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Iterative Non-iterative Integrals in Quantum Field Theory: Single scale Feynman integrals in quantum field theories obey difference or
differential equations with respect to their discrete parameter $N$ or
continuous parameter $x$. The analysis of these equations reveals to which
order they factorize, which can be different in both cases. The simplest
systems are the ones which factorize to first order. For them complete solution
algorithms exist. The next interesting level is formed by those cases in which
also irreducible second order systems emerge. We give a survey on the latter
case. The solutions can be obtained as general $_2F_1$ solutions. The
corresponding solutions of the associated inhomogeneous differential equations
form so-called iterative non-iterative integrals. There are known conditions
under which one may represent the solutions by complete elliptic integrals. In
this case one may find representations in terms of meromorphic modular
functions, out of which special cases allow representations in the framework of
elliptic polylogarithms with generalized parameters. These are in general
weighted by a power of $1/\eta(\tau)$, where $\eta(\tau)$ is Dedekind's
$\eta$-function. Single scale elliptic solutions emerge in the
$\rho$-parameter, which we use as an illustrative example. They also occur in
the 3-loop QCD corrections to massive operator matrix elements and the massive
3-loop form factors. | hep-th |
Black Hole Condensation and Duality in String Theory: This is a non-technical version of a talk presented at the conference,
"S-Duality and Mirror Symmetry in String Theory" Trieste, June, 1996 which will
appear in the proceedings. | hep-th |
Non-gravitational exceptional supermultiplets: We examine non-gravitational minimal supermultiplets which are based on the
tensor gauge fields appearing as matter fields in exceptional generalised
geometry. When possible, off-shell multiplets are given. The fields in the
multiplets describe non-gravitational parts of the internal dynamics of
compactifications of M-theory. In flat backgrounds, they enjoy a global
U-duality symmetry, but also provide multiplets with a possibility of coupling
to a generalised exceptional geometry. | hep-th |
Spin-Statistics Correlations in Various Noncommutative Field Theories: In this thesis we study field theories written on a particular model of
noncommutative spacetime, the Groenewold-Moyal (GM) plane. We start with
briefly reviewing the novel features of field theories on GM plane e.g. the
$\ast$-product, restoration of Poincar\'e-Hopf symmetry and twisted commutation
relations. We then discuss our work on renormalization of field theories on GM
plane. We show that any generic noncommutative theory involving pure matter
fields with polynomial interactions, is a renormalizable theory if the
analogous commutative theory is renormalizable. We further show that all such
noncommutative theories will have same fixed points and $\beta$-functions for
the couplings, as that of the analogous commutative theory. The unique feature
of these field theories is the twisted statistics obeyed by the particles.
Motivated by it, we look at the possibility of twisted statistics by deforming
internal symmetries instead of spacetime symmetries. We construct two different
twisted theories which can be viewed as internal symmetry analogue of the GM
plane and dipole field theories which arise in the low energy limit of certain
string configurations. We further study their various properties like the issue
of causality and the scattering formalism. Having studied the mathematical
properties of noncommutative and twisted internal symmetries we move on to
discuss their potential phenomenological signatures. We first discuss the
noncommutative thermal correlation functions and show that because of the
twisted statistics, all correlation functions except two-point function get
modified. Finally we discuss the modifications in Hanbury-Brown Twiss (HBT)
correlation functions due to twisted statistics on GM plane and the potential
of observing signatures of noncommutativity by doing a HBT correlation
experiment with Ultra High Energy Cosmic Rays (UHECRs). | hep-th |
Thermodynamics of Rotating Black Branes in Gauss-Bonnet-nonlinear
Maxwell Gravity: We consider the Gauss-Bonnet gravity in the presence of a new class of
nonlinear electromagnetic field, namely, power Maxwell invariant. By use of a
suitable transformation, we obtain a class of real rotating solutions with $k$
rotation parameters and investigate some properties of the solutions such as
existence of singularity(ies) and asymptotic behavior of them. Also, we
calculate the finite action, thermodynamic and conserved quantities of the
solutions and using the the Smarr-type formula to check the first law of
thermodynamics. | hep-th |
Reply to `Can infrared gravitons screen $Λ$?': We reply to the recent criticism by Garriga and Tanaka of our proposal that
quantum gravitational loop corrections may lead to a secular screening of the
effective cosmological constant. Their argument rests upon a renormalization
scheme in which the composite operator $(R \sqrt{-g} - 4 \Lambda \sqrt{-g}
)_{\rm ren}$ is defined to be the trace of the renormalized field equations.
Although this is a peculiar prescription, we show that it {\it does not
preclude secular screening}. Moreover, we show that a constant Ricci scalar
{\it does not even classically} imply a constant expansion rate. Other
important points are: (1) the quantity $R_{\rm ren}$ of Garriga and Tanaka is
neither a properly defined composite operator, nor is it constant; (2) gauge
dependence does not render a Green's function devoid of physical content; (3)
scalar models on a non-dynamical de Sitter background (for which there is no
gauge issue) can induce arbitrarily large secular contributions to the stress
tensor; (4) the same secular corrections appear in observable quantities in
quantum gravity; and (5) the prospects seem good for deriving a simple
stochastic formulation of quantum gravity in which the leading secular effects
can be summed and for which the expectation values of even complicated, gauge
invariant operators can be computed at leading order. | hep-th |
Topological Sigma Models with H-Flux: We investigate the topological theory obtained by twisting the N=(2,2)
supersymmetric nonlinear sigma model with target a bihermitian space with
torsion. For the special case in which the two complex structures commute, we
show that the action is a Q-exact term plus a quasi-topological term. The
quasi-topological term is locally given by a closed two-form which corresponds
to a flat gerbe-connection and generalises the usual topological term of the
A-model. Exponentiating it gives a Wilson surface, which can be regarded as a
generalization of a Wilson line. This makes the quantum theory globally
well-defined. | hep-th |
Supertwistor formulation for higher dimensional superstrings: Considered is the formulation for the superstring action in 6 and 10
dimensions involving supertwistor variables that appropriately generalize
4-dimensional Ferber supertwistors. Equations of motion and kappa-symmetry
transformations in terms of the supertwistors are derived. It is shown that
covariant kappa-symmetry gauge fixing reduces superstring action to the
quadratic one with respect to supertwistors. Upon gauge fixing remaining
symmetries it can be cast into the form of the light-cone gauge Green-Schwarz
superstring action. | hep-th |
Supersymmetric gauge theory and the Yangian: This paper develops a new connection between supersymmetric gauge theories
and the Yangian. I show that a twisted, deformed version of the pure N=1
supersymmetric gauge theory is controlled by the Yangian, in the same way that
Chern-Simons theory is controlled by the quantum group. This result is used to
give an exact calculation, in perturbation theory, of the expectation value of
a certain net of n+m Wilson operators in the deformed N=1 gauge theory. This
expectation value coincides with the partition function of a spin-chain
integrable lattice model on an n-by-m doubly-periodic lattice. | hep-th |
Perturbations of General Relativity to All Orders and the General
$n^{\rm th}$ Order Terms: We derive all-order expressions for perturbations of the Einstein-Hilbert
action and the Einstein equation with the general $n$-th order terms. To this
end, we employ Cheung and Remmen's perturbation conventions both in tensor
density and the usual metric tensor formalisms, including the Einstein-dilaton
theory. Remarkably, we find minimal building blocks that generate the entire
perturbations for each of our formulations. We show that the number of terms of
perturbations grows linearly as the order of perturbations increases. We regard
our results as the reference and discuss how to derive perturbations in other
conventions from the reference. As a consistency check, we compute graviton
scattering amplitudes using the perturbiner method based on the perturbative
Einstein equation. Finally we discuss how to generalise the results to curved
backgrounds and incorporate additional matter. | hep-th |
A New Perspective on DGP Gravity: We examine brane induced gravity on codimension-1 branes, a.k.a DGP gravity,
as a theory of five-dimensional gravity containing a certain class
four-dimensional branes. From this perspective, the model suffers from a number
of pathologies which went unnoticed before. By generalizing the 5D geometry
from Minkowski to Schwarzschild, we find that when the bulk mass is large
enough, the brane hits a pressure singularity at finite radius. Further, on the
self-accelerating branch, the five-dimensional energy is unbounded from below,
implying that the self-accelerating backgrounds are unstable. Even in an empty
Minkowski bulk, standard Euclidean techniques suggest that the spontaneous
nucleation of self-accelerating branes is unsuppressed. If so, quantum effects
will strongly modify any classical intuition about the theory. We also note
that unless considered as Z_2-orbifold boundaries, self-accelerating branes
correspond to `wormhole' configurations, which introduces the usual problematic
issues associated with wormholes. Altogether these pathologies present a
serious challenge that any proposed UV completion of the DGP model must
overcome. | hep-th |
Instantons, Monopoles and Toric HyperKaehler Manifolds: In this paper, the metric on the moduli space of the k=1 SU(n) periodic
instanton -or caloron- with arbitrary gauge holonomy at spatial infinity is
explicitly constructed. The metric is toric hyperKaehler and of the form
conjectured by Lee and Yi. The torus coordinates describe the residual
U(1)^{n-1} gauge invariance and the temporal position of the caloron and can
also be viewed as the phases of n monopoles that constitute the caloron. The
(1,1,..,1) monopole is obtained as a limit of the caloron. The calculation is
performed on the space of Nahm data, which is justified by proving the
isometric property of the Nahm construction for the cases considered. An
alternative construction using the hyperKaehler quotient is also presented. The
effect of massless monopoles is briefly discussed. | hep-th |
Energy-momentum tensor of bouncing gravitons: In models of the Universe with extra dimensions gravity propagates in the
whole space-time. Graviton production by matter on the brane is significant in
the early hot Universe. In a model of 3-brane with matter embedded in 5D
space-time conditions for gravitons emitted from the brane to the bulk to
return back to the brane are found. For a given 5-momentum of graviton falling
back to the brane the interval between the times of emission and return to the
brane is calculated. A method to calculate contribution to the energy-momentum
tensor from multiple graviton bouncings is developed. Explicit expressions for
contributions to the energy-momentum tensor of gravitons which have made one,
two and three bounces are obtained and their magnitudes are numerically
calculated. These expressions are used to solve the evolution equation for dark
radiation. A relation connecting reheating temperature and the scale of extra
dimension is obtained. For the reheating temperature $T_R\sim 10^6 GeV$ we
estimate the scale of extra dimension $\m$ to be of order $10^{-9} GeV\,\,\,
(\m^{-1}\sim 10^{-5} cm )$. | hep-th |
Quantization of the anisotropic conformal Horava theory: We perform the Batalin-Fradkin-Vilkovisky quantization of the anisotropic
conformal Horava theory in d spatial dimensions. We introduce a model with a
conformal potential suitable for any dimension. We define an anisotropic and
local gauge-fixing condition that accounts for the spatial diffeomorphisms and
the anisotropic Weyl transformations. We show that the BRST transformations can
be expressed mainly in terms of a spatial diffeomorphism along a ghost field
plus a conformal transformation with another ghost field as argument. We study
the quantum Lagrangian in the d=2 case, obtaining that all propagators are
regular, except for the fields associated with the measure of the second-class
constraints. This behavior is qualitatively equal to the nonconformal case. | hep-th |
Finite Tensor Deformations of Supergravity Solitons: We consider brane solutions where the tensor degrees of freedom are excited.
Explicit solutions to the full non-linear supergravity equations of motion are
given for the M5 and D3 branes, corresponding to finite selfdual tensor or
Born-Infeld field strengths. The solutions are BPS-saturated and
half-supersymmetric. The resulting metric space-times are analysed. | hep-th |
Nonperturbative black hole entropy and Kloosterman sums: Non-perturbative quantum corrections to supersymmetric black hole entropy
often involve nontrivial number-theoretic phases called Kloosterman sums. We
show how these sums can be obtained naturally from the functional integral of
supergravity in asymptotically AdS_2 space for a class of black holes. They are
essentially topological in origin and correspond to charge-dependent phases
arising from the various gauge and gravitational Chern-Simons terms and
boundary Wilson lines evaluated on Dehn-filled solid 2-torus. These corrections
are essential to obtain an integer from supergravity in agreement with the
quantum degeneracies, and reveal an intriguing connection between topology,
number theory, and quantum gravity. We give an assessment of the current
understanding of quantum entropy of black holes. | hep-th |
Sommerfeld effect as the vertex correction in three-dimensional space: It is shown that the correction to the vertex for fermion pair annihilation
and production in the low-energy region is equal to the value of the wave
function for the two-body system at the origin. The procedure also shows
directly that the emergence of the Sommerfeld effect in quantum mechanics is
the product of the reduction of the vertex correction from four spacetime
dimensions to three-dimensional space. Meanwhile, the reciprocal wave function
is introduced into quantum mechanics. | hep-th |
Matching the circular Wilson loop with dual open string solution at
1-loop in strong coupling: We compute the 1-loop correction to the effective action for the string
solution in AdS_5 x S^5 dual to the circular Wilson loop. More generically, the
method we use can be applied whenever the two dimensional spectral problem
factorizes, to regularize and define the fluctuation determinants in terms of
solutions of one-dimensional differential equations. A such it can be applied
to non-homogeneous solutions both for open and closed strings and to various
boundary conditions. In the case of the circular Wilson loop, we obtain, for
the 1-loop partition function a result which up to a factor of two matches the
expectation from the exact gauge theory computation. The discrepancy can be
attributed to an overall constant in the string partition function coming from
the normalization of zero modes, which we have not fixed. | hep-th |
Boundary Effects in Quantum Physics: We analyze the role of boundaries in the infrared behavior of quantum field
theories. By means of a novel method we calculate the vacuum energy for a
massless scalar field confined between two homogeneous parallel plates with the
most general type of boundary properties. This allows the discrimination
between boundary conditions which generate attractive or repulsive Casimir
forces between the plates. In the interface between both regimes we find a very
interesting family of boundary conditions which do not induce any type of
Casimir force. We analyze the effect of the renormalization group flow on these
boundary conditions. Even if the Casimirless conformal invariant conditions are
physically unstable under renormalization group flow they emerge as a new set
of conformally invariant boundary conditions which are anomaly free. | hep-th |
Vibrational modes of Q-balls: We study linear perturbations of classically stable Q-balls in theories
admitting analytic solutions. Although the corresponding boundary value problem
is non-Hermitian, the analysis of perturbations can also be performed
analytically in certain regimes. We show that in theories with the flat
potential, large Q-balls possess soft excitations. We also find a specific
vibrational mode for Q-balls with a near-critical charge, where the
perturbation theory for excitations can be developed. Comparing with the
results on stability of Q-balls provides additional checks of our analysis. | hep-th |
Exploring the Abelian 4D, $\mathcal{N}$ = 4 Vector-Tensor Supermultiplet
and Its Off-Shell Central Charge Structure: An abelian 4D, $\mathcal{N}$ = 4 vector supermultiplet allows for a duality
transformation to be applied to one of its spin-0 states. The resulting theory
can be described as an abelian 4D, $\mathcal{N}$ = 4 vector-tensor
supermultiplet. It is seen to decompose into a direct sum of an off-shell 4D,
$\mathcal{N}$ = 2 vector supermultiplet and an off-shell 4D, $\mathcal{N}$ = 2
tensor supermultiplet. The commutator algebra of the other two supersymmetries
are still found to be on-shell. However, the central charge structure in the
resulting 4D, $\mathcal{N}$ = 4 vector-tensor supermultiplet is considerably
simpler that that of the parent abelian 4D, $\mathcal{N}$ = 4 vector
supermultiplet. This appears to be due to the replacement of the usual SO(4)
symmetry associated with the abelian 4D, $\mathcal{N}$ = 4 vector
supermultiplet being replaced by a
GL(2,$\mathbb{R}$)$\otimes$GL(2,$\mathbb{R}$) symmetry in the 4D, $\mathcal{N}$
= 4 vector-tensor supermultiplet. The $Mathematica$ code detailing the
calculations is available open-source at the HEPTHools Data Repository on
GitHub. | hep-th |
One-Loop N-Point Superstring Amplitudes with Manifest d=4 Supersymmetry: The hybrid formalism for the superstring is used to compute one-loop
amplitudes with an arbitrary number of external d=4 supergravity states. These
one-loop N-point amplitudes are expressed as Koba-Nielsen-like formulas with
manifest d=4 supersymmetry. | hep-th |
Symmetries of post-Galilean expansions: In this letter we study an infinite extension of the Galilei symmetry group
in any dimension that can be thought of as a non-relativistic or post-Galilean
expansion of the Poincare symmetry. We find an infinite-dimensional vector
space on which this generalized Galilei group acts and usual Minkowski space
can be modeled by our construction. We also construct particle and string
actions that are invariant under these transformations. | hep-th |
On quantum corrections to geodesics in de-Sitter spacetime: We find a coordinate-independent wave-packet solution of the massive
Klein-Gordon equation with the conformal coupling to gravity in the de-Sitter
universe. This solution can locally be represented through the superposition of
positive-frequency plane waves at any space-time point, assuming that the
scalar-field mass $M$ is much bigger than the de-Sitter Hubble constant $H$.
The solution is also shown to be related to the two-point function in the
de-Sitter quantum vacuum. Moreover, we study the wave-packet propagation over
cosmological times, depending on the ratio of $M$ and $H$. In doing so, we find
that this wave packet propagates like a point-like particle of the same mass if
$M \ggg H$, but, if otherwise, the wave packet behaves highly non-classically. | hep-th |
Trouble Finding the Optimal AdS/QCD: In the bottom-up approach to AdS/QCD based on a five-dimensional gravity
dilaton action the exponential of the dilaton field is usually identified as
the strong or 't Hooft coupling. There is currently no model known which fits
the measurements of the running coupling and lattice results for pressure at
the same time. With a one parametric toy model we demonstrate the effect of
fitting the pressure on the coupling and vice versa. | hep-th |
Chiral Symmetry Breaking in the $d=3$ Nambu-Jona-Lasinio Model in Curved
Spacetime: The phase structure of the $d=3$ Nambu-Jona-Lasinio model in curved spacetime
is considered to leading order in the $1/N$--expansion and in the linear
curvature approximation. The possibility of a curvature-induced first-order
phase transition is investigated numerically. The dynamically generated
fermionic mass is calculated for some values of the curvature. | hep-th |
Symplectic Fermions: We study two-dimensional conformal field theories generated from a
``symplectic fermion'' - a free two-component fermion field of spin one - and
construct the maximal local supersymmetric conformal field theory generated
from it. This theory has central charge c=-2 and provides the simplest example
of a theory with logarithmic operators.
Twisted states with respect to the global SL(2,C)-symmetry of the symplectic
fermions are introduced and we describe in detail how one obtains a consistent
set of twisted amplitudes. We study orbifold models with respect to finite
subgroups of SL(2,C) and obtain their modular invariant partition functions. In
the case of the cyclic orbifolds explicit expressions are given for all two-,
three- and four-point functions of the fundamental fields. The C_2-orbifold is
shown to be isomorphic to the bosonic local logarithmic conformal field theory
of the triplet algebra encountered previously. We discuss the relation of the
C_4-orbifold to critical dense polymers. | hep-th |
Dual gravity and E11: We consider the equation of motion in the gravity sector that arises from the
non-linear realisation of the semi-direct product of E11 and its first
fundamental representation, denoted by l1, in four dimensions. This equation is
first order in derivatives and at low levels relates the usual field of gravity
to a dual gravity field. When the generalised space-time is restricted to be
the usual four dimensional space-time we show that this equation does correctly
describe Einstein's theory at the linearised level. We also comment on previous
discussions of dual gravity. | hep-th |
Anomaly inflow and RR anomalous couplings: We review the anomaly inflow mechanism on D-branes and O-planes. In
particular, we compute the one-loop world-volume anomalies and derive the RR
anomalous couplings required for their cancellation. | hep-th |
A general holographic insulator/superconductor model away from the probe
limit: We investigate holographic phase transitions affected by dark matter sector
in the AdS soliton background away from the probe limit. When neglecting
backreaction, the scalar charge q can be scaled unity without loss of
generality. While considering backreaction in this work, we obtain much more
richer physics by choosing various scalar charge q. Firstly, we observe
unstable retrograde condensation appears due to the dark matter sector and also
derive stable conditions. For stable solutions, we find that the larger
coupling parameter $\alpha$ makes the gap of condensation shallower and the
critical chemical potential keeps as a constant with a large scalar charge q,
which is similar to cases in the probe limit. In contrast, the dark matter
sector could affect the critical chemical potential and the order of phase
transitions for very small charge q. We also arrive at the same conclusion from
the holographic topological entanglement entropy approach. Moreover, we state
that the entanglement entropy approach is especially powerful in studying the
effects of the dark matter sector in this general insulator/superconductor
system. | hep-th |
Black hole entropy and the renormalization group: Four decades after its first postulation by Bekenstein, black hole entropy
remains mysterious. It has long been suggested that the entanglement entropy of
quantum fields on the black hole gravitational background should represent at
least an important contribution to the total Bekenstein-Hawking entropy, and
that the divergences in the entanglement entropy should be absorbed in the
renormalization of the gravitational couplings. In this talk, we describe how
an improved understanding of black hole entropy is obtained by combining these
notions with the renormalization group. By introducing an RG flow scale, we
investigate whether the total entropy of the black hole can be partitioned in a
"gravitational" part related to the flowing gravitational action, and a
"quantum" part related to the unintegrated degrees of freedom. We describe the
realization of this idea for free fields, and the complications and
qualifications arising for interacting fields. | hep-th |
Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic
Classes: We investigate the generic 3D topological field theory within AKSZ-BV
framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly
cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue
that the perturbative partition function gives rise to secondary characteristic
classes. We investigate a toy model which is an odd analogue of Chern-Simons
theory, and we give some explicit computation of two point functions and show
that its perturbation theory is identical to the Chern-Simons theory. We give
concrete example of the homomorphism taking Lie algebra cocycles to
Q-characteristic classes, and we reinterpreted the Rozansky-Witten model in
this light. | hep-th |
On algebraic structures in supersymmetric principal chiral model: Using the Poisson current algebra of the supersymmetric principal chiral
model, we develop the algebraic canonical structure of the model by evaluating
the fundamental Poisson bracket of the Lax matrices that fits into the rs
matrix formalism of non-ultralocal integrable models. The fundamental Poisson
bracket has been used to compute the Poisson bracket algebra of the monodromy
matrix that gives the conserved quantities in involution. | hep-th |
The simplest non-associative generalization of supersymmetry: Nonassociative generalization of supersymmetry is suggested. 3- and 4-point
associators for supersymmetric generators are considered. On the basis of zero
Jacobiators for three supersymmetric generators, we have obtained the simplest
form of 3-point associators. The connection between 3- and 4-point associators
is considered. On the basis of this connection, 4-point associators are
obtained. The Jacobiators for the product of four supersymmetric generators are
calculated. We discuss the possible physical meaning of numerical coefficients
presented on the right-hand sides of associators. The possible connection
between supersymmetry, hidden variables, and nonassociativity is discussed. | hep-th |
Probing the Constituent Structure of Black Holes: Based on recent ideas, we propose a framework for the description of black
holes in terms of constituent graviton degrees of freedom. Within this
formalism a large black hole can be understood as a bound state of N
longitudinal gravitons. In this context black holes are similar to baryonic
bound states in quantum chromodynamics which are described by fundamental quark
degrees of freedom. As a quantitative tool we employ a quantum bound state
description originally developed in QCD that allows to consider black holes in
a relativistic Hartree like framework. As an application of our framework we
calculate the cross section for scattering processes between graviton emitters
outside of a Schwarzschild black hole and absorbers in its interior, that is
gravitons. We show that these scatterings allow to directly extract structural
observables such as the momentum distribution of black hole constituents. | hep-th |
Universality of anomalous conductivities in theories with
higher-derivative holographic duals: Anomalous chiral conductivities in theories with global anomalies are
independent of whether they are computed in a weakly coupled quantum (or
thermal) field theory, hydrodynamics, or at infinite coupling from holography.
While the presence of dynamical gauge fields and mixed, gauge-global anomalies
can destroy this universality, in their absence, the non-renormalisation of
anomalous Ward identities is expected to be obeyed at all intermediate coupling
strengths. In holography, bulk theories with higher-derivative corrections
incorporate coupling constant corrections to the boundary theory observables in
an expansion around infinite coupling. In this work, we investigate the
coupling constant dependence and universality of anomalous conductivities (and
thus of the anomalous Ward identities) in general, four-dimensional systems
that possess asymptotically anti-de Sitter holographic duals with a
non-extremal black brane in five dimensions, and anomalous transport introduced
into the boundary theory via the bulk Chern-Simons action. We show that in bulk
theories with arbitrary gauge- and diffeomorphism-invariant higher-derivative
actions, anomalous conductivities, which can incorporate an infinite series of
(inverse) coupling constant corrections, remain universal. Owing to the
existence of the membrane paradigm, the proof reduces to a construction of bulk
effective theories at the horizon and the boundary. It only requires us to
impose the condition of horizon regularity and correct boundary conditions on
the fields. We also discuss ways to violate the universality by violating
conditions for the validity of the membrane paradigm, in particular, by adding
mass to the vector fields (a case with a mixed, gauge-global anomaly) and in
bulk geometries with a naked singularity. | hep-th |
Maximally Supersymmetric Yang-Mills in five dimensions in light-cone
superspace: We formulate maximally supersymmetric Yang-Mills theory in five dimensions in
light-cone superspace. The light-cone Hamiltonian is of the quadratic form and
the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory
in four dimensions. We specifically study three-point counterterms and show how
these counterterms vanish on-shell. This study is a preliminary to set up the
technique in order to study possible four-point counterterms. | hep-th |
Weyl Card Diagrams: To capture important physical properties of a spacetime we construct a new
diagram, the card diagram, which accurately draws generalized Weyl spacetimes
in arbitrary dimensions by encoding their global spacetime structure,
singularities, horizons, and some aspects of causal structure including null
infinity. Card diagrams draw only non-trivial directions providing a clearer
picture of the geometric features of spacetimes as compared to Penrose
diagrams, and can change continuously as a function of the geometric
parameters. One of our main results is to describe how Weyl rods are
traversable horizons and the entirety of the spacetime can be mapped out. We
review Weyl techniques and as examples we systematically discuss properties of
a variety of solutions including Kerr-Newman black holes, black rings,
expanding bubbles, and recent spacelike-brane solutions. Families of solutions
will share qualitatively similar cards. In addition we show how card diagrams
not only capture information about a geometry but also its analytic
continuations by providing a geometric picture of analytic continuation. Weyl
techniques are generalized to higher dimensional charged solutions and applied
to generate perturbations of bubble and S-brane solutions by Israel-Khan rods.
This paper is a condensed and simplified presentation of the card diagrams in
hep-th/0409070. | hep-th |
Universal horizons in maximally symmetric spaces: Universal horizons in Ho\v{r}ava-Lifshitz gravity and Einstein-{\ae}ther
theory are the equivalent of causal horizons in general relativity and appear
to have many of the same properties, including a first law of horizon
thermodynamics and thermal radiation. Since universal horizons are infrared
solutions of a putative power counting renormalizable quantum gravitational
theory, fully understanding their thermodynamics will shed light on the
interplay between black hole thermodynamics and quantum gravity. In this paper,
we provide a complete classification, including asymptotic charges, of all four
dimensional static and spherically symmetric universal horizon solutions with
maximally symmetric asymptotics -- the equivalents of the Schwarzschild,
Schwarzschild de Sitter or Schwarzschild anti-de Sitter spacetimes.
Additionally we derive the associated first laws for the universal horizon
solutions. Finally we prove that independent of asymptotic boundary conditions,
any spherically symmetric solution in Ho\v{r}ava-Lifshitz gravity with a
universal horizon is also a solution of Einstein-{\ae}ther theory, thereby
broadening and complementing the known equivalence region of the solution
spaces. | hep-th |
On the Natural Gauge Fields of Manifolds: The gauge symmetry inherent in the concept of manifold has been discussed.
Within the scope of this symmetry the linear connection or displacement field
can be considered as a natural gauge field on the manifold. The gauge invariant
equations for the displacement field have been derived. It has been shown that
the energy-momentum tensor of this field conserves and hence the displacement
field can be treated as one that transports energy and gravitates. To show the
existence of the solutions of the field equations we have derived the general
form of the displacement field in Minkowski space-time which is invariant under
rotation and space and time inversion. With this anzats we found
spherically-symmetric solutions of the equations in question. | hep-th |
Twisted topological structures related to M-branes II: Twisted Wu and
Wu^c structures: Studying the topological aspects of M-branes in M-theory leads to various
structures related to Wu classes. First we interpret Wu classes themselves as
twisted classes and then define twisted notions of Wu structures. These
generalize many known structures, including Pin^- structures, twisted Spin
structures in the sense of Distler-Freed-Moore, Wu-twisted differential
cocycles appearing in the work of Belov-Moore, as well as ones introduced by
the author, such as twisted Membrane and twisted String^c structures. In
addition, we introduce Wu^c structures, which generalize Pin^c structures, as
well as their twisted versions. We show how these structures generalize and
encode the usual structures defined via Stiefel-Whitney classes. | hep-th |
The complete one-loop spin chain for N=2 Super-Yang-Mills: We show that the complete planar one-loop mixing matrix of the N=2 Super
Yang--Mills theory can be obtained from a reduction of that of the N=4 theory.
For composite operators of scalar fields, this yields an anisotropic XXZ spin
chain, whose spectrum of excitations displays a mass gap. | hep-th |
The Family Problem: Hints from Heterotic Line Bundle Models: Within the class of heterotic line bundle models, we argue that N=1 vacua
which lead to a small number of low-energy chiral families are preferred. By
imposing an upper limit on the volume of the internal manifold, as required in
order to obtain finite values of the four-dimensional gauge couplings, and
validity of the supergravity approximation we show that, for a given manifold,
only a finite number of line bundle sums are consistent with supersymmetry. By
explicitly scanning over this finite set of line bundle models on certain
manifolds we show that, for a sufficiently small volume of the internal
manifold, the family number distribution peaks at small values, consistent with
three chiral families. The relation between the maximal number of families and
the gauge coupling is discussed, which hints towards a possible explanation of
the family problem. | hep-th |
From Fusion Hierarchy to Excited State TBA: Functional relations among the fusion hierarchy of quantum transfer matrices
give a novel derivation of the TBA equations, namely without string hypothesis.
This is demonstrated for two important models of 1D highly correlated electron
systems, the supersymmetric $t-J$ model and the supersymmetric extended Hubbard
model. As a consequence, "the excited state TBA" equations, which characterize
correlation lengths, are explicitly derived for the $t-J$ model. To the
authors' knowledge, this is the first explicit derivation of excited state TBA
equations for 1D lattice electron systems. | hep-th |
Hemisphere Partition Function and Analytic Continuation to the Conifold
Point: We show that the hemisphere partition function for certain U(1) gauged linear
sigma models (GLSMs) with D-branes is related to a particular set of
Mellin-Barnes integrals which can be used for analytic continuation to the
singular point in the K\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY)
projective hypersurface. We directly compute the analytic continuation of the
full quantum corrected central charge of a basis of geometric D-branes from the
large volume to the singular point. In the mirror language this amounts to
compute the analytic continuation of a basis of periods on the mirror CY to the
conifold point. However, all calculations are done in the GLSM and we do not
have to refer to the mirror CY. We apply our methods explicitly to the cubic,
quartic and quintic CY hypersurfaces. | hep-th |
A solution of 2D QCD at Finite $N$ using a conformal basis: We study 2D QCD with a fundamental fermion at small-$N$ using the recently
proposed conformal basis approach. We find that effective conformal dominance
still holds, namely that the spectrum converges efficiently, with high
scaling-dimension operators decoupling exponentially quickly from the stable
single-particle states. Consequently, for these stable bound states, accurate,
analytic expressions for wavefunctions and parton distribution functions can be
given, even for $N=3$. | hep-th |
Z_2 x Z_2 Heterotic Orbifold Models of Non Factorisable Six Dimensional
Toroidal Manifolds: We discuss heterotic strings on Z_2 x Z_2 orbifolds of non factorisable
six-tori. Although the number of fixed tori is reduced as compared to the
factorisable case, Wilson lines are still needed for the construction of three
generation models. An essential new feature is the straightforward appearance
of three generation models with one generation per twisted sector. We
illustrate our general arguments for the occurrence of that property by an
explicit example. Our findings give further support for the conjecture that
four dimensional heterotic strings formulated at the free fermionic point are
related to Z_2 x Z_2 orbifolds. | hep-th |
The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and
Celestial Amplitudes: The soft limits of scattering amplitudes have been extensively studied due to
their essential role in the computation of physical observables in collider
physics. The universal factorisation that occurs in these kinematic limits has
been shown to be related to conservation laws associated with asymptotic, or
large, gauge symmetries. This connection has led to a deeper understanding of
the symmetries of gauge and gravitational theories and to a reformulation of
scattering amplitudes in a basis of boost eigenstates which makes manifest the
two-dimensional global conformal symmetry of the celestial sphere. The recast,
or celestial, amplitudes possess many of the properties of conformal field
theory correlation functions which has suggested a path towards a holographic
description of asymptotically flat spacetimes. In this review we consider these
interconnected developments in our understanding of soft theorems, asymptotic
symmetries and conformal field theory with a focus on the structure and
symmetries of the celestial amplitudes and their holographic interpretation. | hep-th |
Feynman rules for Coulomb gauge QCD: The Coulomb gauge in nonabelian gauge theories is attractive in principle,
but beset with technical difficulties in perturbation theory. In addition to
ordinary Feynman integrals, there are, at 2-loop order, Christ-Lee (CL) terms,
derived either by correctly ordering the operators in the Hamiltonian, or by
resolving ambiguous Feynman integrals. Renormalization theory depends on the
subgraph structure of ordinary Feynamn graphs. The CL terms do not have
subgraph structure. We show how to carry out enormalization in the presene of
CL terms, by re-expressing these as `pseudo-Feynman' inegrals. We also explain
how energy divergences cancel. | hep-th |
The evolution of the universe from noncompact Kaluza-Klein theory: We develope a 5D mechanism inspired in the Campbell's theorem, to explain the
(neutral scalar field governed) evolution of the universe from a initially
inflationary expansion that has a change of phase towards a decelerated
expansion and thereinafter evolves towards the present day observed celerated
(quintessential) expansion. | hep-th |
Magnetic-field-driven topological phase transition in the holograpic
Weyl semimetal: We study the magnetic field effects on the quantum critical point (QCP) in
the holographic Weyl semimetal model. We show that it increases quadratically
with the magnetic field for weak field and linear with the magnetic field for
strong field. Our findings are compatible with previous results in the
literature from other approaches. | hep-th |
Runaway directions in O'Raifeartaigh models: R-symmetries, which are needed for supersymmetry (SUSY) breaking in
O'Raifeartaigh models, often lead to SUSY runaway directions trough a
complexified R-transformation. Non-R symmetries also lead to runaway directions
in a similar way. This work investigates the occurrence of runaway directions
of both SUSY and SUSY breaking types. We clarify previous issues on fractional
charges and genericness, and make a refined statement on conditions for runaway
directions related to either R-symmetries or non-R symmetries. We present a
generic and anomaly-free model to show the existence of runaway directions
related to non-R symmetries. We also comment on the possibility to combine the
non-R symmetry case to the R-symmetry case by an R-charge redefinition. | hep-th |
The Static Gauge Potential with a Cutoff: The static potential, corresponding to the interaction of two heavy sources
is computed for $\mathcal{N}=4$ Super Yang Mills in the strong 't Hooft
coupling regime by using the AdS/CFT conjecture and performing a computation of
a rectangular Wilson loop at a finite distance of the boundary. | hep-th |
RG limit cycles: In this review we consider the concept of limit cycles in the renormalization
group flows. The examples of this phenomena in the quantum mechanics and field
theory will be presented. | hep-th |
Operator Product Expansion in Logarithmic Conformal Field Theory: In logarithmic conformal field theory, primary fields come together with
logarithmic partner fields on which the stress-energy tensor acts
non-diagonally. Exploiting this fact and global conformal invariance of two-
and three-point functions, operator product expansions of logarithmic operators
in arbitrary rank logarithmic conformal field theory are investigated. Since
the precise relationship between logarithmic operators and their primary
partners is not yet sufficiently understood in all cases, the derivation of
operator product expansion formulae is only possible under certain assumptions.
The easiest cases are studied in this paper: firstly, where operator product
expansions of two primaries only contain primary fields, secondly, where the
primary fields are pre-logarithmic operators. Some comments on generalization
towards more relaxed assumptions are made, in particular towards the case where
logarithmic fields are not quasi-primary. We identify an algebraic structure
generated by the zero modes of the fields, which proves useful in determining
settings in which our approach can be successfully applied. | hep-th |
Singularities and Gauge Theory Phases: Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we
present a correspondence between networks of small resolutions for singular
elliptic fibrations and Coulomb branches of five-dimensional N=1 gauge
theories. While resolutions correspond to subchambers of the Coulomb branch,
partial resolutions correspond to higher codimension loci at which the Coulomb
branch intersects the Coulomb-Higgs branches. Flops between different
resolutions are identified with reflections on the Coulomb branch. Physics
aside, this correspondence provides an interesting link between elliptic
fibrations and representation theory. | hep-th |
Toward the End of Time: The null-brane space-time provides a simple model of a big crunch/big bang
singularity. A non-perturbative definition of M-theory on this space-time was
recently provided using matrix theory. We derive the fermion couplings for this
matrix model and study the leading quantum effects. These effects include
particle production and a time-dependent potential. Our results suggest that as
the null-brane develops a big crunch singularity, the usual notion of
space-time is replaced by an interacting gluon phase. This gluon phase appears
to constitute the end of our conventional picture of space and time. | hep-th |
Decoupling of High Dimension Operators from the Low Energy Sector in
Holographic Models: We study the decoupling of high dimension operators from the the description
of the low-energy spectrum in theories where conformal symmetry is broken by a
single scale, which we refer to as `broken CFTs'. Holographic duality suggests
that this decoupling occurs in generic backgrounds. We show how the decoupling
of high mass states in the (d+1)-dimensional bulk relates to the decoupling of
high energy states in the d-dimensional broken CFT. In other words, we explain
why both high dimension operators and high mass states in the CFT decouple from
the low-energy physics of the mesons and glueballs. In many cases, the
decoupling can occur exponentially fast in the dimension of the operator.
Holography motivates a new kind of form factor proportional to the two point
function between broken CFT operators with very different scaling dimensions.
This new notion of decoupling can provide a systematic justification for
holographic descriptions of QCD and condensed matter systems with only light
degrees of freedom in the bulk. | hep-th |
Nonlocal vertices and analyticity: Landau equations and general Cutkosky
rule: We study the analyticity properties of amplitudes in theories with nonlocal
vertices of the type occurring in string field theory and a wide class of
nonlocal field theory models. Such vertices are given in momentum space by
entire functions of rapid decay in certain (including Euclidean) directions
ensuring UV finiteness but are necessarily of rapid increase in others. A
parametric representation is obtained by integrating out the loop (Euclidean)
momenta after the introduction of generalized Schwinger parameters. Either in
the original or parametric representation, the well-defined resulting
amplitudes are then continued in the complex space of the external momenta
invariants. We obtain the alternative forms of the Landau equations determining
the singularity surfaces showing that the nonlocal vertices serve as UV
regulators but do not affect the local singularity structure. As a result the
full set of singularities known to occur in local field theory also occurs
here: normal and anomalous thresholds as well as acnodes, crunodes, and cusps
that may under certain circumstances appear even on the physical sheet.
Singularities of the second type also appear as shown from the parametric
representation. We obtain the general Cutkosky discontinuity rule for
encircling a singularity by employing contour deformations only in the finite
plane. The unitarity condition (optical theorem) is then discussed as a special
application of the rule across normal thresholds and the hermitian analyticity
property of amplitudes. | hep-th |
Quantum Cauchy problem in cosmology: We develop a general framework for effective equations of expectation values
in quantum cosmology and pose for them the quantum Cauchy problem with
no-boundary and tunneling wavefunctions. We apply this framework in the model
with a big negative non-minimal coupling, which incorporates a recently
proposed low energy (GUT scale) mechanism of the quantum origin of the
inflationary Universe and study the effects of the quantum inflaton mode. | hep-th |
Infrared Modification of Gravity: In this lecture I address the issue of possible large distance modification
of gravity and its observational consequences. Although, for the illustrative
purposes we focus on a particular simple generally-covariant example, our
conclusions are rather general and apply to large class of theories in which,
already at the Newtonian level, gravity changes the regime at a certain very
large crossover distance $r_c$. In such theories the cosmological evolution
gets dramatically modified at the crossover scale, usually exhibiting a
"self-accelerated" expansion, which can be differentiated from more
conventional "dark energy" scenarios by precision cosmology. However, unlike
the latter scenarios, theories of modified-gravity are extremely constrained
(and potentially testable) by the precision gravitational measurements at much
shorter scales. Despite the presence of extra polarizations of graviton, the
theory is compatible with observations, since the naive perturbative expansion
in Newton's constant breaks down at a certain intermediate scale. This happens
because the extra polarizations have couplings singular in $1/r_c$. However,
the correctly resummed non-linear solutions are regular and exhibit continuous
Einsteinian limit. Contrary to the naive expectation, explicit examples
indicate that the resummed solutions remain valid after the ultraviolet
completion of the theory, with the loop corrections taken into account. | hep-th |
Double Field Theory at SL(2) angles: An extended field theory is presented that captures the full SL(2) x O(6,6+n)
duality group of four-dimensional half-maximal supergravities. The theory has
section constraints whose two inequivalent solutions correspond to minimal D=10
supergravity and chiral half-maximal D=6 supergravity, respectively coupled to
vector and tensor multiplets. The relation with O(6,6+n) (heterotic) double
field theory is thoroughly discussed. Non-Abelian interactions as well as
background fluxes are captured by a deformation of the generalised
diffeomorphisms. Finally, making use of the SL(2) duality structure, it is
shown how to generate gaugings with non-trivial de Roo-Wagemans angles via
generalised Scherk-Schwarz ansaetze. Such gaugings allow for moduli
stabilisation including the SL(2) dilaton. | hep-th |
Functional quantization of Generalized Scalar Duffin-Kemmer-Petiau
Electrodynamics: The main goal of this work is to study systematically the quantum aspects of
the interaction between scalar particles in the framework of Generalized Scalar
Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is
quantized after a constraint analysis following Dirac's methodology by
determining the Hamiltonian transition amplitude. In particular, the covariant
transition amplitude is established in the generalized non-mixing Lorenz gauge.
The complete Green's functions are obtained through functional methods and the
theory's renormalizability is also detailed presented. Next, the radiative
corrections for the Green's functions at $\alpha $-order are computed; and, as
it turns out, an unexpected $m_{P}$-dependent divergence on the DKP sector of
the theory is found. Furthermore, in order to show the effectiveness of the
renormalization procedure on the present theory, a diagrammatic discussion on
the photon self-energy and vertex part at $\alpha ^{2}$-order are presented,
where it is possible to observe contributions from the DKP self-energy
function, and then analyse whether or not this novel divergence propagates to
higher-order contributions. Lastly, an energy range where the theory is well
defined: $m^{2}\ll k^{2}<m_{p}^{2}$ was also found by evaluating the effective
coupling for the GSDKP. | hep-th |
M2-doughnuts: We present a family of new M2-brane solutions in $AdS_7\times S^4$ that
calculate toroidal BPS surface operators in the $\mathcal{N}=(2,0)$ theory.
These observables are conformally invariant and not subject to anomalies so we
are able to evaluate their finite expectation values at leading order at large
$N$. In the limit of a thin torus we find a cylinder, which is a natural
surface generalization of both the circular and parallel lines Wilson loop. We
study and comment on this limit in some detail. | hep-th |
An Etude on Global Vacuum Energy Sequester: Recently two of the authors proposed a mechanism of vacuum energy sequester
as a means of protecting the observable cosmological constant from quantum
radiative corrections. The original proposal was based on using global Lagrange
multipliers, but later a local formulation was provided. Subsequently other
interesting claims of a different non-local approach to the cosmological
constant problem were made, based again on global Lagrange multipliers. We
examine some of these proposals and find their mutual relationship. We explain
that the proposals which do not treat the cosmological constant counterterm as
a dynamical variable require fine tunings to have acceptable solutions.
Furthermore, the counterterm often needs to be retuned at every order in the
loop expansion to cancel the radiative corrections to the cosmological
constant, just like in standard GR. These observations are an important
reminder of just how the proposal of vacuum energy sequester avoids such
problems. | hep-th |
Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries: In a recent paper, we proposed closed-form expressions for the superconformal
indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas (AD)
superconformal field theories (SCFTs) in the Schur limit. Following up on our
results, we turn our attention to the small S^1 regime of these indices. As
expected on general grounds, our study reproduces the S^3 partition functions
of the resulting dimensionally reduced theories. However, we show that in all
cases---with the exception of the reduction of the (A_1, D_4) SCFT---certain
imaginary partners of real mass terms are turned on in the corresponding mirror
theories. We interpret these deformations as R symmetry mixing with the
topological symmetries of the direct S^1 reductions. Moreover, we argue that
these shifts occur in any of our theories whose four-dimensional N=2
superconformal U(1)_R symmetry does not obey an SU(2) quantization condition.
We then use our R symmetry map to find the four-dimensional ancestors of
certain three-dimensional operators. Somewhat surprisingly, this picture turns
out to imply that the scaling dimensions of many of the chiral operators of the
four-dimensional theory are encoded in accidental symmetries of the
three-dimensional theory. We also comment on the implications of our work on
the space of general N=2 SCFTs. | hep-th |
Lectures on nonlinear sigma-models in projective superspace: N = 2 supersymmetry in four space-time dimensions is intimately related to
hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces
for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On
the other hand, when coupled to N = 2 supergravity, the sigma-model target
spaces must be quaternionic Kahler. It is known that such manifolds of
restricted holonomy are difficult to generate explicitly. Projective superspace
is a field-theoretic approach to constructing general N = 2 supersymmetric
nonlinear sigma-models, and hence to generate new hyperkahler and quaternionic
Kahler metrics. Intended for a mixed audience consisting of both physicists and
mathematicians, these lectures provide a pedagogical introduction to the
projective-superspace approach. | hep-th |
Two-Dimensional Chiral Matrix Models and String Theories: We formulate and solve a class of two-dimensional matrix gauge models
describing ensembles of non-folding surfaces covering an oriented, discretized,
two-dimensional manifold. We interpret the models as string theories
characterized by a set of coupling constants associated to worldsheet
ramification points of various orders. Our approach is closely related to, but
simpler than, the string theory describing two-dimensional Yang-Mills theory.
Using recently developed character expansion methods we exactly solve the
models for target space lattices of arbitrary internal connectivity and
topology. | hep-th |
Existence of a Supersymmetric Massless Ground State of the $SU(N)$
Matrix Model globally on its Valleys: In this work we consider the existence and uniqueness of the ground state of
the regularized Hamiltonian of the Supermembrane in dimensions $D= 4,\,5,\,7$
and 11, or equivalently the $SU(N)$ Matrix Model. That is, the 0+1 reduction of
the 10-dimensional $SU(N)$ Super Yang-Mills Hamiltonian. This ground state
problem is associated with the solutions of the inner and outer Dirichlet
problems for this operator, and their subsequent smooth patching (glueing) into
a single state. We have discussed properties of the inner problem in a previous
work, therefore we now investigate the outer Dirichlet problem for the
Hamiltonian operator. We establish existence and uniqueness on unbounded
valleys defined in terms of the bosonic potential. These are precisely those
regions where the bosonic part of the potential is less than a given value
$V_0$, which we set to be arbitrary. The problem is well posed, since these
valleys are preserved by the action of the $SU(N)$ constraint. We first show
that their Lebesgue measure is finite, subject to restrictions on $D$ in terms
of $N$. We then use this analysis to determine a bound on the fermionic
potential which yields the coercive property of the energy form. It is from
this, that we derive the existence and uniqueness of the solution. As a
by-product of our argumentation, we show that the Hamiltonian, restricted to
the valleys, has spectrum purely discrete with finite multiplicity. Remarkably,
this is in contrast to the case of the unrestricted space, where it is well
known that the spectrum comprises a continuous segment. We discuss the relation
of our work with the general ground state problem and the question of
confinement in models with strong interactions. | hep-th |
Time Dependent Cosmologies and Their Duals: We construct a family of solutions in IIB supergravity theory. These are time
dependent or depend on a light-like coordinate and can be thought of as
deformations of AdS_5 x S^5. Several of the solutions have singularities. The
light-like solutions preserve 8 supersymmetries. We argue that these solutions
are dual to the N=4 gauge theory in a 3+1 dimensional spacetime with a metric
and a gauge coupling that is varying with time or the light-like direction
respectively. This identification allows us to map the question of singularity
resolution to the dual gauge theory. | hep-th |
Entanglement between two disjoint universes: We use the replica method to compute the entanglement entropy of a universe
without gravity entangled in a thermofield-double-like state with a disjoint
gravitating universe. Including wormholes between replicas of the latter gives
an entropy functional which includes an "island" on the gravitating universe.
We solve the back-reaction equations when the cosmological constant is negative
to show that this island coincides with a causal shadow region that is created
by the entanglement in the gravitating geometry. At high entanglement
temperatures, the island contribution to the entropy functional leads to a
bound on entanglement entropy, analogous to the Page behavior of evaporating
black holes. We demonstrate that the entanglement wedge of the non-gravitating
universe grows with the entanglement temperature until, eventually, the
gravitating universe can be entirely reconstructed from the non-gravitating
one. | hep-th |
Charged Rotating Black Holes in Five Dimensional U(1)^3 Gauged N=2
Supergravity: We obtain the general solution for non-extremal 3-charge dilatonic rotating
black holes in the U(1)^3 gauged five-dimensional N=2 supergravity coupled to
two vector multiplets, in the case where the two rotation parameters are set
equal. These solutions encompass all the previously-known extremal solutions,
and, by setting the three charges equal, the recently-obtained non-extremal
solutions of N=2 gauged five-dimensional pure supergravity. | hep-th |
A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on
$S^4$: We consider a non-supersymmetric domain-wall version of $\mathcal{N} = 4$ SYM
theory where five out of the six scalar fields have non-zero classical values
on one side of a wall of codimension one. The classical fields have commutators
which constitute an irreducible representation of the Lie algebra
$\mathfrak{so}(5)$ leading to a highly non-trivial mixing between color and
flavor components of the quantum fields. Making use of fuzzy spherical
harmonics on $S^4$, we explicitly solve the mixing problem and derive not only
the spectrum of excitations at the quantum level but also the propagators of
the original fields needed for perturbative quantum computations. As an
application, we derive the one-loop one-point function of a chiral primary and
find complete agreement with a supergravity prediction of the same quantity in
a double-scaling limit which involves a limit of large instanton number in the
dual D3-D7 probe-brane setup. | hep-th |
Mass, Entropy and Holography in Asymptotically de Sitter Spaces: We propose a novel prescription for computing the boundary stress tensor and
charges of asymptotically de Sitter (dS) spacetimes from data at early or late
time infinity. If there is a holographic dual to dS spaces, defined analogously
to the AdS/CFT correspondence, our methods compute the (Euclidean) stress
tensor of the dual. We compute the masses of Schwarzschild-de Sitter black
holes in four and five dimensions, and the masses and angular momenta of
Kerr-de Sitter spaces in three dimensions. All these spaces are less massive
than de Sitter, a fact which we use to qualitatively and quantitatively relate
de Sitter entropy to the degeneracy of possible dual field theories. Our
results in general dimension lead to a conjecture: Any asymptotically de Sitter
spacetime with mass greater than de Sitter has a cosmological singularity.
Finally, if a dual to de Sitter exists, the trace of our stress tensor computes
the RG equation of the dual field theory. Cosmological time evolution
corresponds to RG evolution in the dual. The RG evolution of the c function is
then related to changes in accessible degrees of freedom in an expanding
universe. | hep-th |
Boundary form factors in the Smirnov--Fateev model with a diagonal
boundary $S$ matrix: The boundary conditions with diagonal boundary $S$ matrix and the boundary
form factors for the Smirnov--Fateev model on a half line has been considered
in the framework of the free field representation. In contrast to the case of
the sine-Gordon model, in this case the free field representation is shown to
impose severe restrictions on the boundary $S$ matrix, so that a finite number
of solutions is only consistent with the free field realization. | hep-th |
One-loop corrections in Maxwell-metric-affine bumblebee gravity: In this paper, we consider the coupling of the metric-affine bumblebee
gravity to the Abelian gauge field and obtain the effective model corresponding
to the weak gravity limit of this theory. The effective bumblebee theory
displays new unconventional couplings between the bumblebee field and its field
strength, and the $U(1)$ gauge field along with its respective field strength,
as a result of the non-metricity effects. Thus, being a new gauge-bumblebee
theory, it represents an example of vector-vector couplings which are very
rarely considered, if not entirely overlooked, in the Abelian case. For this
theory we calculate the lower perturbative corrections. We close the paper with
discussions of other possible vector-vector couplings. | hep-th |
$\mathcal{N}=2$ consistent truncations from wrapped M5-branes: We discuss consistent truncations of eleven-dimensional supergravity on a
six-dimensional manifold $M$, preserving minimal $\mathcal{N}=2$ supersymmetry
in five dimensions. These are based on $G_S \subseteq USp(6)$ structures for
the generalised $E_{6(6)}$ tangent bundle on $M$, such that the intrinsic
torsion is a constant $G_S$ singlet. We spell out the algorithm defining the
full bosonic truncation ansatz and then apply this formalism to consistent
truncations that contain warped AdS$_5 \times_{\rm w}M$ solutions arising from
M5-branes wrapped on a Riemann surface. The generalised $U(1)$ structure
associated with the $\mathcal{N}=2$ solution of Maldacena-Nu\~nez leads to
five-dimensional supergravity with four vector multiplets, one hypermultiplet
and $SO(3)\times U(1)\times \mathbb{R}$ gauge group. The generalised structure
associated with "BBBW" solutions yields two vector multiplets, one
hypermultiplet and an abelian gauging. We argue that these are the most general
consistent truncations on such backgrounds. | hep-th |
Holographic Formulation of Quantum Supergravity: We show that ${\cal N}=1$ supergravity with a cosmological constant can be
expressed as constrained topological field theory based on the supergroup
$Osp(1|4)$. The theory is then extended to include timelike boundaries with
finite spatial area. Consistent boundary conditions are found which induce a
boundary theory based on a supersymmetric Chern-Simons theory. The boundary
state space is constructed from states of the boundary supersymmetric
Chern-Simons theory on the punctured two sphere and naturally satisfies the
Bekenstein bound, where area is measured by the area operator of quantum
supergravity. | hep-th |
The c and a-theorems and the Local Renormalisation Group: The Zamolodchikov c-theorem has led to important new insights in our
understanding of the renormalisation group and the geometry of the space of
QFTs. Here, we review the parallel developments of the search for a
higher-dimensional generalisation of the c-theorem and of the Local
Renormalisation Group.
The idea of renormalisation with position-dependent couplings, running under
local Weyl scaling, is traced from its early realisations to the elegant modern
formalism of the local renormalisation group. The key role of the associated
Weyl consistency conditions in establishing RG flow equations for the
coefficients of the trace anomaly in curved spacetime, and their relation to
the c-theorem and four-dimensional a-theorem, is explained in detail.
A number of different derivations of the c-theorem in two dimensions are
presented -- using spectral functions, RG analysis of Green functions of the
energy-momentum tensor T_{mu nu}, and dispersion relations -- and are
generalised to four dimensions. The obstruction to establishing monotonic
C-functions related to the beta_c and beta_b trace anomaly coefficients in four
dimensions is discussed. The possibility of deriving an a-theorem, involving
the coefficient beta_a of the Euler-Gauss-Bonnet density in the trace anomaly,
is explored initially by formulating the QFT on maximally symmetric spaces.
Then the formulation of the weak a-theorem using a dispersion relation for
four-point functions of T^mu_mu is presented.
Finally, we describe the application of the local renormalisation group to
the issue of limit cycles in theories with a global symmetry and it is shown
how this sheds new light on the geometry of the space of couplings in QFT. | hep-th |
't Hooft lines of ADE-type and Topological Quivers: We investigate 4D Chern-Simons theory with ADE gauge symmetries in the
presence of interacting Wilson and 't Hooft line defects. We analyse the
intrinsic properties of these lines' coupling and explicate the building of
oscillator-type Lax matrices verifying the RLL integrability equation. We
propose gauge quiver diagrams Q$_{G}^{\mu }$ encoding the topological data
carried by the Lax operators and give several examples where Darboux
coordinates are interpreted in terms of topological bi-fundamental matter. We
exploit this graphical description $\left( i\right) $ to give new results
regarding solutions in representations beyond the fundamentals of $sl_{N}$, $%
so_{2N}$ and $e_{6,7}$, and $\left( ii\right) $ to classify the Lax operators
for simply laced symmetries in a unified E$_{7}$ CS theory. For quick access, a
summary list of the leading topological quivers Q$% _{ADE}^{\mu }$ is given in
the conclusion section [Figures 29.(a-e), 30.(a-d) and 31.(a-d)]. | hep-th |
Chiral Four-Dimensional Heterotic Covariant Lattices: In the covariant lattice formalism, chiral four-dimensional heterotic string
vacua are obtained from certain even self-dual lattices which completely
decompose into a left-mover and a right-mover lattice. The main purpose of this
work is to classify all right-mover lattices that can appear in such a chiral
model, and to study the corresponding left-mover lattices using the theory of
lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is
employed to calculate a lower bound on the number of left-mover lattices. Also,
the known relationship between asymmetric orbifolds and covariant lattices is
considered in the context of our classification. | hep-th |
Evaluating Feynman Integrals Using D-modules and Tropical Geometry: Feynman integrals play a central role in the modern scattering amplitudes
research program. Advancing our methods for evaluating Feynman integrals will,
therefore, strengthen our ability to compare theoretical predictions with data
from particle accelerators such as the Large Hadron Collider. Motivated by
this, the present manuscript purports to study mathematical concepts related to
Feynman integrals. In particular, we present both numerical and analytical
algorithms for the evaluation of Feynman integrals.
The content is divided into three parts. Part I focuses on the method of DEQs
for evaluating Feynman integrals. An otherwise daunting integral expression is
thereby traded for the comparatively simpler task of solving a system of DEQs.
We use this technique to evaluate a family of two-loop Feynman integrals of
relevance for dark matter detection. Part II situates the study of DEQs for
Feynman integrals within the framework of D-modules, a natural language for
studying PDEs algebraically. Special emphasis is put on a particular D-module
called the GKZ system, a set of higher-order PDEs that annihilate a generalized
version of a Feynman integral. In the course of matching the generalized
integral to a Feynman integral proper, we discover an algorithm for evaluating
the latter in terms of logarithmic series. Part III develops a numerical
integration algorithm. It combines Monte Carlo sampling with tropical geometry,
a particular offspring of algebraic geometry that studies "piecewise-linear"
polynomials. Feynman's i*epsilon-prescription is incorporated into the
algorithm via contour deformation. We present an open-source program named
Feyntrop that implements this algorithm, and use it to numerically evaluate
Feynman integrals between 1-5 loops and 0-5 legs in physical regions of phase
space. | hep-th |
A note on the infinite-dimensional symmetries of classical hamiltonian
systems: We show that any Hamiltonian system with one degree of freedom is invariant
under a $w_\infty$ algebra of symmetries. | hep-th |
Chiral Anomaly in Euler Fluid and Beltrami Flow: We show that the chiral anomaly of quantum field theories with Dirac fermions
subject to an axial background field is an inherent property of kinematics of a
perfect classical fluid. Celebrated Beltrami flows (stationary solutions of
Euler equations with extensive helicity) exhibit the chiral anomaly equivalent
to that known for Dirac fermions. A prominent effect of the chiral anomaly is
the transport electric current at equilibrium. We show that it is also a
property of Beltrami flows. | hep-th |
High spin baryon in hot strongly coupled plasma: We consider a strings-junction holographic model of probe baryon in the
finite-temperature supersymmetric Yang-Mills dual of the AdS-Schwarzschild
black hole background. In particular, we investigate the screening length for
high spin baryon composed of rotating N_c heavy quarks. To rotate quarks by
finite force, we put hard infrared cutoff in the bulk and give quarks finite
mass. We find that N_c microscopic strings are embedded reasonably in the bulk
geometry when they have finite angular velocity \omega, similar to the meson
case. By defining the screening length as the critical separation of quarks, we
compute the \omega dependence of the baryon screening length numerically and
obtain a reasonable result which shows that baryons with high spin dissociate
more easily. Finally, we discuss the relation between J and E^2 for baryons. | hep-th |
Quantization of models with non-compact quantum group symmetry. Modular
XXZ magnet and lattice sinh-Gordon model: We define and study certain integrable lattice models with non-compact
quantum group symmetry (the modular double of U_q(sl_2)) including an
integrable lattice regularization of the sinh-Gordon model and a non-compact
version of the XXZ model. Their fundamental R-matrices are constructed in terms
of the non-compact quantum dilogarithm. Our choice of the quantum group
representations naturally ensures self-adjointness of the Hamiltonian and the
higher integrals of motion. These models are studied with the help of the
separation of variables method. We show that the spectral problem for the
integrals of motion can be reformulated as the problem to determine a subset
among the solutions to certain finite difference equations (Baxter equation and
quantum Wronskian equation) which is characterized by suitable analytic and
asymptotic properties. A key technical tool is the so-called Q-operator, for
which we give an explicit construction. Our results allow us to establish some
connections to related results and conjectures on the sinh-Gordon theory in
continuous space-time. Our approach also sheds some light on the relations
between massive and massless models (in particular, the sinh-Gordon and
Liouville theories) from the point of view of their integrable structures. | hep-th |
All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied
Symbology: Recent progress on scattering amplitudes has benefited from the mathematical
technology of symbols for efficiently handling the types of polylogarithm
functions which frequently appear in multi-loop computations. The symbol for
all two-loop MHV amplitudes in planar SYM theory is known, but explicit
analytic formulas for the amplitudes are hard to come by except in special
limits where things simplify, such as multi-Regge kinematics. By applying
symbology we obtain a formula for the leading behavior of the imaginary part
(the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics
for any number of gluons. Our result predicts a simple recursive structure
which agrees with a direct BFKL computation carried out in a parallel
publication. | hep-th |
Superconnection in the spin factor approach to particle physics: The notion of superconnection devised by Quillen in 1985 and used in
gauge-Higgs field theory in the 1990's is applied to the spin factors
(finite-dimensional euclidean Jordan algebras) recently considered as
representing the finite quantum geometry of one generation of fermions in the
Standard Model of particle physics. | hep-th |
Algebraic Geometry Approach in Theories with Extra Dimensions I.
Application of Lobachevsky Geometry: This present paper has the purpose to find certain physical appications of
Lobachevsky geometry and of the algebraic geometry approach in theories with
extra dimensions. It has been shown how the periodic properties of the
uniformization functions-solutions of cubic algebraic equations in gravity
theory enable the orbifold periodic identification of the points pr{c} and
-pr{c} under compactification. It has been speculated that corrections to the
extradimensional volume in theories with extra dimensions should be taken into
account due to the non-euclidean nature of the Lobachevsky space. It has been
demonstrated that in the Higgs mass generation model with two branes (a
"hidden" and a "visible" one), to any mass on the visible brane there could
correspond a number of physical masses. Algebraic equations for 4D
Schwarzschild Black Holes in higher dimensional brane worlds have been
obtained. | hep-th |
Aspects of superconformal field theories in six dimensions: We introduce the analytic superspace formalism for six-dimensional $(N,0)$
superconformal field theories. Concentrating on the $(2,0)$ theory we write
down the Ward identities for correlation functions in the theory and show how
to solve them. We then consider the four-point function of four energy momentum
multiplets in detail, explicitly solving the Ward identities in this case. We
expand the four-point function using both Schur polynomials, which lead to a
simple formula in terms of a single function of two variables, and (a
supersymmetric generalisation of) Jack polynomials, which allow a conformal
partial wave expansion. We then perform a complete conformal partial wave
analysis of both the free theory four-point function and the AdS dual
four-point function. We also discuss certain operators at the threshold of the
series a) unitary bound, and prove that some such operators may not develop
anomalous dimensions, by finding selection rules for certain three-point
functions. For those operators which are not protected, we find representations
with which they may combine to become long. | hep-th |
Summability of Superstring Theory: Several arguments are given for the summability of the superstring
perturbation series. Whereas the Schottky group coordinatization of moduli
space may be used to provide refined estimates of large-order bosonic string
amplitudes, the super-Schottky group variables define a measure for the
supermoduli space integral which leads to upper bounds on superstring
scattering amplitudes. | hep-th |
No-dipole-hair theorem for higher-dimensional static black holes: We prove that static black holes in n-dimensional asymptotically flat
spacetime cannot support non-trivial electric p-form field strengths when
(n+1)/2<= p <= n-1. This implies in particular that static black holes cannot
possess dipole hair under these fields. | hep-th |
Solvable limit of ETH matrix model for double-scaled SYK: We study the two-matrix model for double-scaled SYK model, called ETH matrix
model introduced by Jafferis et al [arXiv:2209.02131]. If we set the parameters
$q_A,q_B$ of this model to zero, the potential of this two-matrix model is
given by the Gaussian terms and the $q$-commutator squared interaction. We find
that this model is solvable in the large $N$ limit and we explicitly construct
the planar one- and two-point function of resolvents in terms of elliptic
functions. | hep-th |
An Attempt to Remove Quadratic Divergences in the Standard Theory: The quadratic divergences caused by Yukawa interactions in the standard
theory of elementary particle physics is shown to be removed by introducing
finite-mass complex-ghost regulator fields. In this modification of the
standard theory, its manifest covariance, renormalizability, gauge invariance
and unitarity are retained, and no new observable particles are introduced. | hep-th |
Orientifold Planes, Type I Wilson Lines and Non-BPS D-branes: There is a longstanding puzzle concerned with the existence of Op~-planes
with p>=6, which are orientifold p-planes of negative charge with stuck
Dp-branes. We study the consistency of configurations with various orientifold
planes and propose a resolution to this puzzle. It is argued that O6~-planes
are possible in massive IIA theory with odd cosmological constant, while
O7~-planes and O8~-planes are not allowed. Various relations between
orientifold planes and non-BPS D-branes are also addressed. | hep-th |
2d (0,2) Quiver Gauge Theories and D-Branes: We initiate a systematic study of 2d (0,2) quiver gauge theories on the
worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present
an algorithm for efficiently calculating the classical mesonic moduli spaces of
these theories, which correspond to the probed geometries. We also introduce a
systematic procedure for constructing the gauge theories for arbitrary toric
singularities by means of partial resolution, which translates to higgsing in
the field theory. Finally, we introduce Brane Brick Models, a novel class of
brane configurations that consist of D4-branes suspended from an NS5-brane
wrapping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are
the 2d analogues of Brane Tilings and allow a direct connection between
geometry and gauge theory. | hep-th |
Scale Vs. Conformal Invariance in the AdS/CFT Correspondence: We present two examples of non-trivial field theories which are scale
invariant, but not conformally invariant. This is done by placing certain field
theories, which are conformally invariant in flat space, onto curved
backgrounds of a specific type. We define this using the AdS/CFT
correspondence, which relates the physics of gravity in asymptotically Anti-de
Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one
dimension fewer. The AdS rotating (Kerr) black holes in five and seven
dimensions provide us with the examples, since by the correspondence we are
able to define and compute the action and stress tensor of four and six
dimensional field theories residing on rotating Einstein universes, using the
``boundary counterterm'' method. The rotation breaks conformal but not scale
invariance. The AdS/CFT framework is therefore a natural arena for generating
such examples of non-trivial scale invariant theories which are not conformally
invariant. | hep-th |
New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to
Separation of Variables: The supersymmetric intertwining relations with second order supercharges
allow to investigate new two-dimensional model which is not amenable to
standard separation of variables. The corresponding potential being the
two-dimensional generalization of well known one-dimensional P\"oschl-Teller
model is proven to be exactly solvable for arbitrary integer value of parameter
$p:$ all its bound state energy eigenvalues are found analytically, and the
algorithm for analytical calculation of all wave functions is given. The shape
invariance of the model and its integrability are of essential importance to
obtain these results. | hep-th |
Possible Lorentz symmetry violation from broken Weyl invariance: In this work, we investigate a theory of linear Weyl gravity coupled to a
scalar field and study the scenario in which Lorentz symmetry is broken by a
non-vanishing vacuum expectation value of the Weyl field in the flat space
limit after Weyl symmetry breaking. We show that a $CPT$-odd Lorentz-violating
interaction is generated after symmetry breaking. Features of different
symmetry-broken phases and their dependence on the spacetime character of the
generated Lorentz-violating background are discussed. Also, we analyze the
naturalness of the theory by showing that the light mass scale is protected
from large radiative corrections due to an enhanced spacetime symmetry. | hep-th |
Soldering Chiralities II: Non-Abelian Case: We study the non-abelian extension of the soldering process of two chiral WZW
models of opposite chiralities, resulting in a (non-chiral) WZW model living in
a 2D space-time with non trivial Riemanian curvature. | hep-th |
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