be lower
than the one in flat 5D spacetime. The mass spectra of the fermion Kaluza-Klein
(KK) modes are continuous, and there is a series of fermion resonances. The
number and lifetime of the resonances are finite and increase with the
temperature parameter, but the mass of the resonances decreases with the
temperature parameter. Second, in the case of dS brane, we do not find such a
critical value of the temperature parameter. The mass spectra of the fermion KK
modes are also continuous, and there is a series of fermion resonances. The
effects of temperature on resonance number, lifetime, and mass are the same
with the case of flat brane. Last, in the case of AdS brane, {the critical
value of the temperature parameter can less or greater than the one in the flat
5D spacetime.} The spectra of fermion KK modes are discrete, and the mass of
fermion KK modes does not decrease monotonically with increasing temperature
parameter. |
Shedding black hole light on the emergent string conjecture: Asymptotically massless towers of species are ubiquitous in the string
landscape when infinite-distance limits are approached. Due to the remarkable
properties of string dualities, they always comprise Kaluza-Klein states or
higher-spin excitations of weakly coupled, asymptotically tensionless critical
strings. The connection between towers of light species and small black holes
warrants seeking a bottom-up rationale for this dichotomoy, dubbed emergent
string conjecture. In this paper we move a first step in this direction,
exploring bottom-up constraints on towers of light species motivated purely
from the consistency of the corresponding thermodynamic picture for small black
holes. These constraints shed light on the allowed towers in quantum gravity,
and, upon combining them with unitarity and causality constraints from
perturbative graviton scattering, they provide evidence for the emergent string
scenario with no reference to a specific ultraviolet completion. | Affine holomorphic quantization: We present a rigorous and functorial quantization scheme for affine field
theories, i.e., field theories where local spaces of solutions are affine
spaces. The target framework for the quantization is the general boundary
formulation, allowing to implement manifest locality without the necessity for
metric or causal background structures. The quantization combines the
holomorphic version of geometric quantization for state spaces with the Feynman
path integral quantization for amplitudes. We also develop an adapted notion of
coherent states, discuss vacuum states, and consider observables and their
Berezin-Toeplitz quantization. Moreover, we derive a factorization identity for
the amplitude in the special case of a linear field theory modified by a
source-like term and comment on its use as a generating functional for a
generalized S-matrix. |
Analytic study of properties of holographic superconductors in
Born-Infeld electrodynamics: In this paper, based on the Sturm-Liouville eigenvalue problem, we
analytically investigate several properties of holographic s-wave
superconductors in the background of a Schwarzschild-AdS spacetime in the
framework of Born-Infeld electrodynamics. Based on a perturbative approach, we
explicitly find the relation between the critical temperature and the charge
density and also the fact that the Born-Infeld coupling parameter indeed
affects the formation of scalar hair at low temperatures. Higher value of the
Born-Infeld parameter results in a harder condensation to form. We further
compute the critical exponent associated with the condensation near the
critical temperature. The analytical results obtained are found to be in good
agreement with the existing numerical results. | Multimomentum Hamiltonian Formalism in Field Theory. Geometric
Supplementary: The well-known geometric approach to field theory is based on description of
classical fields as sections of fibred manifolds, e.g. bundles with a structure
group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms
including the multiomentum Hamiltonian formalism are phrased in terms of jet
manifolds. Then, configuration and phase spaces of fields are
finite-dimensional. Though the jet manifolds have been widely used for theory
of differential operators, the calculus of variations and differential
geometry, this powerful mathematical methods remains almost unknown for
physicists. This Supplementary to our previous article (hep-th/9403172) aims to
summarize necessary requisites on jet manifolds and general connections. |
Duality Transformations in Supersymmetric Yang-Mills Theories coupled to
Supergravity,: We consider duality transformations in N=2, d=4 Yang--Mills theory coupled to
N=2 supergravity. A symplectic and coordinate covariant framework is
established, which allows one to discuss stringy `classical and quantum duality
symmetries' (monodromies), incorporating T and S dualities. In particular, we
shall be able to study theories (like N=2 heterotic strings) which are
formulated in symplectic basis where a `holomorphic prepotential' F does not
exist, and yet give general expressions for all relevant physical quantities.
Duality transformations and symmetries for the N=1 matter coupled Yang--Mills
supergravity system are also exhibited. The implications of duality symmetry on
all N>2 extended supergravities are briefly mentioned. We finally give the
general form of the central charge and the N=2 semiclassical spectrum of the
dyonic BPS saturated states (as it comes by truncation of the N=4 spectrum). | Comments on N=2 Born-Infeld Attractors: We demonstrated that the new N=2 Born-Infeld action with two N=1 vector
supermultiplets, i.e. n=2 case considered as the example in the recent paper by
S. Ferrara, M. Porrati and A. Sagnotti, is some sort of complexification of J.
Bagger and A. Galperin construction of N=2 Born-Infeld action. Thus, novel
features could be expected only for n>2 cases, if the standard action is
considered. |
Supersymmetry preserving and breaking degenerate vacua, and radiative
moduli stabilization: We propose a new type of moduli stabilization scenario where the
supersymmetric and supersymmetry-breaking minima are degenerate at the leading
level. The inclusion of the loop-corrections originating from the matter fields
resolves this degeneracy of vacua. Light axions are predicted in one of our
models. | Topological strings and large N phase transitions I: Nonchiral expansion
of q-deformed Yang-Mills theory: We examine the problem of counting bound states of BPS black holes on local
Calabi-Yau threefolds which are fibrations over a Riemann surface by computing
the partition function of q-deformed Yang-Mills theory on the Riemann surface.
We study in detail the genus zero case and obtain, at finite $N$, the instanton
expansion of the gauge theory. It can be written exactly as the partition
function for U(N) Chern-Simons gauge theory on a Lens space, summed over all
non-trivial vacua, plus a tower of non-perturbative instanton contributions.
The correspondence between two and three dimensional gauge theories is
elucidated by an explicit mapping between two-dimensional Yang-Mills instantons
and flat connections on the Lens space. In the large $N$ limit we find a
peculiar phase structure in the model. At weak string coupling the theory
reduces exactly to the trivial flat connection sector with instanton
contributions exponentially suppressed, and the topological string partition
function on the resolved conifold is reproduced in this regime. At a certain
critical point all non-trivial vacua contribute, instantons are enhanced and
the theory appears to undergo a phase transition into a strong coupling regime.
We rederive these results by performing a saddle-point approximation to the
exact partition function. We obtain a q-deformed version of the Douglas-Kazakov
equation for two-dimensional Yang-Mills theory on the sphere, whose one-cut
solution below the transition point reproduces the resolved conifold geometry.
Above the critical point we propose a two-cut solution that should reproduce
the chiral-antichiral dynamics found for black holes on the Calabi-Yau
threefold and the Gross-Taylor string in the undeformed limit. |
Black Hole Thermodynamics, Induced Gravity and Gravity in Brane Worlds: One of explanations of the black hole entropy implies that gravity is
entirely induced by quantum effects. By using arguments based on the AdS/CFT
correspondence we give induced gravity interpretation of the gravity in a brane
world in higher dimensional anti-de Sitter (AdS) space. The underlying quantum
theory is SU(N) theory where $N$ is related to the CFT central charge. The
theory includes massless fields which correspond to degrees of freedom of the
boundary CFT. In addition, on the brane there are massive degrees of freedom
with masses proportional to $l^{-1}$ where $l$ is the radius of AdS. At the
conformal boundary of AdS they are infinitely heavy and completely decouple. It
is the massive fields which can explain the black hole entropy. We support our
interpretation by a microscopic model of a 2D brane world in $AdS_3$. | The Algebraic Page Curve: The Page curve describing the process of black hole evaporation is derived in
terms of a family, parametrized in terms of the evaporation time, of finite
type II_1 factors, associated, respectively, to the entanglement wedges of the
black hole and the radiation. The so defined Page curve measures the relative
continuous dimension of the black hole and the radiation along the evaporation
process. The transfer of information is quantitatively defined in terms of the
Murray von Neumann parameter describing the change of the spatial properties of
the factors during the evaporation. In the simplest case the generator of the
evaporation process is defined in terms of the action of the fundamental group
of the hyperfinite type II_1 factor. In this setup the Page curve describes a
phase transition with the transfer of information as order parameter. We
discuss the limits of either a type I or a type III description of the black
hole evaporation. |
Oscillator quantization of the massive scalar particle dynamics on AdS
spacetime: The set of trajectories for massive spinless particles on $AdS_{N+1}$
spacetime is described by the dynamical integrals related to the isometry group
SO(2,N). The space of dynamical integrals is mapped one to one to the phase
space of the $N$-dimensional oscillator. Quantizing the system canonically, the
classical expressions for the symmetry generators are deformed in a consistent
way to preserve the $so(2,N)$ commutation relations. This quantization thus
yields new explicit realizations of the spin zero positive energy UIR's of
SO(2,N) for generic $N$. The representations as usual can be characterized by
their minimal energy $\alpha$ and are valid in the whole range of $\alpha$
allowed by unitarity. | Domain Walls in Strongly Coupled Theories: Domain walls in strongly coupled gauge theories are discussed. A general
mechanism is suggested automatically leading to massless gauge bosons localized
on the wall. In one of the models considered, outside the wall the theory is in
the non-Abelian confining phase, while inside the wall it is in the Abelian
Coulomb phase. Confining property of the non-Abelian theories is a key
ingredient of the mechanism which may be of practical use in the context of the
dynamic compactification scenarios.
In supersymmetric (N=1) Yang-Mills theories the energy density of the wall
can be exactly calculated in the strong coupling regime. This calculation
presents a further example of non-trivial physical quantities that can be found
exactly by exploiting specific properties of supersymmetry. A key observation
is the fact that the wall in this theory is a BPS-saturated state. |
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