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F-brane Dynamics: We generalize the current algebra of constraints of U-duality-covariant
critical superstrings to include the generator responsible for the dynamics of
the fundamental brane. This allows us to define $\kappa$ symmetry and to write
a worldvolume action in Hamiltonian form that is manifestly supersymmetric in
the target space. The Lagrangian form of this action is generally covariant,
but the worldvolume metric has fewer components than expected. | The Bethe Ansatz for the superconformal index with unequal angular
momenta: A few years ago it was shown that the superconformal index of the
$\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory in the large $N$ limit
matches with the entropy of $1/16$-supersymmetric black holes in type IIB
string theory on $AdS_5\times S^5$. In some cases, an even more detailed match
between the two sides is possible. When the two angular momentum chemical
potentials in the index are equal, the superconformal index can be written as a
discrete sum of Bethe ansatz solutions, and it was shown that specific terms in
this sum are in a one-to-one correspondence to stable black hole solutions, and
that the matching can be extended to non-perturbative contributions from
wrapped D3-branes. A Bethe ansatz approach to computing the superconformal
index exists also when the ratio of the angular momentum chemical potentials is
any rational number, but in those cases it involves a sum over a very large
number of terms (growing exponentially with $N$). Benini et al showed that a
specific one of these terms matches with the black hole, but the role of the
other terms is not clear. In this paper we analyze some of the additional
contributions to the index in the Bethe ansatz approach, and we find that their
matching to the gravity side is much more complicated than in the case of equal
chemical potentials. In particular, we find some contributions that are larger
than the one which was found to match the black holes, so that they must cancel
with other large contributions. We give some evidence that cancellations of
this type are possible, but we leave a full understanding of how they work to
the future. |
The deconfinement phase transition in the Hamiltonian approach to
Yang--Mills theory in Coulomb gauge: The deconfinement phase transition of SU(2) Yang--Mills theory is
investigated in the Hamiltonian approach in Coulomb gauge assuming a
quasi-particle picture for the grand canonical gluon ensemble. The thermal
equilibrium state is found by minimizing the free energy with respect to the
quasi-gluon energy. Above the deconfinement phase transition the ghost form
factor remains infrared divergent but its infrared exponent is approximately
halved, while the gluon energy, being infrared divergent in the confined phase,
becomes infrared finite in the deconfined phase. For the effective gluon mass
we find a critical exponent of 0.37. Using the lattice results for the gluon
propagator to fix the scale, the deconfinement transition temperature is
obtained in the range of 275 to 290 MeV. | Conformal symmetry of superstrings on $AdS_3\times S^3\times T^4$ and
D1/D5 system: Conformal field theory of the D1/D5 system and superstrings on $AdS_3\times
S^3\times T^4$ is studied with particular attention to the world-sheet fields
corresponding to the $T^4$ part. A solution to the spacetime N=4 superconformal
symmetry doubling and other problems is proposed. It is argued that the
relevant spacetime symmetry should be based on the middle N=4 superconformal
algebra. It is discussed as to why this superconformal structure has been
missed so far. |
On the correspondence between gravity fields and CFT operators: It is shown that a nonlinear derivative-dependent transformation of gravity
fields changes correlation functions in a boundary CFT, and, therefore,
corresponds to a change of a basis of operators in the CFT. It is argued that
only non-renormalized structures in correlation functions can be changed by
such a field transformation, and that the study of the response of correlation
functions to gravity field transformations allows one to find them. In the case
of 4-point functions of CPOs in SYM_4 several non-renormalized structures are
found, including the extremal and subextremal ones. It is also checked that
quartic couplings of scalar fields s^I that are dual to extended chiral primary
operators vanish in the subextremal case, as dictated by the
non-renormalization theorem for the subextremal 4-point functions and the
AdS/CFT correspondence. | The geometry of RN-AdS fluids: We establish the parameter space geometry of a fluid system characterized by
two constants, whose equation of state mimics that of the RN-AdS black hole. We
call this the RN-AdS fluid. We study the scalar curvature on the parameter
space of this system, and show its equivalence with the RN-AdS black hole, in
the limit of vanishing specific heat at constant volume. Further, an analytical
construction of the Widom line is established. We also numerically study the
behavior of geodesics on the parameter space of the fluid, and find a geometric
scaling relation near its second order critical point. |
Casimir Energy of 5D Warped System and Sphere Lattice Regularization: Casimir energy is calculated for the 5D electromagnetism and 5D scalar theory
in the {\it warped} geometry. It is compared with the flat
case(arXiv:0801.3064). A new regularization, called {\it sphere lattice
regularization}, is taken. In the integration over the 5D space, we introduce
two boundary curves (IR-surface and UV-surface) based on the {\it minimal area
principle}. It is a {\it direct} realization of the geometrical approach to the
{\it renormalization group}. The regularized configuration is {\it
closed-string like}. We do {\it not} take the KK-expansion approach. Instead,
the position/momentum propagator is exploited, combined with the {\it
heat-kernel method}. All expressions are closed-form (not KK-expanded form).
The {\it generalized} P/M propagators are introduced. We numerically evaluate
$\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra
space IR parameter) dependence of the Casimir energy. We present two {\it new
ideas} in order to define the 5D QFT: 1) the summation (integral) region over
the 5D space is {\it restricted} by two minimal surfaces (IR-surface,
UV-surface) ; or 2) we introduce a {\it weight function} and require the
dominant contribution is given by the {\it minimal surface}. Based on these, 5D
Casimir energy is {\it finitely} obtained after the {\it proper renormalization
procedure.} The {\it warp parameter} $\om$ suffers from the {\it
renormalization effect}. We examine the meaning of the weight function and
reach a {\it new definition} of the Casimir energy where {\it the 4D momenta(or
coordinates) are quantized} with the extra coordinate as the Euclidean time
(inverse temperature). We comment on the cosmological constant term and present
an answer to the problem at the end. Dirac's large number naturally appears. | Porting of EPICS to Real Time UNIX, and usage ported EPICS for FEL
automation: This article describes concepts and mechanisms used in porting of EPICS
(Experimental Physical and Industrial Control System) codes to platform of
operating system UNIX. Without destruction of EPICS architecture, new features
of EPICS provides the support for real time operating system LynxOS/x86 and
equipment produced by INP (Budker Institute of Nuclear Physics). Application of
ported EPICS reduces the cost of software and hardware is used for automation
of FEL (Free Electron Laser) complex. |
Supersymmetric vortex defects in two dimensions: We study codimension-two BPS defects in 2d N=(2,2) supersymmetric gauge
theories, focusing especially on those characterized by vortex-like
singularities in the dynamical or non-dynamical gauge field. We classify
possible SUSY-preserving boundary conditions on charged matter fields around
the vortex defects, and derive a formula for defect correlators on the squashed
sphere. We also prove an equivalence relation between vortex defects and 0d-2d
coupled systems. Our defect correlators are shown to be consistent with the
mirror symmetry duality between Abelian gauged linear sigma models and
Landau-Ginzburg models, as well as that between the minimal model and its
orbifold. We also study the vortex defects inserted at conical singularities. | The Quantum Black Hole Specific Heat is Positive: We suggest in this Letter that the Bekenstein-Hawking black hole entropy
accounts for the degrees of freedom which are excited at low temperatures only
and hence it leads to the negative specific heat. Taking into account the
physical degrees of freedom which are excited at high temperatures, the
existence of which we postulate, we compute the total specific heat of the
quantum black hole that appears to be positive. This is done in analogy to the
Planck's treatment of the black body radiation problem. Other thermodynamic
functions are computed as well. Our results and the success of the
thermodynamic description of the quantum black hole suggest an underlying
atomic (discrete) structure of gravitation. The basic properties of these
gravitational atoms are found. |
Worldline Superfield Actions for N=2 Superparticles: We propose doubly supersymmetric actions in terms of n=2(D-2) worldline
superfields for N=2 superparticles in D=3,4 and Type IIA D=6 superspaces. These
actions are obtained by dimensional reduction of superfield actions for N=1
superparticles in D=4,6 and 10, respectively. We show that in all these models
geometrodynamical constraints on target superspace coordinates do not put the
theory on the mass shell, so the actions constructed consistently describe the
dynamics of the corresponding N=2 superparticles. We also find that in contrast
to the IIA D=6 superparticle a chiral IIB D=6 superparticle, which is not
obtainable by dimensional reduction from N=1, D=10, is described by superfield
constraints which produce dynamical equations. This implies that for the IIB
D=6 superparticle the doubly supersymmetric action does not exist in the
conventional form. | Jackson Integral Representations for Solutions to the Quantized
Knizhnik-Zamolodchikov Equation: The quantized Knizhnik-Zamolodchikov equations associated with the
trigonometric R-matrix or the rational R-matrix of the A-type are considered.
Jackson integral representations for solutions of these equations are
described. Asymptotic solutions for a holonomic system of difference equations
are constructed. Relations between the integral representations and the Bethe
ansatz are indicated. |
Proving the dimension-shift conjecture: We prove the conjecture made by Bern, Dixon, Dunbar, and Kosower that
describes a simple dimension shifting relationship between the one-loop
structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure
Yang-Mills theory. The proof captures all orders in dimensional regularisation
using unitarity cuts, by combining massive spinor-helicity with Coulomb-branch
supersymmetry. The form of these amplitudes can be given in terms of pentagon
and box integrals using a generalised D-dimensional unitarity technique which
captures the full amplitude to all multiplicities. | Universality class of alternative phase space and Van der Waals
criticality: A new perspective toward thermodynamic phase space of Reisser-Nordstrom (RN)
black holes in an anti-de-Sitter (AdS) spaces was recently proposed [Phys.
Lett. B 768 (2017) 235], where the square of the electric charge $(Q^2)$ of
black hole was regarded as a thermodynamic variable and the cosmological
constant (pressure) as a fixed quantity. In this paper, we address the
universality class and critical properties of any AdS black hole in this
alternative phase space. We disclose the critical behavior of AdS black hole in
the alternative phase space in which a continuous phase transition happens and
in a very general framework, independent of the spacetime metric. Based on the
expansion of the equation of state and Landau thermodynamic potential in the
neighborhood of a critical point in the alternative phase space, we confirm
that the set of values for critical exponents for generic black hole is
analogous to the Van der Waals fluid system. Finally, we reveal that the scalar
curvature in geometry thermodynamic diverges at the critical point of black
hole. Our study shows that the approach here is powerful enough to investigate
the critical behavior of any black holes and further supports the viability of
the alternative viewpoint toward phase space of black holes suggested in [Phys.
Lett. B 768 (2017) 235]. |
Dynamical Cobordisms in General Relativity and String Theory: We describe a class of time-dependent solutions in string- or M-theory that
are exact with respect to alpha-prime and curvature corrections and interpolate
in physical space between regions in which the low energy physics is
well-approximated by different string theories and string compactifications.
The regions are connected by expanding "domain walls" but are not separated by
causal horizons, and physical excitations can propagate between them. As
specific examples we construct solutions that interpolate between oriented and
unoriented string theories, and also between type II and heterotic theories.
Our solutions can be weakly curved and under perturbative control everywhere
and can asymptote to supersymmetric at late times. | Point-like topological defects in bilayer quantum Hall systems: Following a suggestion given in Phys. Lett. B 571 (2003) 250, we show how a
bilayer Quantum Hall system at fillings nu =m/pm+2 can exhibit a point-like
topological defect in its edge state structure. Indeed our CFT theory for such
a system, the Twisted Model (TM), gives rise in a natural way to such a feature
in the twisted sector. Our results are in agreement with recent experimental
findings (cond-mat/0503478) which evidence the presence of a topological defect
in the bilayer system. |
Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections,
bound states at threshold, and S-duality: We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial
three-torus. The low energy spectrum consists of a number of continua of states
of arbitrarily low energies. Although the theory has no mass-gap, it appears
that the dimensions and discrete abelian magnetic and electric 't Hooft fluxes
of the continua are computable in a semi-classical approximation. The
wave-functions of the low-energy states are supported on submanifolds of the
moduli space of flat connections, at which various subgroups of the gauge group
are left unbroken. The field theory degrees of freedom transverse to such a
submanifold are approximated by supersymmetric matrix quantum mechanics with 16
supercharges, based on the semi-simple part of this unbroken group. Conjectures
about the number of normalizable bound states at threshold in the latter theory
play a crucial role in our analysis. In this way, we compute the low-energy
spectra in the cases where the simply connected cover of the gauge group is
given by SU(n), Spin(2n+1) or Sp(2n). We then show that the constraints of
S-duality are obeyed for unique values of the number of bound states in the
matrix quantum mechanics. In the cases based on Spin(2n+1) and Sp(2n), the
proof involves surprisingly subtle combinatorial identities, which hint at a
rich underlying structure. | Exponentially localized solutions of the Klein-Gordon equation: Exponentially localized solutions of the Klein-Gordon equation for two and
three space variables are presented. The solutions depend on four free
parameters. For some relations between the parameters, the solutions describe
wave packets filled with oscillations whose amplitudes decrease in the Gaussian
way with distance from a point running with group velocity along a straight
line. The solutions are constructed using exact complex solutions of the
eikonal equation and may be regarded as ray solutions with amplitudes involving
one term. It is also shown that the multidimensional nonlinear Klein-Gordon
equation can be reduced to an ordinary differential equation with respect to
the complex eikonal. |
Minimal constrained superfields and the Fayet-Iliopoulos model: We show how the necessary constraints to project out all the components of a
chiral superfield except for some scalar degrees of freedom originate from
simple operators in the microscopic theory. This is in particular useful in
constructing the simplest models of a goldstone boson/inflaton; or extracting
the Standard Model Higgs doublet from a supersymmetric electroweak sector. We
use the Fayet-Iliopoulos model as an example of the origin for the
supersymmetry breaking. We consider the regime where both gauge symmetry and
supersymmetry are spontaneously broken, leaving (in the decoupling limit) the
goldstino as the only light mode in this sector. We show in three different
ways, both in components and in superspace language, how the nilpotent
goldstino superfield emerges. We then use it to write different effective
operators and extract some of the consequences for the low energy spectrum. | Dynkin Diagrams and Integrable Models Based on Lie Superalgebras: An analysis is given of the structure of a general two-dimensional Toda field
theory involving bosons and fermions which is defined in terms of a set of
simple roots for a Lie superalgebra. It is shown that a simple root system for
a superalgebra has two natural bosonic root systems associated with it which
can be found very simply using Dynkin diagrams; the construction is closely
related to the question of how to recover the signs of the entries of a Cartan
matrix for a superalgebra from its Dynkin diagram. The significance for Toda
theories is that the bosonic root systems correspond to the purely bosonic
sector of the integrable model, knowledge of which can determine the bosonic
part of the extended conformal symmetry in the theory, or its classical mass
spectrum, as appropriate. These results are applied to some special kinds of
models and their implications are investigated for features such as
supersymmetry, positive kinetic energy and generalized reality conditions for
the Toda fields. As a result, some new families of integrable theories with
positive kinetic energy are constructed, some containing a mixture of massless
and massive degrees of freedom, others being purely massive and supersymmetric,
involving a number of coupled sine/sinh-Gordon theories. |
Modular Forms and Three Loop Superstring Amplitudes: We study a proposal of D'Hoker and Phong for the chiral superstring measure
for genus three. A minor modification of the constraints they impose on certain
Siegel modular forms leads to a unique solution. We reduce the problem of
finding these modular forms, which depend on an even spin structure, to finding
a modular form of weight 8 on a certain subgroup of the modular group. An
explicit formula for this form, as a polynomial in the even theta constants, is
given. We checked that our result is consistent with the vanishing of the
cosmological constant. We also verified a conjecture of D'Hoker and Phong on
modular forms in genus 3 and 4 using results of Igusa. | Rotating Black Droplet: We construct the gravitational dual, in the Unruh state, of the "jammed"
phase of a CFT at strong coupling and infinite N on a fixed five-dimensional
rotating Myers-Perry black hole with equal angular momenta. When the angular
momenta are all zero, the solution corresponds to the five-dimensional
generalization of the solution first studied by Figueras, Lucietti, and
Wiseman. In the extremal limit, when the angular momenta of the Myers-Perry
black hole are maximum, the Unruh, Boulware and Hartle-Hawking states
degenerate. We give a detailed analysis of the corresponding holographic stress
energy tensor for all values of the angular momenta, finding it to be regular
at the horizon in all cases. We compare our results with existent literature on
thermal states of free field theories on black hole backgrounds. |
Double Soft Limit of Graviton Amplitude from the Cachazo-He-Yuan
Formalism: We present a complete analysis for double soft limit of graviton scattering
amplitude using the formalism proposed by Cachazo, He and Yuan. Our results
agree with that obtained via BCFW recursion relations in arXiv:1504.05558. In
addition we find precise relations between degenerate and nondegenerate
solutions of scattering equations with local and nonlocal terms in the soft
factor. | Unitary matrix with a Penner-like potential also yields N_f=2: It has been known for some time that a hermitian matrix model with a
Penner-like potential yields as its large-N free energy the prepotential of N=2
N_f=2 SU(2) SUSY gauge theory. We give a rigorous proof that a unitary matrix
model with the identical potential also yields the same prepotential, although
the parameter identifications are slightly different. This result has been
anticipated by Itoyama et. al. |
$κ$-deformed complex scalar field: conserved charges, symmetries
and their impact on physical observables: In this paper we revisit the model of $\kappa$-deformed complex scalar field.
We find that this model possesses ten conserved Noether charges that form,
under commutators, a representation of (undeformed) Poincar\'e algebra. It
follows that the theory is relativistic and does not break Lorentz invariance.
However the spacetime representation of boosts is not standard, and contains a
non-local translation, different for positive and negative energy modes. It
then follows that although the masses of particles and anti-particles are
equal, the theory violates CPT symmetry in a subtle way. We explain why the
Jost-Wightman-Greenberg theorem of equivalence of the Poincar\'e symmetry and
CPT fails in our case. Finally, we discuss the phenomenological consequences of
the theory and its possible observational signatures. | Spinor Green function in higher-dimensional cosmic string space-time in
the presence of magnetic flux: In this paper we investigate the vacuum polarization effects associated with
quantum fermionic charged fields in a generalized $(d+1)-$dimensional cosmic
string space-times considering the presence of a magnetic flux along the
string. In order to develop this analysis we calculate a general expression for
the respective Green function, valid for several different values of $d$, which
is expressed in terms of a bispinor associated with the square of the Dirac
operator. Adopting this result, we explicitly calculate the renormalized vacuum
expectation values of the energy-momentum tensors, $<T^A_B>_{Ren.}$, associated
with massless fields. Moreover, for specific values of the parameters which
codify the cosmic string and the fractional part of the ratio of the magnetic
flux by the quantum one, we were able to present in closed forms the bispinor
and the respective Green function for massive fields. |
Scalar Casimir effect between Dirichlet spheres or a plate and a sphere: We present a simple formalism for the evaluation of the Casimir energy for
two spheres and a sphere and a plane, in case of a scalar fluctuating field,
valid at any separations. We compare the exact results with various
approximation schemes and establish when such schemes become useful. The
formalism can be easily extended to any number of spheres and/or planes in
three or arbitrary dimensions, with a variety of boundary conditions or
non-overlapping potentials/non-ideal reflectors. | Compactified Twistor Fibration and Topology of Ward Unitons: We use the compactified twistor correspondence for the (2+1)-dimensional
integrable chiral model to prove a conjecture of Ward. In particular, we
construct the correspondence space of a compactified twistor fibration and use
it to prove that the second Chern numbers of the holomorphic vector bundles,
corresponding to the uniton solutions of the integrable chiral model, equal the
third homotopy classes of the restricted extended solutions of the unitons.
Therefore we deduce that the total energy of a time-dependent uniton is
proportional to the second Chern number. |
Matter representations from geometry: under the spell of Dynkin: In the traditional Katz-Vafa method, matter representations are determined by
decomposing the adjoint representation of a parent simple Lie algebra
$\mathfrak{m}$ as the direct sum of irreducible representations of a semisimple
subalgebra $\mathfrak{g}$. The Katz-Vafa method becomes ambiguous as soon as
$\mathfrak{m}$ contains several subalgebras isomorphic to $\mathfrak{g}$ but
giving different decompositions of the adjoint representation. We propose a
selection rule that characterizes the matter representations observed in
generic constructions in F-theory and M-theory: the matter representations in
generic F-theory compactifications correspond to linear equivalence classes of
subalgebras $\mathfrak{g}\subset \mathfrak{m}$ with Dynkin index one along each
simple components of $\mathfrak{g}$. This simple yet elegant selection rule
allows us to apply the Katz-Vafa method to a much large class of models. We
illustrate on numerous examples how this proposal streamlines the derivation of
matter representations in F-theory and resolves previously ambiguous cases. | More on Homological Supersymmetric Quantum Mechanics: In this work, we first solve complex Morse flow equations for the simplest
case of a bosonic harmonic oscillator to discuss localization in the context of
Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the
bosonized supersymmetric quantum mechanics on algebraic geometric grounds and
report that their complex phases can be accessed through the cohomology of WKB
1-form of the underlying singular spectral curve subject to necessary
cohomological corrections for non-zero genus. Motivated by Picard-Lefschetz
theory, we write down a general formula for the index of $\mathcal{N} = 4$
quantum mechanics with background $R$-symmetry gauge fields. We conjecture that
certain symmetries of the refined Witten index and singularities of the moduli
space may be used to determine the correct intersection coefficients. A few
examples, where this conjecture holds, are shown in both linear and closed
quivers with rank-one quiver gauge groups. The $R$-anomaly removal along the
"Morsified" relative homology cycles also called "Lefschetz thimbles" is shown
to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos
(FI) parameters appear in the intersection coefficients for the relative
homology of the quiver quantum mechanics resulting from dimensional reduction
of $2d$ $\mathcal{N}=(2,2)$ gauge theory on a circle and explicitly calculate
integrals along the Lefschetz thimbles in $\mathcal{N}=4$ $\mathbb{CP}^{k-1}$
model. The Stokes jumping of coefficients and its relation to wall crossing
phenomena is briefly discussed. We also find that the notion of "on-the-wall"
index is related to the invariant Lefschetz thimbles under Stokes phenomena. An
implication of the Lefschetz thimbles in constructing knots from quiver quantum
mechanics is indicated. |
Gravity versus Noncommutative Gauge Theory: A Double Copy Perspective: We discuss how Moyal deformations of gauge theories, which arise naturally
from open string theory, fit into the paradigm of colour-kinematics duality and
the double copy of gauge theory to gravity. Along the way we encounter novel
noncommutative scalar field theories with rigid colour symmetry that have no
interacting commutative counterparts. These scalar theories offer new
perspectives on old ideas that rank one noncommutative gauge theories are
gravitational theories. This is rendered explicit in four dimensions where they
and their double copy images yield deformations of integrable theories
describing the self-dual sectors of Yang-Mills theory and gravity. | Chiral gauge theory and gravity from unconventional supersymmetry: From a gauge $SU(2,2|2)$ model with broken supersymmetry, we construct an
action for $SU(2)\times U(1)$ Yang-Mills theory coupled to gravity and matter.
The connection components for AdS boosts and special conformal translations are
auxiliary fields and their fixing reduces the theory to two distintive sectors:
a vector-like gauge theory with general relativity and a chiral gauge theory
where gravity drops out. We discuss some of the main classical features of the
model such as the predicted tree level gauge couplings, cosmological constant
value, mass-like terms and the Einstein equations. |
Particle-physics constraints on multifractal spacetimes: We study electroweak interactions in the multiscale theory with
$q$-derivatives, a framework where spacetime has the typical features of a
multifractal. In the simplest case with only one characteristic time, length
and energy scale $t_*$, $\ell_*$, and $E_*$, we consider (i) the muon decay
rate and (ii) the Lamb shift in the hydrogen atom, and constrain the
corrections to the ordinary results. We obtain the independent absolute upper
bounds (i) $t_* < 10^{-13}{\rm s}$ and (ii) $E_*>35\,\text{MeV}$. Under some
mild theoretical assumptions, the Lamb shift alone yields the even tighter
ranges $t_*<10^{-27}\,{\rm s}$, $\ell_*<10^{-19}\,{\rm m}$, and
$E_*>450\,\text{GeV}$. To date, these are the first robust constraints on the
scales at which the multifractal features of the geometry can become important
in a physical process. | 't Hooft-Polyakov monopole of higher generalized angular momenta: We recall the quaternionic fomulation, which can simplify the computation of
the linearized Yang-Mills-Higgs equation in the background of a 't
Hooft-Polyakov monopole. We then study the solutions in the cases $j=0$, $j=1$
and $j\geq 2$ separately. In particular, we investigate the spectral properties
of the monopoles. We focus on some of the bound states and show that as the
generalized momentum increases, the $k-$th eigenvalue tends to 1. We show the
existence of Feshbach resonance for $\om <1$ in the coupled system and
calculated the partial cross section when $\om >1$. |
Electromagnetic instability and Schwinger effect in the
Witten-Sakai-Sugimoto model with D0-D4 background: Using the Witten-Sakai-Sugimoto model in the D0-D4 background, we
holographically compute the vacuum decay rate of the Schwinger effect in this
model. Our calculation contains the influence of the D0-brane density which
could be identified as the $\theta$ angle or chiral potential in QCD. Under the
strong electromagnetic fields, the instability appears due to the creation of
quark-antiquark pairs and the associated decay rate can be obtained by
evaluating the imaginary part of the effective Euler-Heisenberg action which is
identified as the action of the probe brane with a constant electromagnetic
field. In the bubble D0-D4 configuration, we find the decay rate decreases when
the $\theta$ angle increases since the vacuum becomes heavier in the present of
the glue condensate in this system. And the decay rate matches to the result in
the black D0-D4 configuration at zero temperature limit according to our
calculations. In this sense, the Hawking-Page transition of this model could be
consistently interpreted as the confined/deconfined phase transition.
Additionally there is another instability from the D0-brane itself in this
system and we suggest that this instability reflects to the vacuum decay
triggered by the $\theta$ angle as it is known in the $\theta$-dependent QCD. | Tropological Sigma Models: With the use of mathematical techniques of tropical geometry, it was shown by
Mikhalkin some twenty years ago that certain Gromov-Witten invariants
associated with topological quantum field theories of pseudoholomorphic maps
can be computed by going to the tropical limit of the geometries in question.
Here we examine this phenomenon from the physics perspective of topological
quantum field theory in the path integral representation, beginning with the
case of the topological sigma model before coupling it to topological gravity.
We identify the tropicalization of the localization equations, investigate its
geometry and symmetries, and study the theory and its observables using the
standard cohomological BRST methods. We find that the worldsheet theory
exhibits a nonrelativistic structure, similar to theories of the Lifshitz type.
Its path-integral formulation does not require a worldsheet complex structure;
instead, it is based on a worldsheet foliation structure. |
Quasinormal modes of supersymmetric microstate geometries from the D1-D5
CFT: We revisit the study of the probe scalar quasinormal modes of a class of
three-charge supersymmetric microstate geometries. We compute the real and
imaginary parts of the quasinormal modes and show that in the parameter range
when the geometries have large AdS region, the spectrum is precisely reproduced
from a D1-D5 orbifold CFT analysis. The spectrum includes the slow decaying
modes pointed out by Eperon, Reall, and Santos. We analyse in detail the nature
of the quasinormal modes by studying the scalar wavefunction. We show that
these modes correspond to slow leakage of excitation from AdS throat to
infinity. | Ghost-spin chains, entanglement and $bc$-ghost CFTs: We study 1-dimensional chains of ghost-spins with nearest neighbour
interactions amongst them, developing further the study of ghost-spins in
previous work, defined as 2-state spin variables with indefinite norm. First we
study finite ghost-spin chains with Ising-like nearest neighbour interactions:
this helps organize and clarify the study of entanglement earlier and we
develop this further. Then we study a family of infinite ghost-spin chains with
a different Hamiltonian containing nearest neighbour hopping-type interactions.
By defining fermionic ghost-spin variables through a Jordan-Wigner
transformation, we argue that these ghost-spin chains lead in the continuum
limit to the $bc$-ghost CFTs. |
On the Hagedorn Transition and Collective Dynamics of D0-branes: Banks, Fischler, Klebanov and Susskind have proposed a model for black hole
thermodynamics based on the principle that the entropy is of order the number
of particles at the phase transition point in a Boltzmann gas of D0-branes. We
show that the deviations from Boltzmann scaling found in $d<6$ noncompact
spatial dimensions have a simple explanation in the analysis of
self-gravitating random walks due to Horowitz and Polchinski. In the special
case of $d=4$ we find evidence for the onset of a phase transition in the
Boltzmann gas analogous to the well-known Hagedorn transition in a gas of free
strings. Our result relies on an estimate of the asymptotic density of states
in a dilute gas of D0-branes. | Page curves for a family of exactly solvable evaporating black holes: We study the entanglement entropy of a one-parameter family of exactly
solvable gravities in the 2-dimensional asymptotically-flat space. The islands
and Page curves of eternal, evaporating and bath-removed black holes are
investigated. The different theories in this parameter class are identified
through field redefinitions which leave the island invariant. The Page
transition is found to occur at the first a third of the black hole life time
in the evaporating case for this family of solutions. In addition, we consider
gluing the equilibrium black hole and the evaporating one along a null
trajectory and study the effect of gluing on the islands and Page curves. In
the glued space, the island jumps across two different geometries at a certain
retarded time. As a result, the Page transition is stretched and split into two
separate ones -- the first transition happens when the net entropy generation
stops and the second one occurs as the early radiation effectively starts to
become purified. Finally, we discuss the issues concerning the inconsistent
rates of purification and the paradox related to the state of the radiation. |
On the Holographic Nature Of Rindler Energy: We show that the dimensionless Rindler energy of a black hole, $E_R$, is
exactly the surface Hamiltonian obtained from the Einstein--Hilbert action
evaluated on the horizon. Therefore, $E_R$ is given by a surface integral over
the horizon and manifestly holographic. In the context of the AdS/CFT duality,
Rindler energy corresponds, on the boundary, to a dimensionless energy given by
the product of the AdS radius and the extensive part of the CFT energy. We find
that, beyond General Relativity, $E_R$ is still holographic but not necessarily
given by the surface Hamiltonian of the theory. | BRST-antifield-treatment of metric-affine gravity: The metric-affine gauge theory of gravity provides a broad framework in which
gauge theories of gravity can be formulated. In this article we fit
metric-affine gravity into the covariant BRST--antifield formalism in order to
obtain gauge fixed quantum actions. As an example the gauge fixing of a general
two-dimensional model of metric-affine gravity is worked out explicitly. The
result is shown to contain the gauge fixed action of the bosonic string in
conformal gauge as a special case. |
Equal charge black holes and seven dimensional gauged supergravity: We present various supergravity black holes of different dimensions with some
U(1) charges set equal in a simple, common form. Black hole solutions of seven
dimensional U(1)^2 gauged supergravity with three independent angular momenta
and two equal U(1) charges are obtained. We investigate the thermodynamics and
the BPS limit of this solution, and find that there are rotating supersymmetric
black holes without naked closed timelike curves. There are also supersymmetric
topological soliton solutions without naked closed timelike curves that have a
smooth geometry. | Sigma Model Corrections to the Confining Background: Sigma model ($\alpha^{\prime}$) corrections to the confining string
background are obtained. The main result is that the Poincar\'e invariant
ansatz is maintained. Physical conditions for the dissapearance of the naked
singularity are discussed. |
Line Operators in Chern-Simons-Matter Theories and Bosonization in Three
Dimensions: We study Chern-Simons theories at large $N$ with either bosonic or fermionic
matter in the fundamental representation. The most fundamental operators in
these theories are mesonic line operators, the simplest example being Wilson
lines ending on fundamentals. We classify the conformal line operators along an
arbitrary smooth path as well as the spectrum of conformal dimensions and
transverse spins of their boundary operators at finite 't Hooft coupling. These
line operators are shown to satisfy first-order chiral evolution equations, in
which a smooth variation of the path is given by a factorized product of two
line operators. We argue that this equation together with the spectrum of
boundary operators are sufficient to uniquely determine the expectation values
of these operators. We demonstrate this by bootstrapping the two-point function
of the displacement operator on a straight line. We show that the line
operators in the theory of bosons and the theory of fermions satisfy the same
evolution equation and have the same spectrum of boundary operators. | Extended MQCD and SUSY/non-SUSY duality: We study the SUSY/non-SUSY duality proposed by Aganagic et al. from Type IIA
string and M-theory perspectives. We find that our brane configuration
generalizes the so-called $extended$ Seiberg-Witten theory on the one hand, and
provides a way to realize non-SUSY vacua by intersecting NS5-branes on the
other hand. We also argue how the partial SUSY breaking from $\Ncal=2$ down to
$\Ncal=1$ can be clearly visualized through the brane picture. |
Gauge Supergravities for all Odd Dimensions: Recently proposed supergravity theories in odd dimensions whose fields are
connection one-forms for the minimal supersymmetric extensions of anti-de
Sitter gravity are discussed. Two essential ingredients are required for this
construction: (1) The superalgebras, which extend the adS algebra for different
dimensions, and (2) the lagrangians, which are Chern-Simons $(2n-1)$-forms. The
first item completes the analysis of van Holten and Van Proeyen, which was
valid for N=1 only. The second ensures that the actions are invariant by
construction under the gauge supergroup and, in particular, under local
supersymmetry. Thus, unlike standard supergravity, the local supersymmetry
algebra closes off-shell and without requiring auxiliary fields. \\
The superalgebras are constructed for all dimensions and they fall into three
families: $osp(m|N)$ for $D=2,3,4$, mod 8, $osp(N|m)$ for $D=6,7,8$, mod 8, and
$su(m-2,2|N)$ for D=5 mod 4, with $m=2^{[D/2]}$. The lagrangian is constructed
for $D=5, 7$ and 11. In all cases the field content includes the vielbein
($e_{\mu}^{a}$), the spin connection ($\omega_{\mu}^{ab}$), $N$ gravitini
($\psi_{\mu}^{i}$), and some extra bosonic "matter" fields which vary from one
dimension to another. | Diagonal $K$-matrices and transfer matrix eigenspectra associated with
the $G^{(1)}_2$ $R$-matrix: We find all the diagonal $K$-matrices for the $R$-matrix associated with the
minimal representation of the exceptional affine algebra $G^{(1)}_2$. The
corresponding transfer matrices are diagonalized with a variation of the
analytic Bethe ansatz. We find many similarities with the case of the
Izergin-Korepin $R$-matrix associated with the affine algebra $A^{(2)}_2$. |
Generalized Measures in Gauge Theory: Let P -> M be a principal G-bundle. Using techniques from the loop
representation of gauge theory, we construct well-defined substitutes for
``Lebesgue measure'' on the space A of connections on P and for ``Haar
measure'' on the group Ga of gauge transformations. More precisely, we define
algebras of ``cylinder functions'' on the spaces A, Ga, and A/Ga, and define
generalized measures on these spaces as continuous linear functionals on the
corresponding algebras. Borrowing some ideas from lattice gauge theory, we
characterize generalized measures on A, Ga, and A/Ga in terms of graphs
embedded in M. We use this characterization to construct generalized measures
on A and Ga, respectively. The ``uniform'' generalized measure on A is
invariant under the group of automorphisms of P. It projects down to the
generalized measure on A/Ga considered by Ashtekar and Lewandowski in the case
G = SU(n). The ``generalized Haar measure'' on Ga is right- and left-invariant
as well as Aut(P)-invariant. We show that averaging any generalized measure on
A against generalized Haar measure gives a gauge-invariant generalized measure
on A. | Fixing D7 Brane Positions by F-Theory Fluxes: To do realistic model building in type IIB supergravity, it is important to
understand how to fix D7-brane positions by the choice of fluxes. More
generally, F-theory model building requires the understanding of how fluxes
determine the singularity structure (and hence gauge group and matter content)
of the compactification. We analyse this problem in the simple setting of
M-theory on K3xK3. Given a certain flux which is consistent with the F-theory
limit, we can explicitly derive the positions at which D7 branes or stacks of
D7 branes are stabilised. The analysis is based on a parameterization of the
moduli space of type IIB string theory on T^2/Z_2 (including D7-brane
positions) in terms of the periods of integral cycles of M-theory on K3. This
allows us, in particular, to select a specific desired gauge group by the
choice of flux numbers. |
Examining the weak cosmic censorship conjecture by gedanken experiments
for Kerr-Sen black holes: In this paper, we investigate the weak cosmic censorship conjecture for the
Kerr-Sen black holes by considering the new version of the gedanken experiments
proposed recently by Sorce and Wald. After deriving the first two order
perturbation inequalities in the low energy limit of heterotic string theory
based on the Iyer-Wald formalism and applying it into the Kerr-Sen black hole,
we find that the Kerr-Sen black hole can not be overspun or overcharged by the
charged matter collision after taking into account the second-order
perturbation inequality, although they can be destroyed by the scene only
considering the first-order perturbation inequality. Therefore, the weak cosmic
censorship conjecture is preserved in the Kerr-Sen black hole at this level. | Microscopic origin of the entropy of black holes in general relativity: We construct an infinite family of microstates with geometric interiors for
eternal black holes in general relativity with negative cosmological constant
in any dimension. Wormholes in the Euclidean path integral for gravity cause
these states to have small, but non-zero, quantum mechanical overlaps that have
a universal form. The overlaps have a dramatic consequence: the microstates
span a Hilbert space of log dimension equal to the Bekenstein-Hawking entropy.
The semiclassical microstates we construct contain Einstein-Rosen bridges of
arbitrary size behind their horizons. Our results imply that all these bridges
can be interpreted as quantum superpositions of wormholes of size at most
exponential in the entropy. |
Dynamics of Gauge Field Inflation: We analyze the existence and stability of dynamical attractor solutions for
cosmological inflation driven by the coupling between fermions and a gauge
field. Assuming a spatially homogeneous and isotropic gauge field and fermion
current, the interacting fermion equation of motion reduces to that of a free
fermion up to a phase shift. Consistency of the model is ensured via the
Stuckelberg mechanism. We prove the existence of exactly one stable solution,
and demonstrate the stability numerically. Inflation arises without fine
tuning, and does not require postulating any effective potential or
non-standard coupling. | Black hole information and Reeh-Schlieder theorem: The Reeh-Schlieder theorem, with the time-slice axiom of quantum field
theory, may be used to recover the information which falls into a black hole.
Analyticity of quantum fields in states with finite energy plays the crucial
role. In AdS spacetime, our argument based on the Reeh-Schlieder theorem is
consistent with the argument that there is no information loss because of the
AdS/CFT correspondence. |
Ruppeiner Geometry of RN Black Holes: Flat or Curved?: In some recent studies \cite{aman1, aman2, aman3}, Aman {\it et al.} used the
Ruppeiner scalar as a measure of underlying interactions of
Reissner-Nordstr\"{o}m black holes, indicating that it is a non-interacting
statistical system for which classical thermodynamics could be used at any
scale. Here, we show that if we use the complete set of thermodynamic
variables, a non-flat state space will be produced. Furthermore, the Ruppeiner
curvature diverges at extremal limits, as it would for other types of black
holes. | Innocuous Implications of a Minimum Length in Quantum Gravity: A modification to the time-energy uncertainty relation in quantum gravity has
been interpreted as increasing the duration of fluctuations producing virtual
black holes with masses greater than the Planck mass. I point out that such
virtual black holes have an exponential factor arising from the action such
that their contribution to proton decay is suppressed, rather than enhanced,
relative to Planck-mass black holes. |
Loop equations for multi-cut matrix models: The loop equation for the complex one-matrix model with a multi-cut structure
is derived and solved in the planar limit. An iterative scheme for higher genus
contributions to the free energy and the multi-loop correlators is presented
for the two-cut model, where explicit results are given up to and including
genus two. The double-scaling limit is analyzed and the relation to the one-cut
solution of the hermitian and complex one-matrix model is discussed. | Mapping of relativistic Green's functions under extended point canonical
transformations: Given a relativistic two-point Green's function for a spinor system with
spherical symmetry we show how to obtain another in the same class by extended
point canonical transformations (XPCT). |
BCFW construction of the Veneziano Amplitude: In this note we demonstrate how one can compute the Veneziano amplitude for
bosonic string theory using the BCFW method. We use an educated ansatz for the
cubic amplitude of two tachyons and an arbitrary level string state. | A stringy perspective on the quantum integrable model/gauge
correspondence: We present a string theory realization for the correspondence between quantum
integrable models and supersymmetric gauge theories. The quantization results
from summing the effects of fundamental strings winding around a compact
direction. We discuss the examples of the XXZ gauge/Bethe correspondence and
five-dimensional \Omega--deformed SYM on M x S^1. |
Stability of flux vacua in the presence of charged black holes: In this letter we consider a charged black hole in a flux compactification of
type IIB string theory. Both the black hole and the fluxes will induce
potentials for the complex structure moduli. We choose the compact dimensions
to be described locally by a deformed conifold, creating a large hierarchy. We
demonstrate that the presence of a black hole typically will not change the
minimum of the moduli potential in a substantial way. However, we also point
out a couple of possible loop-holes, which in some cases could lead to
interesting physical consequences such as changes in the hierarchy. | D0-branes in Gepner models and N=2 black holes: In this paper D-brane boundary states constructed in Gepner models are used
to analyze some aspects of the dynamics of D0-branes in Calabi-Yau
compactifications of type II theories to four dimensions. It is shown that the
boundary states correspond to BPS objects carrying dyonic charges. By analyzing
the couplings to closed string fields a correspondence between the D0-branes
and extremal charged black holes in N=2 supergravity is found. |
The Casimir effect for pistons with transmittal boundary conditions: This work focuses on the analysis of the Casimir effect for pistons subject
to transmittal boundary conditions. In particular we consider, as piston
configuration, a direct product manifold of the type $I\times N$ where $I$ is a
closed interval of the real line and $N$ is a smooth compact Riemannian
manifold. By utilizing the spectral zeta function regularization technique, we
compute the Casimir energy of the system and the Casimir force acting on the
piston. Explicit results for the force are provided when the manifold $N$ is a
$d$-dimensional ball. | On F-term contribution to effective action: We apply equivariant integration technique, developed in the context of
instanton counting, to two dimensional N=2 supersymmetric Yang-Mills models.
Twisted superpotential for U(N) model is computed. Connections to the four
dimensional case are discussed. Also we make some comments about the eight
dimensional model which manifests similar features. |
Phase and Scaling Properties of Determinants Arising in Topological
Field Theories: In topological field theories determinants of maps with negative as well as
positive eigenvalues arise. We give a generalisation of the zeta-regularisation
technique to derive expressions for the phase and scaling-dependence of these
determinants. For theories on odd-dimensional manifolds a simple formula for
the scaling dependence is obtained in terms of the dimensions of certain
cohomology spaces. This enables a non-perturbative feature of Chern-Simons
gauge theory to be reproduced by path-integral methods. | Confinement from gluodynamics in curved space-time: We determine the static potential for a heavy quark-antiquark pair from
gluodynamics in curved space-time. Our calculation is done within the framework
of the gauge-invariant, path-dependent, variables formalism. The potential
energy is the sum of a Yukawa and a linear potential, leading to the
confinement of static charges. |
Superstring Perturbation Theory and Ramond-Ramond Backgrounds: We consider perturbative Type II superstring theory in the covariant NSR
formalism in the presence of NSNS and RR backgrounds. A concrete example that
we have in mind is the geometry of D3-branes which in the near-horizon region
is AdS_5 x S_5, although our methods may be applied to other backgrounds as
well. We show how conformal invariance of the string path integral is
maintained order by order in the number of holes. This procedure makes uses of
the Fischler-Susskind mechanism to build up the background geometry. A simple
formal expression is given for a \sigma-model Lagrangian. This suggests a
perturbative expansion in 1/g^2N and 1/N. As applications, we consider at
leading order the mixing of RR and NSNS states, and the realization of the
spacetime supersymmetry algebra. | Thermal Giant Graviton with Non-commutative Dipole Field: Using the type II near-extremal 3D-branes solution we apply the T-duality and
smeared twist to construct the supergravity backgrounds which dual to the 4D
finite temperature non-commutative dipole field theories. We first consider the
zero-temperature system in which, depending on the property of dipole vectors
it may be N=2, N=1 or N=0 theory. We investigate the rotating D3-brane
configurations moving on the spactimes and show that, for the cases of N=2 and
N =1 the rotating D3-brane could be blowed up to the stable spherical
configuration which is called as giant graviton and has a less energy than the
point-like graviton. The giant graviton configuration is stable only if its
angular momentum was less than a critical value of $P_c$ which is an increasing
function of the dipole strength. For the case of non-supersymmetric theory,
however, the spherical configuration has a larger energy than the point-like
graviton. We also find that the dipole field always render the dual giant
graviton to be more stable than the point-like graviton. The relation of dual
giant graviton energy with its angular momentum, which in the AdS/CFT
correspondence being the operator anomalous dimension is obtained. We
furthermore show that the temperature does not change the property of the giant
graviton, while it will render the dual giant graviton to be unstable. |
Orthogonal black di-ring solution: We construct a five dimensional exact solution of the orthogonal black
di-ring which has two black rings whose $S^1$-rotating planes are orthogonal.
This solution has four free parameters which represent radii of and speeds of
$S^1$-rotation of the black rings. We use the inverse scattering method. This
method needs the seed metric. We also present a systematic method how to
construct a seed metric. Using this method, we can probably construct other
solutions having many black rings on the two orthogonal planes with or without
a black hole at the center. | Left-handed string and CHY amplitude at one loop: We propose a generalized left-handed (chiral) gauge choice for the genus one
Riemann surface, realized through a singular gauge transformation of worldsheet
coordinates. The transformation predominantly affects the logarithmic non-zero
modes of the Green's function, leaving non-holomorphic and non-logarithmic
modes unchanged. This procedure yields $\delta$-functions for chiral
coordinates and box-diagram-like integrals in terms of modular parameters. The
resulting $\delta$-functions formulate one-loop level Scattering Equations that
simplify to satisfy the tree-level solutions, constraining the locations of the
marked points. Subsequent integrals agree with the field-theoretic box diagram
for the four-point amplitude, in accordance with the divergent $\epsilon$
expansions derived from dimensional regularization in the infrared limit. We
conclude by highlighting potential avenues for future research, including the
exploration of methodologies that preclude the need for worldsheet coordinates
reparametrization and their implications for accurately capturing infrared
behavior from modular parameter integrals. |
3D van der Waals $σ$-model and its Topological Excitations: It is shown that 3D vector van der Waals (conformal) nonlinear $\sigma$-model
(NSM) on a sphere $S^2$ has two types of topological excitations reminiscent
vortices and instantons of 2D NSM. The first, the hedgehogs, are described by
homotopic group $\pi_2(S^2) = \mathbb {Z}$ and have the logarithmic energies.
They are an analog of 2D vortices. The energy and interaction of these
excitations are found. The second, corresponding to 2D instantons, are
described by hpmotopic group $\pi_3(S^2) = \mathbb {Z}$ or the Hopf invariant
$H \in \mathbb {Z}$. A possibility of the topological phase transition in this
model and its applications are briefly discussed. | Painlevé I and exact WKB: Stokes phenomenon for two-parameter
transseries: For more than a century, the Painlev\'e I equation has played an important
role in both physics and mathematics. Its two-parameter family of solutions was
studied in many different ways, yet still leads to new surprises and
discoveries. Two popular tools in these studies are the theory of isomonodromic
deformation that uses the exact WKB method, and the asymptotic description of
transcendents in terms of two-parameter transseries. Combining methods from
both schools of thought, and following work by Takei and collaborators, we find
complete, two-parameter connection formulae for solutions when they cross
arbitrary Stokes lines in the complex plane. These formulae allow us to study
Stokes phenomenon for the full two-parameter family of transseries solutions.
In particular, we recover the exact expressions for the Stokes data that were
recently found by Baldino, Schwick, Schiappa and Vega and compare our
connection formulae to theirs. We also explain several ambiguities in relating
transseries parameter choices to actual Painlev\'e transcendents, study the
monodromy of formal solutions, and provide high-precision numerical tests of
our results. |
Rotating Strings in Six-Dimensional Higher-Derivative Supergravity: We construct the first rotating string solution in 6-dimensional
Einstein-Gauss-Bonnet supergravity, carrying both electric and magnetic
charges. By embedding the known rotating string solution of the 2-derivative
theory into 6-dimensional off-shell supergravity, the Killing spinors
associated with the underlying supersymmetry can be made off-shell and are
universal to all off-shell supergravity models based on the same field content.
The near-horizon geometry is S^3 fibred over the extremal BTZ black hole,
locally isomorphic to AdS_3*S^3. We compute the higher-derivative corrections
to the Brown-Henneaux central charges in a particular R+R^2 model resulting
from K3 compactification of type IIA string theory. | Kink in dual dilaton-axion theories with potential: The representation in terms of Ernst's complex potential is used to describe
and analyze dilaton-axion theories with potential. The set of such systems is
divided into pairs of dual systems with respect to the inversion of the Ernst
potential. Using duality, a theory is constructed that is invariant with
respect to the nonlinear Ehlers transformation. For this theory, a soliton
solution is obtained that is dual to a dilaton kink in a system that is
invariant with respect to the axion shift transformation. |
Absence of Radiation Reaction for an Extended Particle in Classical
Electrodynamics: There are known problems with the standard Lorentz-Dirac description of
radiation reaction in classical electrodynamics. The model of extended in one
dimension particle is proposed and is shown that for this model there is no
total change in particle momentum due to radiation reaction | Non-abelian vortices on compact Riemann surfaces: We consider the vortex equations for a U(n) gauge field coupled to a Higgs
field with values on the n times n square matrices. It is known that when these
equations are defined on a compact Riemann surface, their moduli space of
solutions is closely related to a moduli space of tau-stable holomorphic
n-pairs on that surface. Using this fact and a local factorization result for
the Higgs matrix, we show that the vortex solutions are entirely characterized
by (1) the location in the surface of the zeros of the determinant of the Higgs
matrix and (2) by the choice of a vortex internal structure at each of these
zeros. We describe explicitly the vortex internal spaces and show that they are
compact and connected spaces. |
Self-Completeness in Alternative Theories of Gravity: It has recently been shown via an equivalence of gravitational radius and
Compton wavelength in four dimensions that the trans-Planckian regime of
gravity may by semi-classical, and that this point is defined by a minimum
horizon radius commensurate with the Planck mass. We extend the formalism to
gravity in the context of Randall-Sundrum and the generalized uncertainty
principle. | Soft Algebras for Leaf Amplitudes: Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes
associated to an AdS$_3$ leaf of a foliation of flat spacetime. It is shown
here that the leaf amplitudes are governed by the same infinite-dimensional
soft `$S$-algebra' as their celestial counterparts. Moreover, taking the soft
limit of the smooth three-point MHV leaf amplitude yields a nondegenerate
minus-minus two-point leaf amplitude. The two- and three-point MHV leaf
amplitudes are used to compute the plus-minus-minus leaf operator product
coefficients. |
Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills: After reduction techniques, two-loop amplitudes in N=4 super Yang-Mills
theory can be written in a basis of integrals containing scalar double-box
integrals with rational coefficients, though the complete basis is unknown.
Generically, at two loops, the leading singular behavior of a scalar double box
integral with seven propagators is captured by a hepta-cut. However, it turns
out that a certain class of such integrals has an additional propagator-like
singularity. One can then formally cut the new propagator to obtain an octa-cut
which localizes the cut integral just as a quadruple cut does at one-loop. This
immediately gives the coefficient of the scalar double box integral as a
product of six tree-level amplitudes. We compute, as examples, several
coefficients of the five- and six-gluon non-MHV two-loop amplitudes. We also
discuss possible generalizations to higher loops. | A Four-Reggeon Vertex for ${\bf Z}_3$ Twisted Fermionic Fields: Using operator sewing techniques we construct the Reggeon vertex involving
four external ${\bf Z}_3$-twisted complex fermionic fields. Generalizing a
procedure recently applied to the ordinary Ramond four-vertex, we deduce the
closed form of the ${\bf Z}_3$ vertex by demanding it to reproduce the results
obtained by sewing. |
Holographic flavor on the Higgs branch: In this paper we study the holographic dual, in several spacetime dimensions,
of the Higgs branch of gauge theories with fundamental matter. These theories
contain defects of various codimensionalities, where the matter fields are
located. In the holographic description the matter is added by considering
flavor brane probes in the supergravity backgrounds generated by color branes,
while the Higgs branch is obtained when the color and flavor branes recombine
with each other. We show that, generically, the holographic dual of the Higgs
phase is realized by means of the addition of extra flux on the flavor branes
and by choosing their appropriate embedding in the background geometry. This
suggests a dielectric interpretation in terms of the color branes, whose vacuum
solutions precisely match the F- and D-flatness conditions obtained on the
field theory side. We further compute the meson mass spectra in several cases
and show that when the defect added has codimension greater than zero it
becomes continuous and gapless. | Holomorphic subgraph reduction of higher-point modular graph forms: Modular graph forms are a class of modular covariant functions which appear
in the genus-one contribution to the low-energy expansion of closed string
scattering amplitudes. Modular graph forms with holomorphic subgraphs enjoy the
simplifying property that they may be reduced to sums of products of modular
graph forms of strictly lower loop order. In the particular case of dihedral
modular graph forms, a closed form expression for this holomorphic subgraph
reduction was obtained previously by D'Hoker and Green. In the current work, we
extend these results to trihedral modular graph forms. Doing so involves the
identification of a modular covariant regularization scheme for certain
conditionally convergent sums over discrete momenta, with some elements of the
sum being excluded. The appropriate regularization scheme is identified for any
number of exclusions, which in principle allows one to perform holomorphic
subgraph reduction of higher-point modular graph forms with arbitrary
holomorphic subgraphs. |
Machine Learning of Calabi-Yau Volumes: We employ machine learning techniques to investigate the volume minimum of
Sasaki-Einstein base manifolds of non-compact toric Calabi-Yau 3-folds. We find
that the minimum volume can be approximated via a second order multiple linear
regression on standard topological quantities obtained from the corresponding
toric diagram. The approximation improves further after invoking a
convolutional neural network with the full toric diagram of the Calabi-Yau
3-folds as the input. We are thereby able to circumvent any minimization
procedure that was previously necessary and find an explicit mapping between
the minimum volume and the topological quantities of the toric diagram. Under
the AdS/CFT correspondence, the minimum volumes of Sasaki-Einstein manifolds
correspond to central charges of a class of 4d N=1 superconformal field
theories. We therefore find empirical evidence for a function that gives values
of central charges without the usual extremization procedure. | Global strings in extra dimensions: a full map of solutions, matter
trapping and the hierarchy problem: We consider (d_0+2)-dimensional configurations with global strings in the two
extra dimensions and a flat metric in d_0 dimensions, endowed with a warp
factor e^{2\gamma} depending on the distance l from the string center. All
possible regular solutions to the field equations are classified by the
behavior of the warp factor and the extra-dimensional circular radius r(l).
Solutions with r\to \infty and r\to \const >0 as l\to \infty are interpreted in
terms of thick brane world models. Solutions with r \to 0 as l \to l_c > 0,
i.e., those with a second center, are interpreted as either multi-brane systems
(which is appropriate for large enough distances l_c between the centers) or as
Kaluza-Klein type configurations with extra dimensions invisible due to their
smallness. For the case of the Mexican-hat symmetry breaking potential, we
build a full map of regular solutions on the (\epsilon,\Gamma) parameter plane,
where \epsilon acts as an effective cosmological constant while \Gamma
characterizes the strength of gravity. The trapping properties of candidate
brane worlds for test scalar fields are discussed. Good trapping properties for
massive fields are found for models with growing warp factors. Kaluza-Klein
type models are shown to possess nontrivial warp factor behaviors, leading to
matter particle mass spectra which seem promising from the standpoint of
hierarchy problems. |
Topologican Gauging of N=16 Supergravity in Three-Dimensions: We present a topologically non-trivial generalization of gauged N=16
supergravity on the coset E_8 / SO(16) in three-dimensions. This formulation is
based on a combination of BF-term and a Chern-Simons term for an SO(16) gauge
field A_\m{}^{I J}. The fact that an additional vector field B_\m{}^{I J} is
physical and propagating with couplings to \sigma-model fields makes our new
gauging non-trivial and different from the conventional one. Even though the
field strength of the A_\m{}^{I J}-field vanishes on-shell, the action is
topologically non-trivial due to non-vanishing \pi_3-homotopy. We also present
an additional modifications by an extra Chern-Simons term. As by-products, we
give also an application to N=9 supergravity coupled to a \sigma-model on the
coset F_4 / SO(9), and a new BF-Chern-Simons theory coupled to ^\forall N
extended supergravity. | Towards a Holographic Bose-Hubbard Model: We present a holographic construction of the large-N Bose-Hubbard model. The
model is based on Maxwell fields coupled to charged scalar fields on the AdS2
hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model
and find that the model admits Mott insulator ground states in the limit of
large Coulomb repulsion. In the Mott insulator phases, the bosons are localized
on each site. At zero hopping we find that the transitions between Mott
insulating phases with different fillings correspond to first order
level-crossing phase transitions. At finite hopping we find a holographic phase
transition between the Mott phase and a non-homogeneous phase. We then analyze
the perturbations of fields around both the Mott insulator phase and
inhomogeneous phase. We find almost zero modes in the non-homogeneous phase. |
Hypersymmetry: a Z_3-graded generalization of supersymmetry: We propose a generalization of non-commutative geometry and gauge theories
based on ternary Z_3-graded structures. In the new algebraic structures we
define, we leave all products of two entities free, imposing relations on
ternary products only. These relations reflect the action of the Z_3-group,
which may be either trivial, i.e. abc=bca=cab, generalizing the usual
commutativity, or non-trivial, i.e. abc=jbca, with j=e^{(2\pi i)/3}. The usual
Z_2-graded structures such as Grassmann, Lie and Clifford algebras are
generalized to the Z_3-graded case. Certain suggestions concerning the eventual
use of these new structures in physics of elementary particles are exposed. | Linking number of vortices as baryon number: We show that the topological degree of a Skyrmion field is the same as the
Hopf charge of the field under the Hopf map and thus equals the linking number
of the preimages of two points on the 2-sphere under the Hopf map. We further
interpret two particular points on the 2-sphere as vortex zeros and the linking
of these zero lines follows from the latter theorem. Finally we conjecture that
the topological degree of the Skyrmion can be interpreted as the product of
winding numbers of vortices corresponding to the zero lines, summing over
clusters of vortices. |
Presymplectic AKSZ formulation of Einstein gravity: Any local gauge theory can be represented as an AKSZ sigma model (upon
parameterization if necessary). However, for non-topological models in
dimension higher than 1 the target space is necessarily infinite-dimensional.
The interesting alternative known for some time is to allow for degenerate
presymplectic structure in the target space. This leads to a very concise
AKSZ-like representation for frame-like Lagrangians of gauge systems. In this
work we concentrate on Einstein gravity and show that not only the Lagrangian
but also the full-scale Batalin--Vilkovisky formulation is naturally encoded in
the presymplectic AKSZ formulation, giving an elegant supergeometrical
construction of BV for Cartan-Weyl action. The same applies to the main
structures of the respective Hamiltonian BFV formulation. | The role of singletons in $S^7$ compactifications: We derive the isometry irrep content of squashed seven-sphere
compactifications of eleven-dimensional supergravity, i.e., the left-squashed
($LS^7$) with ${\mathcal N}=1$ and right-squashed ($RS^7$) with ${\mathcal
N}=0$ supersymmetry, in a manner completely independent of the round sphere.
Then we compare this result with the spectrum obtained by Higgsing the round
sphere spectrum. This way we discover features of the spectra which makes it
possible to argue that the only way the round spectrum can be related by a
Higgs mechanism to the one of $LS^7$ is if the singletons are included in the
round sphere spectrum. For this to work also in the $RS^7$ case it seems that
the gravitino of the $LS^7$ spectrum must be replaced by a fermionic singleton
present in the $RS^7$ spectrum. |
Towards Relativistic Skyrmions: We revisit baryons in the Skyrme model. Starting from static baryons in the
helicity eigenstates, we generalize their wavefunctions to the non-static and
relativistic regime. A new representation for gamma matrices in the soliton
collective space is constructed and the corresponding Dirac equation is
obtained. As an example, we draw consideration on how to apply this new
representation on the calculus of vector current vacuum expectation values for
baryon states of spin and isospin half and arbitrary momenta and we show how
elastic form factors can be derived. | Hadron production in electron-positron annihilation computed from the
gauge gravity correspondence: We provide a non-perturbative expression for the hadron production in
electron-positron annihilation at zero temperature in a strongly coupled,
large-Nc SU(Nc) field theory with Nf << Nc quark flavors. The resulting
expressions are valid to leading order in the electromagnetic coupling constant
but non-perturbatively in the SU(Nc) interactions and the mass of the quark. We
obtain this quantity by computing the imaginary part of the hadronic vacuum
polarization function Pi_q using holographic techniques, providing an
alternative to the known method that uses the spectrum of infinitely stable
mesons determined by the normalizable modes of the appropriated fields in the
bulk. Our result exhibits a structure of poles localized at specific real
values of q^2, which coincide with the ones found using the normalizable modes,
and extends it offering the unique analytic continuation of this distribution
to a function defined for values of q^2 over the complex plane. This analytic
continuation permits to include a finite decay width for the mesons. By
comparison with experimental data we find qualitatively good agreement on the
shape of the first pole, when using the rho meson parameters and choosing a
proper normalization factor. We then estimate the contribution to the anomalous
magnetic moment of the muon finding an agreement within 25%, for this choice of
parameters. |
Entanglement Entropy in Quantum Gravity and the Plateau Problem: In a quantum gravity theory the entropy of entanglement $S$ between the
fundamental degrees of freedom spatially divided by a surface is discussed. The
classical gravity is considered as an emergent phenomenon and arguments are
presented that: 1) $S$ is a macroscopical quantity which can be determined
without knowing a real microscopical content of the fundamental theory; 2) $S$
is given by the Bekenstein-Hawking formula in terms of the area of a
co-dimension 2 hypesurface $\cal B$; 3) in static space-times $\cal B$ can be
defined as a minimal hypersurface of a least volume separating the system in a
constant time slice. It is shown that properties of $S$ are in agreement with
basic properties of the von Neumann entropy. Explicit variational formulae for
$S$ in different physical examples are considered. | Membranes Wrapped on Holomorphic Curves: We construct supergravity solutions dual to the twisted field theories
arising when M-theory membranes wrap holomorphic curves in Calabi-Yau n-folds.
The solutions are constructed in an Abelian truncation of maximal D=4 gauged
supergravity and then uplifted to D=11. For four-folds and five-folds we find
new smooth AdS/CFT examples and for all cases we analyse the nature of the
singularities that arise. Our results provide an interpretation of certain
charged topological AdS black holes. We also present the generalised
calibration two-forms for the solutions. |
Super-Higgs in Superspace: We determine the effective gravitational couplings in superspace whose
components reproduce the supergravity Higgs effect for the constrained
Goldstino multiplet. It reproduces the known Gravitino sector whilst
constraining the off-shell completion. We show that these components arise by
computing the effective action. This may be useful for phenomenological studies
and model building: We give an example of its application to multiple
Goldstini. | Deducing the symmetry of the standard model from the automorphism and
structure groups of the exceptional Jordan algebra: We continue the study undertaken in \cite{DV} of the exceptional Jordan
algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an
almost classical space-time approach to particle physics. Along with reviewing
known properties of $J$ and of the associated exceptional Lie groups we argue
that the symmetry of the model can be deduced from the Borel-de Siebenthal
theory of maximal connected subgroups of simple compact Lie groups. |
Coming to Terms with Strongly Coupled Strings: The holomorphy of the superpotential along with symmetries gives very strong
constraints on any stringy non-perturbative effects. This observation suggests
an approach to string phenomenology. (Presented at ``Strings 95'', March 1995. | New five-dimensional Bianchi type magnetically charged hairy topological
black hole solutions in string theory: We construct black hole solutions to the leading order of string effective
action in five dimensions with the source given by dilaton and magnetically
charged antisymmetric gauge $B$-field. Presence of the considered $B$-field
leads to the unusual asymptotic behavior of solutions which are neither
asymptotically flat nor asymptotically (A)dS. We consider the three-dimensional
space part to correspond to the Bianchi classes and so the horizons of these
topological black hole solutions are modeled by seven homogeneous Thurston
geometries of $E^3$, $S^3$, $H^3$, $H^2 \times E^1$, $\widetilde{{SL_2R}}$,
nilgeometry, and solvegeometry. Calculating the quasi-local mass, temperature,
entropy, dilaton charge, and magnetic potential, we show that the first law of
black hole thermodynamics is satisfied by these quantities and the dilaton hair
is of the secondary type. Furthermore, for Bianchi type $V$, the $T$-dual black
hole solution is obtained which carries no charge associated with $B$-field and
possesses a dilaton hair of secondary kind. Also, the entropy turns to be
invariant under the $T$-duality. |
Locality, Causality and Noncommutative Geometry: We analyse the causality condition in noncommutative field theory and show
that the nonlocality of noncommutative interaction leads to a modification of
the light cone to the light wedge. This effect is generic for noncommutative
geometry. We also check that the usual form of energy condition is violated and
propose that a new form is needed in noncommutative spacetime. On reduction
from light cone to light wedge, it looks like the noncommutative dimensions are
effectively washed out and suggests a reformulation of noncommutative field
theory in terms of lower dimensional degree of freedom. This reduction of
dimensions due to noncommutative geometry could play a key role in explaining
the holographic property of quantum gravity. | High energy scattering and AdS/CFT: In this talk we describe the application of the AdS/CFT correspondence for a
confining background to the study of high energy scattering amplitudes in gauge
theory. We relate the energy behaviour of scattering amplitudes to properties
of minimal surfaces of the helicoidal type. We describe the results of
hep-th/0003059 and hep-th/0010069 for amplitudes with vacuum quantum number
exchange and, very briefly, hep-th/0110024 on the extension of this formalism
to Reggeon exchange. |
D-brane Configurations for Domain Walls and Their Webs: Supersymmetric U(Nc) gauge theory with Nf massive hypermultiplets in the
fundamental representation admits various BPS solitons like domain walls and
their webs. In the first part we show as a review of the previous paper
hep-th/0412024 that domain walls are realized as kinky fractional D3-branes
interpolating between separated D7-branes. In the second part we discuss brane
configurations for domain wall webs. This is a contribution to the conference
based on the talk given by MN. | Kahler Moduli Stabilization and the Propagation of Decidability: Diophantine equations are in general undecidable, yet appear readily in
string theory. We demonstrate that numerous classes of Diophantine equations
arising in string theory are decidable and propose that decidability may
propagate through networks of string vacua due to additional structure in the
theory. Diophantine equations arising in index computations relevant for
D3-instanton corrections to the superpotential exhibit propagation of
decidability, with new and existing solutions propagating through networks of
geometries related by topological transitions. In the geometries we consider,
most divisor classes appear in at least one solution, significantly improving
prospects for Kahler moduli stabilization across large ensembles of string
compactifications. |
On Detecting Discrete Cheshire Charge: We analyze the charges carried by loops of string in models with non-abelian
local discrete symmetry. The charge on a loop has no localized source, but can
be detected by means of the Aharonov--Bohm interaction of the loop with another
string. We describe the process of charge detection, and the transfer of charge
between point particles and string loops, in terms of gauge--invariant
correlation functions. | On the trace anomaly for Weyl fermions: This note is a comment on some recent papers that have raised a controversy
about the existence of the odd-parity trace anomaly in a four-dimensional
theory of Weyl fermions. Without going into too technical details we explain
why the methods employed in those papers cannot detect it. |
Pole-skipping of gravitational waves in the backgrounds of
four-dimensional massive black holes: Pole-skipping is a property of gravitational waves dictated by their
behaviour at horizons of black holes. It stems from the inability to
unambiguously impose ingoing boundary conditions at the horizon at an infinite
discrete set of Fourier modes. The phenomenon has been best understood, when
such a description exists, in terms of dual holographic (AdS/CFT) correlation
function that take the value of `$0/0$' at these special points. In this work,
we investigate details of pole-skipping purely from the point of view of
classical gravity in 4$d$ massive black hole geometries with flat, spherical
and hyperbolic horizons, and with an arbitrary cosmological constant. We show
that pole-skipping points naturally fall into two categories: the algebraically
special points and a set of pole-skipping points that is common to the even and
odd channels of perturbations. Our analysis utilises and generalises (to
arbitrary maximally symmetric horizon topology and cosmological constant) the
`integrable' structure of the Darboux transformations, which relate the master
field equations that describe the evolution of gravitational perturbations in
the two channels. Finally, we provide new insights into a number of special
cases: spherical black holes, asymptotically Anti-de Sitter black branes and
pole-skipping at the cosmological horizon in de Sitter space. | The G_Newton --> 0 Limit of Euclidean Quantum Gravity: Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit
of Euclidean or complexified general relativity is not a free field theory, but
is a theory that describes a linearized self-dual connection propagating on an
arbitrary anti-self-dual background. This theory is quantized in the loop
representation and, as in the full theory, an infinite dimnensional space of
exact solutions to the constraint is found. An inner product is also proposed.
The path integral is constructed from the Hamiltonian theory and the measure is
explicitly computed nonperturbatively, without relying on a semiclassical
expansion. This theory could provide the starting point for a new approach to
perturbation theory in $G_{Newton}$ that does not rely on a background field
expansion and in which full diffeomorphism invariance is satisfied at each
order. |
Branes and Quantized Fields: It is shown that the Dirac-Nambu-Goto brane can be described as a point
particle in an infinite dimensional space with a particular metric. This can be
considered as a special case of a general theory in which branes are points in
the brane space ${\cal M}$, whose metric is dynamical, just like in general
relativity. Such a brane theory, amongst others, includes the flat brane space,
whose metric is the infinite dimensional analog of the Minkowski space metric
$\eta_{\mu \nu}$. A brane living in the latter space will be called "flat
brane"; it is like a bunch of non-interacting point particles. Quantization of
the latter system leads to a system of non-interacting quantum fields.
Interactions can be included if we consider a non trivial metric in the space
of fields. Then the effective classical brane is no longer a flat brane. For a
particular choice of the metric in the field space we obtain the
Dirac-Nambu-Goto brane. We also show how a Stueckelberg-like quantum field
arises within the brane space formalism. With the Stueckelberg fields, we avoid
certain well-known intricacies, especially those related to the position
operator that is needed in our construction of effective classical branes from
the systems of quantum fields. | Thick branes in Horndeski gravity: We investigate thick brane solutions in the Horndeski gravity. In this setup,
we found analytical solutions, applying the first-order formalism to two scalar
fields where the first field comes from the non-minimal scalar-tensor coupling
and the second is due to the matter contribution sector. With these analytical
solutions, we evaluate the symmetric thick brane solutions in Horndeski gravity
with four-dimensional geometry. In such a setup, we evaluate the gravity
fluctuations to find ``almost massless modes'', for any values of the Horndeski
parameters. These modes were used to compute the corrections to the Newtonian
potential and evaluate the limit four-dimensional gravity. |
A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory: In frames of the nonlocal and nonpolynomial quantum theory of the one
component scalar field in $D$-dimensional spacetime, stated by Gariy
Vladimirovich Efimov, the expansion of the $\mathcal{S}$-matrix is revisited
for different interaction Lagrangians and for some kinds of Gaussian
propagators modified by different ultraviolet form factors $F$ which depend on
some length parameter $l$. The expansion of the $\mathcal{S}$-matrix is of the
form of a grand canonical partition function of some $D+N$-dimensional ($N\geq
1$) classical gas with interaction. The toy model of the realistic quantum
field theory (QFT) is considered where the $\mathcal{S}$-matrix is calculated
in closed form. Then, the functional Schwinger-Dyson and Schr\"{o}dinger
equations for the $\mathcal{S}$-matrix in Efimov representation are derived.
These equations play a central role in the present paper. The functional
Schwinger-Dyson and Schr\"{o}dinger equations in Efimov representation do not
involve explicit functional derivatives but involve a shift of the field which
is the $\mathcal{S}$-matrix argument. The asymptotic solutions of the
Schwinger-Dyson equation are obtained in different limits. Also, the solution
is found in one heuristic case allowing us to study qualitatively the behavior
of the $\mathcal{S}$-matrix for an arbitrary finite value of its argument.
Self-consistency equations, which arise during the process of derivation, are
of a great interest. Finally, in the light of the discussion of QFT functional
equations, ultraviolet form factors and extra dimensions, the connection with
functional (in terms of the Wilson-Polchinski and Wetterich-Morris functional
equations) and holographic renormalization groups (in terms of the functional
Hamilton-Jacobi equation) is made. In addition the Hamilton-Jacobi equation is
formulated in an unconventional way. | Catalysis of Dynamical Symmetry Breaking by a Magnetic Field: A constant magnetic field in 3+1 and 2+1 dimensions is a strong catalyst of
dynamical chiral symmetry breaking, leading to the generation of a fermion mass
even at the weakest attractive interaction between fermions. The essence of
this effect is the dimensional reduction $D/rightarrow D-2$ in the dynamics of
fermion pairing in a magnetic field. The effect is illustrated in the
Nambu-Jona-Lasinio model and QED. Possible applications of this effect and its
extension to inhomogeneous field configurations are discussed. |
Plane Gravitational Waves in String Theory: We analyze the coset model $(E_2^c \ti E_2^c)/E_2^c$ and construct a class of
exact string vacua which describe plane gravitational waves and their duals,
generalizing the plane wave background found by Nappi and Witten. In
particular, the vector gauging describes a two-parameter family of singular
geometries with two isometries, which is dual to plane gravitational waves. In
addition, there is a mixed vector-axial gauging which describes a one-parameter
family of plane waves with five isometries. These two backgrounds are related
by a duality transformation which generalizes the known axial-vector duality
for abelian subgroups. | Relation between space-time inversion and particle-antiparticle symmetry
and the microscopic essence of special relativity: After analyzing the implication of investigations on the C, P and T
transformations since 1956, we propose that there is a basic symmetry in
particle physics. The combined space-time inversion is equivalent to
particle-antiparticle transformation, denoted by ${\cal PT=C}$. It is shown
that the relativistic quantum mechanics and quantum field theory do contain
this invariance explicitly or implicitly. In particular, (a) the appearance of
negative energy or negative probability density in single particle theory --
corresponding to the fact of existence of antiparticle, (b) spin- statistics
connection, (c) CPT theorem, (d) the Feynman propagator are linked together via
this symmetry. Furthermore, we try to derive the main results of special
relativity, especially, (e) the mass-energy relation, (f) the Lorentz
transformation by this one ``relativistic'' postulate and some
``nonrelativistic'' knowledge. |
The BMS-like symmetry of extremal horizons: I revisit the calculation of infinite-dimensional symmetries that emerge in
the vicinity of isolated horizons. I focus the attention on extremal black
holes, for which the isometry algebra that preserves a sensible set of
asymptotic boundary conditions at the horizon strictly includes the BMS
algebra. The conserved charges that correspond to this BMS sector, however,
reduce to those of superrotation, generating only two copies of Witt algebra.
For more general horizon isometries, in contrast, the charge algebra does
include both Witt and supertranslations, being similar to BMS but s.str.
differing from it.
This work has been prepared for the proceedings of the XXII Simposio Sofichi
2020, held in Chile in November 2020. The material herein is based on my work
in collaboration with Laura Donnay, Hernan Gonzalez and Miguel Pino, and it is
included in arXiv:1511.08687 and arXiv:1607.05703. | A Practical Approach to the Hamilton-Jacobi Formulation of Holographic
Renormalization: We revisit the subject of holographic renormalization for asymptotically AdS
spacetimes. For many applications of holography, one has to handle the
divergences associated with the on-shell gravitational action. The brute force
approach uses the Fefferman-Graham (FG) expansion near the AdS boundary to
identify the divergences, but subsequent reversal of the expansion is needed to
construct the infinite counterterms. While in principle straightforward, the
method is cumbersome and application/reversal of FG is formally unsatisfactory.
Various authors have proposed an alternative method based on the
Hamilton-Jacobi equation. However, this approach may appear to be abstract,
difficult to implement, and in some cases limited in applicability. In this
paper, we clarify the Hamilton-Jacobi formulation of holographic
renormalization and present a simple algorithm for its implementation to
extract cleanly the infinite counterterms. While the derivation of the method
relies on the Hamiltonian formulation of general relativity, the actual
application of our algorithm does not. The work applies to any $D$-dimensional
holographic dual with asymptotic AdS boundary, Euclidean or Lorentzian, and
arbitrary slicing. We illustrate the method in several examples, including the
FGPW model, a holographic model of 3d ABJM theory, and cases with marginal
scalars such as a dilaton-axion system. |
The emergence of fermions and the E11 content: Claudio's warm and endearing personality adds to our admiration for his
achievements in physics a sense of friendliness. His constant interest in
fundamental questions motivated the following presentation of our attempt to
understand the nature of fermions. This problem is an essential element of the
quantum world and might be related to the quest for quantum gravity. We shall
review how space-time fermions can emerge out of bosons in string theory and
how this fact affects the extended Kac-Moody approach to the M-theory project. | A new branch of inflationary speed limits: We present a new mechanism for inflation which exhibits a speed limit on
scalar motion, generating accelerated expansion even on a steep potential. This
arises from explicitly integrating out the short modes of additional fields
coupled to the inflaton $\phi$ via a dimension six operator, yielding an
expression for the effective action which includes a nontrivial (logarithmic)
function of $(\partial\phi)^2$. The speed limit appears at the branch cut of
this logarithm arising in a large flavor expansion, similarly to the square
root branch cut in DBI inflation arising in a large color expansion. Finally,
we describe observational constraints on the parameters of this model. |
Four-Dimensional N=2(4) Superstring Backgrounds and The Real Heavens: We study N=2(4) superstring backgrounds which are four-dimensional
non-\Kahlerian with non-trivial dilaton and torsion fields. In particular we
consider the case that the backgrounds possess at least one $U(1)$ isometry and
are characterized by the continual Toda equation and the Laplace equation. We
obtain a string background associated with a non-trivial solution of the
continual Toda equation, which is mapped, under the T-duality transformation,
to the hyper-\Kahler Taub-NUT instanton background. It is shown that the
integrable property of the non-\Kahlerian spaces have the direct origin in the
real heavens: real, self-dual, euclidean, Einstein spaces. The Laplace equation
and the continual Toda equation imposed on quasi-\Kahler geometry for
consistent string propagation are related to the self-duality conditions of the
real heavens with ``translational'' and ``rotational''Killing symmetry
respectively. | Aspects of 5d Seiberg-Witten Theories on $\mathbb{S}^1$: We study the infrared physics of 5d $\cal N=1$ Yang-Mills theories
compactified on $\mathbb{S}^1$, with a view toward 4d and 5d limits. Global
structures of the simplest Coulombic moduli spaces are outlined, with an
emphasis on how multiple planar 4d Seiberg-Witten geometries are embedded in
the cigar geometry of a single 5d theory on $\mathbb{S}^1$. The Coulomb phase
boundaries in the decompactification limit are given particular attention and
related to how the wall-crossings by 5d BPS particles turn off. On the other
hand, the elliptic genera of magnetic BPS strings do wall-cross and retain the
memory of 4d wall-crossings, which we review with the example of dP$_2$ theory.
Along the way, we also offer a general field theory proof of the odd shift of
electric charge on Sp$(k)_\pi$ instanton solitons, previously observed via
geometric engineering for low-rank supersymmetric theories. |
Quantum corrections for (anti)-evaporating black hole: In this paper we analyse the quantum correction for Schwarzschild black hole
in the Unruh state in the framework of spherically symmetric gravity (SSG)
model. SSG is a two-dimensional dilaton model which is obtained by spherically
symmetric reduction from the four-dimensional theory. We find the one-loop
geometry of the (anti)-evaporating black hole and corrections for mass, entropy
and apparent horizon. | Instantons in Partially Broken Gauge Groups: We discuss the effects of instantons in partially broken gauge groups on the
low-energy effective gauge theory. Such effects arise when some of the
instantons of the original gauge group G are no longer contained in (or can not
be gauge rotated into) the unbroken group H. In cases of simple G and H, a good
indicator for the existence of such instantons is the ``index of embedding.''
However, in the general case one has to examine \pi_3(G/H) to decide whether
there are any instantons in the broken part of the gauge group. We give several
examples of supersymmetric theories where such instantons exist and leave their
effects on the low-energy effective theory. |
Smirnov's Integrals and Quantum Knizhnik-Zamolodchikov Equation of Level
$0$: We study the quantum Knizhnik-Zamolodchikov equation of level $0$ associated
with the spin $1/2$ representation of $U_q \bigl(\widehat{\frak s \frak l
_{2}}\bigr)$. We find an integral formula for solutions in the case of an
arbitrary total spin and $|q|<1$. In the formula, different solutions can be
obtained by taking different integral kernels with the cycle of integration
being fixed. | Memory effects from holonomies: We provide a uniform treatment of electromagnetic and gravitational memory
effects, based on the gravito-electromagnetic formulation of GR and a
generalization of the geodesic deviation equation. This allows us to find novel
results: in gauge theory, we derive relativistic corrections to the well-known
kick memory observable, and a general expression for the displacement memory
observable, typically overlooked in the literature. In GR, we find relativistic
corrections to displacement and kick memory observables. In both theories, we
find novel radial memory effects. Next, we show that electromagnetic and
gravitational memory observables can be formulated in terms of certain
holonomies on a holographic screen in asymptotically flat spacetimes. In gauge
theory, the displacement and kick memory effects form a Hamiltonian vector
field which is canonically generated by a Wilson loop. In the first order
formulation of GR, we show that the holonomy naturally splits into
translational and Lorentz parts. While the former encodes the leading and
subleading displacement and kick memory observables, the latter reproduces the
gyroscopic memory effect. |
Towards a supersymmetric classification of D-brane configurations with
odd spin structure: We consider the construction of a general tree level amplitude for the
interactions between dynamical D-branes where the configurations have non-zero
odd spin structure. Using Riemann Theta Identities we map the conditions for
the preservation of some supersymmetry to a set of integer matrices satisfying
a simple but non-trivial equation. We also show how the regularization of the
RR zero modes plays an important role in determining which configurations are
permitted. | Accelerating Black Hole Thermodynamics with Boost Time: We derive a thermodynamic first law for the electrically charged C-metric
with vanishing cosmological constant. This spacetime describes a pair of
identical accelerating black holes each pulled by a cosmic string. Treating the
"boost time" of this spacetime as the canonical time, we find a thermodynamic
first law in which every term has an unambiguous physical meaning. We then show
how this first law can be derived using Noetherian methods in the covariant
phase space formalism. We argue that the area of the acceleration horizon
contributes to the entropy and that the appropriate notion of energy of this
spacetime is a "boost mass", which vanishes identically. The recovery of the
Reissner-Nordstrom first law in the limit of small string tension is also
demonstrated. Finally, we compute the action of the Euclidean section of the
C-metric and show it agrees with the thermodynamic grand potential, providing
an independent confirmation of the validity of our first law. We also briefly
speculate on the significance of firewalls in this spacetime. |
N=4 mechanics with diverse (4,4,0) multiplets: explicit examples of HKT,
CKT, and OKT geometries: We present simple models of N=4 supersymmetric mechanics with ordinary and
mirror linear (4,4,0) multiplets that give a transparent description of HKT,
CKT, and OKT geometries. These models are treated in the N=4 and N=2 superfield
approaches, as well as in the component approach. Our study makes manifest that
the CKT and OKT supersymmetric sigma models are distinguished from the more
simple HKT models by the presence of extra holomorphic torsions in the
supercharges. | Quantum field theory based on birefringent modified Maxwell theory: In the current paper the properties of a birefringent Lorentz-violating
extension of quantum electrodynamics is considered. The theory results from
coupling modified Maxwell theory, which is a CPT-even Lorentz-violating
extension of the photon sector, to a Dirac theory of standard spin-1/2
particles. It is then restricted to a special birefringent case with one
nonzero Lorentz-violating coefficient. The modified dispersion laws of
electromagnetic waves are obtained plus their phase and group velocities are
considered. After deriving the photon propagator and the polarization vectors
for a special momentum configuration we prove both unitarity at tree-level and
microcausality for the quantum field theory based on this Lorentz-violating
modification. These analytical proofs are done for a spatial momentum with two
vanishing components and the proof of unitarity is supported by numerical
investigations in case all components are nonvanishing. The upshot is that the
theory is well-behaved within the framework of our assumptions where there is a
possible issue for negative Lorentz-violating coefficients. The paper shall
provide a basis for the future analysis of alternative birefringent quantum
field theories. |
Conformal couplings of Galileons to other degrees of freedom: We discuss a formulation of Galileon actions in terms of matrix determinants
in four dimensions. This approach allows one to straightforwardly determine
derivative couplings between Galileons and scalar or vector degrees of freedom
that lead to equations of motion with at most two space-time derivatives. We
use this method to easily build generalizations of Galileon set-ups preserving
conformal symmetry, finding explicit examples of couplings between Galileons
and additional degrees of freedom that preserve the Galileon conformal
invariance. We discuss various physical applications of our method and of our
results. | Analytical Study of Mode Coupling in Hybrid Inflation: We provide an analytical study of the coupling of short and long wavelength
fluctuation modes during the initial phase of reheating in two field models
like hybrid inflation. In these models, there is - at linear order in
perturbation theory - an instability in the entropy modes of cosmological
perturbations which, if not cut off, could lead to curvature fluctuations which
exceed the current observational values. Here, we demonstrate that the
back-reaction of short wavelength fluctuations is too weak to lead to a
truncation of the instability for the long wavelength modes on time scales
comparable to the typical instability time scale of the long wavelength entropy
modes. Hence, unless there are other mechanisms which truncate the instability,
then in models such as hybrid inflation the curvature perturbations produced
during reheating on scales of current observational interest may be very
important. |
The field nature of spin for electromagnetic particle: The field nature of spin in the framework of the field electromagnetic
particle concept is considered. A mathematical character of the fine structure
constant is discussed. Three topologically different field models for charged
particle with spin are investigated in the scope of the linear electrodynamics.
A using of these field configurations as an initial approximation for an
appropriate particle solution of nonlinear electrodynamics is discussed. | Quarter-BPS solutions in three-dimensional N=16 supergravity and the
Liouville equation: We show how by assuming at least 8 real timelike supersymmetries in the
maximally supersymmetric three-dimensional ungauged supergravity and a further
simplifying Ansatz, we are naturally led to a pair of Liouville field
equations. We also show that there are no solutions that preserve only 6 real
timelike supersymmetries. The solution relies on the classification of complex
spinors of Spin(8) to which the problem quickly reduces. |
Multicritical Phase Transitions in Lovelock AdS Black Holes: We demonstrate that black holes in order $N\ge 4$ Lovelock gravity can
exhibit multicritical phase behaviour. We show an explicit example of a
quadruple point in $d=10$ fourth-order Lovelock gravity and a quintuple point
in $d=14$ sixth-order Lovelock gravity. We also demonstrate that
multi-criticality can be realized for uncharged, non-rotating black holes by
highlighting a new type of multi-critical point between black holes and thermal
radiation. We discuss the methodology used and make comparisons to other black
hole multi-critical points in terms of the Gibbs phase rule. | A Rule of Thumb Derivation of Born-Infeld Action for D-branes: A rule of thumb derivation of the Dirac-Born-Infeld action for D-branes is
studied \`a la Fradkin and Tseytlin, by simply integrating out of the
superstring coordinates in a narrow strip attached to the D-branes. In case of
superstrings, the coupling of Ramond-Ramond fields as well as the
Dirac-Born-Infeld type coupling of the Neveu Schwarz-Neveu Schwarz fields come
out in this way. |
Noncommutative Gravity in two Dimensions: We deform two-dimensional topological gravity by making use of its gauge
theory formulation. The obtained noncommutative gravity model is shown to be
invariant under a class of transformations that reduce to standard
diffeomorphisms once the noncommutativity parameter is set to zero. Some
solutions of the deformed model, like fuzzy AdS_2, are obtained. Furthermore,
the transformation properties of the model under the Seiberg-Witten map are
studied. | Most General Spherically Symmetric M2-branes and Type IIB Strings: We obtain the most general spherically symmetric M2-branes and type IIB
strings, with \R^{1,2}\times SO(8) and \R^{1,1}\times SO(8) isometries
respectively. We find that there are twelve different classes of M2-branes, and
we study their curvature properties. In particular we obtain new smooth
M2-brane wormholes that connect two asymptotic regions: one is flat and the
other can be either flat or AdS_4\times S^7. We find that these wormholes are
traversable with certain time-like trajectories. We also obtain the most
general Ricci-flat solutions in five dimensions with \R^{1,1}\times SO(3)
isometries. |
Tensor Perturbations in Quantum Cosmological Backgrounds: In the description of the dynamics of tensor perturbations on a homogeneous
and isotropic background cosmological model, it is well known that a simple
Hamiltonian can be obtained if one assumes that the background metric satisfies
Einstein classical field equations. This makes it possible to analyze the
quantum evolution of the perturbations since their dynamics depends only on
this classical background. In this paper, we show that this simple Hamiltonian
can also be obtained from the Einstein-Hilbert lagrangian without making use of
any assumption about the dynamics of the background metric. In particular, it
can be used in situations where the background metric is also quantized, hence
providing a substantial simplification over the direct approach originally
developed by Halliwell and Hawking. | E_{11}, ten forms and supergravity: We extend the previously given non-linear realisation of E_{11} for the
decomposition appropriate to IIB supergravity to include the ten forms that
were known to be present in the adjoint representation. We find precise
agreement with the results on ten forms found by closing the IIB supersymmetry
algebra. |
Can codimension-two branes solve the cosmological constant problem?: It has been suggested that codimension-two braneworlds might naturally
explain the vanishing of the 4D effective cosmological constant, due to the
automatic relation between the deficit angle and the brane tension. To
investigate whether this cancellation happens dynamically, and within the
context of a realistic cosmology, we study a codimension-two braneworld with
spherical extra dimensions compactified by magnetic flux. Assuming Einstein
gravity, we show that when the brane contains matter with an arbitrary equation
of state, the 4D metric components are not regular at the brane, unless the
brane has nonzero thickness. We construct explicit 6D solutions with thick
branes, treating the brane matter as a perturbation, and find that the universe
expands consistently with standard Friedmann-Robertson-Walker (FRW) cosmology.
The relation between the brane tension and the bulk deficit angle becomes
$\Delta=2\pi G_6(\rho-3 p)$ for a general equation of state. However, this
relation does not imply a self-tuning of the effective 4D cosmological constant
to zero; perturbations of the brane tension in a static solution lead to
deSitter or anti-deSitter braneworlds. Our results thus confirm other recent
work showing that codimension-two braneworlds in nonsupersymmetric Einstein
gravity do not lead to a dynamical relaxation of the cosmological constant, but
they leave open the possibility that supersymmetric versions can be compatible
with self-tuning. | Catching the phantom: the MSSM on the Z6-orientifold: These lecture notes give a short introduction of the derivation of the
supersymmetric standard model on the Z6-orientifold as published in
hep-th/0404055. Untwisted and twisted cycles are constructed and one specific
model is discussed in more detail. |
Proca Q-balls and Q-shells: Non-topological solitons such as Q-balls and Q-shells have been studied for
scalar fields invariant under global and gauged U(1) symmetries. We generalize
this framework to include a Proca mass for the gauge boson, which can arise
either from spontaneous symmetry breaking or via the St\"uckelberg mechanism. A
heavy (light) gauge boson leads to solitons reminiscent of the global (gauged)
case, but for intermediate values these Proca solitons exhibit completely novel
features such as disconnected regions of viable parameter space and Q-shells
with unbounded radius. We provide numerical solutions and excellent analytic
approximations for both Proca Q-balls and Q-shells. These allow us to not only
demonstrate the novel features numerically, but also understand and predict
their origin analytically. | An Algebraic Approach to Solving Evolution Problems in Some Nonlinear
Quantum Models: A new general Lie-algebraic approach is proposed to solving evolution tasks
in some nonlinear problems of quantum physics with polynomially deformed Lie
algebras $su_{pd}(2)$ as their dynamic symmetry algebras.
The method makes use of an expansion of the evolution operators by power
series in the $su_{pd}(2)$ shift operators and a (recursive) reduction of
finding coefficient functions to solving auxiliary exactly solvable $su(2)$
problems with quadratic Hamiltonians.
PACS numbers: 03.70; 02.20; 42.50 |
Representations and characters of the Virasoro algebra and N=1
super-Virasoro algebras: We present the list of irreducible (generalized) highest weight modules over
the Virasoro algebra and N=1 super-Virasoro algebras obtained as factor-modules
of (generalized) Verma modules. We present also the character formulae of all
these modules and single out the unitary irreducible ones. Most formulas are
valid for the three algebras under consideration, the different cases being
distinguished by two parameters. This is a slightly extended version of an
Encyclopedia entry. | Supersymmetric Oscillator: Novel Symmetries: We discuss various continuous and discrete symmetries of the supersymmetric
simple harmonic oscillator (SHO) in one (0 + 1)-dimension of spacetime and show
their relevance in the context of mathematics of differential geometry. We show
the existence of a novel set of discrete symmetries in the theory which has,
hitherto, not been discussed in the literature on theoretical aspects of SHO.
We also point out the physical relevance of our present investigation. |
Massive flows in AdS$_6$/CFT$_5$: We study five-dimensional ${\cal N}=1$ Superconformal Field Theories of the
linear quiver type. These are deformed by a relevant operator, corresponding to
a homogeneous mass term for certain matter fields. The free energy is
calculated at arbitrary values of the mass parameter. After a careful
regularisation procedure, the result can be put in correspondence with a
calculation in the supergravity dual background. The F-theorem is verified for
these flows, both in field theory and in supergravity. This letter presents
some of the results in the companion paper arXiv:2211.13240. | Fermion Determinant Calculus: The path-integral of the fermionic oscillator with a time-dependent frequency
is analyzed. We give the exact relation between the boundary condition to
define the domain in which the path-integral is performed and the transition
amplitude that the path-integral calculates. According to this relation, the
amplitude suppressed by a zero mode does not indicate any special dynamics,
unlike the analogous situation in field theories. It simply says the
path-integral picks up a combination of the amplitudes that vanishes. The zero
mode that is often neglected in the reason of not being normalizable is
necessary to obtain the correct answer for the propagator and to avoid an
anomaly on the fermion number. We give a method to obtain the fermionic
determinant by the determinant of a simple (2\times 2) matrix, which enables us
to calculate it for a variety of boundary conditions. |
Inflationary Universe in Higher Derivative Induced Gravity: In an induced-gravity model, the stability condition of an inflationary
slow-rollover solution is shown to be $\phi_0
\partial_{\phi_0}V(\phi_0)=4V(\phi_0)$. The presence of higher derivative terms
will, however, act against the stability of this expanding solution unless
further constraints on the field parameters are imposed. We find that these
models will acquire a non-vanishing cosmological constant at the end of
inflation. Some models are analyzed for their implication to the early
universe. | Why Matrix Theory is Hard: Recently Sen and Seiberg gave a prescription for constructing the matrix
theory in any superstring background. We use their prescription to test the
finite N matrix theory conjecture on an ALE space. Based on our earlier work
with Shenker, we find a sharper discrepancy between matrix theory computation
and supergravity prediction. We discuss subtleties in the light-front
quantization which may lead to a resolution to the discrepancy. |
Inflationary Potentials from the Exact Renormalisation Group: We show that an inflationary slow-roll potential can be derived as an IR
limit of the non-perturbative exact renormalisation group equation for a scalar
field within the mean-field approximation. The result follows without having to
specify a Lagrangian for the UV theory at the Planck scale. We assume that the
theory contains a scalar mode with suppressed coupling to other UV fields, and
that higher derivative couplings are suppressed. The resulting effective
potential gives rise to slow-roll inflation, which is fully consistent with the
recent observations. As an example of how the proposed renormalisation group
procedure works, we perform an explicit calculation in the $\phi^4$ theory. | $A_\infty$-Algebra from Supermanifolds: Inspired by the analogy between different types of differential forms on
supermanifolds and string fields in superstring theory, we construct new
multilinear non-associative products of forms which yield an
$A_\infty$-algebra. |
Integrable strings for AdS/CFT: In this PhD thesis we review some aspects of integrable models related to
string backgrounds or their deformations. In the first part we develop methods
to obtain exact results in the AdS3/CFT2 correspondence. We consider the AdS_3
x S^3 x T^4 background with pure Ramond-Ramond flux and we find the all-loop
worldsheet S-matrix by exploiting the symmetries of the model in light-cone
gauge. As we naturally include the massless modes on the worldsheet, we derive
the full set of Bethe-Yang equations. In the massive sector we give also a
spin-chain description and we write down solutions compatible with crossing for
the scalar factors which are not constrained by simmetries. In the second part
of the thesis we consider the so-called "eta-deformation" of the superstring on
AdS_5 x S^5. We first discuss the effects of the deformation at the level of
the bosonic sigma-model, and we match the tree-level worldsheet scattering
processes to the expansion of the q-deformed S-matrix. To identify the missing
Ramond-Ramond fields we then compute the action quadratic in fermions, and we
provide an alternative derivation by looking at the kappa-symmetry variations.
The resulting background fields do not solve the equations of motion of type
IIB supergravity and we comment on this. | Lorentzian worldline path integral approach to Schwinger effect: We demonstrate that the positive frequency modes for a complex scalar field
in a constant electric field (Schwinger modes), in three different gauges, can
be represented as exact Lorentzian worldline path integral amplitudes. Although
the mathematical forms of the mode functions differ in each gauge, we show that
a simple prescription for Lorentzian worldlines' boundary conditions dispenses
the Schwinger modes in all three gauges (that we considered) in a unified
manner. Following that, using our formalism, we derive the exact Bogoliubov
coefficients and, hence, the particle number, \textit{without} appealing to the
well-known connection formulas for parabolic cylinder functions. This result is
especially relevant in view of the fact that in a general electromagnetic field
configuration, one does not have the luxury of closed-form solutions. We argue
that the real time worldline path integral approach may be a promising
alternative in such non-trivial cases. We also demonstrate, using
Picard-Lefschetz theory, how the so-called worldline instantons emerge
naturally from relevant saddle points that are complex. |
Unification of Spacetime Symmetries of Massive and Massless Particles: The internal space-time symmetries of relativistic particles are dictated by
Wigner's little groups. The $O(3)$-like little group for a massive particle at
rest and the $E(2)$-like little group of a massless particle are two different
manifestations of the same covariant little group. Likewise, the quark model
and parton pictures are two different manifestations of the one covariant
entity. | The quantum description of BF model in superspace: We consider the BRST symmetric four dimensional BF theory, a topological
theory, containing antysymmetric tensor fields in Landau gauge and extend the
BRST symmetry by introducing a shift symmetry to it. Within this formulation,
the antighost fields corresponding to shift symmetry coincide with antifields
of standard field/antifield formulation. Further, we provide a superspace
description for the BF model possessing extended BRST and extended anti-BRST
transformations. |
The mass of the adjoint pion in N=1 supersymmetric Yang-Mills theory: In Monte Carlo simulations of N=1 supersymmetric Yang-Mills theory the mass
of the unphysical adjoint pion, which is easily obtained numerically, is being
used for the tuning to the limit of vanishing gluino mass. In this article we
show how to define the adjoint pion in the framework of partially quenched
chiral perturbation theory and we derive a relation between its mass and the
mass of the gluino analogous to the Gell-Mann-Oakes-Renner relation of QCD. | The equation of state for scalar-tensor gravity: We show that the field equation of Brans-Dicke gravity and scalar-tensor
gravity can be derived as the equation of state of Rindler spacetime, where the
local thermodynamic equilibrium is maintained. Our derivation implies that the
effective energy can not feel the heat flow across the Rindler horizon. |
Screening length in plasma winds: We study the screening length L_s of a heavy quark-antiquark pair in strongly
coupled gauge theory plasmas flowing at velocity v. Using the AdS/CFT
correspondence we investigate, analytically, the screening length in the
ultra-relativistic limit. We develop a procedure that allows us to find the
scaling exponent for a large class of backgrounds. We find that for conformal
theories the screening length is (boosted energy density)^{-1/d}. As examples
of conformal backgrounds we study R-charged black holes and
Schwarzschild-anti-deSitter black holes in (d+1)-dimensions. For non-conformal
theories, we find that the exponent deviates from -1/d and as examples we study
the non-extremal Klebanov-Tseytlin and Dp-brane geometries. We find an
interesting relation between the deviation of the scaling exponent from the
conformal value and the speed of sound. | The 2nd order renormalization group flow for non-linear sigma models in
2 dimensions: We show that for two dimensional manifolds M with negative Euler
characteristic there exists subsets of the space of smooth Riemannian metrics
which are invariant and either parabolic or backwards-parabolic for the 2nd
order RG flow. We also show that solutions exists globally on these sets.
Finally, we establish the existence of an eternal solution that has both a UV
and IR limit, and passes through regions where the flow is parabolic and
backwards-parabolic. |
Quantum Gravitational Corrections to the Entropy of a
Reissner-Nordström Black Hole: Starting from an effective action for quantum gravity, we calculate the
quantum gravitational corrections to the Wald entropy of a four dimensional
non-extremal Reissner-Nordstr\"om (RN) black hole in the limit of small
electric charge, generalising a previous calculation carried out by Calmet and
Kuipers [1] for a Schwarzschild black hole. We show that, at second order in
the Ricci curvature, the RN metric receives quantum corrections which shift the
classical position of the event horizon. We apply the Wald entropy formula by
integrating over the perimeter of the quantum corrected event horizon. We then
compute the quantum gravitational corrections to the temperature and the
pressure of the black hole. | K-theory and phase transitions at high energies: The duality between $E_8\times E_8$ heteritic string on manifold $K3\times
T^2$ and Type IIA string compactified on a Calabi-Yau manifold induces a
correspondence between vector bundles on $K3\times T^2$ and Calabi-Yau
manifolds. Vector bundles over compact base space $K3\times T^2$ form the set
of isomorphism classes, which is a semi-ring under the operation of Whitney sum
and tensor product. The construction of semi-ring $Vect\ X$ of isomorphism
classes of complex vector bundles over X leads to the ring $KX=K(Vect\ X)$,
called Grothendieck group. As K3 has no isometries and no non-trivial
one-cycles, so vector bundle winding modes arise from the $T^2$
compactification. Since we have focused on supergravity in d=11, there exist
solutions in d=10 for which space-time is Minkowski space and extra dimensions
are $K3\times T^2$. The complete set of soliton solutions of supergravity
theory is characterized by RR charges, identified by K-theory. Toric
presentation of Calabi-Yau through Batyrev's toric approximation enables us to
connect transitions between Calabi-Yau manifolds, classified by enhanced
symmetry group, with K-theory classification. |
Dark energy from bulk matter: We consider the possibility of getting accelerated expansion and w=-1
crossing in the context of a braneworld cosmological setup, endowed with a bulk
energy-momentum tensor. For a given ansatz of the bulk content, we demonstrate
that the bulk pressures dominate the dynamics at late times and can lead to
accelerated expansion. We also analyze the constraints under which we can get a
realistic profile for the effective equation of state and conclude that matter
in the bulk has the effect of dark energy on the brane. Furthermore, we show
that it is possible to simulate the behavior of a Chaplygin gas using
non-exotic bulk matter. | Snowmass White Paper: The Quest to Define QFT: This article provides a review of the literature on rigorous definitions and
constructions in Quantum Field Theory, spanning the period of seven decades.
Comparing with the ideas and constructions found in the modern physics
literature, we conclude that none of the existing systems of QFT axioms can
cover all the physical situations. Therefore, it is still an outstanding open
problem to formulate a complete definition of QFT. We argue that the question
is of relevance for both physicists and mathematicians. |
QCD at High Energies and Two-Dimensional Field Theory: Previous studies of high-energy scattering in QCD have shown a remarkable
correspondence with two-dimensional field theory. In this paper we formulate a
simple effective model in which this two-dimensional nature of the interactions
is manifest. Starting from the (3+1)-dimensional Yang-Mills action, we
implement the high energy limit $s\! >\! > \! t$ via a scaling argument and we
derive from this a simplified effective theory. This effective theory is still
(3+1)-dimensional, but we show that its interactions can to leading order be
summarized in terms of a two-dimensional sigma-model defined on the transverse
plane. Finally, we verify that our formulation is consistent with known
perturbative results. This is a revised and extended version of hep-th 9302104.
In particular, we have added a section that clarifies the connection with
Lipatov's gluon emission vertex. | Heterotic String Model Building with Monad Bundles and Reinforcement
Learning: We use reinforcement learning as a means of constructing string
compactifications with prescribed properties. Specifically, we study heterotic
SO(10) GUT models on Calabi-Yau three-folds with monad bundles, in search of
phenomenologically promising examples. Due to the vast number of bundles and
the sparseness of viable choices, methods based on systematic scanning are not
suitable for this class of models. By focusing on two specific manifolds with
Picard numbers two and three, we show that reinforcement learning can be used
successfully to explore monad bundles. Training can be accomplished with
minimal computing resources and leads to highly efficient policy networks. They
produce phenomenologically promising states for nearly 100% of episodes and
within a small number of steps. In this way, hundreds of new candidate standard
models are found. |
An Alternative To The Horizontality Condition In Superfield Approach To
BRST Symmetries: We provide an alternative to the gauge covariant horizontality condition
which is responsible for the derivation of the nilpotent (anti-)BRST symmetry
transformations for the gauge and (anti-)ghost fields of a (3 + 1)-dimensional
(4D) interacting 1-form non-Abelian gauge theory in the framework of the usual
superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. The above
covariant horizontality condition is replaced by a gauge invariant restriction
on the (4, 2)-dimensional supermanifold, parameterized by a set of four
spacetime coordinates x^\mu (\mu = 0, 1, 2, 3) and a pair of Grassmannian
variables \theta and \bar\theta. The latter condition enables us to derive the
nilpotent (anti-)BRST symmetry transformations for all the fields of an
interacting 4D 1-form non-Abelian gauge theory where there is an explicit
coupling between the gauge field and the Dirac fields. The key differences and
striking similarities between the above two conditions are pointed out clearly. | Where does curvaton reside? Differences between bulk and brane frames: Some classes of inflationary models naturally introduce two distinct
metrics/frames, and their equivalence in terms of observables has often been
put in question. D-brane inflation proposes candidates for an inflaton embedded
in the string theory and possesses descriptions on the brane and bulk
metrics/frames, which are connected by a conformal/disformal transformation
that depends on the inflaton and its derivatives. It has been shown that
curvature perturbations generated by the inflaton are identical in both frames,
meaning that observables such as the spectrum of cosmic microwave background
(CMB) anisotropies are independent of whether matter fields---including those
in the standard model of particle physics---minimally couple to the brane or
the bulk metric/frame. This is true despite the fact that the observables are
eventually measured by the matter fields and that the total action including
the matter fields is different in the two cases. In contrast, in curvaton
scenarios, the observables depend on the frame to which the curvaton minimally
couples. Among all inflationary scenarios, we focus on two models motivated by
the KKLMMT fine-tuning problem: a slow-roll inflation with an inflection-point
potential and a model of a rapidly rolling inflaton that conformally couples to
gravity. In the first model, the difference between the frames in which the
curvaton resides is encoded in the spectral index of the curvature
perturbations, depicting the nature of the frame transformation. In the second
model, the curvaton on the brane induces a spectral index significantly
different from that in the bulk and is even falsified by the observations. This
work thus demonstrates that two frames connected by a conformal/disformal
transformation lead to different physical observables such as CMB anisotropies
in curvaton models. |
Note on I-brane Near Horizon PP-wave Background: We find out a PP-wave spacetime with constant Neveu-Schwarz (NS) three form
flux by taking a Penrose limit on the 1+1 dimensional intersection of two
orthogonal stacks of fivebranes in type IIB string theory. We further find out
an intersecting (D1-D5)-brane solution in this background and analyze its
supersymmetry properties by solving the dilatino and gravitino variations
explicitly. | Noncommutative Space-time from Quantized Twistors: We consider the relativistic phase space coordinates (x_{\mu},p_{\mu}) as
composite, described by functions of the primary pair of twistor coordinates.
It appears that if twistor coordinates are canonicaly quantized the composite
space-time coordinates are becoming noncommutative. We obtain deformed
Heisenberg algebra which in order to be closed should be enlarged by the
Pauli-Lubanski four-vector components. We further comment on star-product
quantization of derived algebraic structures which permit to introduce
spin-extended deformed Heisenberg algebra. |
Thermofield Dynamics and Casimir Effect for Fermions: A generalization of the Bogoliubov transformation is developed to describe a
space compactified fermionic field. The method is the fermionic counterpart of
the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F.
C. Khanna and A. E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on
the thermofield dynamics approach. We analyse the energy-momentum tensor for
the Casimir effect of a free massless fermion field in a $d$-dimensional box at
finite temperature. As a particular case the Casimir energy and pressure for
the field confined in a 3-dimensional parallelepiped box are calculated. It is
found that the attractive or repulsive nature of the Casimir pressure on
opposite faces changes depending on the relative magnitude of the edges. We
also determine the temperature at which the Casimir pressure in a cubic boc
changes sign and estimate its value when the edge of the cybe is of the order
of confining lengths for baryons. | Universal Subleading Spectrum of Effective String Theory: We analyse the spectrum of the D-dimensional Poincare invariant effective
string model of Polchinski and Strominger. It is shown that the leading terms
beyond the Casimir term in the long distance expansion of the spectrum have a
universal character which follows from the constraint of Poincare invariance. |
Masses, Sheets and Rigid SCFTs: We study mass deformations of certain three dimensional $\mathcal{N}=4$
Superconformal Field Theories (SCFTs) that have come to be called $T^\rho[G]$
theories. These are associated to tame defects of the six dimensional $(0,2)$
SCFT $X[\mathfrak{j}]$ for $\mathfrak{j}=A,D,E$. We describe these deformations
using a refined version of the theory of sheets, a subject of interest in
Geometric Representation Theory. In mathematical terms, we parameterize local
mass-like deformations of the tamely ramified Hitchin integrable system and
identify the subset of the deformations that do admit an interpretation as a
mass deformation for the theories under consideration. We point out the
existence of non-trivial Rigid SCFTs among these theories. We classify the
Rigid theories within this set of SCFTs and give a description of their Higgs
and Coulomb branches. We then study the implications for the endpoints of RG
flows triggered by mass deformations in these 3d $\mathcal{N}=4$ theories.
Finally, we discuss connections with the recently proposed idea of Symplectic
Duality and describe some conjectures about its action. | Quantum supertwistors: In this paper we give an explicit expression for a star product on the super
Minkowski space written in the supertwistor formalism. The big cell of the
super Grassmannian Gr(2|0, 4|1) is identified with the chiral, super Minkowki
space. The super Grassmannian is an homogeneous space under the action of the
complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4,
signature (1,3) and supersymmetry N=1. The quantization is done by substituting
the groups and homogeneous spaces by their quantum deformed counterparts. The
calculations are done in Manin's formalism. When we restrict to the big cell we
can compute explicitly an expression for the super star product in the
Minkowski superspace associated to this deformation and the choice of a certain
basis of monomials. |
Large N and double scaling limits in two dimensions: Recently, the author has constructed a series of four dimensional
non-critical string theories with eight supercharges, dual to theories of light
electric and magnetic charges, for which exact formulas for the central charge
of the space-time supersymmetry algebra as a function of the world-sheet
couplings were obtained. The basic idea was to generalize the old matrix model
approach, replacing the simple matrix integrals by the four dimensional matrix
path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov
critical points by the Argyres-Douglas critical points. In the present paper,
we study qualitatively similar toy path integrals corresponding to the two
dimensional N=2 supersymmetric non-linear sigma model with target space CP^n
and twisted mass terms. This theory has some very strong similarities with N=2
super Yang-Mills, including the presence of critical points in the vicinity of
which the large n expansion is IR divergent. The model being exactly solvable
at large n, we can study non-BPS observables and give full proofs that double
scaling limits exist and correspond to universal continuum limits. A complete
characterization of the double scaled theories is given. We find evidence for
dimensional transmutation of the string coupling in some non-critical string
theories. We also identify en passant some non-BPS particles that become
massless at the singularities in addition to the usual BPS states. | Logarithmic conformal field theory approach to topologically massive
gravity: We study the topologically massive gravity at the chiral point (chiral
gravity) by using the logarithmic conformal field theory. Two new tensor fields
of $\psi^{new}$ and $X$ are introduced for a candidate of propagating physical
field at the chiral point. However, we show that ($\psi^{new},\psi^L$) form a
dipole ghost pair of unphysical fields and $X$ is not a primary. This implies
that there is no physically propagating degrees of freedom at the chiral point. |
On the complex structure in the Gupta-Bleuler quantization method: We examine the general conditions for the existence of the complex structure
intrinsic in the Gupta-Bleuler quantization method for the specific case of
mixed first and second class fermionic constraints in an arbitrary space-time
dimension. The cases d=3 and 10 are shown to be of prime importance. The
explicit solution for d=10 is presented. | Born-Infeld Gravity in any Dimension: We develop a Born-Infeld type theory for gravity in any dimension. We show
that in four dimensions our formalism allows a self-dual (or anti-self dual)
Born-Infeld gravity description. Moreover, we show that such a self-dual action
is reduced to both the Deser-Gibbons and the Jacobson-Smolin-Samuel action of
Ashtekar formulation. A supersymmetric generalization of our approach is
outlined. |
de Sitter Swampland Conjecture in String Field Inflation: In this paper, we study a particular type of inflation by using non-local
Friedman equations that are somehow derived from the zero levels of string
field theory and express a tachyonic action. Then, we challenge it by further
refining de Sitter (dS) swampland conjecture (FRdSSC) monitoring. Therefore, we
investigate some quantities, such as potential and Hubble parameters. We also
consider slow-roll parameters to examine quantities such as the scalar spectrum
index and the tensor-to-scalar ratio. Using straightforward calculations, we
investigate this model from the swampland conjecture perspective in terms of
the cosmological parameters, i.e., ($n_s$), ($r$), and observable data such as
Planck 2018, by constructing some structures such as $(c_1,2-n_s)$ and
$(c_1,2-r_s)$. Then, we make a new restriction for this conjecture as
$c_12c_22$ and get a limit for this model in the range $c0.0942$. We find this
inflationary model is strongly in tension with the dS swampland conjecture
(dSSC), i.e., $c_1=c_2 \neq \mathcal{O}(1)$. So, we shall challenge it with the
FRdSSC, which has some free parameters, viz., $a,b>0$, $a+b=1$, and $q>2$. By
setting these parameters, we examine the compatibility of the mentioned
conjecture with this inflationary model. Finally, we infer from this string
field inflation model that it satisfies the FRdSSC with the constraint of its
free parameters $a$, $b$, and $q$. | Phenomenological characterisation of semi-holographic non-Fermi liquids: We analyse some phenomenological implications of the most general
semi-holographic models for non-Fermi liquids that have emerged with inputs
from the holographic correspondence. We find generalizations of Landau-Silin
equations with few parameters governing thermodynamics, low energy response and
collective excitations. We show that even when there is a Fermi surface with
well-defined quasi-particle excitations, the collective excitations can behave
very differently from Landau's theory. |
Islands with Gravitating Baths: Towards ER = EPR: We study the Page curve and the island rule for black holes evaporating into
gravitating baths, with an eye towards establishing a connection with the
ER=EPR proposal. We consider several models of two entangled 2d black holes in
Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first,
"doubled PSSY," model is one in which the black holes have end-of-the-world
(ETW) branes with a flavour degree of freedom. We study highly entangled states
of this flavour degree of freedom and find an entanglement-induced
Hawking-Page-like transition from a geometry with two disconnected black holes
to one with a pair of black holes connected by a wormhole, thus realising the
ER = EPR proposal. The second model is a dynamical one in which the ETW branes
do not have internal degrees of freedom but the JT gravity is coupled to a 2d
CFT, and we entangle the black holes by coupling the two CFTs at the $AdS$
boundary and evolving for a long time. We study the entanglement entropy
between the two black holes and find that the story is substantially similar to
that with a non-gravitating thermal bath. In the third model, we couple the two
ends of a two-sided eternal black hole and evolve for a long time. Finally, we
discuss the possibility of a Hawking-Page-like transition induced by real-time
evolution that realises the ER = EPR proposal in this dynamical setting. | Analytical bound-state solutions of the Klein-Fock-Gordon equation for
the sum of Hulthén and Yukawa potential within SUSY quantum mechanics: The relativistic wave equations determine the dynamics of quantum fields in
the context of quantum field theory. One of the conventional tools for dealing
with the relativistic bound-state problem is the Klein-Fock-Gordon equation. In
this work, using a developed scheme, we present how to surmount the centrifugal
part and solve the modified Klein-Fock-Gordon equation for the linear
combination of Hulth\'en and Yukawa potentials. In particular, we show that the
relativistic energy eigenvalues and corresponding radial wave functions are
obtained from supersymmetric quantum mechanics by applying the shape invariance
concept. Here, both scalar potential conditions, which are whether equal and
non-equal to vector potential, are considered in the calculation. The energy
levels and corresponding normalized eigenfunctions are represented as a
recursion relation regarding the Jacobi polynomials for arbitrary $l$ states.
Beyond that, a closed-form of the normalization constant of the wave functions
is found. Furthermore, we state that the energy eigenvalues are quite sensitive
with potential parameters for the quantum states. The non-relativistic and
relativistic results obtained within SUSY QM overlap entirely with the results
obtained by ordinary quantum mechanics, and it displays that the mathematical
implementation of SUSY quantum mechanics is quite perfect. |
$S^7$ Current Algebras: We present $S^7$-algebras as generalized Kac-Moody algebras. A number of
free-field representations is found. We construct the octonionic projective
spaces ${\O}P^N$. | M-theory description of BPS string in 7-brane background: We discuss the BPS configurations of IIB strings in the 7-brane background
from M-theory viewpoint. We first obtain the hyperkahler geometry background of
M-theory expected from the 7-brane solutions of the type IIB supergravity. We
choose the appropriate complex structures of the background geometries and
embed a membrane of M-theory holomorphically to obtain a BPS string
configuration. The recently discussed BPS string configurations such as
3-string junctions and string networks in the flat background are generalized
to the cases with the 7-brane backgrounds. The property of the BPS string
configurations in the 7-brane backgrounds is in agreement with the previously
known results from the IIB string viewpoint. |
Strings in Plane Wave Backgrounds Revisited: String theory in an exact plane wave background is explored. A new example of
singularity in the sense of string theory for nonsingular spacetime metric is
presented. The 4-tachyon scattering amplitude is constructed. The spectrum of
states found from the poles in the factorization turns out to be equivalent to
that of the theory in flat space-time. The massless vertex operator is obtained
from the residue of the first order pole. | The Background-Field Method and Noninvariant Renormalization: We investigate the consistency of the background-field formalism when
applying various regularizations and renormalization schemes. By an example of
a two-dimensional $\sigma$ model it is demonstrated that the background-field
method gives incorrect results when the regularization (and/or renormalization)
is noninvariant. In particular, it is found that the cut-off regularization and
the differential renormalization belong to this class and are incompatible with
the background-field method in theories with nonlinear symmetries. |
Quantization of fields based on Generalized Uncertainty Principle: We construct a quantum theory of free scalar field in 1+1 dimensions based on
a `Generalized Uncertainty Principle'. Both canonical and path integral
formalism are employed. Higher dimensional extension is easily performed in the
path integral formalism. | Hyperbolic vortices with large magnetic flux: There has been some recent interest in the study of non-abelian BPS monopoles
in the limit of large magnetic charge. Most investigations have used a magnetic
bag approximation, in which spherical symmetry is assumed within an abelian
description. In particular, this approach has been used to suggest the
existence of two types of magnetic bag, with differing distributions of the
zeros of the Higgs field, together with multi-layer structures, containing
several magnetic bags. This paper is concerned with the analogous situation of
abelian BPS vortices in the hyperbolic plane, in the limit of large magnetic
flux. This system has the advantage that explicit exact solutions can be
obtained and compared with a magnetic bag approximation. Exact BPS vortex
solutions are presented that are analogous to the two types of magnetic bags
predicted for BPS monopoles and it is shown that these structures can be
combined to produce exact multi-layer solutions. |
Conformal and Uniformizing Maps in Borel Analysis: Perturbative expansions in physical applications are generically divergent,
and their physical content can be studied using Borel analysis. Given just a
finite number of terms of such an expansion, this input data can be analyzed in
different ways, leading to vastly different precision for the extrapolation of
the expansion parameter away from its original asymptotic regime. Here we
describe how conformal maps and uniformizing maps can be used, in conjunction
with Pad'e approximants, to increase the precision of the information that can
be extracted from a finite amount of perturbative input data. We also summarize
results from the physical interpretation of Pad'e approximations in terms of
electrostatic potential theory. | Cosmic No-hair Conjecture and Inflation with an SU(3) Gauge Field: We study inflationary universes with an SU(3) gauge field coupled to an
inflaton through a gauge kinetic function. Although the SU(3) gauge field grows
at the initial stage of inflation due to the interaction with the inflaton,
nonlinear self-couplings in the kinetic term of the gauge field become
significant and cause nontrivial dynamics after sufficient growth. We
investigate the evolution of the SU(3) gauge field numerically and reveal
attractor solutions in the Bianchi type I spacetime. In general cases where all
the components of the SU(3) gauge field have the same magnitude initially, they
all tend to decay eventually because of the nonlinear self-couplings.
Therefore, the cosmic no-hair conjecture generically holds in a mathematical
sense. Practically, however, the anisotropy can be generated transiently in the
early universe, even for an isotropic initial condition. Moreover, we find
particular cases for which several components of the SU(3) gauge field survive
against the nonlinear self-couplings. It occurs due to flat directions in the
potential of a gauge field for Lie groups whose rank is higher than one. Thus,
an SU(2) gauge field has a specialty among general non-Abelian gauge fields. |
Instabilities of D-brane Bound States and Their Related Theories: We investigate the Gregory-Laflamme instability for bound states of branes in
type II string theory and in M-theory. We examine systems with two different
constituent branes: for instance, D3-F1 or D4-D0. For the cases in which the
Gregory-Laflamme instability can occur, we describe the boundary of
thermodynamic stability. We also present an argument for the validity of the
Correlated Stability Conjecture, generalizing earlier work by Reall. We discuss
the implications for OM theory and NCOS theory, finding that in both cases,
there exists some critical temperature above which the system becomes unstable
to clumping of the open strings/membranes. | The p-bar p --> pi_0 pi_0 Puzzle: According to conventional theory, the annihilation reaction p-bar p --> pi_0
pi_0 cannot occur from a p-bar p atomic S state. However, this reaction occurs
so readily for antiprotons stopping in liquid hydrogen, that it would require
30% P-wave annihilations. Experimental results from other capture and p-bar p
annihilation channels show that the fraction of P-wave annihilations is less
than 6% in agreement with theoretical expectations. An experimental test to
determine whether this reaction can occur from an atomic S state is suggested.
If indeed this reaction is occurring from an atomic S state, then certain
neutral vector mesons should exhibit a pi_0 pi_0 decay mode, and this can also
be tested experimentally. |
Multiparticle Amplitudes in a Scalar EFT: At sufficiently high energies the production of a very large number of
particles is kinematically allowed. However, it is well-known that already in
the simplest case of a weakly-coupled massive $\lambda \varphi^4$ theory,
$n$-particle amplitudes become non-perturbative in the limit where $n$ scales
with energy. In this case, the effective expansion parameter, $\lambda n$, is
no longer small and the perturbative approach breaks down. In general, the
associated $n$-particle production rates were argued to be described by an
exponential that, depending on the specifics of the underlying Quantum Field
Theory model, could be either growing or decaying in the large-$n$ regime. We
investigate such processes in general settings of Effective Field Theory (EFT),
involving arbitrary higher-dimensional operators of $\varphi$. We perform the
resummation of all leading loop corrections arising from EFT vertices for
amplitudes at the multiparticle threshold. We find that the net effect of
higher-dimensional operators amounts to an exponentially growing factor. We
show that if an exponential growth was already generated by the renormalizable
interactions, it would then be further enhanced by the EFT contributions. On
the other hand, if the multiparticle rates computed in the renormalizable part
of the theory were suppressed, this suppression would not be lifted in the EFT. | Winding number versus Chern--Pontryagin charge: In the usual d dimensional SO(d) gauged Higgs models with $d$-component Higgs
fields, the 'energies' of the topologically stable solitons are bounded from
below by the Chern-Pontryagin charges. A new class of Higgs models is proposed
here, whose 'energies' are stabilised instead by the winding number of the
Higgs field itself, with no reference to the gauge group. Consequently, such
Higgs models can be gauged by SO(N), with 2 \le N \le d. |
Topological Recursion in The Ramond Sector: We investigate supereigenvalue models in the Ramond sector and their
recursive structure. We prove that the free energy truncates at quadratic order
in Grassmann coupling constants, and consider super loop equations of the
models with the assumption that the 1/N expansion makes sense. Subject to this
assumption, we obtain the associated genus-zero algebraic curve with two
ramification points (one regular and the other irregular) and also the
supersymmetric partner polynomial equation. Starting with these polynomial
equations, we present a recursive formalism that computes all the correlation
functions of these models. Somewhat surprisingly, correlation functions
obtained from the new recursion formalism have no poles at the irregular
ramification point due to a supersymmetric correction -- the new recursion may
lead us to a further development of supersymmetric generalizations of the
Eynard-Orantin topological recursion. | From Black Hole to Qubits: Evidence of Fast Scrambling in BMN theory: BMN Matrix theory admits vacua in the shape of large spherical membranes.
Per- turbing around such vacua, the setup provides for a controlled
computational frame- work for testing information evolution in Matrix black
holes. The theory realizes excitations in the supergravity multiplet as qubits.
These qubits are coupled to matrix degrees of freedom that describe
deformations of the spherical shape of the membrane. Arranging the ripples on
the membrane into a heat bath, we use the qubit system as a probe and compute
the associated Feynman-Vernon density matrix at one loop order. This allows us
to trace the evolution of entanglement in the system and extract the
characteristic scrambling timescale. We find that our numerical analysis is
consistent with this time scaling logarithmically with the entropy of the qubit
system, in tune with suggestions by Sekino and Susskind. |
Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim
Gravity: In this paper we use the covariant Peierls bracket to compute the algebra of
a sizable number of diffeomorphism-invariant observables in classical
Jackiw-Teitelboim gravity coupled to fairly arbitrary matter. We then show that
many recent results, including the construction of traversable wormholes, the
existence of a family of $SL(2,\mathbb{R})$ algebras acting on the matter
fields, and the calculation of the scrambling time, can be recast as simple
consequences of this algebra. We also use it to clarify the question of when
the creation of an excitation deep in the bulk increases or decreases the
boundary energy, which is of crucial importance for the "typical state"
versions of the firewall paradox. Unlike the "Schwarzian" or "boundary
particle" formalism, our techniques involve no unphysical degrees of freedom
and naturally generalize to higher dimensions. We do a few higher-dimensional
calculations to illustrate this, which indicate that the results we obtain in
JT gravity are fairly robust. | Spinning operators and defects in conformal field theory: We study the kinematics of correlation functions of local and extended
operators in a conformal field theory. We present a new method for constructing
the tensor structures associated to primary operators in an arbitrary bosonic
representation of the Lorentz group. The recipe yields the explicit structures
in embedding space, and can be applied to any correlator of local operators,
with or without a defect. We then focus on the two-point function of traceless
symmetric primaries in the presence of a conformal defect, and explain how to
compute the conformal blocks. In particular, we illustrate various techniques
to generate the bulk channel blocks either from a radial expansion or by acting
with differential operators on simpler seed blocks. For the defect channel, we
detail a method to compute the blocks in closed form, in terms of projectors
into mixed symmetry representations of the orthogonal group. |
On duality of the noncommutative extension of the Maxwell-Chern-Simons
model: We study issues of duality in 3D field theory models over a canonical
noncommutative spacetime and obtain the noncommutative extension of the
Self-Dual model induced by the Seiberg-Witten map. We apply the dual projection
technique to uncover some properties of the noncommutative Maxwell-Chern-Simons
theory up to first-order in the noncommutative parameter. A duality between
this theory and a model similar to the ordinary self-dual model is
estabilished. The correspondence of the basic fields is obtained and the
equivalence of algebras and equations of motion are directly verified. We also
comment on previous results in this subject. | Low energy dynamics of self-dual A_1 strings: We examine the interrelation between the (2,0) supersymmetric six dimensional
effective action for the A_1 theory, and the corresponding low-energy theory
for the collective coordinates associated to supersymmetric selfdual BPS
strings. We argue that this low-energy theory is a two-dimensional N = 4
supersymmetric sigma model. |
From classical Lagrangians to Hamilton operators in the Standard-Model
Extension: In this article we investigate whether a theory based on a classical
Lagrangian for the minimal Standard-Model Extension (SME) can be quantized such
that the result is equal to the corresponding low-energy Hamilton operator
obtained from the field-theory description. This analysis is carried out for
the whole collection of minimal Lagrangians found in the literature. The upshot
is that first quantization can be performed consistently. The unexpected
observation is made that at first order in Lorentz violation and at second
order in the velocity the Lagrangians are related to the Hamilton functions by
a simple transformation. Under mild assumptions, it is shown that this holds
universally. This result is used successfully to obtain classical Lagrangians
for two complicated sectors of the minimal SME that have not been considered in
the literature so far. Therefore, it will not be an obstacle anymore to derive
such Lagrangians even for involved sets of coefficients - at least to the level
of approximation stated above. | A Two-Form Formulation of the Vector-Tensor Multiplet in Central Charge
Superspace: A two-form formulation for the N=2 vector-tensor multiplet is constructed
using superfield methods in central charge superspace. The N=2 non-Abelian
standard supergauge multiplet in central charge superspace is also discussed,
as is with the associated Chern-Simons form. We give the constraints, solve the
Bianchi identities and present the action for a theory of the vector-tensor
multiplet coupled to the non-Abelian supergauge multiplet via the Chern-Simons
form. |
Stepwise Projection: Toward Brane Setups for Generic Orbifold
Singularities: The construction of brane setups for the exceptional series E6,E7,E8 of SU(2)
orbifolds remains an ever-haunting conundrum. Motivated by techniques in some
works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic
outlook, a method which we call stepwise projection, that may shed some light
on this puzzle. We exemplify this method, consisting of transformation rules
for obtaining complex quivers and brane setups from more elementary ones, to
the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we
demonstrate the generality of the stepwise procedure by appealing to Frobenius'
theory of Induced Representations. Our algorithm suggests the existence of
generalisations of the orientifold plane in string theory. | Probing the Holographic Fermi Arc with scalar field: Numerical and
analytical study: Fermi arcs are disconnected contour of Fermi surface, which can be observed
in the pseudo-gap phase of high temperature superconductors. Aiming to
understand this pseudo-gap phenomena, we study a holographic Fermionic system
coupled with a massive scalar field in an AdS black hole background. Depending
on the boundary condition on the scalar field mode, we discuss two possible
scenarios. When the scalar condenses below a critical temperature $T_c$, the
Fermi surface undergoes a transition from normal phase to pseudo-gap phase.
Hence $T_c$ can be the reminiscent of well-known cross over temperature $T^*$
in cuprate superconductor, below which pseudo-gap appears at constant doping.
In the second scenario, the bulk scalar develops a non-normalizable profile at
arbitrary temperature for non-zero source at the boundary. Therefore, we can
tune the Fermi spectrum by tuning a dual source at the boundary. The dual
source for this case can be the reminiscent of hole doping in the real cuprate
superconductor. For both the cases we have studied Fermi spectrum and observed
anisotropic gap in the spectral function depending on the model parameter and
studied the properties of Fermi arcs across different phases. |
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