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Causality Constraints in Conformal Field Theory: Causality places nontrivial constraints on QFT in Lorentzian signature, for
example fixing the signs of certain terms in the low energy Lagrangian. In
d-dimensional conformal field theory, we show how such constraints are encoded
in crossing symmetry of Euclidean correlators, and derive analogous constraints
directly from the conformal bootstrap (analytically). The bootstrap setup is a
Lorentzian four-point function corresponding to propagation through a
shockwave. Crossing symmetry fixes the signs of certain log terms that appear
in the conformal block expansion, which constrains the interactions of
low-lying operators. As an application, we use the bootstrap to rederive the
well known sign constraint on the $(\partial\phi)^4$ coupling in effective
field theory, from a dual CFT. We also find constraints on theories with higher
spin conserved currents. Our analysis is restricted to scalar correlators, but
we argue that similar methods should also impose nontrivial constraints on the
interactions of spinning operators.
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Trefoil Solitons, Elementary Fermions, and SU_q(2): By utilizing the gauge invariance of the SU_q(2) algebra we sharpen the basis
of the q-knot phenomenology.
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Chains of topological oscillators with instantons and calculable
topological observables in topological quantum mechanics: We extend to a possibly infinite chain the conformally invariant mechanical
system that was introduced earlier as a toy model for understanding the
topological Yang-Mills theory. It gives a topological quantum model that has
interesting and computable zero modes and topological invariants. It confirms
the recent conjecture by several authors that supersymmetric quantum mechanics
may provide useful tools for understanding robotic mechanical systems (Vitelli
et al.) and condensed matter properties (Kane et al.), where trajectories of
effective models are allowed or not by the conservation of topological indices.
The absences of ground state and mass gaps are special features of such
systems.
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$T\bar{T}$ deformed YM$_{2}$ on general backgrounds from an integral
transformation: We consider the $T\bar{T}$ deformation of two dimensional Yang--Mills theory
on general curved backgrounds. We compute the deformed partition function
through an integral transformation over frame fields weighted by a Gaussian
kernel. We show that this partition function satisfies a flow equation which
has been derived previously in the literature, which now holds on general
backgrounds. We connect ambiguities associated to first derivative terms in the
flow equation to the normalization of the functional integral over frame
fields. We then compute the entanglement entropy for a general state in the
theory. The connection to the string theoretic description of the theory is
also investigated.
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String Dualities and Toric Geometry: An Introduction: This note is supposed to be an introduction to those concepts of toric
geometry that are necessary to understand applications in the context of string
and F-theory dualities. The presentation is based on the definition of a toric
variety in terms of homogeneous coordinates, stressing the analogy with
weighted projective spaces. We try to give both intuitive pictures and precise
rules that should enable the reader to work with the concepts presented here.
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Black String Solutions with arbitrary Tension: We consider 1+4 dimensional black string solutions which are invariant under
translation along the fifth direction. The solutions are characterized by the
two parameters, mass and tension, of the source. The Gregory-Laflamme solution
is shown to be characterized by the tension whose magnitude is one half of the
mass per unit length of the source. The general black string solution with
arbitrary tension is presented and its properties are discussed.
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Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de
Sitter space: We consider critical gravity as van Dam-Vletman-Zakharov (vDVZ) discontinuity
in anti de Sitter space. For this purpose, we introduce the higher curvature
gravity. This discontinuity can be confirmed by calculating the residues of
relevant poles explicitly. For the non-critical gravity of
$0<m_2^2<-2\Lambda/3$, the scalar residue of a massive pole is given by 2/3
when taking the $\Lambda \to 0$ limit first and then the $m^2_2 \to 0$ limit.
This indicates that the vDVZ discontinuity occurs in the higher curvature
theory, showing that propagating degrees of freedom is decreased from 5 to 3.
However, at the critical point of $m^2_2=-2\Lambda/3$, the tensor residue of a
massive pole blows up and scalar residue is -5/36, showing the unpromising
feature of the critical gravity.
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Geometric tool kit for higher spin gravity (part II): An introduction to
Lie algebroids and their enveloping algebras: These notes provide a self-contained introduction to Lie algebroids,
Lie-Rinehart algebras and their universal envelopes. This review is motivated
by the speculation that higher-spin gauge symmetries should admit a natural
formulation as enveloping algebras of Lie algebroids since rigid higher-spin
algebras are enveloping algebras of Lie algebras. Nevertheless, the material
covered here may be of general interest to anyone interested in the description
of gauge symmetries, connections and covariant derivatives, in terms of Lie
algebroids. In order to be self-contained, a concise introduction to the
algebraic characterisation of vector bundles as projective modules over the
algebra of functions on the base manifold is provided.
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Momentum-space formulae for AdS correlators for diverse theories in
diverse dimensions: In this paper, we explore correlators of a series of theories in anti-de
Sitter space: we present comprehensive results for interactions involving
scalars, gluons, and gravitons in multiple dimensions. One aspect of our
investigation is the establishment of an intriguing connection between the
kinematic factors of these theories; indeed, such a connection directly relates
these theories among themselves and with other theories of higher spin fields.
Besides providing several explicit results throughout the paper, we also
highlight the interconnections and relationships between these different
theories, providing valuable insights into their similarities and distinctions.
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Dressed Dirac Propagator from a Locally Supersymmetric ${\cal N}=1$
Spinning Particle: We study the Dirac propagator dressed by an arbitrary number $N$ of photons
by means of a worldline approach, which makes use of a supersymmetric ${\cal N}
= 1$ spinning particle model on the line, coupled to an external Abelian vector
field. We obtain a compact off-shell master formula for the tree level
scattering amplitudes associated to the dressed Dirac propagator. In
particular, unlike in other approaches, we express the particle fermionic
degrees of freedom using a coherent state basis, and consider the gauging of
the supersymmetry, which ultimately amounts to integrating over a worldline
gravitino modulus, other than the usual worldline einbein modulus which
corresponds to the Schwinger time integral. The path integral over the
gravitino reproduces the numerator of the dressed Dirac propagator.
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Full Unitarity and the Moments of Scattering Amplitudes: We study the impact of full unitarity on the moment structure of forward
scattering amplitudes. We introduce the semiarcs, calculable quantities in the
EFT dispersively related to both real and imaginary parts of the UV amplitude
for a fixed number of subtractions. It is observed that large hierarchies
between consecutive moments are forbidden by unitarity. Bounds from full
unitarity compete with the ones stemming from convexity, and become more
important in EFTs where the loop expansion is more important than the
derivative expansion.
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Coset Space Dimensional Reduction of Einstein--Yang--Mills theory: In the present contribution we extend our previous work by considering the
coset space dimensional reduction of higher-dimensional Einstein--Yang--Mills
theories including scalar fluctuations as well as Kaluza--Klein excitations of
the compactification metric and we describe the gravity-modified rules for the
reduction of non-abelian gauge theories.
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Emergent Spacetime and Holographic CFTs: We discuss universal properties of conformal field theories with holographic
duals. A central feature of these theories is the existence of a low-lying
sector of operators whose correlators factorize. We demonstrate that
factorization can only hold in the large central charge limit. Using conformal
invariance and factorization we argue that these operators are naturally
represented as fields in AdS as this makes the underlying linearity of the
system manifest. In this class of CFTs the solution of the conformal bootstrap
conditions can be naturally organized in structures which coincide with Witten
diagrams in the bulk. The large value of the central charge suggests that the
theory must include a large number of new operators not captured by the
factorized sector. Consequently we may think of the AdS hologram as an
effective representation of a small sector of the CFT, which is embedded inside
a much larger Hilbert space corresponding to the black hole microstates.
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7D Randall-Sundrum cosmology, brane-bulk energy exchange and holography: We discuss the cosmological implications and the holographic dual theory of
the 7D Randall-Sundrum (RS) gravitational set-up. Adding generic matter in the
bulk on the 7D gravity side we study the cosmological evolution inferred by the
non vanishing value of the brane-bulk energy exchange parameter. This analysis
is achieved in detail for specific assumptions on the internal space evolution,
including analytical considerations and numerical results. The dual theory is
then constructed, making use of the holographic renormalization procedure. The
resulting renormalized 6D CFT is anomalous and coupled to 6D gravity plus
higher order corrections. The critical point analysis on the brane is
performed. Finally, we sketch a comparison between the two dual descriptions.
We moreover generalize the AdS/CFT dual theory to the non conformal and
interacting case, relating the energy exchange parameter of the bulk gravity
description to the new interactions between hidden and visible sectors.
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Quantum K-Theory of Calabi-Yau Manifolds: The disk partition function of certain 3d N=2 supersymmetric gauge theories
computes a quantum K-theoretic ring for Kahler manifolds X. We study the 3d
gauge theory/quantum K-theory correspondence for global and local Calabi-Yau
manifolds with several Kahler moduli. We propose a multi-cover formula that
relates the 3d BPS world-volume degeneracies computed by quantum K-theory to
Gopakumar-Vafa invariants.
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Chiral formulation for hyperkaehler sigma-models on cotangent bundles of
symmetric spaces: Starting with the projective-superspace off-shell formulation for
four-dimensional N = 2 supersymmetric sigma-models on cotangent bundles of
arbitrary Hermitian symmetric spaces, their on-shell description in terms of N
= 1 chiral superfields is developed. In particular, we derive a universal
representation for the hyperkaehler potential in terms of the curvature of the
symmetric base space. Within the tangent-bundle formulation for such
sigma-models, completed recently in arXiv:0709.2633 and realized in terms of N
= 1 chiral and complex linear superfields, we give a new universal formula for
the superspace Lagrangian. A closed form expression is also derived for the
Kaehler potential of an arbitrary Hermitian symmetric space in Kaehler normal
coordinates.
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Four-Point Amplitude from Open Superstring Field Theory: An open superstring field theory action has been proposed which does not
suffer from contact term divergences. In this paper, we compute the on-shell
four-point tree amplitude from this action using the Giddings map. After
including contributions from the quartic term in the action, the resulting
amplitude agrees with the first-quantized prescription.
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Towards the determination of the dimension of the critical surface in
asymptotically safe gravity: We compute the beta functions of Higher Derivative Gravity within the
Functional Renormalization Group approach, going beyond previously studied
approximations. We find that the presence of a nontrivial Newtonian coupling
induces, in addition to the free fixed point of the one-loop approximation,
also two nontrivial fixed points, of which one has the right signs to be free
from tachyons. Our results are consistent with earlier suggestions that the
dimension of the critical surface for pure gravity is three.
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Anomalies and symmetric mass generation for Kaehler-Dirac fermions: We show that massless Kaehler-Dirac (KD) fermions exhibit a mixed
gravitational anomaly involving an exact $U(1)$ symmetry which is unique to KD
fields. Under this $U(1)$ symmetry the partition function transforms by a phase
depending only on the Euler character of the background space. Compactifying
flat space to a sphere we learn that the anomaly vanishes in odd dimensions but
breaks the symmetry down to $Z_4$ in even dimensions. This $Z_4$ is sufficient
to prohibit bilinear terms from arising in the fermionic effective action. Four
fermion terms are allowed but require multiples of two flavors of KD field. In
four dimensional flat space each KD field can be decomposed into four Dirac
spinors and hence these anomaly constraints ensure that eight Dirac fermions
or, for real representations, sixteen Majorana fermions are needed for a
consistent interacting theory. These constraints on fermion number agree with
known results for topological insulators and recent work on discrete anomalies
rooted in the Dai-Freed theorem. Our work suggests that KD fermions may offer
an independent path to understanding these constraints. Finally we point out
that this anomaly survives intact under discretization and hence is relevant in
understanding recent numerical results on lattice models possessing massive
symmetric phases.
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The Standard Model and The Four Dimensional Superstring: Starting from the Nambu-Goto bosonic string, a four dimensional superstring
model is constructed using the equivalence of one boson to two Majorana-Weyl
fermions. The conditions of anomaly cancellation in a 'heterotic' string theory
lead to the correct result and is found to be consistent with the requirements
of the standard model.
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Effective long distance $q\bar{q} $ potential in holographic RG flows: We study the $q\bar{q}$ potential in strongly coupled non-conformal field
theories with a non-trivial renormalization group flow via holography. We focus
on the properties of this potential at an inter-quark separation $L$ large
compared to the characteristic scale of the field theory. These are determined
by the leading order IR physics plus a series of corrections, sensitive to the
properties of the RG-flow. To determine those corrections, we propose a general
method applying holographic Wilsonian renormalization to a dual string. We
apply this method to examine in detail two sets of examples, $3+1$-dimensional
theories with an RG flow ending in an IR fixed point; and theories that are
confining in the IR, in particular, the Witten QCD and Klebanov-Strassler
models. In both cases, we find corrections with a universal dependence on the
inter-quark separation. When there is an IR fixed point, that correction decays
as a power $\sim 1/L^4$. We explain that dependence in terms of a double-trace
deformation in a one-dimensional defect theory. For a confining theory, the
decay is exponential $\sim e^{-ML}$, with $M$ a scale of the order of the
glueball mass. We interpret this correction using an effective flux tube
description as produced by a background internal mode excitation induced by
sources localized at the endpoints of the flux tube. We discuss how these
results could be confronted with lattice QCD data to test whether the
description of confinement via the gauge/gravity is qualitatively correct.
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Non-perturbative tests for the Asymptotic Freedom in the $\mathcal{PT}%
$-symmetric $(-φ^{4})_{3+1}$ theory: In the literature, the asymptotic freedom property of the $(-\phi^{4})$
theory is always concluded from real-line calculations while the theory is
known to be a non-real-line one. In this article, we test the existence of the
asymptotic freedom in the $(-\phi^{4})_{3+1}$ theory using mean field approach.
In this approach and contrary to the original Hamiltonian, the obtained
effective Hamiltonian is rather a real-line one. Accordingly, this work
resembles the first reasonable analysis for the existence of the asymptotic
freedom property in the $\mathcal{PT}$-symmetric $(-\phi^{4})$ theory. In this
respect, we calculated three different amplitudes of different positive
dimensions (in mass units) and find that all of them goes to very small values
at high energy scales (small coupling) in agreement with the spirit of the
asymptotic freedom property of the theory. To test the validity of our
calculations, we obtained the asymptotic behavior of the vacuum condensate in
terms of the coupling, analytically, and found that the controlling factor
$\Lambda$ has the value $\frac{(4 \pi)^{2}}{6}= 26. 319$ compared to the result
$\Lambda=26.3209$ from the literature which was obtained via numerical
predictions. We assert that the non-blow up of the massive quantities at high
energy scales predicted in this work strongly suggests the possibility of the
solution of the famous hierarchy puzzle in a standard model with
$\mathcal{PT}$-symmetric Higgs mechanism.
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Annihilation into Channels with Strangeness and the OZI Rule Violation: Two-step mechanisms in the $N\bar{N}$ annihilation and their role in the OZI
rule violating reactions are discussed. In particular the two meson
rescattering mechanism for $\pi\phi$ channel including all off-shell effects is
typically two orders of magnitude bigger than the OZI tree level expectation
and explains the observed ratio $\phi \pi/\omega \pi$ in the annihilation at
rest. The rates for the final states including photons, $\gamma\omega$ and
$\gamma\phi$, can be explained in the vector dominance model. The observed rate
for $p\bar{p}\to\gamma\omega$ is suppressed due to destructive interference
between the intermediate $\rho$ and $\omega$ states while the interference in
$p\bar{p}\to\gamma\phi$ is required to be constructive leading to a large ratio
$\gamma\phi/\gamma\omega$.
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GAMMA: A Mathematica package for performing gamma-matrix algebra and
Fierz transformations in arbitrary dimensions: We have developed a Mathematica package capable of performing gamma-matrix
algebra in arbitrary (integer) dimensions. As an application we can compute
Fierz transformations.
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String Model Building, Reinforcement Learning and Genetic Algorithms: We investigate reinforcement learning and genetic algorithms in the context
of heterotic Calabi-Yau models with monad bundles. Both methods are found to be
highly efficient in identifying phenomenologically attractive three-family
models, in cases where systematic scans are not feasible. For monads on the
bi-cubic Calabi-Yau either method facilitates a complete search of the
environment and leads to similar sets of previously unknown three-family
models.
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Phase Transitions in Higher Derivative Gravity: This paper deals with black holes, bubbles and orbifolds in Gauss-Bonnet
theory in five dimensional anti de Sitter space. In particular, we study
stable, unstable and metastable phases of black holes from thermodynamical
perspective. By comparing bubble and orbifold geometries, we analyse associated
instabilities. Assuming AdS/CFT correspondence, we discuss the effects of this
higher derivative bulk coupling on a specific matrix model near the critical
points of the boundary gauge theory at finite temperature. Finally, we propose
another phenomenological model on the boundary which mimics various phases of
the bulk space-time.
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Algebraic aspects of when and how a Feynman diagram reduces to simpler
ones: The method of Symmetries of Feynman Integrals defines for any Feynman diagram
a set of partial differential equations. On some locus in parameter space the
equations imply that the diagram can be reduced to a linear combination of
simpler diagrams. This paper provides a systematic method to determine this
locus and the associated reduction through an algebraic method involving
factorization of maximal minors.
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On the fundamental representation of Borcherds algebras with one
imaginary simple root: Borcherds algebras represent a new class of Lie algebras which have almost
all the properties that ordinary Kac-Moody algebras have, and the only major
difference is that these generalized Kac-Moody algebras are allowed to have
imaginary simple roots. The simplest nontrivial examples one can think of are
those where one adds ``by hand'' one imaginary simple root to an ordinary
Kac-Moody algebra. We study the fundamental representation of this class of
examples and prove that an irreducible module is given by the full tensor
algebra over some integrable highest weight module of the underlying Kac-Moody
algebra. We also comment on possible realizations of these Lie algebras in
physics as symmetry algebras in quantum field theory.
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Sigma model of near-extreme rotating black holes and their microstates: Five-dimensional non-extreme rotating black holes with large NS-NS five-brane
and fundamental string charge are shown to be described by a conformal sigma
model, which is a marginal integrable deformation of six-dimensional SL(2,R) x
SU(2) WZW model. The two WZW levels are equal to the five-brane charge, while
the parameters of the two marginal deformations generated by the left and right
chiral SU(2) currents are proportional to the two angular momentum components
of the black hole. The near-horizon description is effectively in terms of a
free fundamental string whose tension is rescaled by the five-brane charge. The
microstates are identified with those of left and right moving superconformal
string oscillations in the four directions transverse to the five-brane. Their
statistical entropy reproduces precisely the Bekenstein-Hawking entropy of the
rotating black hole.
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Schnabl's Solution and Boundary States in Open String Field Theory: We discuss that Schnabl's solution is an off-shell extension of the boundary
state describing a D-brane in the closed string sector. It gives the physical
meaning of the gauge invariant overlaps for the solution in our previous paper
and supports Ellwood's recent proposal in the operator formalism.
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Charged 4D Einstein-Gauss-Bonnet-AdS Black Holes: Shadow, Energy
Emission, Deflection Angle and Heat Engine: Recently, there has been a surge of interest in the 4D Einstein-Gauss-Bonnet
(4D EGB) gravity theory which bypasses the Lovelock theorem and avoids
Ostrogradsky's instability. Such a novel theory has nontrivial dynamics and
presents several predictions for cosmology and black hole physics. Motivated by
recent astrophysical observations and the importance of anti-de Sitter
spacetime, we investigate shadow geometrical shapes and deflection angle of
light from the charged AdS black holes in 4D EGB gravity theory. We explore the
shadow behaviors and photon sphere around such black holes, and inspect the
effect of different parameters on them. Then, we present a study regarding the
energy emission rate of such black holes and analyze the significant role of
the Gauss-Bonnet (GB) coupling constant in the radiation process. Then, we
perform a discussion of holographic heat engines of charged 4D EGB-AdS black
holes by obtaining the efficiency of a rectangular engine cycle. Finally, by
comparing heat engine efficiency with the Carnot efficiency, we indicate that
the ratio $\frac{\eta }{\eta_{c}}$ is always less than one which is consistent
with the thermodynamic second law.
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Yang--Mills sphalerons in all even spacetime dimensions $d=2k$, $k>2$ :
$k$=3,4: The classical solutions to higher dimensional Yang--Mills (YM) systems, which
are integral parts of higher dimensional Einstein--YM (EYM) systems, are
studied. These are the gravity decoupling limits of the fully gravitating EYM
solutions. In odd spacetime dimensions, depending on the choice of gauge group,
these are either topologically stable or unstable. Both cases are analysed, the
latter numerically only. In even spacetime dimensions they are always unstable,
describing saddle points of the energy, and can be described as {\it
sphalerons}. This instability is analysed by constructing the noncontractible
loops and calculating the Chern--Simons (CS) charges, and also perturbatively
by numerically constructing the negative modes. This study is restricted to the
simplest YM system in spacetime dimensions $d=6,7,8$, which is amply
illustrative of the generic case.
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Entanglement entropy of subtracted geometry black holes: We compute the entanglement entropy of minimally coupled scalar fields on
subtracted geometry black hole backgrounds, focusing on the logarithmic
corrections. We notice that matching between the entanglement entropy of
original black holes and their subtracted counterparts is only at the order of
the area term. The logarithmic correction term is not only different but also,
in general, changes sign in the subtracted case. We apply Harrison
transformations to the original black holes and find out the choice of the
Harrison parameters for which the logarithmic corrections vanish.
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On the induced gauge invariant mass: We derive a general expression for the gauge invariant mass (m_G) for an
Abelian gauge field, as induced by vacuum polarization, in 1+1 dimensions. From
its relation to the chiral anomaly, we show that m_G has to satisfy a certain
quantization condition. This quantization can be, on the other hand, explicitly
verified by using the exact general expression for the gauge invariant mass in
terms of the fermion propagator. This result is applied to some explicit
examples, exploring the possibility of having interesting physical situations
where the value of $m_G$ departs from its canonical value. We also study the
possibility of generalizing the results to the 2+1 dimensional case at finite
temperature, showing that there are indeed situations where a finite and
non-vanishing gauge invariant mass is induced.
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Shuffling quantum field theory: We discuss shuffle identities between Feynman graphs using the Hopf algebra
structure of perturbative quantum field theory. For concrete exposition, we
discuss vertex function in massless Yukawa theory.
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N=2 Heterotic-Type II duality and bundle moduli: Heterotic string compactifications on a $K3$ surface $\mathfrak{S}$ depend on
a choice of hyperk\"ahler metric, anti-self-dual gauge connection and
Kalb-Ramond flux, parametrized by hypermultiplet scalars. The metric on
hypermultiplet moduli space is in principle computable within the $(0,2)$
superconformal field theory on the heterotic string worldsheet, although little
is known about it in practice. Using duality with type II strings compactified
on a Calabi-Yau threefold, we predict the form of the quaternion-K\"ahler
metric on hypermultiplet moduli space when $\mathfrak{S}$ is elliptically
fibered, in the limit of a large fiber and even larger base. The result is in
general agreement with expectations from Kaluza-Klein reduction, in particular
the metric has a two-stage fibration structure, where the $B$-field moduli are
fibered over bundle and metric moduli, while bundle moduli are themselves
fibered over metric moduli. A more precise match must await a detailed analysis
of $R^2$-corrected ten-dimensional supergravity.
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Scalar and Vector Massive Fields in Lyra's Manifold: The problem of coupling between spin and torsion is analysed from a Lyra's
manifold background for scalar and vector massive fields using the
Duffin-Kemmer-Petiau (DKP) theory. We found the propagation of the torsion is
dynamical, and the minimal coupling of DKP field corresponds to a non-minimal
coupling in the standard Klein-Gordon-Fock and Proca approaches. The origin of
this difference in the couplings is discussed in terms of equivalence by
surface terms.
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Monopoles in AdS: Applications to holographic theories have led to some recent interest in
magnetic monopoles in four-dimensional Anti-de Sitter spacetime. This paper is
concerned with a study of these monopoles, using both analytic and numerical
methods. An approximation is introduced in which the fields of a charge N
monopole are explicitly given in terms of a degree N rational map. Within this
approximation, it is shown that the minimal energy monopole of charge N has the
same symmetry as the minimal energy Skyrmion with baryon number N in Minkowski
spacetime. Beyond charge two the minimal energy monopole has only a discrete
symmetry, which is often Platonic. The rational map approximation provides an
upper bound on the monopole energy and may be viewed as a smooth non-abelian
refinement of the magnetic bag approximation, to which it reverts under some
additional approximations. The analytic results are supported by numerical
solutions obtained from simulations of the non-abelian field theory. A similar
analysis is performed on the monopole wall that emerges in the large N limit,
to reveal a hexagonal lattice as the minimal energy architecture.
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Short-lived modes from hydrodynamic dispersion relations: We consider the dispersion relation of the shear-diffusion mode in
relativistic hydrodynamics, which we generate to high order as a series in
spatial momentum q for a holographic model. We demonstrate that the
hydrodynamic series can be summed in a way that extends through branch cuts
present in the complex q plane, resulting in the accurate description of
multiple sheets. Each additional sheet corresponds to the dispersion relation
of a different non-hydrodynamic mode. As an example we extract the frequencies
of a pair of oscillatory non-hydrodynamic black hole quasinormal modes from the
hydrodynamic series. The analytic structure of this model points to the
possibility that the complete spectrum of gravitational quasinormal modes may
be accessible from the hydrodynamic derivative expansion.
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PT-symmetric interpretation of double-scaling: The conventional double-scaling limit of an O(N)-symmetric quartic quantum
field theory is inconsistent because the critical coupling constant is
negative. Thus, at the critical coupling the Lagrangian defines a quantum
theory with an upside-down potential whose energy appears to be unbounded
below. Worse yet, the integral representation of the partition function of the
theory does not exist. It is shown that one can avoid these difficulties if one
replaces the original theory by its PT-symmetric analog. For a zero-dimensional
O(N)-symmetric quartic vector model the partition function of the PT-symmetric
analog is calculated explicitly in the double-scaling limit.
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The Bethe Roots of Regge Cuts in Strongly Coupled N=4 SYM Theory: We describe a general algorithm for the computation of the remainder function
for n-gluon scattering in multi-Regge kinematics for strongly coupled planar
N=4 super Yang-Mills theory. This regime is accessible through the infrared
physics of an auxiliary quantum integrable system describing strings in
AdS5xS5. Explicit formulas are presented for n=6 and n=7 external gluons. Our
results are consistent with expectations from perturbative gauge theory. This
paper comprises the technical details for the results announced in
arXiv:1405.3658 .
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Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM: It was recently shown that the string theory duals of certain deformations of
the N=4 gauge theory can be obtained by a combination of T-duality
transformations and coordinate shifts. Here we work out the corresponding
procedure of twisting the dual integrable spin chain and its Bethe ansatz. We
derive the Bethe equations for the complete twisted N=4 gauge theory at one and
higher loops. These have a natural generalization which we identify as twists
involving the Cartan generators of the conformal algebra. The underlying model
appears to be a form of noncommutative deformation of N=4 SYM.
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Photon and Axion Splitting in an Inhomogeneous Magnetic Field: The axion photon system in an external magnetic field, when the direction of
propagation of axions and photons is orthogonal to the direction of the
external magnetic field, displays a continuous axion-photon duality symmetry in
the limit the axion mass is neglected. The conservation law that follow in this
effective 2+1 dimensional theory from this symmetry is obtained. The magnetic
field interaction is seen to be equivalent to first order to the interaction of
a complex charged field with an external electric potential, where this
ficticious "electric potential" is proportional to the external magnetic field.
This allows one to solve for the scattering amplitudes using already known
scalar QED results. From the scalar QED analog the axion and the photon are
symmetric and antisymmetric combinations of particle and antiparticle. If one
considers therefore scattering experiments in which the two spatial dimensions
of the effective theory are involved non trivially, one observes that both
particle and antiparticle components of photons and axions are preferentially
scattered in different directions, thus producing the splitting or
decomposition of the photon and axion into their particle and antiparticle
components in an inhomogeneous magnetic field. This observable in principle
effect is of first order in the axion photon coupling, unlike the "light
shining through a wall phenomena ", which is second order.
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Charged black rings from inverse scattering: The inverse scattering method of Belinsky and Zakharov is a powerful method
to construct solutions of vacuum Einstein equations. In particular, in five
dimensions this method has been successfully applied to construct a large
variety of black hole solutions. Recent applications of this method to
Einstein-Maxwell-dilaton (EMd) theory, for the special case of Kaluza-Klein
dilaton coupling, has led to the construction of the most general black ring in
this theory. In this contribution, we review the inverse scattering method and
its application to the EMd theory. We illustrate the efficiency of these
methods with a detailed construction of an electrically charged black ring.
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On First Order Symmetry Operators for the Field Equations of
Differential Forms: We consider first order symmetry operators for the equations of motion of
differential $p$-form fields in general $D$-dimensional background geometry of
any signature for both massless and massive cases. For $p=1$ and $p=2$ we give
the general forms of the symmetry operators. Then we find a class of symmetry
operators for arbitrary $p$ and $D$, which is naturally suggested by the lower
$p$ results.
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Stringy surprises: There are many conceivable possibilities of embedding the MSSM in string
theory. These proceedings describe an approach which is based on grand
unification in higher dimensions. This allows one to obtain global
string-derived models with the exact MSSM spectrum and built-in gauge coupling
unification. It turns out that these models exhibit various appealing features
such as (i) see-saw suppressed neutrino masses, (ii) an order one top Yukawa
coupling and potentially realistic flavor structures, (iii) non-Abelian
discrete flavor symmetries relaxing the supersymmetric flavor problem, (iv) a
hidden sector whose scale of strong dynamics is consistent with TeV-scale soft
masses, and (v) a solution to the mu-problem. The crucial and unexpected
property of these features is that they are not put in by hand nor explicitly
searched for but happen to occur automatically, and might thus be viewed as
"stringy surprises".
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q-Functional Field Theory for particles with exotic statistics: In the paper we give consecutive description of functional methods of quantum
field theory for systems of interacting q-particles. These particles obey
exotic statistics and appear in many problems of condensed matter physics,
magnetism and quantum optics. Motivated by the general ideas of standard field
theory we derive formulae in q-functional derivatives for the partition
function and Green's functions generating functional for systems of exotic
particles. This leads to a corresponding perturbation series and a diagram
technique. Results are illustrated by a consideration of an one-dimensional
q-particle system and compared with some exact expressions obtained earlier.
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Branes and Calibrated Geometries: The fivebrane worldvolume theory in eleven dimensions is known to contain BPS
threebrane solitons which can also be interpreted as a fivebrane whose
worldvolume is wrapped around a Riemann surface. By considering configurations
of intersecting fivebranes and hence intersecting threebrane solitons, we
determine the Bogomol'nyi equations for more general BPS configurations. We
obtain differential equations, generalising Cauchy-Riemann equations, which
imply that the worldvolume of the fivebrane is wrapped around a calibrated
geometry.
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NSR superstring measures in genus 5: Currently there are two proposed ansatze for NSR superstring measures: the
Grushevsky ansatz and the OPSMY ansatz, which for genera g<=4 are known to
coincide. However, neither the Grushevsky nor the OPSMY ansatz leads to a
vanishing two point function in genus four, which can be constructed from the
genus five expressions for the respective ansatze. This is inconsistent with
the known properties of superstring amplitudes.
In the present paper we show that the Grushevsky and OPSMY ansatze do not
coincide in genus five. Then, by combining these ansatze, we propose a new
ansatz for genus five, which now leads to a vanishing two-point function in
genus four. We also show that one cannot construct an ansatz from the currently
known forms in genus 6 that satisfies all known requirements for superstring
measures.
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A Note on the BPS Spectrum of the Matrix Model: We calculate, using noncommutative supersymmetric Yang-Mills gauge theory,
the part of the spectrum of the toroidally compactified Matrix theory which
corresponds to quantized electric fluxes.
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Reconstructing the universe history, from inflation to acceleration,
with phantom and canonical scalar fields: We consider the reconstruction technique in theories with a single or
multiple (phantom and/or canonical) scalar fields. With the help of several
examples, it is demonstrated explicitly that the universe expansion history,
unifying early-time inflation and late-time acceleration, can be realized in
scalar-tensor gravity. This is generalized to the theory of a scalar field
coupled non-minimally to the curvature and to a Brans-Dicke-like theory.
Different examples of unification of inflation with cosmic acceleration, in
which de Sitter, phantom, and quintessence type fields play the fundamental
role--in different combinations--are worked out. Specifically, the frame
dependence and stability properties of de Sitter space scalar field theory are
studied. Finally, for two-scalar theories, the late-time acceleration and
early-time inflation epochs are successfully reconstructed, in realistic
situations in which the more and more stringent observational bounds are
satisfied, using the freedom of choice of the scalar field potential, and of
the kinetic factor.
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Superresonance effect from a rotating acoustic black hole and Lorentz
symmetry breaking: We investigate the possibility of the acoustic superresonance phenomenon
(analog to the superradiance in black hole physics), i.e., the amplification of
a sound wave by reflection from the ergoregion of a rotating acoustic black
hole with Lorentz symmetry breaking. For rotating black holes the effect of
superradiance corresponds to the situation where the incident waves has
reflection coefficient greater than one, and energy is extracted from them. For
an acoustic Kerr-like black hole its rate of loss of mass is affected by the
Lorentz symmetry breaking. We also have shown that for suitable values of the
Lorentz violating parameter a wider spectrum of particle wave function can be
scattered with increased amplitude by the acoustic black hole.
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Revisiting 3D Flat Holography: Causality Structure and Modular flow: Flat space holography is an open and hard problem existing several different
approaches, which may finally turn out to be consistent with each other, in the
literature to tackle it. Focusing on how bulk emergent spacetime is encoded in
quantum information of null boundaries, we choose a specific toy model called
the flat$_3$/BMSFT model, which conjectures the duality between boundary
BMS$_3$ invariant field theory and bulk quantum gravity in 3D asymptotic flat
spacetimes (AFS), to explore. Aiming to find an entanglement wedge like
quantity for single interval and a connected entanglement wedge for
multi-intervals in flat$_3$/BMSFT model, we explore the bulk causality
structures related to the holographic swing surface proposal through both
boundary and bulk local modular flow, make a corresponding decomposition of the
global Minkowski spacetime and look at the entanglement phase transition. As a
byproduct, we solve the problem about the existence of partial entanglement
entropy (PEE) correspondence in this model which is a bit nontrivial due to the
unusual behavior of boundary modular flow in BMS$_3$ field theory. Among the
literature considering quantum information aspects of flat$_3$/BMSFT model,
there are several substantial, unusual but overlooked phenomena which need to
be emphasized and revisited to gain more deserved attention. Thus another
motivation of this paper is to find where these unusual phenomena come from,
and physically show in a manifest way what they may imply. After reading we
hope readers can feel sincerely what we present about the above mentioned
second aim is more valuable than the mathematical results in the present paper.
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Non-linear integral equations in {\cal {N}}=4 SYM: We survey and discuss the applications of the non-linear integral equation in
the framework of the Bethe Ansatz type equations which are conjectured to give
the eigenvalues of the dilatation operator in ${\cal {N}}=4$ SYM. Moreover, an
original idea (different from that of \cite {FMQR}) to derive a non-linear
integral equation is briefly depicted in Section 4.
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Exact solutions of higher dimensional black holes: We review exact solutions of black holes in higher dimensions, focusing on
asymptotically flat black hole solutions and Kaluza-Klein type black hole
solutions. We also summarize some properties which such black hole solutions
reveal.
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Instanton Counting and Chern-Simons Theory: The instanton partition function of N=2, D=4 SU(2) gauge theory is obtained
by taking the field theory limit of the topological open string partition
function, given by a Chern-Simons theory, of a CY3-fold. The CY3-fold on the
open string side is obtained by geometric transition from local F_0 which is
used in the geometric engineering of the SU(2) theory. The partition function
obtained from the Chern-Simons theory agrees with the closed topological string
partition function of local F_0 proposed recently by Nekrasov. We also obtain
the partition functions for local F_1 and F_2 CY3-folds and show that the
topological string amplitudes of all local Hirzebruch surfaces give rise to the
same field theory limit. It is shown that a generalization of the topological
closed string partition function whose field theory limit is the generalization
of the instanton partition function, proposed by Nekrasov, can be determined
easily from the Chern-Simons theory.
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Trapped Brane Features in DBI Inflation: We consider DBI inflation with a quadratic potential and the effect of
trapped branes on the inflationary fluctuations. When going through a trapped
brane the effective potential of the inflaton receives a contribution whose
effect is to induce a jump in the power spectrum of the inflaton perturbations.
This feature appears in the power spectrum at a scale corresponding to the size
of the sound horizon when the two branes cross each other.
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The Final Model Building for the Supersymmetric Pati-Salam Models from
Intersecting D6-Branes: All the possible three-family ${\cal N}=1$ supersymmetric Pati-Salam models
constructed with intersecting D6-branes from Type IIA orientifolds on
$T^6/(\mathbb{Z}_2\times \mathbb{Z}_2)$ are recently presented in arXiv:
2112.09632. Taking models with largest wrapping number $5$ and approximate
gauge coupling unification at GUT scale as examples, we show string scale gauge
coupling unification can be realized through two-loop renormalization group
equation running by introducing seven pairs of vector-like particles from
${\cal N}=2$ sector. The number of these introduced vector-like particles are
fully determined by the brane intersection numbers while there are two D6-brane
parallel to each other along one two-torus. We expect this will solve the gauge
coupling unification problem in the generic intersecting brane worlds by
introducing vector-like particles that naturally included in the ${\cal N}=2$
sector.
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Axion RG flows and the holographic dynamics of instanton densities: Axionic holographic RG flow solutions are studied in the context of general
Einstein-Axion-Dilaton theories. A non-trivial axion profile is dual to the
(non-perturbative) running of the $\theta$-term for the corresponding instanton
density operator. It is shown that a non-trivial axion solution is incompatible
with a non-trivial (holographic) IR conformal fixed point. Imposing a suitable
axion regularity condition allows to select the IR geometry in a unique way.
The solutions are found analytically in the asymptotic UV and IR regimes, and
it is shown that in those regimes the axion backreaction is always negligible.
The axion backreaction may become important in the intermediate region of the
bulk. To make contact with the axion probe limit solutions, a systematic
expansion of the solution is developed. Several concrete examples are worked
out numerically. It is shown that the regularity condition always implies a
finite allowed range for the axion source parameter in the UV. This translates
into the existence of a finite (but large) number of saddle-points in the large
$N_c$ limit. This ties in well with axion-swampland conjectures.
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Effective Action and Conformal Phase Transition in Three-Dimensional QED: The effective action for local composite operators in $QED_3$ is considered.
The effective potential is calculated in leading order in $1/N_f$ ($N_f$ is the
number of fermion flavors) and used to describe the features of the phase
transition at $N_f=N_{\rm cr}$, $3<N_{\rm cr}<5$. It is shown that this
continuous phase transition satisfies the criteria of the conformal phase
transition, considered recently in the literature. In particular, there is an
abrupt change of the spectrum of light excitations at the critical point,
although the phase transition is continuous, and the structure of the equation
for the divergence of the dilatation current is essentially different in the
symmetric and nonsymmetric phases. The connection of this dynamics with the
dynamics in $QCD_4$ is briefly discussed.
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Supersymmetric Localization in GLSMs for Supermanifolds: In this paper we apply supersymmetric localization to study gauged linear
sigma models (GLSMs) describing supermanifold target spaces. We use the
localization method to show that A-twisted GLSM correlation functions for
certain supermanifolds are equivalent to A-twisted GLSM correlation functions
for hypersurfaces in ordinary spaces under certain conditions. We also argue
that physical two-sphere partition functions are the same for these two types
of target spaces. Therefore, we reproduce the claim of arXiv:hep-th/9404186,
arXiv:hep-th/9506070. Furthermore, we explore elliptic genera and (0,2)
deformations and find similar phenomena.
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Jet Quenching and Holographic Thermalization: We employ the AdS/CFT correspondence to investigate the thermalization of the
strongly-coupled plasma and the jet quenching of a hard probe traversing such a
thermalizing medium.
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Features of ghost-gluon and ghost-quark bound states related to BRST
quartets: The BRST quartet mechanism in infrared Landau gauge QCD is investigated.
Based on the observed positivity violation for transverse gluons $A_{\mathrm
{tr}}$ the field content of the non-perturbative BRST quartet generated by
$A_{\mathrm {tr}}$ is derived. To identify the gluon's BRST-daughter state as
well as the Faddeev-Popov--charge conjugated second parent state, a truncated
Bethe-Salpeter equation for the gluon-ghost bound state in the adjoint colour
representation is derived and studied. This equation is found to be compatible
with the so-called scaling solutions of functional approaches. Repeating the
same construction for quarks instead of $A_{\mathrm {tr}}$ leads in a similar
way to a truncated Bethe-Salpeter equation for the quark-ghost bound state in
the fundamental representation. Within the scaling solution the infrared
divergence of the quark-gluon vertex is exactly the right one to make this
Bethe-Salpeter equation infrared consistent.
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Integrability, Einstein spaces and holographic fluids: Using holographic-fluid techniques, we discuss some aspects of the
integrability properties of Einstein's equations in asymptotically anti-de
Sitter spacetimes. We review and we amend the results of 1506.04813 on how
exact four-dimensional Einstein spacetimes, which are algebraically special
with respect to Petrov's classification, can be reconstructed from boundary
data: this is possible if the boundary metric supports a traceless, symmetric
and conserved complex rank-two tensor, which is related to the boundary Cotton
and energy-momentum tensors, and if the hydrodynamic congruence is shearless.
We illustrate the method when the hydrodynamic congruence has vorticity and the
boundary metric has two commuting isometries. This leads to the complete
Plebanski-Demianski family. The structure of the boundary consistency
conditions depict a U(1) invariance for the boundary data, which is reminiscent
of a Geroch-like solution-generating pattern for the bulk.
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$T\bar{T}$-deformed 2D Yang-Mills at large N: collective field theory
and phase transitions: We consider the $T\bar T$ deformation of 2d large $N$ YM theory on a
cylinder, sphere and disk. The collective field theory Hamiltonian for the
deformed theory is derived and the particular solutions to the equations of
motion of the collective theory are found for the sphere. The account of the
non-perturbative branch of the solution amounts to the first-order phase
transition at the $(A,\tau)$ plane. We analyze the third-order phase transition
in the deformed theory on the disk and derive the critical area as a function
of the boundary holonomy. A kind of Hagedorn behavior in the spectral density
is discussed.
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Black Hole Final State Conspiracies: The principle that unitarity must be preserved in all processes, no matter
how exotic, has led to deep insights into boundary conditions in cosmology and
black hole theory. In the case of black hole evaporation, Horowitz and
Maldacena were led to propose that unitarity preservation can be understood in
terms of a restriction imposed on the wave function at the singularity.
Gottesman and Preskill showed that this natural idea only works if one
postulates the presence of "conspiracies" between systems just inside the event
horizon and states at much later times, near the singularity. We argue that
some AdS black holes have unusual internal thermodynamics, and that this may
permit the required "conspiracies" if real black holes are described by some
kind of sum over all AdS black holes having the same entropy.
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Topological Two Dimensional Dilaton Supergravity: We present a topological version of two dimensional dilaton supergravity. It
is obtained by gauging an extension of the super-Poincar\'e algebra in two
space-time dimensions. This algebra is obtained by an unconventional
contraction of the super de Sitter algebra. Besides the generators of the super
de Sitter algebra it has one more fermionic generator and two more bosonic
generators one of them being a central charge. The gauging of this algebra is
performed in the usual way. Unlike some proposals for a dilaton supergravity
theory we obtain a model which is non-local in the gravitino field.
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Holographic quantization of linearized higher-spin gravity in the de
Sitter causal patch: We study the dS/CFT duality between minimal type-A higher-spin gravity and
the free Sp(2N) vector model. We consider the bulk spacetime as "elliptic" de
Sitter space dS_4/Z_2, in which antipodal points have been identified. We apply
a technique from arXiv:1509.05890, which extracts the quantum-mechanical
commutators (or Poisson brackets) of the linearized bulk theory in an
*observable patch* of dS_4/Z_2 directly from the boundary 2-point function.
Thus, we construct the Lorentzian commutators of the linearized bulk theory
from the Euclidean CFT. In the present paper, we execute this technique for the
entire higher-spin multiplet, using a higher-spin-covariant language, which
provides a promising framework for the future inclusion of bulk interactions.
Aside from its importance for dS/CFT, our construction of a Hamiltonian
structure for a bulk causal region should be of interest within higher-spin
theory itself. The price we pay is a partial symmetry breaking, from the full
dS group (and its higher-spin extension) to the symmetry group of an observable
patch. While the boundary field theory plays a role in our arguments, the
results can be fully expressed within a boundary *particle mechanics*. Bulk
fields arise from this boundary mechanics via a version of second quantization.
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Nonstandard Parafermions and String Compactification: Nonstandard parafermions are built and their central charges and dimensions
are calculated. We then construct new N=2 superconformal field theories by
tensoring the parafermions with a free boson. We study the spectrum and modular
transformations of these theories. Superstring and heterotic strings in four
dimensions are then obtained by tensoring the new superconformal field theories
along with some minimal models. The generations and antigenerations are
studied. We give an example of the $1^2(5,7)$ theory which is shown to have
three net generations.
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Reduction of Dual Theories: In view of the presence of a superpotential, the dual of a gauge theory like
SQCD contains two coupling parameters. The method of the Reduction of Couplings
is used in order to express the parameter of the superpotential in terms of the
dual gauge coupling. In the conformal window and above it, a unique, isolated
solution is obtained. The coupling parameter of the superpotential is given
simply by f times the square of the gauge coupling. Here f is a function of the
the number of colors and the number of flavors, and it is known explicitly. The
solution is valid to all orders in the asymptotic expansion, and it is the
appropriate choice for the dual theory. The same solution exists in the free
magnetic interval. A `general' solution with non-integer powers is discussed,
as are some exceptional cases.
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The Holographic Principle: After a pedagogical overview of the present status of High-Energy Physics,
some problems concerning physics at the Planck scale are formulated, and an
introduction is given to a notion that became known as ``the holographic
principle" in Planck scale physics, which is arrived at by studying quantum
mechanical features of black holes.
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Massive vector particles tunneling from Kerr and Kerr-Newman black holes: In this paper, we investigate the Hawking radiation of massive spin-1
particles from 4-dimensional Kerr and Kerr-Newman black holes. By applying the
Hamilton-Jacobi ansatz and the WKB approximation to the field equations of the
massive bosons in Kerr and Kerr-Newman space-time, the quantum tunneling method
is successfully implemented. As a result, we obtain the tunneling rate of the
emitted vector particles and recover the standard Hawking temperature of both
the two black holes.
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Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM: We study a three-dimensional U(k) Yang-Mills Chern-Simons theory with adjoint
matter preserving two supersymmetries. According to Acharya and Vafa, this
theory describes the low-energy worldvolume dynamics of BPS domain walls in
four-dimensional N=1 SYM theory. We demonstrate how to obtain the same theory
in a brane configuration of type IIB string theory that contains threebranes
and fivebranes. A combination of string and field theory techniques allows us
to re-formulate some of the well-known properties of N=1 SYM domain walls in a
geometric language and to postulate a Seiberg-like duality for the Acharya-Vafa
theory. In the process, we obtain new information about the dynamics of branes
in setups that preserve two supersymmetries. Using similar methods we also
study other N=1 CS theories with extra matter in the adjoint and fundamental
representations of the gauge group.
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Regularisation : many recipes, but a unique principle : Ward identities
and Normalisation conditions. The case of CPT violation in QED: We analyse the recent controversy on a possible Chern-Simons like term
generated through radiative corrections in QED with a CPT violating term : we
prove that, if the theory is correctly defined through Ward identities and
normalisation conditions, no Chern-Simons term appears, without any ambiguity.
This is related to the fact that such a term is a kind of minor modification of
the gauge fixing term, and then no renormalised. The past year literature on
that subject is discussed, and we insist on the fact that any absence of an
{\sl a priori} divergence should be explained by some symmetry or some
non-renormalisation theorem.
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Tits-Satake projections of homogeneous special geometries: We organize the homogeneous special geometries, describing as well the
couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small
number of universality classes. This relates manifolds on which similar types
of dynamical solutions can exist. The mathematical ingredient is the
Tits-Satake projection of real simple Lie algebras, which we extend to all
solvable Lie algebras occurring in these homogeneous special geometries. Apart
from some exotic cases all the other, 'very special', homogeneous manifolds can
be grouped in seven universality classes. The organization of these classes,
which capture the essential features of their basic dynamics, commutes with the
r- and c-map. Different members are distinguished by different choices of the
paint group, a notion discovered in the context of cosmic billiard dynamics of
non maximally supersymmetric supergravities. We comment on the usefulness of
this organization in universality classes both in relation with cosmic billiard
dynamics and with configurations of branes and orbifolds defining special
geometry backgrounds.
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Hawking Radiation of Extended Objects: We compute the effects on the temperature and precise spectrum of Hawking
radiation from a Schwarzschild black hole when the emitted object is taken to
be spatially extended. We find that in the low-momentum regime, the power
emitted is exponentially suppressed for sufficiently large radiated objects, or
sufficiently small black holes, though the temperature of emission is
unchanged. We numerically determine the magnitude of this suppression as a
function of the size and mass of the object and the black hole, and discuss the
implications for various extended objects in nature.
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Ghost Free Mimetic Massive Gravity: The mass of the graviton can be generated using a Brout-Englert-Higgs
mechanism with four scalar fields. We show that when one of these fields is
costrained as in mimetic gravity, the massive gravity obtained is ghost free
and consistent. The mass term is not of the Fierz-Pauli type. There are only
five degrees of freedom and the sixth degree of freedom associated with the
Boulware-Deser ghost is constrained and replaced by mimetic matter to all
orders. The van Dam-Veltman-Zakharov discontinuity is also absent.
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Comments on Penrose Limit of AdS_4 x M^{1,1,1}: We construct a Penrose limit of AdS_4 x M^{1,1,1} where M^{1,1,1}= SU(3) x
SU(2) x U(1)/(SU(2) x U(1) x U(1)) that provides the pp-wave geometry equal to
the one in the Penrose limit of AdS_4 x S^7. There exists a subsector of three
dimensional N=2 dual gauge theory which has enhanced N=8 maximal supersymmetry.
We identify operators in the N=2 gauge theory with supergravity KK excitations
in the pp-wave geometry and describe how the gauge theory operators made out of
two kinds of chiral fields of conformal dimension 4/9, 1/3 fall into N=8
supermultiplets.
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3d mirror for Argyres-Douglas theories: 3d mirrors for all 4d $\mathcal{N}=2$ Argyres-Douglas (AD) theories
engineered using 6d $(2,0)$ theory are found. The basic steps are: 1): Find a
punctured sphere representation for the AD theories (this is achieved in our
previous studies of S duality); 2): Attach a 3d theory for each puncture; 3):
Glue together the 3d theory for each puncture. We found the 3d mirror quiver
gauge theory for the AD theories engineered using 6d $A$ and $D$ type theories.
These 3d mirrors are useful for studying the properties of original 4d theory
such as Higgs branch, S-duality, etc; We also construct many new 3d
$\mathcal{N}=4$ SCFTs.
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One-loop Wilson loops and the particle-interface potential in AdS/dCFT: We initiate the calculation of quantum corrections to Wilson loops in a class
of four-dimensional defect conformal field theories with vacuum expectation
values based on N=4 super Yang-Mills theory. Concretely, we consider an
infinite straight Wilson line, obtaining explicit results for the one-loop
correction to its expectation value in the large-N limit. This allows us to
extract the particle-interface potential of the theory. In a further
double-scaling limit, we compare our results to those of a previous calculation
in the dual string-theory set-up consisting of a D5-D3 probe-brane system with
flux, and we find perfect agreement.
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Colored knot polynomials for Pretzel knots and links of arbitrary genus: A very simple expression is conjectured for arbitrary colored Jones and
HOMFLY polynomials of a rich $(g+1)$-parametric family of Pretzel knots and
links. The answer for the Jones and HOMFLY polynomials is fully and explicitly
expressed through the Racah matrix of U_q(SU_N), and looks related to a modular
transformation of toric conformal block.
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The Bisognano-Wichmann Theorem for Massive Theories: The geometric action of modular groups for wedge regions (Bisognano-Wichmann
property) is derived from the principles of local quantum physics for a large
class of Poincare covariant models in d=4. As a consequence, the CPT theorem
holds for this class. The models must have a complete interpretation in terms
of massive particles. The corresponding charges need not be localizable in
compact regions: The most general case is admitted, namely localization in
spacelike cones.
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Prescriptive Unitarity from Positive Geometries: In this paper, we define the momentum amplituhedron in the four-dimensional
split-signature space of dual momenta. It encodes scattering amplitudes at tree
level and loop integrands for N=4 super Yang-Mills in the planar sector. In
this description, every point in the tree-level geometry is specified by a null
polygon. Using the null structure of this kinematic space, we find a geometry
whose canonical differential form produces loop-amplitude integrands.
Remarkably, at one loop it is a curvy version of a simple polytope, whose
vertices are specified by maximal cuts of the amplitude. This construction
allows us to find novel formulae for the one-loop integrands for amplitudes
with any multiplicity and helicity. The formulae obtained in this way agree
with the ones derived via prescriptive unitarity. It makes prescriptive
unitarity naturally emerge from this geometric description.
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Global anomalies on Lorentzian space-times: We formulate an algebraic criterion for the presence of global anomalies on
globally hyperbolic space-times in the framework of locally covariant field
theory. We discuss some consequences and check that it reproduces the
well-known global $SU(2)$ anomaly in four space-time dimensions.
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Copernican Crystallography: Redundancies are pointed out in the widely used extension of the
crystallographic concept of Bravais class to quasiperiodic materials. Such
pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary
crystallography on microscopic periodicity. The broadening of crystallography
to include quasiperiodic materials is accomplished by defining the point group
in terms of indistinguishable (as opposed to identical) densities.
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Ward Identities in the Derivation of Hawking Radiation from Anomalies: Robinson and Wilczek suggested a new method of deriving Hawking radiation by
the consideration of anomalies. The basic idea of their approach is that the
flux of Hawking radiation is determined by anomaly cancellation conditions in
the Schwarzschild black hole (BH) background. Iso et al. extended the method to
a charged Reissner-Nordstroem BH and a rotating Kerr BH, and they showed that
the flux of Hawking radiation can also be determined by anomaly cancellation
conditions and regularity conditions of currents at the horizon. Their
formulation gives the correct Hawking flux for all the cases at infinity and
thus provides a new attractive method of understanding Hawking radiation. We
present some arguments clarifying for this derivation. We show that the Ward
identities and boundary conditions for covariant currents without referring to
the Wess-Zumino terms and the effective action are sufficient to derive Hawking
radiation. Our method, which does not use step functions, thus simplifies some
of the technical aspects of the original formulation.
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New boundary conditions in Einstein-scalar gravity in three dimensions: We analyze the backreaction of a class of scalar field self-interactions with
the possibility of evolving from an AdS vacuum to a fixed point where the
scalar field potential vanishes. Exact solutions which interpolate between
these regions, ranging from stationary black hole to dynamical spacetimes are
constructed. Their surface charges are finite but non-integrable. We study the
properties of these charges on the solutions. In particular, we show that the
integrable part of the charges provides a realization of the conformal algebra
by means of a modification of the Dirac bracket proposed by Barnich and
Troessaert. The latter construction allows for a field dependent central
extension, whose value tends to the Brown-Henneaux central charge at late
times.
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Quantization of Even-Dimensional Actions of Chern-Simons Form with
Infinite Reducibility: We investigate the quantization of even-dimensional topological actions of
Chern-Simons form which were proposed previously. We quantize the actions by
Lagrangian and Hamiltonian formulations {\`a} la Batalin, Fradkin and
Vilkovisky. The models turn out to be infinitely reducible and thus we need
infinite number of ghosts and antighosts. The minimal actions of Lagrangian
formulation which satisfy the master equation of Batalin and Vilkovisky have
the same Chern-Simons form as the starting classical actions. In the
Hamiltonian formulation we have used the formulation of cohomological
perturbation and explicitly shown that the gauge-fixed actions of both
formulations coincide even though the classical action breaks Dirac's
regularity condition. We find an interesting relation that the BRST charge of
Hamiltonian formulation is the odd-dimensional fermionic counterpart of the
topological action of Chern-Simons form. Although the quantization of two
dimensional models which include both bosonic and fermionic gauge fields are
investigated in detail, it is straightforward to extend the quantization into
arbitrary even dimensions. This completes the quantization of previously
proposed topological gravities in two and four dimensions.
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Moduli Corrections to Gauge and Gravitational Couplings in four
dimensional Superstrings: We study one-loop, moduli-dependent corrections to gauge and gravitational
couplings in supersymmetric vacua of the heterotic string. By exploiting their
relation to the integrability condition for the associated CP-odd couplings, we
derive general expressions for them, both for $(2,2)$ and $(2,0)$ models, in
terms of tree level four-point functions in the internal $N=2$ superconformal
theory. The $(2,2)$ case, in particular symmetric orbifolds, is discussed in
detail.
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Central Charges for AdS Black Holes: Nontrivial diffeomorphisms act on the horizon of a generic 4D black holes and
create distinguishing features referred to as soft hair. Amongst these are a
left-right pair of Virasoro algebras with associated charges that reproduce the
Bekenstein-Hawking entropy for Kerr black holes. In this paper we show that if
one adds a negative cosmological constant, there is a similar set of
infinitesimal diffeomorphisms that act non-trivially on the horizon. The
algebra of these diffeomorphisms gives rise to a central charge. Adding a
boundary counterterm, justified to achieve integrability, leads to well-defined
central charges with cL = cR. The macroscopic area law for Kerr-AdS black holes
follows from the assumption of a Cardy formula governing the black hole
microstates.
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Elliptic genera and real Jacobi forms: We construct real Jacobi forms with matrix index using path integrals. The
path integral expressions represent elliptic genera of two-dimensional N=(2,2)
supersymmetric theories. They arise in a family labeled by two integers N and k
which determine the central charge of the infrared fixed point through the
formula c=3N(1+ 2N/k). We decompose the real Jacobi form into a mock modular
form and a term arising from the continuous spectrum of the conformal field
theory. We argue that the Jacobi form represents the elliptic genus of a theory
defined on a 2N dimensional background with U(N) isometry, containing a complex
projective space section, a circle fiber and a linear dilaton direction. We
also present formulas for the elliptic genera of orbifolds of these models.
|
Mirror Mediation: I show that the effective action of string compactifications has a structure
that can naturally solve the supersymmetric flavour and CP problems. At leading
order in the g_s and \alpha' expansions, the hidden sector factorises. The
moduli space splits into two mirror parts that depend on Kahler and complex
structure moduli. Holomorphy implies the flavour structure of the Yukawa
couplings arises in only one part. In type IIA string theory flavour arises
through the Kahler moduli sector and in type IIB flavour arises through the
complex structure moduli sector. This factorisation gives a simple solution to
the supersymmetric flavour and CP problems: flavour physics is generated in one
sector while supersymmetry is broken in the mirror sector. This mechanism does
not require the presence of gauge, gaugino or anomaly mediation and is
explicitly realised by phenomenological models of IIB flux compactifications.
|
Tachyon Condensation in Superstring Field Theory: It has been conjectured that at the stationary point of the tachyon potential
for the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstring
theories, the negative energy density cancels the brane tensions. We study this
conjecture using a Wess-Zumino-Witten-like open superstring field theory free
of contact term divergences and recently shown to give 60% of the vacuum energy
by condensation of the tachyon field alone. While the action is non-polynomial,
the multiscalar tachyon potential to any fixed level involves only a finite
number of interactions. We compute this potential to level three, obtaining 85%
of the expected vacuum energy, a result consistent with convergence that can
also be viewed as a successful test of the string field theory. The resulting
effective tachyon potential is bounded below and has two degenerate global
minima. We calculate the energy density of the kink solution interpolating
between these minima finding good agreement with the tension of the D-brane of
one lower dimension.
|
Chiral Random Two-Matrix Theory and QCD with imaginary chemical
potential: We summarise recent results for the chiral Random Two-Matrix Theory
constructed to describe QCD in the epsilon-regime with imaginary chemical
potential. The virtue of this theory is that unquenched Lattice simulations can
be used to determine both low energy constants Sigma and F in the leading order
chiral Lagrangian, due to their respective coupling to quark mass and chemical
potential. We briefly recall the analytic formulas for all density and
individual eigenvalue correlations and then illustrate them in detail in the
simplest, quenched case with imaginary isospin chemical potential. Some
peculiarities are pointed out for this example: i) the factorisation of density
and individual eigenvalue correlation functions for large chemical potential
and ii) the factorisation of the non-Gaussian weight function of bi-orthogonal
polynomials into Gaussian weights with ordinary orthogonal polynomials.
|
Calculating Extra (Quasi)Moduli on the Abrikosov-Nielsen-Olesen string
with Spin-Orbit Interaction: Using a representative set of parameters we numerically calculate the
low-energy Lagrangian on the world sheet of the Abrikosov-Nielsen-Olesen string
in a model in which it acquires rotational (quasi)moduli. The bulk model is
deformed by a spin-orbit interaction generating a number of "entangled" terms
on the string world sheet.
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New potentials from Scherk-Schwarz reductions: We study compactifications of eleven-dimensional supergravity on Calabi-Yau
threefolds times a circle, with a duality twist along the circle a la
Scherk-Schwarz. This leads to four-dimensional N=2 gauged supergravity with a
semi-positive definite potential for the scalar fields, which we derive
explicitly. Furthermore, inspired by the orientifold projection in string
theory, we define a truncation to N=1 supergravity. We determine the D-terms,
Kaehler- and superpotentials for these models and study the properties of the
vacua. Finally, we point out a relation to M-theory compactifications on
seven-dimensional manifolds with G2 structure.
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The chiral WZNW phase space as a quasi-Poisson space: It is explained that the chiral WZNW phase space is a quasi-Poisson space
with respect to the `canonical' Lie quasi-bialgebra which is the classical
limit of Drinfeld's quasi-Hopf deformation of the universal enveloping algebra.
This exemplifies the notion of quasi-Poisson-Lie symmetry introduced recently
by Alekseev and Kosmann-Schwarzbach, and also permits us to generalize certain
dynamical twists considered previously in this example.
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Scalar Boundary Conditions in Hyperscaling Violating Geometry: We study the possible boundary conditions of scalar field modes in a
hyperscaling violation(HV) geometry with Lifshitz dynamical exponent $z
(z\geqslant1)$ and hyperscaling violation exponent $\theta (\theta\neq0)$. For
the case with $\theta>0$, we show that in the parameter range with $1\leq z\leq
2,~-z+d-1<\theta\leq (d-1)(z-1)$ or $z>2,~-z+d-1<\theta\leq d-1$, the boundary
conditions have different types, including the Neumann, Dirichlet and Robin
conditions, while in the range with $\theta\leq-z+d-1$, only Dirichlet type
condition can be set. In particular, we further confirm that the mass of the
scalar field does not play any role in determining the possible boundary
conditions for $\theta>0$, which has been addressed in Ref. \cite{1201.1905}.
Meanwhile, we also do the parallel investigation in the case with $\theta<0$.
We find that for $m^2<0$, three types of boundary conditions are available, but
for $m^2>0$, only one type is available.
|
Quantum Channels in Quantum Gravity: The black hole final state proposal implements manifest unitarity in the
process of black hole formation and evaporation in quantum gravity, by
postulating a unique final state boundary condition at the singularity. We
argue that this proposal can be embedded in the gauge/gravity context by
invoking a path integral formalism inspired by the Schwinger-Keldysh like
thermo-field double construction in the dual field theory. This allows us to
realize the gravitational quantum channels for information retrieval to
specific deformations of the field theory path integrals and opens up new
connections between geometry and information theory.
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Coulomb and Higgs Phases of $G_2$-manifolds: Ricci flat manifolds of special holonomy are a rich framework as models of
the extra dimensions in string/$M$-theory. At special points in vacuum moduli
space, special kinds of singularities occur and demand a physical
interpretation. In this paper we show that the topologically distinct
$G_2$-holonomy manifolds arising from desingularisations of codimension four
orbifold singularities due to Joyce and Karigiannis correspond physically to
Coulomb and Higgs phases of four dimensional gauge theories. The results
suggest generalisations of the Joyce-Karigiannis construction to arbitrary
ADE-singularities and higher order twists which we explore in detail in
explicitly solvable local models. These models allow us to derive an
isomorphism between moduli spaces of Ricci flat metrics on these non-compact
$G_2$-manifolds and flat ADE-connections on compact flat 3-manifolds which we
establish explicitly for $\operatorname{SU}(n)$.
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New hyper-Kaehler manifolds by fixing monopoles: The construction of new hyper-Kaehler manifolds by taking the infinite
monopole mass limit of certain Bogomol'nyi-Prasad-Sommerfield monopole moduli
spaces is considered. The one-parameter family of hyperkaehler manifolds due to
Dancer is shown to be an example of such manifolds. A new family of fixed
monopole spaces is constructed. They are the moduli spaces of four SU(4)
monopoles, in the infinite mass limit of two of the monopoles. These manifolds
are shown to be nonsingular when the fixed monopole positions are distinct.
|
A note on Burgers' turbulence: In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for
the velocity-difference PDF, with the exciting force correlation function
$\kappa (y)\sim1-y^{\alpha}$ is analyzed. Several solvable cases are
considered, which are in a good agreement with available numerical results.
Then it is shown how the method developed by A. Polyakov can be applied to
turbulence with short-scale-correlated forces, a situation considered in models
of self-organized criticality.
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Three-Dimensional Extremal Black Holes and the Maldacena Duality: We discuss the microscopic states of the extremal BTZ black holes. Degeneracy
of the primary states corresponding to the extremal BTZ black holes in the
boundary N=(4,4) SCFT is obtained by utilizing the elliptic genus and the
unitary representation theory of N=4 SCA. The degeneracy is consistent with the
Bekenstein-Hawking entropy.
|
A Proof Of Ghost Freedom In de Rham-Gabadadze-Tolley Massive Gravity: We identify different helicity degrees of freedom of Fierz-Paulian massive
gravity around generic backgrounds. We show that the two-parameter family
proposed by de Rham, Gabadadze, and Tolley always propagates five degrees of
freedom and therefore is free from the Boulware-Deser ghost. The analysis has a
number of byproducts, among which (a) it shows how the original decoupling
limit construction ensures ghost freedom of the full theory, (b) it reveals an
enhanced symmetry of the theory around linearized backgrounds, and (c) it
allows us to give an algorithm for finding dispersion relations. The proof
naturally extends to generalizations of the theory with a reference metric
different from Minkowski.
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Conifolds From D-branes: In this note we study the resolution of conifold singularity by D-branes by
considering compactification of D-branes on $\C^3/(\Z_2\times\Z_2)$. The
resulting vacuum moduli space of D-branes is a toric variety which turns out to
be a resolved conifold, that is a nodal variety in $\C^4$. This has the
implication that all the corresponding phases of Type--II string theory are
geometrical and are accessible to the D-branes, since they are related by
flops.
|
Yang-Mills fields for Cosets: We consider theories with degenerate kinetic terms such as those that arise
at strong coupling in $N=2$ super Yang-Mills theory. We compute the components
of generalized $N=1,2$ supersymmetric sigma model actions in two dimensions.
The target space coordinates may be matter and/or Yang-Mills superfield
strengths.
|
1+1 Gauge Theories in the Light-Cone Representation: We present a representation independent solution to the continuum Schwinger
model in light-cone ($A^+ = 0$) gauge. We then discuss the problem of finding
that solution using various quantization schemes. In particular we shall
consider equal-time quantization and quantization on either characteristic
surface, $x^+ = 0$ or $x^- = 0$.
|
The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces: The Swampland Distance Conjecture claims that effective theories derived from
a consistent theory of quantum gravity only have a finite range of validity.
This will imply drastic consequences for string theory model building. The
refined version of this conjecture says that this range is of the order of the
naturally built in scale, namely the Planck scale. It is investigated whether
the Refined Swampland Distance Conjecture is consistent with proper field
distances arising in the well understood moduli spaces of Calabi-Yau
compactification. Investigating in particular the non-geometric phases of
Kahler moduli spaces of dimension $h^{11}\in\{1,2,101\}$, we always found
proper field distances that are smaller than the Planck-length.
|
Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological
Theories: We study the holomorphic twist of 3d N = 2 supersymmetric field theories,
discuss the perturbative bulk local operators in general, and explicitly
construct non perturbative bulk local operators for abelian gauge theories. Our
construction is verified by matching the character of the algebra with the
superconformal index. We test a conjectural relation between the derived center
of boundary algebras and bulk algebras in various cases, including
Landau-Ginzburg models with an arbitrary superpotential and some abelian gauge
theories. In the latter cases, monopole operators appear in the derived center
of a perturbative boundary algebra. We briefly discuss the higher structures in
both boundary and bulk algebras.
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A Family of Quasi-solvable Quantum Many-body Systems: We construct a family of quasi-solvable quantum many-body systems by an
algebraic method. The models contain up to two-body interactions and have
permutation symmetry. We classify these models under the consideration of
invariance property. It turns out that this family includes the rational,
hyperbolic (trigonometric) and elliptic Inozemtsev models as the particular
cases.
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Analytic DC thermo-electric conductivities in holography with massive
gravitons: We provide an analytical derivation of the thermo-electric transport
coefficients of the simplest momentum-dissipating model in gauge/gravity where
the lack of momentum conservation is realized by means of explicit graviton
mass in the bulk. We rely on the procedure recently described by Donos and
Gauntlett in the context of Q-lattices and holographic models where momentum
dissipation is realized through non-trivial scalars. The analytical approach
confirms the results found previously by means of numerical computations.
|
Abelian vortices from Sinh--Gordon and Tzitzeica equations: It is shown that both the sinh--Gordon equation and the elliptic Tzitzeica
equation can be interpreted as the Taubes equation for Abelian vortices on a
CMC surface embedded in $\R^{2, 1}$, or on a surface conformally related to a
hyperbolic affine sphere in $\R^3$. In both cases the Higgs field and the U(1)
vortex connection are constructed directly from the Riemannian data of the
surface corresponding to the sinh--Gordon or the Tzitzeica equation. Radially
symmetric solutions lead to vortices with a topological charge equal to one,
and the connection formulae for the resulting third Painlev\'e transcendents
are used to compute explicit values for the strength of the vortices.
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Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and
quaternionic o^*(4) symmetries in unified o(4;C) setting: We employ new calculational technique and present complete list of classical
$r$-matrices for $D=4$ complex homogeneous orthogonal Lie algebra
$\mathfrak{o}(4;\mathbb{C})$, the rotational symmetry of four-dimensional
complex space-time. Further applying reality conditions we obtain the classical
$r$-matrices for all possible real forms of $\mathfrak{o}(4;\mathbb{C})$:
Euclidean $\mathfrak{o}(4)$, Lorentz $\mathfrak{o}(3,1)$, Kleinian
$\mathfrak{o}(2,2)$ and quaternionic $\mathfrak{o}^{\star}(4)$ Lie algebras.
For $\mathfrak{o}(3,1)$ we get known four classical $D=4$ Lorentz $r$-matrices,
but for other real Lie algebras (Euclidean, Kleinian, quaternionic) we provide
new results and mention some applications.
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A quantum field theory of simplicial geometry and the emergence of
spacetime: We present the case for a fundamentally discrete quantum spacetime and for
Group Field Theories as a candidate consistent description of it, briefly
reviewing the key properties of the GFT formalism. We then argue that the
outstanding problem of the emergence of a continuum spacetime and of General
Relativity from fundamentally discrete quantum structures should be tackled
from a condensed matter perspective and using purely QFT methods, adapted to
the GFT context. We outline the picture of continuum spacetime as a condensed
phase of a GFT and a research programme aimed at realizing this picture in
concrete terms.
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Exactly solvable models of supersymmetric quantum mechanics and
connection to spectrum generating algebra: For nonrelativistic Hamiltonians which are shape invariant, analytic
expressions for the eigenvalues and eigenvectors can be derived using the well
known method of supersymmetric quantum mechanics. Most of these Hamiltonians
also possess spectrum generating algebras and are hence solvable by an
independent group theoretic method. In this paper, we demonstrate the
equivalence of the two methods of solution by developing an algebraic framework
for shape invariant Hamiltonians with a general change of parameters, which
involves nonlinear extensions of Lie algebras.
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Coleman-Weinberg Phase Transition in Two-Scalar Models: We explore the Coleman-Weinberg phase transition in regions outside the
validity of perturbation theory. For this purpose we study a Euclidean field
theory with two scalars and discrete symmetry in four dimensions. The phase
diagram is established by a numerical solution of a suitable truncation of
exact non-perturbative flow equations. We find regions in parameter space where
the phase transition (in dependence on the mass term) is of the second or the
first order, separated by a triple point. Our quantitative results for the
first order phase transition compare well to the standard perturbative
Coleman-Weinberg calculation of the effective potential.
|
Accessory parameters for Liouville theory on the torus: We give an implicit equation for the accessory parameter on the torus which
is the necessary and sufficient condition to obtain the monodromy of the
conformal factor. It is shown that the perturbative series for the accessory
parameter in the coupling constant converges in a finite disk and give a
rigorous lower bound for the radius of convergence. We work out explicitly the
perturbative result to second order in the coupling for the accessory parameter
and to third order for the one-point function. Modular invariance is discussed
and exploited. At the non perturbative level it is shown that the accessory
parameter is a continuous function of the coupling in the whole physical region
and that it is analytic except at most a finite number of points. We also prove
that the accessory parameter as a function of the modulus of the torus is
continuous and real-analytic except at most for a zero measure set. Three
soluble cases in which the solution can be expressed in terms of hypergeometric
functions are explicitly treated.
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Konishi Anomaly and Central Extension in N=1/2 Supersymmetry: We show that the 4-dimensional N=1/2 supersymmetry algebra admits central
extension. The central charges are supported by domain wall and the central
charges are computed. We also determine the Konishi anomaly for N=1/2
supersymmetric gauge theory. Due to the new couplings in the Lagrangian, many
terms appears. We show that these terms sum up to give the expected form for
the holomorphic part of the Konishi anomaly. For the anti-holomorphic part, we
give a simple argument that the naive generalization has to be modified. We
suggest that the anti-holomorphic Konishi anomaly is given by a gauge invariant
completion using open Wilson line.
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Effective Schroedinger equations for nonlocal and/or dissipative systems: The projection formalism for calculating effective Hamiltonians and
resonances is generalized to the nonlocal and/or nonhermitian case, so that it
is applicable to the reduction of relativistic systems (Bethe-Salpeter
equations), and to dissipative systems modeled by an optical potential.
It is also shown how to recover all solutions of the time-independent
Schroedinger equation in terms of solutions of the effective Schroedinger
equation in the reduced state space and a Schroedinger equation in a reference
state space.
For practical calculations, it is important that the resulting formulas can
be used without computing any projection operators. This leads to a modified
coupled reaction channel/resonating group method framework for the calculation
of multichannel scattering information.
|
Origin of Matter from Vacuum in Conformal Cosmology: We introduce the hypothesis that the matter content of the universe can be a
product of the decay of primordial vector bosons.
The effect of the intensive cosmological creation of these primordial vector
$W, ~Z $ bosons from the vacuum is studied in the framework of General
Relativity and the Standard Model where the relative standard of measurement
identifying conformal quantities with the measurable ones is accepted.
The relative standard leads to the conformal cosmology with the z-history of
masses with the constant temperature, instead of the conventional z-history of
the temperature with constant masses in inflationary cosmology.
In conformal cosmology both the latest supernova data and primordial
nucleosynthesis are compatible with a stiff equation of state associated with
one of the possible states of the infrared gravitation field.
The distribution function of the created bosons in the lowest order of
perturbation theory exposes a cosmological singularity as a consequence of the
theorem about the absence of the massless limit of massive vector fields in
quantum theory. This singularity can be removed by taking into account the
collision processes leading to a thermalization of the created particles. The
cosmic microwave background (CMB) temperature T=(M_W^2H_0)^{1/3} ~ 2.7 K occurs
as an integral of motion for the universe in the stiff state. We show that this
temperature can be attained by the CMB radiation being the final product of the
decay of primordial bosons.
The effect of anomalous nonconservation of baryon number due to the
polarization of the Dirac sea vacuum by these primordial bosons is considered.
|
A Note on Fluxes and Superpotentials in M-theory Compactifications on
Manifolds of G_2 Holonomy: We consider the breaking of N=1 supersymmetry by non-zero G-flux when
M-theory is compactified on a smooth manifold X of G_2 holonomy. Gukov has
proposed a superpotential W to describe this breaking in the low-energy
effective theory. We check this proposal by comparing the bosonic potential
implied by W with the corresponding potential deduced from the
eleven-dimensional supergravity action. One interesting aspect of this check is
that, though W depends explicitly only on G-flux supported on X, W also
describes the breaking of supersymmetry by G-flux transverse to X.
|
The target space dependence of the Hagedorn temperature: The effect of certain simple backgrounds on the Hagedorn temperature in
theories of closed strings is examined. The background of interest are constant
Neveu-Schwarz $B$-fields, a constant offset of the space-time metric and a
compactified spatial dimension. We find that the Hagedorn temperature of string
theory depends on the parameters of the background. We comment on an
interesting non-extensive feature of the Hagedorn transition, including a
subtlety with decoupling of closed strings in the NCOS limit of open string
theory and on the large radius limit of discrete light-cone quantized closed
strings.
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Some Speculations on the Gauge Coupling in the AdS/CFT Approach: We propose the principle that the scale of the glueball masses in the AdS/CFT
approach to QCD should be set by the square root of the string tension. It then
turns out that the strong bare coupling runs logarithmically with the
ultraviolet cutoff T if first order world sheet fluctuations are included. We
also point out that in the end, when all corrections are included, one should
obtain an equation for the coupling running with T which has some similarity
with the equation for the strong bare coupling.
|
Yang-Mills Gauge Conditions from Witten's Open String Field Theory: We construct the Zinn-Justin-Batalin-Vilkovisky action for tachyons and gauge
bosons from Witten's 3-string vertex of the bosonic open string without gauge
fixing. Through canonical transformations, we find the off-shell, local,
gauge-covariant action up to 3-point terms, satisfying the usual field theory
gauge transformations. Perturbatively, it can be extended to higher-point
terms. It also gives a new gauge condition in field theory which corresponds to
the Feynman-Siegel gauge on the world-sheet.
|
A Defect in AdS3/CFT2 Duality: $AdS_3$ string theory in the stringy regime $k=(R_{AdS}/\ell_{str})^2 < 1$
provides a laboratory for the study of holography in which both sides of
AdS/CFT duality are under fairly good control. Worldsheet string theory is
solvable, and for closed strings the dual spacetime CFT is a deformation of a
symmetric product orbifold. Here we extend this construction to include open
strings by adding a probe D-string, described semi-classically by an $AdS_2$
D-brane in $AdS_3$. The dual defect or boundary conformal field theory (BCFT)
is again a deformed symmetric product, which now describes the Fock space of
long open and closed strings near the AdS boundary, with a boundary deformation
implementing the open/closed transition in addition to the symmetric product
${\mathbb Z}_2$ twist deformation that implements closed string
joining/splitting. The construction thus provides an explicit example of an
$AdS_3/BCFT_2$ duality.
|
A companion to "Knot invariants and M-theory I'' [arXiv:1608.05128]:
proofs and derivations: We construct two distinct yet related M-theory models that provide suitable
frameworks for the study of knot invariants. We then focus on the
four-dimensional gauge theory that follows from appropriately compactifying one
of these M-theory models. We show that this theory has indeed all required
properties to host knots. Our analysis provides a unifying picture of the
various recent works that attempt an understanding of knot invariants using
techniques of four-dimensional physics.
This is a companion paper to arXiv:1608.05128, covering all but section 3.3.
It presents a detailed mathematical derivation of the main results there, as
well as additional material. Among the new insights, those related to
supersymmetry and the topological twist are highlighted. This paper offers an
alternative, complementary formulation of the contents
in~\cite{Dasgupta:2016rhc}, but is self-contained and can be read
independently.
|
't Hooft Operators on an Interface and Bubbling D5-Branes: We consider a brane configuration consisting of a D5-brane, D1-branes and
D3-branes. According to the AdS/CFT correspondence this system realizes a 't
Hooft operator embedded in the interface in the gauge theory side. In the
gravity side the near-horizon geometry is AdS_5 x S^5. The D5-brane is treated
as a probe in the AdS_5 x S^5 and the D1-branes become the gauge flux on the
D5-brane. We examine the condition for preserving appropriate amount of
supersymmetry and derive a set of differential equations which is the
sufficient and necessary condition. This supersymmetric configuration shows
bubbling behavior. We try to derive the relation between the probe D5-brane and
the Young diagram which labels the corresponding 't Hooft operator. We propose
the dictionary of the correspondence between the Young diagram and the probe
D5-brane configuration.
|
Finite Heisenberg Groups in Quiver Gauge Theories: We show by direct construction that a large class of quiver gauge theories
admits actions of finite Heisenberg groups. We consider various quiver gauge
theories that arise as AdS/CFT duals of orbifolds of C^3, the conifold and its
orbifolds and some orbifolds of the cone over Y(p,q). Matching the gauge theory
analysis with string theory on the corresponding spaces implies that the
operators counting wrapped branes do not commute in the presence of flux.
|
Batalin-Vilkovisky quantization of fuzzy field theories: We apply the modern Batalin-Vilkovisky quantization techniques of Costello
and Gwilliam to noncommutative field theories in the finite-dimensional case of
fuzzy spaces. We further develop a generalization of this framework to theories
that are equivariant under a triangular Hopf algebra symmetry, which in
particular leads to quantizations of finite-dimensional analogs of the field
theories proposed recently through the notion of `braided $L_\infty$-algebras'.
The techniques are illustrated by computing perturbative correlation functions
for scalar and Chern-Simons theories on the fuzzy $2$-sphere, as well as for
braided scalar field theories on the fuzzy $2$-torus.
|
Compatibility of symmetric quantization with general covariance in the
Dirac equation and spin connections: By requiring unambiguous symmetric quantization leading to the Dirac equation
in a curved space, we obtain a special representation of the spin connections
in terms of the Dirac gamma matrices and their space-time derivatives. We also
require that squaring the equation give the Klein-Gordon equation in a curved
space in its canonical from (without spinor components coupling and with no
first order derivatives). These requirements result in matrix operator algebra
for the Dirac gamma matrices that involves a universal curvature constant. We
obtain exact solutions of the Dirac and Klein-Gordon equations in 1+1
space-time for a given static metric.
|
Exponential potential for an inflaton with nonminimal kinetic coupling
and its supergravity embedding: In the light of the new observational results we discuss the status of the
exponential potentials driving inflation. We depart form the minimal scenario
and study an inflaton kinetically coupled to the Einstein tensor. We find that
in this case the exponential potentials are well compatible with observations.
Their predictions coincide with those of the chaotic type quadratic potential
for an inflaton minimally coupled to gravity. We show that there exists a
simple mapping between the two models. Moreover, a novel aspect of our model is
that it features a natural exit from the inflationary phase even in the absence
of a minimum. We also turn to supergravity and motivate these sort of
potentials and the non-minimal kinetic coupling as possible effective dilaton
theories.
|
Electrodynamics with Weinberg's Photons: The interaction of the spinor field with the Weinberg's $2(2S+1)$- component
massless field is considered. New interpretation of the Weinberg's spinor is
proposed. The equation analogous to the Dirac oscillator is obtained.
|
On the fate of black string instabilities: An Observation: Gregory and Laflamme (hep-th/9301052) have argued that an instability causes
the Schwarzschild black string to break up into disjoint black holes. On the
other hand, Horowitz and Maeda (arXiv:hep-th/0105111) derived bounds on the
rate at which the smallest sphere can pinch off, showing that, if it happens at
all, such a pinch-off can occur only at infinite affine parameter along the
horizon. An interesting point is that, if a singularity forms, such an infinite
affine parameter may correspond to a finite advanced time -- which is in fact a
more appropriate notion of time at infinity. We argue below that pinch-off at a
finite advanced time is in fact a natural expectation under the bounds derived
by Horowitz and Maeda.
|
Membranes from monopole operators in ABJM theory: large angular momentum
and M-theoretic AdS_4/CFT_3: We consider states with large angular momentum to facilitate the study of the
M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between
M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with
gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this
regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes
the gravity side difficult, while the CFT is strongly coupled and the planar
approximation is not applicable. To overcome these difficulties, we focus on
states on the gravity side with large angular momentum J>>1 and identify the
dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this
sector. Natural approximation schemes arise on both sides thanks to the
presence of the small parameter 1/J. On the AdS side, we use the matrix model
of M-theory on the maximally supersymmetric pp-wave background with matrices of
size J/k. A perturbative treatment of this matrix model provides a good
approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT
side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer
type expansion arises naturally for large J in spite of the theory being
strongly coupled. The energy spectra on the two sides agree at leading order.
This provides a non-trivial test of the AdS_4/CFT_3 correspondence including
near-BPS observables associated with membrane degrees of freedom, thus
verifying the duality beyond the previously studied sectors corresponding to
either BPS observables or the type IIA string regime.
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AdS-CFT and the RHIC fireball: In this talk I will review my work on the description of high energy
scattering in QCD, in particular the fireball observed at RHIC, as well as
predictions for the LHC. The aim is to see how much we can learn about actual
QCD (nonsupersymmetric, $N_c=3$), without knowing the details of the gravity
dual of QCD. Experimental predictions are consistent with data, and important
consequences are obtained for the LHC, in particular for the $pp$ collisions.
The RHIC and LHC correspond to the regime of Froissart bound saturation, in the
Heisenberg model. Asymptotically, the RHIC fireball is mapped to a dual black
hole in the IR of the dual. A simple (and unique) scalar field theory model for
the RHIC fireball indeed exhibits the properties of the dual black hole: a
thermal horizon and aparent information loss.
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Callan-Symanzik method for $m$-axial Lifshitz points: We introduce the Callan-Symanzik method in the description of anisotropic as
well as isotropic Lifshitz critical behaviors. Renormalized perturbation
theories are defined by normalization conditions with nonvanishing masses and
at zero external momenta. The orthogonal approximation is employed to obtain
the critical indices $\eta_{L2}$, $\nu_{L2}$, $\eta_{L4}$ and $\nu_{L4}$
diagramatically at least up to two-loop order in the anisotropic criticalities.
This approximation is also utilized to compute the exponents $\eta_{L4}$ and
$\nu_{L4}$ in the isotropic case. Furthermore, we compute those exponents
exactly for the isotropic behaviors at the same loop order. The results
obtained for all exponents are in perfect agreement with those previously
derived in the massless theories renormalized at nonzero external momenta.
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From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by
Virasoro operators: In this letter,we present our conjecture on the connection between the
Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula
connects these two tau-functions by means of the $GL(\infty)$ group element. An
important feature of this group element is its simplicity: this is a group
element of the Virasoro subalgebra of $gl(\infty)$. If proved, this conjecture
would allow to derive the Virasoro constraints for the Hurwitz tau-function,
which remain unknown in spite of existence of several matrix model
representations, as well as to give an integrable operator description of the
Kontsevich--Witten tau-function.
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Curvature-induced phase transition in three-dimensional Thirring model: The effective potential of composite fermion fields in three-dimensional
Thirring model in curved spacetime is calculated in linear curvature
approximation. The phase transition accompanied by the creation of non-zero
chiral invariant bifermionic vector-like condensate is shown to exist. The type
of this phase transition is discussed.
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Fractional Klein-Gordon Equation on AdS$_{2+1}$: We propose a covariant definition of the fractional Klein-Gordon equation
with long-range interactions independent of the metric of the underlying
manifold. As an example we consider the fractional Klein-Gordon equation on
AdS$_{2+1}$, computing the explicit kernel representation of the fractional
Laplace-Beltrami operator as well as the two-point propagator of the fractional
Klein-Gordon equation. Our results suggest that the propagator only exists if
the mass is small compared to the inverse AdS radius, presumably because the
AdS space expands faster with distance as a flat space of the same dimension.
Our results are expected to be useful in particular for new applications of the
AdS/CFT correspondence within statistical mechanics and quantum information.
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The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory
Compactifications: We study seven-branes in $O(10^{15})$ four-dimensional F-theory
compactifications where seven-brane moduli must be tuned in order to achieve
non-abelian gauge symmetry. The associated compact spaces $B$ are the set of
all smooth weak Fano toric threefolds. By a study of fine star regular
triangulations of three dimensional reflexive polytopes, the number of such
spaces is estimated to be $5.8\times 10^{14}\lesssim N_\text{bases}\lesssim
1.8\times 10^{17}$. Typically hundreds or thousands of moduli must be tuned to
achieve symmetry for $h^{11}(B)<10$, but the average number drops sharply into
the range $O(25)$-$O(200)$ as $h^{11}(B)$ increases. For some low rank groups,
such as $SU(2)$ and $SU(3)$, there exist examples where only a few moduli must
be tuned in order to achieve seven-brane gauge symmetry.
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$O(α)$ Radiative Correction to the Casimir Energy for Penetrable
Mirrors: The leading radiative correction to the Casimir energy for two parallel
penetrable mirrors is calculated within QED perturbation theory. It is found to
be of the order $\alpha$ like the known radiative correction for ideally
reflecting mirrors from which it differs only by a monotonic, powerlike
function of the frequency at which the mirrors become transparent. This shows
that the $O(\alpha^2)$ radiative correction calculated recently by Kong and
Ravndal for ideally reflecting mirrors on the basis of effective field theory
methods remains subleading even for the physical case of penetrable mirrors.
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The cosmic QCD phase transition with dense matter and its gravitational
waves from holography: Consistent with cosmological constraints, there are scenarios with the large
lepton asymmetry which can lead to the finite baryochemical potential at the
cosmic QCD phase transition scale. In this paper, we investigate this
possibility in the holographic models. Using the holographic renormalization
method, we find the first order Hawking-Page phase transition, between
Reissner-Nordstr$\rm\ddot{o}$m AdS black hole and thermal charged AdS space,
corresponding to the de/confinement phase transition. We obtain the
gravitational wave spectra generated during the evolution of bubbles for a
range of the bubble wall velocity and examine the reliability of the scenarios
and consequent calculations by gravitational wave experiments.
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Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity
Theories: A description of the bosonic sector of ten-dimensional N=1 supergravity as a
non-linear realisation is given. We show that if a suitable extension of this
theory were invariant under a Kac-Moody algebra, then this algebra would have
to contain a rank eleven Kac-Moody algebra, that can be identified to be a
particular real form of very-extended D_8. We also describe the extension of
N=1 supergravity coupled to an abelian vector gauge field as a non-linear
realisation, and find the Kac-Moody algebra governing the symmetries of this
theory to be very-extended B_8. Finally, we discuss the related points for the
N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields.
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Boundary Operators of BCFW Recursion Relation: We show that boundary contributions of BCFW recursions can be interpreted as
the form factors of some composite operators which we call 'boundary
operators'. The boundary operators can be extracted from the operator product
expansion of deformed fields. We also present an algorithm to compute the
boundary operators using path integral.
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Gradient flow exact renormalization group: The gradient flow bears a close resemblance to the coarse graining, the
guiding principle of the renormalization group (RG). In the case of scalar
field theory, a precise connection has been made between the gradient flow and
the RG flow of the Wilson action in the exact renormalization group (ERG)
formalism. By imitating the structure of this connection, we propose an ERG
differential equation that preserves manifest gauge invariance in Yang--Mills
theory. Our construction in continuum theory can be extended to lattice gauge
theory.
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Black Holes and the Holographic Principle: This lecture reviews the black hole information paradox and briefly appraises
some proposed resolutions in view of developments in string theory. It goes on
to give an elementary introduction to the holographic principle.
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String Theory in Magnetic Monopole Backgrounds: We discuss string propagation in the near-horizon geometry generated by
Neveu-Schwarz fivebranes, Kaluza-Klein monopoles and fundamental strings. When
the fivebranes and KK monopoles are wrapped around a compact four-manifold
$\MM$, the geometry is $AdS_3\times S^3/\ZZ_N\times \MM$ and the spacetime
dynamics is expected to correspond to a local two dimensional conformal field
theory. We determine the moduli space of spacetime CFT's, study the spectrum of
the theory and compare the chiral primary operators obtained in string theory
to supergravity expectations.
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Galilei covariance and (4,1) de Sitter space: A vector space G is introduced such that the Galilei transformations are
considered linear mappings in this manifold. The covariant structure of the
Galilei Group (Y. Takahashi, Fortschr. Phys. 36 (1988) 63; 36 (1988) 83) is
derived and the tensor analysis is developed. It is shown that the Euclidean
space is embedded the (4,1) de Sitter space through in G. This is an
interesting and useful aspect, in particular, for the analysis carried out for
the Lie algebra of the generators of linear transformations in G.
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The Ostrogradskian Instability of Lagrangians with Nonlocality of Finite
Extent: I reply to the objections recently raised by J. Llosa to my constructive
proof that Lagrangians with nonlocality of finite extent inherit the full
Ostrogradskian instability.
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Conservation Laws from Asymptotic Symmetry and Subleading Charges in QED: We present several results on memory effects, asymptotic symmetry and soft
theorems in massive QED. We first clarify in what sense the memory effects are
interpreted as the charge conservation of the large gauge transformations, and
derive the leading and subleading memory effects in classical electromagnetism.
We also show that the sub-subleading charges are not conserved without
including contributions from the spacelike infinity. Next, we study QED in the
BRST formalism and show that parts of large gauge transformations are physical
symmetries by justifying that they are not gauge redundancies. Finally, we
obtain the expression of charges associated with the subleading soft photon
theorem in massive scalar QED.
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$W_{\infty}$ Algebras and Incompressibility in the Quantum Hall Effect: We discuss how a large class of incompressible quantum Hall states can be
characterized as highest weight states of different representations of the
\Winf algebra. Second quantized expressions of the \Winf generators are
explicitly derived in the cases of multilayer Hall states, the states proposed
by Jain to explain the hierarchical filling fractions and the ones related by
particle-hole conjugation.
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On timelike supersymmetric solutions of Abelian gauged 5-dimensional
supergravity: We consider 5-dimensional gauged supergravity coupled to Abelian vector
multiplets, and we look for supersymmetric solutions for which the
4-dimensional K\"ahler base space admits a holomorphic isometry. Taking
advantage of this isometry, we are able to find several supersymmetric
solutions for the ST$[2,n_v+1]$ special geometric model with arbitrarily many
vector multiplets. Among these there are three families of solutions with
$n_v+2$ independent parameters, which for one of the families can be seen to
correspond to $n_v+1$ electric charges and one angular momentum. These
solutions generalize the ones recently found for minimal gauged supergravity in
JHEP 1704 (2017) 017 and include in particular the general supersymmetric
asymptotically-AdS$_5$ black holes of Gutowski and Reall, analogous black hole
solutions with non-compact horizon, the three near horizon geometries
themselves, and the singular static solutions of Behrndt, Chamseddine and
Sabra.
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Towards a Field Theory of F-theory: We make a proposal for a bosonic field theory in twelve dimensions that
admits the bosonic sector of eleven-dimensional supergravity as a consistent
truncation. It can also be consistently truncated to a ten-dimensional
Lagrangian that contains all the BPS p-brane solitons of the type IIB theory.
The mechanism allowing the consistent truncation in the latter case is unusual,
in that additional fields with an off-diagonal kinetic term are non-vanishing
and yet do not contribute to the dynamics of the ten-dimensional theory. They
do, however, influence the oxidation of solutions back to twelve dimensions. We
present a discussion of the oxidations of all the basic BPS solitons of
M-theory and the type IIB string to D=12. In particular, the NS-NS and R-R
strings of the type IIB theory arise as the wrappings of membranes in D=12
around one or other circle of the compactifying 2-torus.
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Algebra of operators in an AdS-Rindler wedge: We discuss the algebra of operators in AdS-Rinlder wedge, particularly in
AdS$_{5}$/CFT$_{4}$. We explicitly construct the algebra at $N=\infty$ limit
and discuss its Type III$_{1}$ nature. We will consider $1/N$ corrections to
the theory and using a novel way of renormalizing the area of Ryu-Takayanagi
surface, describe how several divergences can be renormalized and the algebra
becomes Type II$_{\infty}$. This will make it possible to associate a density
matrix to any state in the Hilbert space and thus a von Neumann entropy.
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BRST Formalism and Zero Locus Reduction: In the BRST quantization of gauge theories, the zero locus $Z_Q$ of the BRST
differential $Q$ carries an (anti)bracket whose parity is opposite to that of
the fundamental bracket. We show that the on-shell BFV/BV gauge symmetries are
in a 1:1 correspondence with Hamiltonian vector fields on $Z_Q$, and
observables of the BRST theory are in a 1:1 correspondence with characteristic
functions of the bracket on $Z_Q$. By reduction to the zero locus, we obtain
relations between bracket operations and differentials arising in different
complexes (the Gerstenhaber, Schouten, Berezin-Kirillov, and Sklyanin
brackets); the equation ensuring the existence of a nilpotent vector field on
the reduced manifold can be the classical Yang-Baxter equation. We also
generalize our constructions to the bi-QP-manifolds which from the BRST theory
viewpoint corresponds to the BRST-anti-BRST-symmetric quantization.
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Haag-Ruelle scattering theory in presence of massless particles: Within the framework of local quantum physics we construct a scattering
theory of stable, massive particles without assuming mass gaps. This extension
of the Haag-Ruelle theory is based on advances in the harmonic analysis of
local operators. Our construction is restricted to theories complying with a
regularity property introduced by Herbst. The paper concludes with a brief
discussion of the status of this assumption.
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The continuation method and the real analyticity of the accessory
parameters: the general elliptic case: We apply the Le Roy-Poincar\'e continuation method to prove the real analytic
dependence of the accessory parameters on the position of the sources in
Liouville theory in presence of any number of elliptic sources. The treatment
is easily extended to the case of the torus with any number of elliptic
singularities. A discussion is given of the extension of the method to
parabolic singularities and higher genus surfaces.
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On Perturbative Gravity and Gauge Theory: We review some applications of tree-level (classical) relations between
gravity and gauge theory that follow from string theory. Together with
$D$-dimensional unitarity, these relations can be used to perturbatively
quantize gravity theories, i.e. they contain the necessary information for
obtaining loop contributions. We also review recent applications of these ideas
showing that N=1 D=11 supergravity diverges, and review arguments that N=8 D=4
supergravity is less divergent than previously thought, though it does appear
to diverge at five loops. Finally, we describe field variables for the
Einstein-Hilbert Lagrangian that help clarify the perturbative relationship
between gravity and gauge theory.
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Integrable System Constructed out of Two Interacting Superconformal
Fields: We describe how it is possible to introduce the interaction between
superconformal fields of the same conformal dimensions. In the classical case
such construction can be used to the construction of the Hirota - Satsuma
equation. We construct supersymmetric Poisson tensor for such fields, which
generates a new class of Hamiltonin systems. We found Lax representation for
one of equation in this class by supersymmetrization Lax operator responsible
for Hirota - Satsuma equation. Interestingly our supersymmetric equation is not
reducible to classical Hirota - Satsuma equation. We show that our generalized
system is reduced to the one of the supersymmetric KDV equation (a=4) but in
this limit integrals of motion are not reduced to integrals of motion of the
supersymmetric KdV equation.
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Energy dynamics, information and heat flow in quenched cooling and the
crossover from quantum to classical thermodynamics: The dynamics when a hot many-body quantum system is brought into
instantaneous contact with a cold many-body quantum system can be understood as
a combination of early time quantum correlation (von Neumann entropy) gain and
late time energy relaxation. We show that at the shortest timescales there is
an energy increase in each system linked to the entropy gain, even though
equilibrium thermodynamics does not apply. This energy increase is of quantum
origin and results from the collective binding energy between the two systems.
Counter-intuitively, this implies that also the hotter of the two systems
generically experiences an initial energy increase when brought into contact
with the other colder system. In the limit where the energy relaxation
overwhelms the (quantum) correlation build-up, classical energy dynamics
emerges where the energy in the hot system decreases immediately upon contact
with a cooler system. We use both strongly correlated SYK systems and weakly
correlated mixed field Ising chains to exhibit these characteristics, and
comment on its implications for both black hole evaporation and quantum
thermodynamics.
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Boundary-Value Problems for the Squared Laplace Operator: The squared Laplace operator acting on symmetric rank-two tensor fields is
studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this
fourth-order elliptic operator is obtained provided that such tensor fields and
their first (or second) normal derivatives are set to zero at the boundary.
Strong ellipticity of the resulting boundary-value problems is also proved.
Mixed boundary conditions are eventually studied which involve complementary
projectors and tangential differential operators. In such a case, strong
ellipticity is guaranteed if a pair of matrices are non-degenerate. These
results find application to the analysis of quantum field theories on manifolds
with boundary.
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Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple
M2-branes: We review various generalizations of the notion of Lie algebras, in
particular those appearing in the recently proposed Bagger-Lambert-Gustavsson
model, and study their interrelations. We find that Filippov's n-Lie algebras
are a special case of strong homotopy Lie algebras. Furthermore, we define a
class of homotopy Maurer-Cartan equations, which contains both the Nahm and the
Basu-Harvey equations as special cases. Finally, we show how the super
Yang-Mills equations describing a Dp-brane and the Bagger-Lambert-Gustavsson
equations supposedly describing M2-branes can be rewritten as homotopy
Maurer-Cartan equations, as well.
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3D String Theory and Umbral Moonshine: The simplest string theory compactifications to 3D with 16 supercharges --
the heterotic string on $T^7$, and type II strings on $K3 \times T^3$ -- are
related by U-duality, and share a moduli space of vacua parametrized by
$O(8,24; \mathbb{Z}) \backslash O(8,24) / (O(8) \times O(24))$. One can think
of this as the moduli space of even, self-dual 32-dimensional lattices with
signature (8,24). At 24 special points in moduli space, the lattice splits as
$\Gamma^{8,0} \oplus \Gamma^{0,24}$. $\Gamma^{0,24}$ can be the Leech lattice
or any of 23 Niemeier lattices, while $\Gamma^{8,0}$ is the $E_8$ root lattice.
We show that starting from this observation, one can find a precise connection
between the Umbral groups and type IIA string theory on $K3$. This provides a
natural physical starting point for understanding Mathieu and Umbral moonshine.
The maximal unbroken subgroups of Umbral groups in 6D (or any other limit) are
those obtained by starting at the associated Niemeier point and moving in
moduli space while preserving the largest possible subgroup of the Umbral
group. To illustrate the action of these symmetries on BPS states, we discuss
the computation of certain protected four-derivative terms in the effective
field theory, and recover facts about the spectrum and symmetry representations
of 1/2-BPS states.
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Mathematical structures of non-perturbative topological string theory:
from GW to DT invariants: We study the Borel summation of the Gromov-Witten potential for the resolved
conifold. The Stokes phenomena associated to this Borel summation are shown to
encode the Donaldson-Thomas invariants of the resolved conifold, having a
direct relation to the Riemann-Hilbert problem formulated by T. Bridgeland.
There exist distinguished integration contours for which the Borel summation
reproduces previous proposals for the non-perturbative topological string
partition functions of the resolved conifold. These partition functions are
shown to have another asymptotic expansion at strong topological string
coupling. We demonstrate that the Stokes phenomena of the strong-coupling
expansion encode the DT invariants of the resolved conifold in a second way.
Mathematically, one finds a relation to Riemann-Hilbert problems associated to
DT invariants which is different from the one found at weak coupling. The
Stokes phenomena of the strong-coupling expansion turn out to be closely
related to the wall-crossing phenomena in the spectrum of BPS states on the
resolved conifold studied in the context of supergravity by D. Jafferis and G.
Moore.
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Punctures and p-spin curves from matrix models III. Dl type and
logarithmic potential: The intersection numbers for p spin curves of the moduli space M(g,n) are
considered for D type by a matrix model. The asymptotic behavior of the large
genus g limit and large p limit are derived. The remarkable features of the
cases of p= 1/2, - 1/2, -2, -3 are examined in the Laurent expansion for
multiple correlation functions. The strong coupling expansions for the negative
p cases are considered.
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Renyi entropy, stationarity, and entanglement of the conformal scalar: We extend previous work on the perturbative expansion of the Renyi entropy,
$S_q$, around $q=1$ for a spherical entangling surface in a general CFT.
Applied to conformal scalar fields in various spacetime dimensions, the results
appear to conflict with the known conformal scalar Renyi entropies. On the
other hand, the perturbative results agree with known Renyi entropies in a
variety of other theories, including theories of free fermions and vector
fields and theories with Einstein gravity duals. We propose a resolution
stemming from a careful consideration of boundary conditions near the
entangling surface. This is equivalent to a proper treatment of
total-derivative terms in the definition of the modular Hamiltonian. As a
corollary, we are able to resolve an outstanding puzzle in the literature
regarding the Renyi entropy of ${\cal N}=4$ super-Yang-Mills near $q=1$. A
related puzzle regards the question of stationarity of the renormalized
entanglement entropy (REE) across a circle for a (2+1)-dimensional massive
scalar field. We point out that the boundary contributions to the modular
Hamiltonian shed light on the previously-observed non-stationarity. Moreover,
IR divergences appear in perturbation theory about the massless fixed point
that inhibit our ability to reliably calculate the REE at small non-zero mass.
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Free fermionic higher spin fields in AdS(5): Totally symmetric massless fermionic fields of arbitrary spins in AdS(5) are
described as su(2,2) multispinors. The approach is based on the well-known
isomorfism o(4,2)=su(2,2). Explicitly gauge invariant higher spin free actions
are constructed and free field equations are analyzed.
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Holomorphy, Minimal Homotopy and the 4D, N = 1 Supersymmetric
Bardeen-Gross-Jackiw Anomaly: By use of a special homotopy operator, we present an explicit, closed-form
and simple expression for the left-right Bardeen-Gross-Jackiw anomalies
described as the proper superspace integral of a superfunction.
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String theory in Lorentz-invariant light cone gauge - II: We perform a quantization of 4-dimensional Nambu-Goto theory of open string
in light cone gauge, related in Lorentz-invariant way with the world sheet.
This allows to obtain a quantum theory without anomalies in Lorentz group. We
consider a special type of gauge fixing conditions, imposed in oscillator
sector of the theory, which lead to a relatively simple Hamiltonian mechanics,
convenient for canonical quantization. We discuss the algebraic and geometric
properties of this mechanics and determine its mass spectrum for the states of
spin singlet S=0.
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"Short" spinning strings and structure of quantum AdS_5 x S^5 spectrum: Using information from the marginality conditions of vertex operators for the
AdS_5 x S^5 superstring, we determine the structure of the dependence of the
energy of quantum string states on their conserved charges and the string
tension proportional to lambda^(1/2). We consider states on the leading Regge
trajectory in the flat space limit which carry one or two (equal) spins in
AdS_5 or S^5 and an orbital momentum in S^5, with Konishi multiplet states
being particular cases. We argue that the coefficients in the energy may be
found by using a semiclassical expansion. By analyzing the examples of folded
spinning strings in AdS_5 and S^5 as well as three cases of circular two-spin
strings we demonstrate the universality of transcendental (zeta-function) parts
of few leading coefficients. We also show the consistency with target space
supersymmetry with different states belonging to the same multiplet having the
same non-trivial part of the energy. We suggest, in particular, that a rational
coefficient (found by Basso for the folded string using Bethe Ansatz
considerations and which, in general, is yet to be determined by a direct
two-loop string calculation) should, in fact, be universal.
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Superstring dualities and p-brane bound states: We show that the M-theory/IIA and IIA/IIB superstring dualities together with
the diffeomorphism invariance of the underlying theories require the presence
of certain p-brane bound states in IIA and IIB superstring theories preserving
1/2 of the spacetime supersymmetry. We then confirm the existence of IIA and
IIB supergravity solutions having the appropriate p-brane bound states
interpretation.
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String Quantum Symmetries and the SL(2,Z) Group: We prove, using arguments relying only on the "special K\"ahler" structure of
the moduli space of the Calabi-Yau three-fold, that in the case of one single
modulus the quantum modular group of the string effective action corresponding
to Calabi-Yau vacua can not be SL(2,${Z\kern -4.6pt Z}$).
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The Emergence of Anticommuting Coordinates and the Dirac-Ramond-Kostant
operators: The history of anticommuting coordinates is decribed.
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Tackling tangledness of cosmic strings by knot polynomial topological
invariants: Cosmic strings in the early universe have received revived interest in recent
years. In this paper we derive these structures as topological defects from
singular distributions of the quintessence field of dark energy. Our emphasis
is placed on the topological charge of tangled cosmic strings, which originates
from the Hopf mapping and is a Chern-Simons action possessing strong inherent
tie to knot topology. It is shown that the Kauffman bracket knot polynomial can
be constructed in terms of this charge for un-oriented knotted strings, serving
as a topological invariant much stronger than the traditional Gauss linking
numbers in characterizing string topology. Especially, we introduce a
mathematical approach of breaking-reconnection which provides a promising
candidate for studying physical reconnection processes within the
complexity-reducing cascades of tangled cosmic strings.
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Open AdS/CFT via a Double Trace Deformation: A concrete model of extracting the physics from the bulk of a gravitational
universe is important to the study of quantum gravity and its possible
relationship with experiments. Such a model can be constructed in the AdS/CFT
correspondence by gluing a bath on the asymptotic boundary of the bulk anti-de
Sitter (AdS) spacetime. This bath models a laboratory and is described by a
quantum field theory. In the dual conformal field theory (CFT) description this
coupling is achieved by a double-trace deformation that couples the CFT with
the bath. This suggests that the physics observed by the laboratory is fully
unitary. In this paper, we analyze the quantum aspects of this model in detail
which conveys new lessons about the AdS/CFT correspondence, and we discuss the
potential usefulness of this model in understanding subregion physics in a
gravitational universe.
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Phase structure of the $O(2)$ ghost model with higher-order gradient
term: The phase structure and the infrared behaviour of the Euclidean 3-dimensional
$O(2)$ symmetric ghost scalar field model with higher-order derivative term has
been investigated in Wegner and Houghton's renormalization group framework. The
symmetric phase in which no ghost condensation occurs and the phase with
restored symmetry but with a transient presence of a ghost condensate have been
identified. Finiteness of the correlation length at the phase boundary hints to
a phase transition of first order. The results are compared with those for the
ordinary $O(2)$ symmetric scalar field model.
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On Problems of the Lagrangian Quantization of W3-gravity: We consider the two-dimensional model of W3-gravity within Lagrangian
quantization methods for general gauge theories. We use the Batalin-Vilkovisky
formalism to study the arbitrariness in the realization of the gauge algebra.
We obtain a one-parametric non-analytic extension of the gauge algebra, and a
corresponding solution of the classical master equation, related via an
anticanonical transformation to a solution corresponding to an analytic
realization. We investigate the possibility of closed solutions of the
classical master equation in the Sp(2)-covariant formalism and show that such
solutions do not exist in the approximation up to the third order in ghost and
auxiliary fields.
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Symmetry Reduction in Twisted Noncommutative Gravity with Applications
to Cosmology and Black Holes: As a preparation for a mathematically consistent study of the physics of
symmetric spacetimes in a noncommutative setting, we study symmetry reductions
in deformed gravity. We focus on deformations that are given by a twist of a
Lie algebra acting on the spacetime manifold. We derive conditions on those
twists that allow a given symmetry reduction. A complete classification of
admissible deformations is possible in a class of twists generated by commuting
vector fields. As examples, we explicitly construct the families of vector
fields that generate twists which are compatible with
Friedmann-Robertson-Walker cosmologies and Schwarzschild black holes,
respectively. We find nontrivial isotropic twists of FRW cosmologies and
nontrivial twists that are compatible with all classical symmetries of black
hole solutions.
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Heterotic mini-landscape (II): completing the search for MSSM vacua in a
Z_6 orbifold: We complete our search for MSSM vacua in the Z_6-II heterotic orbifold by
including models with 3 Wilson lines. We estimate the total number of
inequivalent models in this orbifold to be 10^7. Out of these, we find almost
300 models with the exact MSSM spectrum, gauge coupling unification and a heavy
top quark. Models with these features originate predominantly from local GUTs.
The scale of gaugino condensation in the hidden sector is correlated with
properties of the observable sector such that soft masses in the TeV range are
preferred.
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The partition function of the supersymmetric two-dimensional black hole
and little string theory: We compute the partition function of the supersymmetric two-dimensional
Euclidean black hole geometry described by the SL(2,R)/U(1) superconformal
field theory. We decompose the result in terms of characters of the N=2
superconformal symmetry. We point out puzzling sectors of states besides
finding expected discrete and continuous contributions to the partition
function. By adding an N=2 minimal model factor of the correct central charge
and projecting on integral N=2 charges we compute the partition function of the
background dual to little string theory in a double scaling limit. We show the
precise correspondence between this theory and the background for NS5-branes on
a circle, due to an exact description of the background as a null gauging of
SL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection and
target space geometry.
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The Vortex Structure of SU(2) Calorons: We reveal the center vortex content of SU(2) calorons and ensembles of them.
We use Laplacian Center Gauge as well as Maximal Center Gauges to show that the
vortex in a single caloron consists of two parts. The first one connects the
constituent dyons of the caloron (which are monopoles in Laplacian Abelian
Gauge) and extends in time. The second part is predominantly spatial, encloses
one of the dyons and can be related to the twist in the caloron gauge field.
This part depends strongly on the caloron holonomy and degenerates to a plane
when the holonomy is maximally nontrivial, i.e. when the asymptotic Polyakov
loop is traceless. Correspondingly, we find the spatial vortices in caloron
ensembles to percolate in this case. This finding fits perfectly in the
confinement scenario of vortices and shows that calorons are suitable to
facilitate the vortex confinement mechanism.
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Dark Monopoles in Grand Unified Theories: We consider a Yang-Mills-Higgs theory with gauge group $G=SU(n)$ broken to
$G_{v} = [SU(p)\times SU(n-p)\times U(1)]/Z$ by a Higgs field in the adjoint
representation. We obtain monopole solutions whose magnetic field is not in the
Cartan Subalgebra. Since their magnetic field vanishes in the direction of the
generator of the electromagnetic group $U(1)_{em}$, we call them Dark
Monopoles. These Dark Monopoles must exist in some Grand Unified Theories
(GUTs) without the need to introduce a dark sector. We analyze the particular
case of $SU(5)$ GUT, where we obtain that their mass is $M = 4\pi v
\widetilde{E}(\lambda/e^{2})/e$, where $\widetilde{E}(\lambda/e^{2})$ is a
monotonically increasing function of $\lambda/e^{2}$ with
$\widetilde{E}(0)=1.294$ and $\widetilde{E}(\infty)=3.262.$ We also give a
geometrical interpretation to their non-abelian magnetic charge.
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Metric On Quantum Spaes: We introduce the analogue of the metric tensor in case of $q$-deformed
differential calculus. We analyse the consequences of the existence of such
metric, showing that this enforces severe restrictions on the parameters of the
theory. We discuss in detail the examples of the Manin plane and the
$q$-deformation of $SU(2)$. Finally we touch the topic of relations with the
Connes' approach.
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Semi-naive dimensional renormalization: We propose a treatment of $\gamma^5$ in dimensional regularization which is
based on an algebraically consistent extension of the Breitenlohner-Maison-'t
Hooft-Veltman (BMHV) scheme; we define the corresponding minimal
renormalization scheme and show its equivalence with a non-minimal BMHV scheme.
The restoration of the chiral Ward identities requires the introduction of
considerably fewer finite counterterms than in the BMHV scheme. This scheme is
the same as the minimal naive dimensional renormalization in the case of
diagrams not involving fermionic traces with an odd number of $\gamma^5$, but
unlike the latter it is a consistent scheme. As a simple example we apply our
minimal subtraction scheme to the Yukawa model at two loops in presence of
external gauge fields.
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3d Modularity: We find and propose an explanation for a large variety of modularity-related
symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$
theories where such structures a priori are not manifest. These modular
structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil
representations, quantum modular forms, non-semisimple modular tensor
categories, and chiral algebras of logarithmic CFTs.
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On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS
Symmetries: We consider a BMS-type symmetry action on isolated horizons in asymptotically
flat spacetimes. From the viewpoint of the non-relativistic field theory on a
horizon membrane, supertranslations shift the field theory spatial momentum.
The latter is related by a Ward identity to the particle number symmetry
current and is spontaneously broken. The corresponding Goldstone boson shifts
the horizon angular momentum and can be detected quantum mechanically.
Similarly, area preserving superrotations are spontaneously broken on the
horizon membrane and we identify the corresponding gapless modes. In
asymptotically AdS spacetimes we study the BMS-type symmetry action on the
horizon in a holographic superfluid dual. We identify the horizon
supertranslation Goldstone boson as the holographic superfluid Goldstone mode.
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Nonlinear Field Space Theory and Quantum Gravity: Phase spaces with nontrivial geometry appear in different approaches to
quantum gravity and can also play a role in e.g. condensed matter physics.
However, so far such phase spaces have only been considered for particles or
strings. We propose an extension of the usual field theories to the framework
of fields with nonlinear phase space of field values, which generally means
nontrivial topology or geometry. In order to examine this idea we construct a
prototype scalar field with the spherical phase space and then study its
quantized version with the help of perturbative methods. As the result we
obtain a variety of predictions that are known from the quantum gravity
research, including algebra deformations, generalization of the uncertainty
relation and shifting of the vacuum energy.
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Axionic and nonaxionic electrodynamics in plane and circular geometry: Various aspects of axion electrodynamics in the presence of a homogeneous and
isotropic dielectric medium are discussed. 1. We consider first the
"antenna-like" property of a planar dielectric surface in axion
electrodynamics, elaborating on the treatment given earlier on this topic by
Millar {\it et al.} (2017). We calculate the electromagnetic energy
transmission coefficient for a dielectric plate, and compare with the
conventional expression in ordinary electrodynamics. 2. We consider the
situation where the medium exterior to the plate, assumed elastic, is "bent
back" and glued together, so that we obtain a circular dielectric string in
which the waves can propagate clockwise or counterclockwise. As will be shown,
a stationary wave pattern is permitted by the formalism, and we show how the
amplitudes for the two counterpropagating waves can be found. 3. As a special
case, by omitting axions for a moment, we analyze the Casimir effect for the
string, showing its similarity as well as its difference with the Casimir
effect of a scalar field for a piecewise uniform string (Brevik and Nielsen
1990). 4. Finally, including axions again we analyze the enhancement of the
surface-generated electromagnetic radiation near the center of a cylindrical
haloscope, where the interior region is a vacuum and the exterior region a
metal. This enhancement is caused by the curvature of the boundary, and is
mathematically a consequence of the behavior of the Hankel function of the
second kind for small arguments. A simple estimate shows that enhancement may
be quite significant, and can therefore be of experimental interest. This
proposal is suggested as an alternative to the reflector arrangement in a
similar arrangement recently discussed by Liu {\it et al.} (2022).
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Gauge-Invariant Quantum Fields: Gauge-invariant quantum fields are constructed in an Abelian power-counting
renormalizable gauge theory with both scalar, vector and fermionic matter
content. This extends previous results already obtained for the gauge-invariant
description of the Higgs mode via a propagating gauge-invariant field. The
renormalization of the model is studied in the Algebraic Renormalization
approach.
The decomposition of Slavnov-Taylor identities into separately invariant
sectors is analyzed.
We also comment on some non-renormalizable extensions of the model whose 1-PI
Green's functions are the flows of certain differential equations of the
homogeneous Euler type, exactly resumming the dependence on a certain set of
dim. 6 and dim. 8 derivative operators.
The latter are identified uniquely by the condition that they span the mass
and kinetic terms in the gauge-invariant dynamical fields.
The construction can be extended to non-Abelian gauge groups.
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Symmetry Breaking for Bosonic Systems on Orbifolds: We discuss a general class of boundary conditions for bosons living in an
extra spatial dimension compactified on S^1/Z_2. Discontinuities for both
fields and their first derivatives are allowed at the orbifold fixed points. We
analyze examples with free scalar fields and interacting gauge vector bosons,
deriving the mass spectrum, that depends on a combination of the twist and the
jumps. We discuss how the same physical system can be characterized by
different boundary conditions, related by local field redefinitions that turn a
twist into a jump or vice-versa. When the description is in term of
discontinuous fields, appropriate lagrangian terms should be localized at the
orbifold fixed points.
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Emergent Lorentz invariance with chiral fermions: We study renormalization group flows in strongly interacting field theories
with fermions that correspond to transitions between a theory without Lorentz
invariance at high energies down to a theory with approximate Lorentz symmetry
in the infrared. Holographic description of the strong coupling is used. The
emphasis is made on emergence of chiral fermions in the low-energy theory.
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Replica-deformation of the SU(2)-invariant Thirring model via solutions
of the qKZ equation: The response of an integrable QFT under variation of the Unruh temperature
has recently been shown to be computable from an S-matrix preserving
(`replica') deformation of the form factor approach. We show that
replica-deformed form factors of the SU(2)-invariant Thirring model can be
found among the solutions of the rational $sl_2$-type quantum
Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved
charge solutions the deformed form factors are in one-to-one correspondence to
the ones at level zero and use this to conjecture the deformed form factors of
the Noether current in our model.
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Supersymmetric massive truncations of IIb supergravity on
Sasaki-Einstein manifolds: Motivated by recent interest in applications of the AdS/CFT correspondence to
condensed matter applications involving fermions, we present the supersymmetric
completion of the recent massive truncations of IIB supergravity on
Sasaki-Einstein manifolds. In particular, we reduce the fermionic sector of IIB
supergravity to obtain five dimensional N=2 supergravity coupled to one
hypermultiplet and one massive vector multiplet. The supersymmetry
transformations and equations of motion are presented and analyzed. Finally, a
particularly interesting truncation to N=2 supergravity coupled to a single
hypermultiplet is presented which is the supersymmetric completion of the
recently constructed bosonic theory dual to a 3+1 dimensional system exhibiting
a superconducting phase transition.
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A Finite Landscape?: We present evidence that the number of string/$M$ theory vacua consistent
with experiments is a finite number. We do this both by explicit analysis of
infinite sequences of vacua and by applying various mathematical finiteness
theorems.
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Modular Average and Weyl Anomaly in Two-Dimensional Schwarzian Theory: The gauge formulation of Einstein gravity in AdS$_3$ background leads to a
boundary theory that breaks modular symmetry and loses the covariant form. We
examine the Weyl anomaly for the cylinder and torus manifolds. The divergent
term is the same as the Liouville theory when transforming from the cylinder to
the sphere. The general Weyl transformation on the torus also reproduces the
Liouville theory. The Weyl transformation introduces an additional boundary
term for reproducing the Liouville theory, which allows the use of CFT
techniques to analyze the theory. The torus partition function in this boundary
theory is one-loop exact, and an analytical solution to disjoint two-interval
R\'enyi-2 mutual information can be obtained. We also discuss a first-order
phase transition for the separation length of two intervals, which occurs at
the classical level but is smoothed out by non-perturbative effects captured by
averaging over a modular group in the boundary theory.
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Entanglement entropy of near-extremal black hole: We study how the entanglement entropy of the Hawking radiation derived using
island recipe for the Reissner-Nordstr\"om black hole behaves as the black hole
mass decreases. A general answer to the question essentially depends not only
on the character of decreasing of the mass but also on decreasing of the
charge. We assume the specific relationship between the charge and mass
$Q^2=GM^2[1-\left(\frac{M}{\mu}\right)^{2\nu} ]$, which we call the constraint
equation. We discuss whether it is possible to have a constraint so that the
entanglement entropy does not have an explosion at the end of evaporation, as
happens in the case of thermodynamic entropy and the entanglement entropy for
the Schwarzschild black hole. We show that for some special scaling parameters,
the entanglement entropy of radiation does not explode as long as the mass of
the evaporating black hole exceeds the Planck mass.
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Kinky Brane Worlds: We present a toy model for five-dimensional heterotic M-theory where bulk
three-branes, originating in 11 dimensions from M five-branes, are modelled as
kink solutions of a bulk scalar field theory. It is shown that the vacua of
this defect model correspond to a class of topologically distinct M-theory
compactifications. Topology change can then be analysed by studying the time
evolution of the defect model. In the context of a four-dimensional effective
theory, we study in detail the simplest such process, that is the time
evolution of a kink and its collision with a boundary. We find that the kink is
generically absorbed by the boundary thereby changing the boundary charge. This
opens up the possibility of exploring the relation between more complicated
defect configurations and the topology of brane-world models.
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High-energy properties of the graviton scattering in quadratic gravity: We obtain the matter-graviton scattering amplitude in the gravitational
theory of quadratic curvature, which has $R_{\mu\nu}^2$ term in the action.
Unitarity bound is not satisfied because of the existence of negative norm
states, while an analog of unitarity bound for $S$-matrix unitarity holds due
to the cancelation among the positive norm states and negative norm ones in the
unitarity summation in the optical theorem. The violation of unitarity bound is
a counter example of Llewellyn Smith's conjecture on the relation between
tree-level unitarity and renormalizability. We have recently proposed a new
conjecture that an analog of the unitarity bound for $S$-matrix unitarity gives
the equivalent conditions to those for renormalizability. We show that the
gravitational theory of quadratic curvature is a nontrivial example consistent
with our conjecture.
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Constraints on modular inflation in supergravity and string theory: We perform a general algebraic analysis on the possibility of realising
slow-roll inflation in the moduli sector of string models. This problem turns
out to be very closely related to the characterisation of models admitting
metastable vacua with non-negative cosmological constant. In fact, we show that
the condition for the existence of viable inflationary trajectories is a
deformation of the condition for the existence of metastable de Sitter vacua.
This condition depends on the ratio between the scale of inflation and the
gravitino mass and becomes stronger as this parameter grows. After performing a
general study within arbitrary supergravity models, we analyse the implications
of our results in several examples. More concretely, in the case of heterotic
and orientifold string compactifications on a Calabi-Yau in the large volume
limit we show that there may exist fully viable models, allowing both for
inflation and stabilisation. Additionally, we show that subleading corrections
breaking the no-scale property shared by these models always allow for
slow-roll inflation but with an inflationary scale suppressed with respect to
the gravitino scale. A scale of inflation larger than the gravitino scale can
also be achieved under more restrictive circumstances and only for certain
types of compactifications.
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Wrapped membranes, matrix string theory and an infinite dimensional Lie
algebra: We examine the algebraic structure of the matrix regularization for the
wrapped membrane on $R^{10}\times S^1$ in the light-cone gauge. We give a
concrete representation for the algebra and obtain the matrix string theory
having the boundary conditions for the matrix variables corresponding to the
wrapped membrane, which is referred to neither Seiberg and Sen's arguments nor
string dualities. We also embed the configuration of the multi-wrapped membrane
in matrix string theory.
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