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Positivity of Curvature-Squared Corrections in Gravity: We study the Gauss-Bonnet (GB) term as the leading higher-curvature
correction to pure Einstein gravity. Assuming a tree-level ultraviolet
completion free of ghosts or tachyons, we prove that the GB term has a
nonnegative coefficient in dimensions greater than four. Our result follows
from unitarity of the spectral representation for a general ultraviolet
completion of the GB term.
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Poincaré Covariant k-Minkowski Spacetime: A fully Poincare' covariant model is constructed out of the k-Minkowski
spacetime. Covariance is implemented by a unitary representation of the
Poincare' group, and thus complies with the original Wigner approach to quantum
symmetries. This provides yet another example (besides the DFR model), where
Poincare' covariance is realised a` la Wigner in the presence of two
characteristic dimensionful parameters: the light speed and the Planck length.
In other words, a Doubly Special Relativity (DSR) framework may well be
realised without deforming the meaning of "Poincare covariance".
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Dynamical Correlation Functions and Finite-size Scaling in
Ruijsenaars-Schneider Model: The trigonometric Ruijsenaars-Schneider model is diagonalized by means of the
Macdonald symmetric functions. We evaluate the dynamical density-density
correlation function and the one-particle retarded Green function as well as
their thermodynamic limit. Based on these results and finite-size scaling
analysis, we show that the low-energy behavior of the model is described by the
$C=1$ Gaussian conformal field theory under a new fractional selection rule for
the quantum numbers labeling the critical exponents.
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Star product and interacting fields on $κ$-Minkowski space: In this note we extend the methods developed by Freidel et al.
[arXiv:hep-th/0612170] to derive the form of $\phi^4$ interaction term in the
case of scalar field theory on $\kappa$-Minkowski space, defined in terms of
star product. We present explicit expressions for the $\kappa$-Minkowski star
product. Having obtained the the interaction term we use the resulting deformed
conservation rules to investigate if they lead to any threshold anomaly, and we
find that in the leading order they do not, as expected.
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Quantum Affine Symmetry as Generalized Supersymmetry: The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is
an even root of unity. The structure of this algebra allows a natural
generalization of N=2 supersymmetry algebra. In particular it is found that the
momentum operators $P ,\bar{P}$, and thus the Hamiltonian, can be written as
generalized multi-commutators, and can be viewed as new central elements of the
algebra $\CU_q (\hat{sl(2)})$. We show that massive particles in (deformations
of) integer spin representions of $sl(2)$ are not allowed in such theories.
Generalizations of Witten's index and Bogomolnyi bounds are presented and a
preliminary attempt in constructing manifestly $\CU_q (\hat{sl(2)})$ invariant
actions as generalized supersymmetric Landau-Ginzburg theories is made.
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Supergravity field equations from the superconnection: Withdrawn due to the existence of the main result in Phys.Rev. D69 (2004)
105010, hep-th/0312266 (based on earlier results in JHEP 0304 (2003) 039,
hep-th/0212008).
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Parametric phase transition for Gauss-Bonnet AdS black hole: With the help of the parametric solution of the Maxwell equal area law for
the Gauss-Bonnet AdS black hole in five dimensions, we find the second
analytical solution to the first order phase transition. We analyze the
asymptotic behaviors of some characteristic thermodynamic properties for the
small and large black holes at the critical and zero temperatures and also
calculate the critical exponents and the corresponding critical amplitudes in
detail. Moreover, we give the general form of the thermodynamic scalar
curvature based on the Ruppeiner geometry and point out that the attractive
interaction dominates in both the small and large black hole phases when the
first order phase transition occurs in the five dimensional Gauss-Bonnet AdS
black hole.
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Wilson loops in supersymmetric Chern-Simons-matter theories and duality: We study the algebra of BPS Wilson loops in 3d gauge theories with N=2
supersymmetry and Chern-Simons terms. We argue that new relations appear on the
quantum level, and that in many cases this makes the algebra
finite-dimensional. We use our results to propose the mapping of Wilson loops
under Seiberg-like dualities and verify that the proposed map agrees with the
exact results for expectation values of circular Wilson loops. In some cases we
also relate the algebra of Wilson loops to the equivariant quantum K-ring of
certain quasi projective varieties. This generalizes the connection between the
Verlinde algebra and the quantum cohomology of the Grassmannian found by
Witten.
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On the vacuum energy in the Einstein Universe and the conformal anomaly: An oldish question is resurrected concerning the significance of the
ambiguous `b-type' terms encountered in calculations of the vacuum, Casimir
energy on the Einstein Universe for conformally coupled scalar fields. Some
remarks in the literature are hopefully clarified and the relevance of much
earlier evaluations is pointed out. A consistency principle is suggested.
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Emergent Dark Gravity from (Non)Holographic Screens: In this work, a clear connection is made between E. Verlinde's recent theory
of emergent gravity in de Sitter space and the earlier work that described
emergent gravity using holographic screens. A modified (non)holographic screen
scenario is presented, wherein the screen fails to encode an emergent mass in
the bulk "unemerged" part of space for sufficiently large length-scales, where
the volume-law of the non-holographic bulk degrees of freedom overtakes the
area-law scaling of the entropy of the screen. Within this framework, we can
describe both an emergent dark gravitational force, which scales like
$\frac{1}{r}$, and also a version of the baryonic Tully-Fisher relation. We
therefore recast these results within an emergent gravity framework in which
there is an explicit violation of holography for sufficiently large
length-scales.
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Component on shell actions of supersymmetric 3-brane I. 3-brane in D=6: In the present and accompanying papers we explicitly construct the on-shell
supersymmetric component actions for 3-branes moving in D=6 and in D=8 within
the nonlinear realizations framework.
In the first paper we apply our schema to construct the action of
supersymmetric 3-brane in D=6. It turns out that all ingredients entering the
component action can be obtained almost algorithmically by using the nonlinear
realizations approach. Within this approach, properly adapted to the
construction of on-shell component actions, we pay much attention to broken
supersymmetry. Doing so, we were able to write the action in terms of purely
geometric objects (vielbeins and covariant derivatives of the physical bosonic
components), covariant with respect to broken supersymmetry. It turns out that
all terms of the higher orders in the fermions, are hidden inside these
covariant derivatives and vielbeins. Moreover, the main part of the component
action just mimics its bosonic cousin in which the ordinary space-time
derivatives and the bosonic world volume are replaced by their covariant
supersymmetric analogs. The Wess-Zumino term in the action, which does not
exist in the bosonic case, can be also easily constructed in terms of reduced
Cartan forms. Keeping the broken supersymmetry almost explicit, one may write
the Ansatz for the component action, fully defined up to two constant
parameters. The role of the unbroken supersymmetry is just to fix these
parameters.
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Thermalization in the D1D5 CFT: It is generally agreed that black hole formation in gravity corresponds to
thermalization in the dual CFT. It is sometimes argued that if the CFT
evolution shows evidence of large redshift in gravity, then we have seen black
hole formation in the CFT. We argue that this is not the case: a clock falling
towards the horizon increases its redshift but remains intact as a clock; thus
it is not `thermalized'. Instead, thermalization should correspond to a new
phase after the phase of large redshift, where the infalling object turns into
fuzzballs on reaching within planck distance of the horizon. We compute simple
examples of the scattering vertex in the D1D5 CFT which, after many iterations,
would lead to thermalization. An initial state made of two left-moving and two
right-moving excitations corresponds, in gravity, to two gravitons heading
towards each other. The thermalization vertex in the CFT breaks these
excitations into multiple excitations on the left and right sides; we compute
the amplitudes for several of these processes. We find secular terms that grow
as $t^2$ instead of oscillating with $t$; we conjecture that this may be a
feature of processes leading to thermalization.
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Abelian Vortices on Nodal and Cuspidal Curves: We compute the Euler characteristics of the moduli spaces of abelian vortices
on curves with nodal and cuspidal singularities. This generalizes our previous
work where only nodes were taken into account. The result we obtain is again
consistent with the expected reconciliation between the vortex picture of D2-D0
branes and the proposal by Gopakumar and Vafa.
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Scale and Conformal Invariance on (A)dS: We examine the question of scale versus conformal invariance on maximally
symmetric curved backgrounds and study general 2-derivative conformally
invariant free theories of vectors and tensors. For spacetime dimension $D>4$,
these conformal theories can be diagonalized into standard massive fields in
which unbroken conformal symmetry non-trivially mixes components of different
spins. In $D=4$, the tensor case becomes a conformal theory mixing a partially
massless spin-2 field with a massless spin-1 field. For massless linearized
gravity in $D = 4$, we confirm through direct calculation that correlation
functions of gauge-invariant operators take the conformally invariant form,
despite the absence of standard conformal symmetry at the level of the action.
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Note about Yang Mills, QCD and their supersymmetric counterparts: We analyze in an effective Lagrangian framework the connection between Super
QCD (Super Yang Mills) and QCD (Yang Mills) by highlighting the crucial role
that the zero modes play in the process of decoupling gluinos and squarks.
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Exponential mapping for non semisimple quantum groups: The concept of universal T matrix, recently introduced by Fronsdal and
Galindo in the framework of quantum groups, is here discussed as a
generalization of the exponential mapping. New examples related to
inhomogeneous quantum groups of physical interest are developed, the duality
calculations are explicitly presented and it is found that in some cases the
universal T matrix, like for Lie groups, is expressed in terms of usual
exponential series.
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Fusion & Tensoring of Conformal Field Theory and Composite Fermion
Picture of Fractional Quantum Hall Effect: We propose a new way for describing the transition between two quantum Hall
effect states with different filling factors within the framework of rational
conformal field theory. Using a particular class of non-unitary theories, we
explicitly recover Jain's picture of attaching flux quanta by the fusion rules
of primary fields. Filling higher Landau levels of composite fermions can be
described by taking tensor products of conformal theories. The usual projection
to the lowest Landau level corresponds then to a simple coset of these tensor
products with several U(1)-theories divided out. These two operations -- the
fusion map and the tensor map -- can explain the Jain series and all other
observed fractions as exceptional cases. Within our scheme of transitions we
naturally find a field with the experimentally observed universal critical
exponent 7/3.
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Power-law Behavior of High Energy String Scatterings in Compact Spaces: We calculate high energy massive scattering amplitudes of closed bosonic
string compactified on the torus. We obtain infinite linear relations among
high energy scattering amplitudes. For some kinematic regimes, we discover that
some linear relations break down and, simultaneously, the amplitudes enhance to
power-law behavior due to the space-time T-duality symmetry in the compact
direction. This result is consistent with the coexistence of the linear
relations and the softer exponential fall-off behavior of high energy string
scattering amplitudes as we pointed out prevously. It is also reminiscent of
hard (power-law) string scatterings in warped spacetime proposed by Polchinski
and Strassler.
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A universal attractor for inflation at strong coupling: We introduce a novel non-minimal coupling between gravity and the inflaton
sector. Remarkably, for large values of this coupling all models asymptote to a
universal attractor. This behavior is independent of the original scalar
potential and generalizes the attractor in the phi^4 theory with non-minimal
coupling to gravity. The attractor is located in the `sweet spot' of Planck's
recent results.
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Temperature of D3-branes off extremality: We discuss non-extremal rotating D3-branes. We solve the wave equation for
scalars in the supergravity background of certain distributions of branes and
compute the absorption coefficients. The form of these coefficients is similar
to the gray-body factors associated with black-hole scattering. They are given
in terms of two different temperature parameters, indicating that fields (open
string modes) do not remain in thermal equilibrium as we move off extremality.
This should shed some light on the origin of the disagreement between the
supergravity and conformal field theory results on the free energy of a system
of non-coincident D-branes.
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Codimension Two Branes in Einstein-Gauss-Bonnet Gravity: Codimension two branes play an interesting role in attacking the cosmological
constant problem. Recently, in order to handle some problems in codimension two
branes in Einstein gravity, Bostock {\it et al.} have proposed using
six-dimensional Einstein-Gauss-Bonnet (EGB) gravity instead of six-dimensional
Einstein gravity. In this paper, we present the solutions of codimension two
branes in six-dimensional EGB gravity. We show that Einstein's equations take a
"factorizable" form for a factorized metric tensor ansatz even in the presence
of the higher-derivative Gauss-Bonnet term. Especially, a new feature of the
solution is that the deficit angle depends on the brane geometry. We discuss
the implication of the solution to the cosmological constant problem. We also
comment on a possible problem of inflation model building on codimension two
branes.
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Quantum fluctuations and thermal dissipation in higher derivative
gravity: In this paper, based on the $ AdS_{2}/CFT_{1} $ prescription, we explore the
low frequency behavior of quantum two point functions for a special class of
strongly coupled CFTs in one dimension whose dual gravitational counterpart
consists of \textit{extremal} black hole solutions in higher derivative
theories of gravity defined over an asymptotically AdS space time. The quantum
critical points thus described are supposed to correspond to a very large value
of the dynamic exponent ($ z\rightarrow \infty $). In our analysis, we find
that quantum fluctuations are enhanced due to the higher derivative corrections
in the bulk which in turn increases the possibility of quantum phase transition
near the critical point. On the field theory side, such higher derivative
effects would stand for the corrections appearing due to the finite coupling in
the gauge theory. Finally, we compute the coefficient of thermal diffusion at
finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black
holes in the bulk. We observe an important crossover corresponding to $ z=5 $
fixed point.
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On cosmic natural selection: The rate of black hole formation can be increased by increasing the value of
the cosmological constant. This falsifies Smolin's conjecture that the values
of all constants of nature are adjusted to maximize black hole production.
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Y-systems and generalized associahedra: We prove, for an arbitrary finite root system, the periodicity conjecture of
Al.B.Zamolodchikov concerning Y-systems, a particular class of functional
relations arising in the theory of thermodynamic Bethe ansatz. Algebraically,
Y-systems can be viewed as families of rational functions defined by certain
birational recurrences formulated in terms of the underlying root system. In
the course of proving periodicity, we obtain explicit formulas for all these
rational functions, which turn out to always be Laurent polynomials.
In a closely related development, we introduce and study a family of
simplicial complexes that can be associated to arbitrary root systems. In type
A, our construction produces Stasheff's associahedron, whereas in type B, it
gives the Bott-Taubes polytope, or cyclohedron. We enumerate the faces of these
complexes, prove that their geometric realization is always a sphere, and
describe them in concrete combinatorial terms for the classical types ABCD.
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A lattice Poisson algebra for the Pohlmeyer reduction of the AdS_5 x S^5
superstring: The Poisson algebra of the Lax matrix associated with the Pohlmeyer reduction
of the AdS_5 x S^5 superstring is computed from first principles. The resulting
non-ultralocality is mild, which enables to write down a corresponding lattice
Poisson algebra.
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Relativistic fluctuations in stochastic fluid dynamics: The state-of-the-art theoretical formalism for a covariant description of
non-Gaussian fluctuation dynamics in relativistic fluids is discussed.
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Expansion of All Multitrace Tree Level EYM Amplitudes: In this paper, we investigate the expansion of tree level multitrace
Einstein-Yang-Mills (EYM) amplitudes. First, we propose two types of recursive
expansions of tree level EYM amplitudes with an arbitrary number of gluons,
gravitons and traces by those amplitudes with fewer traces or/and gravitons.
Then we give many support evidence, including proofs using the Cachazo-He-Yuan
(CHY) formula and Britto-Cachazo-Feng-Witten (BCFW) recursive relation. As a
byproduct, two types of generalized BCJ relations for multitrace EYM are
further proposed, which will be useful in the BCFW proof. After one applies the
recursive expansions repeatedly, any multitrace EYM amplitudes can be given in
the Kleiss-Kuijf (KK) basis of tree level color ordered Yang-Mills (YM)
amplitudes. Thus the Bern-Carrasco-Johansson (BCJ) numerators, as the expansion
coefficients, for all multitrace EYM amplitudes are naturally constructed.
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A rough end for smooth microstate geometries: Supersymmetric microstate geometries with five non-compact dimensions have
recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear
instability featuring the growth of excitations at an "evanescent ergosurface"
of infinite redshift. We argue that this growth may be treated as adiabatic
evolution along a family of exactly supersymmetric solutions in the limit where
the excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge system
such solutions may be constructed explicitly, incorporating full backreaction,
and are in fact special cases of known microstate geometries. In a near-horizon
limit, they reduce to Aichelburg-Sexl shockwaves in $AdS_3 \times S^3$
propagating along one of the angular directions of the sphere. Noting that the
ERS analysis is valid in the limit of large microstate angular momentum $j$, we
use the above identification to interpret their instability as a transition
from rare smooth microstates with large angular momentum to more typical
microstates with smaller angular momentum. This entropic driving terminates
when the angular momentum decreases to $j \sim \sqrt{n_1n_5}$ where the density
of microstates is maximal. We argue that, at this point, the large stringy
corrections to such microstates will render them non-linearly stable. We
identify a possible mechanism for this stabilization and detail an illustrative
toy model.
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On Euclidean spinors and Wick rotations: We propose a continuous Wick rotation for Dirac, Majorana and Weyl spinors
from Minkowski spacetime to Euclidean space which treats fermions on the same
footing as bosons. The result is a recipe to construct a supersymmetric
Euclidean theory from any supersymmetric Minkowski theory. This Wick rotation
is identified as a complex Lorentz boost in a five-dimensional space and acts
uniformly on bosons and fermions. For Majorana and Weyl spinors our approach is
reminiscent of the traditional Osterwalder Schrader approach in which spinors
are ``doubled'' but the action is not hermitean. However, for Dirac spinors our
work provides a link to the work of Schwinger and Zumino in which hermiticity
is maintained but spinors are not doubled. Our work differs from recent work by
Mehta since we introduce no external metric and transform only the basic
fields.
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APS $η$-invariant, path integrals, and mock modularity: We show that the Atiyah-Patodi-Singer $\eta$-invariant can be related to the
temperature dependent Witten index of a noncompact theory and give a new proof
of the APS theorem using scattering theory. We relate the $\eta$-invariant to a
Callias index and compute it using localization of a supersymmetric path
integral. We show that the $\eta$-invariant for the elliptic genus of a finite
cigar is related to quantum modular forms obtained from the completion of a
mock Jacobi form which we compute from the noncompact path integral.
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A proper scalar product for tachyon representations in configuration
space: We propose a new inner product for scalar fields that are solutions of the
Klein-Gordon equation with $m^2<0$. This inner product is non-local, bearing an
integral kernel including Bessel functions of the second kind, and the
associated norm proves to be positive definite in the subspace of oscillatory
solutions, as opposed to the conventional one. Poincar\'e transformations are
unitarily implemented on this subspace, which is the support of a unitary and
irreducible representation of the proper orthochronous Poincar\'e group. We
also provide a new Fourier Transform between configuration and momentum spaces
which is unitary, and recover the projection onto the representation space.
This new scenario suggests a revision of the corresponding quantum field
theory.
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Quantum corrections in Galileon theories: We calculate the one-loop quantum corrections in the cubic Galileon theory,
using cutoff regularization. We confirm the expected form of the one-loop
effective action and that the couplings of the Galileon theory do not get
renormalized. However, new terms, not included in the tree-level action, are
induced by quantum corrections. We also consider the one-loop corrections in an
effective brane theory, which belongs to the Horndeski or generalized Galileon
class. We find that new terms are generated by quantum corrections, while the
tree-level couplings are also renormalized. We conclude that the structure of
the generalized Galileon theories is altered by quantum corrections more
radically than that of the Galileon theory.
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Crystallographic T-duality: We introduce the notion of crystallographic T-duality, inspired by the
appearance of $K$-theory with graded equivariant twists in the study of
topological crystalline materials. Besides giving a range of new topological
T-dualities, it also unifies many previously known dualities, motivates
generalisations of the Baum-Connes conjecture to graded groups, provides a
powerful tool for computing topological phase classification groups, and
facilitates the understanding of crystallographic bulk-boundary correspondences
in physics.
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Holonomy from wrapped branes: Compactifications of M-theory on manifolds with reduced holonomy arise as the
local eleven-dimensional description of D6-branes wrapped on supersymmetric
cycles in manifolds of lower dimension with a different holonomy group.
Whenever the isometry group SU(2) is present, eight-dimensional gauged
supergravity is a natural arena for such investigations. In this paper we use
this approach and review the eleven dimensional description of D6-branes
wrapped on coassociative 4-cycles, on deformed 3-cycles inside Calabi-Yau
threefolds and on Kahler 4-cycles.
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Monstrous Product CFTs in the Grand Canonical Ensemble: We study symmetric products of the chiral 'Monster' conformal field theory
with c=24 in the grand canonical ensemble by introducing a complex parameter
\rho, whose imaginary part represents the chemical potential \mu conjugate to
the number of copies of the CFT. The grand canonical partition function is
given by the DMVV product formula in terms of the multiplicities of the seed
CFT. It possesses an O(2,2;\ZZ) symmetry that enhances the familiar SL(2,\ZZ)
modular invariance of the canonical ensemble and mixes the modular parameter
\tau with the parameter \rho. By exploiting this enhanced modular symmetry and
the pole structure of the DMVV product formula we are able to extend the region
of validity of Cardy's formula, and explain why it matches the semi-classical
Bekenstein-Hawking formula for black holes all the way down to the AdS-scale.
We prove that for large c the spectrum contains a universal perturbative sector
whose degeneracies obey Hagedorn growth. The transition from Cardy to Hagedorn
growth is found to be due to the formation of a Bose-Einstein condensate of
ground state CFTs at low temperatures. The grand canonical partition function
has an interesting phase structure, which in addition to the standard
Hawking-Page transition between low and high temperature, exhibits a
wall-crossing transition that exchanges the roles of \tau and \rho.
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A geometric discretisation scheme applied to the Abelian Chern-Simons
theory: We give a detailed general description of a recent geometrical discretisation
scheme and illustrate, by explicit numerical calculation, the scheme's ability
to capture topological features. The scheme is applied to the Abelian
Chern-Simons theory and leads, after a necessary field doubling, to an
expression for the discrete partition function in terms of untwisted
Reidemeister torsion and of various triangulation dependent factors. The
discrete partition function is evaluated computationally for various
triangulations of $S^3$ and of lens spaces. The results confirm that the
discretisation scheme is triangulation independent and coincides with the
continuum partition function
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$\mathcal{N} = 1$ superconformal theories with $D_N$ blocks: We study the chiral ring of four-dimensional superconformal field theories
obtained by wrapping M5-branes on a complex curve inside a Calabi-Yau
three-fold. We propose a field theoretic construction of all the theories found
by Bah, Beem, Bobev and Wecht by introducing new building blocks, and prove
several $\mathcal{N} = 1$ dualities featuring the latter. We match the central
charges with those computed from the M5-brane anomaly polynomial, perform the
counting of relevant operators and analyze unitarity bound violations. As a
byproduct, we compute the exact dimension of "heavy operators" obtained by
wrapping an M2-brane on the complex curve.
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On Tensionless Strings in $3+1$ Dimensions: We argue for the existence of phase transitions in $3+1$ dimensions
associated with the appearance of tensionless strings. The massless spectrum of
this theory does not contain a graviton: it consists of one $N=2$ vector
multiplet and one linear multiplet, in agreement with the light-cone analysis
of the Green-Schwarz string in $3+1$ dimensions. In M-theory the string
decoupled from gravity arises when two 5-branes intersect over a
three-dimensional hyperplane. The two 5-branes may be connected by a 2-brane,
whose boundary becomes a tensionless string with $N=2$ supersymmetry in $3+1$
dimensions. Non-critical strings on the intersection may also come from
dynamical 5-branes intersecting the two 5-branes over a string and wrapped over
a four-torus. The near-extremal entropy of the intersecting 5-branes is
explained by the non-critical strings originating from the wrapped 5-branes.
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Spectral Distance on Lorentzian Moyal Plane: We present here a completely operatorial approach, using Hilbert-Schmidt
operators, to compute spectral distances between time-like separated "events ",
associated with the pure states of the algebra describing the Lorentzian Moyal
plane, using the axiomatic framework given by [13, 14]. The result shows no
deformations of non-commutative origin, as in the Euclidean case.
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Structural aspects of asymptotically safe black holes: We study the quantum modifications of classical, spherically symmetric
Schwarzschild (Anti-) de Sitter black holes within Quantum Einstein Gravity.
The quantum effects are incorporated through the running coupling constants
$G_k$ and $\Lambda_k$, computed within the exact renormalization group
approach, and a common scale-setting procedure. We find that, in contrast to
common intuition, it is actually the cosmological constant that determines the
short-distance structure of the RG-improved black hole: in the asymptotic UV
the structure of the quantum solutions is universal and given by the classical
Schwarzschild-de Sitter solution, entailing a self-similarity between the
classical and quantum regime. As a consequence asymptotically safe black holes
evaporate completely and no Planck-size remnants are formed. Moreover, the
thermodynamic entropy of the critical Nariai-black hole is shown to agree with
the microstate count based on the effective average action, suggesting that the
entropy originates from quantum fluctuations around the mean-field geometry.
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Electrons and Photons: Fact not Fiction: The particle Fock space of the matter fields in QED can be constructed using
the free creation and annihilation operators. However, these particle operators
are not, even at asymptotically large times, the modes of the matter fields
that enter the QED Lagrangian. In this letter we construct the fields which do
recover such particle modes at large times. We are thus able to demonstrate for
the first time that, contrary to statements found in the literature, a
relativistic description of charged particles in QED exists.
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Feynman Rules for Scalar Conformal Blocks: We complete the proof of "Feynman rules" for constructing $M$-point conformal
blocks with external and internal scalars in any topology for arbitrary $M$ in
any spacetime dimension by combining the rules for the blocks (based on their
Witten diagram interpretation) with the rules for the construction of conformal
cross ratios (based on OPE flow diagrams). The full set of Feynman rules leads
to blocks as power series of the hypergeometric type in the conformal cross
ratios. We then provide a proof by recursion of the Feynman rules which relies
heavily on the first Barnes lemma and the decomposition of the topology of
interest in comb-like structures. Finally, we provide a nine-point example to
illustrate the rules.
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Cluster Adjacency for m=2 Yangian Invariants: We classify the rational Yangian invariants of the $m=2$ toy model of
$\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the
amplituhedron $\mathcal{A}_{n,k}^{(2)}$. We enumerate and provide an explicit
formula for all invariants for any number of particles $n$ and any helicity
degree $k$. Each invariant manifestly satisfies cluster adjacency with respect
to the $Gr(2,n)$ cluster algebra.
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Boundary WZW, G/H, G/G and CS theories: We extend the analysis of the canonical structure of the Wess-Zumino-Witten
theory to the bulk and boundary coset G/H models. The phase spaces of the coset
theories in the closed and in the open geometry appear to coincide with those
of a double Chern-Simons theory on two different 3-manifolds. In particular, we
obtain an explicit description of the canonical structure of the boundary G/G
coset theory. The latter may be easily quantized leading to an example of a
two-dimensional topological boundary field theory.
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Superconformal Boundaries in $4-ε$ dimensions: Boundaries in three-dimensional $\mathcal{N}=2$ superconformal theories may
preserve one half of the original bulk supersymmetry. There are two
possibilities which are characterized by the chirality of the leftover
supercharges. Depending on the choice, the remaining $2d$ boundary algebra
exhibits $\mathcal{N}=(0,2)$ or $\mathcal{N}=(1,1)$ supersymmetry. In this work
we focus on correlation functions of chiral fields for both types of
supersymmetric boundaries. We study a host of correlators using superspace
techniques and calculate superconformal blocks for two- and three-point
functions. For $\mathcal{N}=(1,1)$ supersymmetry, some of our results can be
analytically continued in the spacetime dimension while keeping the codimension
fixed. This opens the door for a bootstrap analysis of the $\epsilon$-expansion
in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we
prove that in the free theory limit two-point functions of chiral (and
antichiral) fields are unique. The first order correction, which already
describes interactions, is universal up to two free parameters. As a check of
our analysis, we study the Wess-Zumino model with a supersymmetric boundary
using Feynman diagrams, and find perfect agreement between the perturbative and
bootstrap results.
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Fermion zero modes for the mixed-flux AdS$_3$ giant magnon: We explicitly construct the four and two fermion zero modes for the
mixed-flux generalization of the Hofman-Maldacena giant magnon on two of the
AdS$_3$ backgrounds with maximal amount of supersymmetry, AdS$_3 \times$S$^3
\times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. We also show how
to get the $\mathfrak{psu}(1|1)^4$ and $\mathfrak{su}(1|1)^2$ superalgebras
from the semiclassically quantized fermion zero modes.
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Deformation, non-commutativity and the cosmological constant problem: In this talk we provide arguments on possible relation between the
cosmological constant in our space and the non-commutativity parameter of the
internal space of compactified string theory. The arguments are valid in the
context of D3/D7 brane cosmological model of inflation/acceleration.
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Phase Structure of Supersymmetric Models at Finite Temperature: We study O(N) symmetric supersymmetric models in three dimensions at finite
temperature. These models are known to have an interesting phase structures. In
particular, in the limit $N \to \infty$ one finds spontaneous breaking of scale
invariance with no explicit breaking. Supersymmetry is softly broken at finite
temperature and the peculiar phase structure and properties seen at T=0 are
studied here at finite temperature.
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Harmonic oscillator with minimal length, minimal momentum, and maximal
momentum uncertainties in SUSYQM framework: We consider a Generalized Uncertainty Principle (GUP) framework which
predicts a maximal uncertainty in momentum and minimal uncertainties both in
position and momentum. We apply supersymmetric quantum mechanics method and the
shape invariance condition to obtain the exact harmonic oscillator eigenvalues
in this GUP context. We find the supersymmetric partner Hamiltonians and show
that the harmonic oscillator belongs to a hierarchy of Hamiltonians with a
shift in momentum representation and different masses and frequencies. We also
study the effect of a uniform electric field on the harmonic oscillator energy
spectrum in this setup.
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A Note on ODEs from Mirror Symmetry: We give close formulas for the counting functions of rational curves on
complete intersection Calabi-Yau manifolds in terms of special solutions of
generalized hypergeometric differential systems. For the one modulus cases we
derive a differential equation for the Mirror map, which can be viewed as a
generalization of the Schwarzian equation. We also derive a nonlinear seventh
order differential equation which directly governs the instanton corrected
Yukawa coupling.
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Interaction of higher spin massive fields with gravity in string theory: Derivations of consistent equations of motion for the massive spin two field
interacting with gravity is reviewed. From the field theoretical point of view
the most general classical action describing consistent causal propagation in
vacuum Einstein spacetime is given. It is also shown that the massive spin two
field can be consistently described in arbitrary background by means of
lagrangian equations representing an infinite series in curvature. Within
string theory equations of motion for the massive spin two field coupled to
gravity is derived from the requirement of quantum Weyl invariance of the
corresponding two dimensional sigma-model. In the lowest order in string length
the effective equations of motion are demonstrated to coincide with the general
form of consistent equations derived in field theory.
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Low energy effective string cosmology: We give the general analytic solutions derived from the low energy string
effective action for four dimensional Friedmann-Robertson-Walker models with
dilaton and antisymmetric tensor field, considering both long and short
wavelength modes of the $H$-field. The presence of a homogeneous $H$-field
significantly modifies the evolution of the scale factor and dilaton. In
particular it places a lower bound on the allowed value of the dilaton. The
scale factor also has a lower bound but our solutions remain singular as they
all contain regions where the spacetime curvature diverges signalling a
breakdown in the validity of the effective action. We extend our results to the
simplest Bianchi I metric in higher dimensions with only two scale factors. We
again give the general analytic solutions for long and short wavelength modes
for the $H$ field restricted to the three dimensional space, which produces an
anisotropic expansion. In the case of $H$ field radiation (wavelengths within
the Hubble length) we obtain the usual four dimensional radiation dominated FRW
model as the unique late time attractor.
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Explicit field realizations of W algebras: The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the
inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$
algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct
the explicit field realizations of linear $W_{1,2,s}$ algebras with
double-scalar and double-spinor, respectively. Then, after a change of basis,
the realizations of $W_{2,s}$ algebras are presented. The results show that all
these realizations are Romans-type realizations.
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Bubbling the NHEK: We build the first family of smooth bubbling microstate geometries that are
asymptotic to the near-horizon region of extremal five-dimensional Kerr black
holes (NHEK). These black holes arise as extremal non-supersymmetric
highly-rotating D1-D5-P solutions in type IIB string theory on
T$^4\times$S$^1$. Our solutions are asymptotically NHEK in the UV and end in
the IR with a smooth cap. In the context of the Kerr/CFT correspondence, these
bubbling geometries are dual to pure states of the 1+1 dimensional chiral
conformal field theory dual to NHEK. Since our solutions have a bubbling
structure in the IR, they correspond to an IR phase of broken conformal
symmetry, and their existence supports the possibility that all the pure states
whose counting gives the Kerr black hole entropy correspond to horizonless bulk
configurations.
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Fayet-Iliopoulos terms in supergravity without gauged R-symmetry: We construct a supergravity-Maxwell theory with a novel embedding of the
Fayet-Iliopoulos D-term, leading to spontaneous supersymmetry breaking. The
gauging of the R-symmetry is not required and a gravitino mass is allowed for a
generic vacuum. When matter couplings are introduced, an uplift through a
positive definite contribution to the scalar potential is obtained. We observe
a notable similarity to the $\overline{D3}$ uplift constructions and we give a
natural description in terms of constrained multiplets.
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Classical electron model with non static conformal symmetry: Lorentz proposed a classical model of electron in which electron was assumed
to have only 'electromagnetic mass'. We modeled electron as charged anisotropic
perfect fluid sphere admitting non static conformal symmetry. It is noticed
that the pressure and density fail to be regular at the origin but effective
gravitational mass is regular everywhere and vanishes at the limit r->0 i.e. it
does not have to tolerate the problem of singularity. Further, we have matched
interior metric with exterior (Reissner-Nordstr\"om) metric and determine the
values of the parameters k and r_0 (occurring in the solutions) in functions of
mass, charge and radius of the spherically symmetric charged objects i.e.
electron.
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Mass Screening in Modified Gravity: Models of modified gravity introduce extra degrees of freedom, which for
consistency with the data, should be suppressed at observable scales. In the
models that share properties of massive gravity such a suppression is due to
nonlinear interactions: An isolated massive astrophysical object creates a halo
of a nonzero curvature around it, shielding its vicinity from the influence of
the extra degrees of freedom. We emphasize that the very same halo leads to a
screening of the gravitational mass of the object, as seen by an observer
beyond the halo. We discuss the case when the screening could be very
significant and may rule out, or render the models observationally interesting.
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The overarching finite symmetry group of Kummer surfaces in the Mathieu
group M_24: In view of a potential interpretation of the role of the Mathieu group M_24
in the context of strings compactified on K3 surfaces, we develop techniques to
combine groups of symmetries from different K3 surfaces to larger 'overarching'
symmetry groups.
We construct a bijection between the full integral homology lattice of K3 and
the Niemeier lattice of type (A_1)^24, which is simultaneously compatible with
the finite symplectic automorphism groups of all Kummer surfaces lying on an
appropriate path in moduli space connecting the square and the tetrahedral
Kummer surfaces. The Niemeier lattice serves to express all these symplectic
automorphisms as elements of the Mathieu group M_24, generating the
'overarching finite symmetry group' (Z_2)^4:A_7 of Kummer surfaces. This group
has order 40320, thus surpassing the size of the largest finite symplectic
automorphism group of a K3 surface by orders of magnitude. For every Kummer
surface this group contains the group of symplectic automorphisms leaving the
Kaehler class invariant which is induced from the underlying torus. Our results
are in line with the existence proofs of Mukai and Kondo, that finite groups of
symplectic automorphisms of K3 are subgroups of one of eleven subgroups of
M_23, and we extend their techniques of lattice embeddings for all Kummer
surfaces with Kaehler class induced from the underlying torus.
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Chern-Simons 5-form and Holographic Baryons: In the top-down holographic model of QCD based on D4/D8-branes in type IIA
string theory and some of the bottom up models, the low energy effective theory
of mesons is described by a 5 dimensional Yang-Mills-Chern-Simons theory in a
certain curved background with two boundaries. The 5 dimensional Chern-Simons
term plays a crucial role to reproduce the correct chiral anomaly in 4
dimensional massless QCD. However, there are some subtle ambiguities in the
definition of the Chern-Simons term for the cases with topologically
non-trivial gauge bundles, which include the configurations with baryons. In
particular, for the cases with three flavors, it was pointed out by Hata and
Murata that the naive Chern-Simons term does not lead to an important
constraint on the baryon spectrum, which is needed to pick out the correct
baryon spectrum observed in nature. In this paper, we propose a formulation of
well-defined Chern-Simons term which can be used for the cases with baryons,
and show that it recovers the correct baryon constraint as well as the chiral
anomaly in QCD.
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Integrable Gross-Neveu models with fermion-fermion and
fermion-antifermion pairing: The massless Gross-Neveu and chiral Gross-Neveu models are well known
examples of integrable quantum field theories in 1+1 dimensions. We address the
question whether integrability is preserved if one either replaces the
four-fermion interaction in fermion-antifermion channels by a dual interaction
in fermion-fermion channels, or if one adds such a dual interaction to an
existing integrable model. The relativistic Hartree-Fock-Bogoliubov approach is
adequate to deal with the large N limit of such models. In this way, we
construct and solve three integrable models with Cooper pairing. We also
identify a candidate for a fourth integrable model with maximal kinematic
symmetry, the "perfect" Gross-Neveu model. This type of field theories can
serve as exactly solvable toy models for color superconductivity in quantum
chromodynamics.
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Index Theory, Gerbes, and Hamiltonian Quantization: We give an Atiyah-Patodi-Singer index theory construction of the bundle of
fermionic Fock spaces parametrized by vector potentials in odd space dimensions
and prove that this leads in a simple manner to the known Schwinger terms
(Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS
construction to the bundle gerbe approach discussed recently by Carey and
Murray, including an explicit computation of the Dixmier-Douady class. An
advantage of our method is that it can be applied whenever one has a form of
the APS theorem at hand, as in the case of fermions in an external
gravitational field.
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Singular limits in STU supergravity: We analyse the STU sectors of the four-dimensional maximal gauged
supergravities with gauge groups ${\rm SO(8)}$, ${\rm
SO(6)}\ltimes\mathbb{R}^{12}$ and $[{\rm SO(6)}\times{\rm
SO(2)}]\ltimes\mathbb{R}^{12}$, and construct new domain-wall black-hole
solutions in $D=4$. The consistent Kaluza-Klein embedding of these theories is
obtained using the techniques of Exceptional Field Theory combined with the
4$d$ tensor hierarchies, and their respective uplifts into $D=11$ and type IIB
supergravities are connected through singular limits that relate the different
gaugings.
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Quantum Heisenberg groups and Sklyanin algebras: We define new quantizations of the Heisenberg group by introducing new
quantizations in the universal enveloping algebra of its Lie algebra. Matrix
coefficients of the Stone--von Neumann representation are preserved by these
new multiplications on the algebra of functions on the Heisenberg group. Some
of the new quantizations provide also a new multiplication in the algebra of
theta functions; we obtain in this way Sklyanin algebras.
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Temperature effects for $e^-+e^+\rightarrow μ^-+μ^+$ scattering in
very special relativity: The electron-positron scattering process is investigated in the context of
very special relativity (VSR). This theory assumes that the true symmetry of
nature is not the full Lorentz group, but some of its subgroups, such as the
subgroups $SIM(2)$ and $HOM(2)$. In this context, the cross-section for
electron-positron scattering at finite temperature is calculated. The effects
of temperature are introduced using the Thermo Field Dynamics (TFD) formalism.
Our result shows that the cross-section is changed due to both effects, the VSR
contributions and temperature effects. An estimated value for the VSR parameter
using experimental data available in the literature is discussed.
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Planar System and $w_\infty$ Algebra: We study the exotic particles symmetry in the background of noncommutative
two-dimensional phase-space leading to realize in physicswise the deformed
version of $C_{\lambda}$-extended Heisenberg algebra and $\om_\infty$ symmetry.
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Monopole correlation functions and holographic phases of matter in 2+1
dimensions: The strong coupling dynamics of a 2+1 dimensional U(1) gauge theory coupled
to charged matter is holographically modeled via a top-down construction with
intersecting D3- and D5-branes. We explore the resulting phase diagram at
finite temperature and charge density using correlation functions of monopole
operators, dual to magnetically charged particles in the higher-dimensional
bulk theory, as a diagnostic.
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Influence functionals and black body radiation: The Feynman-Vernon formalism is used to obtain a microscopic, quantum
mechanical derivation of black body radiation, for a massless scalar field in
1+1 dimensions, weakly coupled to an environment of finite size. The model
exhibits the absorption, thermal equilibrium, and emission properties of a
canonical black body, but shows that the thermal radiation propagates outwards
from the body, with the Planckian spectrum applying inside a wavefront region
of finite thickness. The black body environment used in the derivation can be
considered to represent a very fine, granular medium, such as lampblack. In the
course of developing the model for black body radiation, thermalization of a
single harmonic oscillator by a heat bath with slowly varying spectral density
is demonstrated. Bargmann-Fock coherent state variables, being convenient for
problems involving harmonic oscillators and free fields, are reviewed and then
used throughout the paper. An appendix reviews the justification for using
baths of independent harmonic oscillators to model generic quantum
environments.
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Non-supersymmetric Attractor with the Cosmological Constant: As a test for the non-supersymmetric attractor mechanism, we consider
extremal Reissner-Nordstr\"{o}m-(anti-)de Sitter black holes. Based on the
simple observation that the near-horizon geometry of a generic extremal black
hole contains two-dimensional anti-de Sitter factor even in the presence of the
positive cosmological constant, we apply Ashoke Sen's entropy function method
to compute the entropy of these black holes. We find the results which exactly
agree with the Bekenstein-Hawking entropy. We also obtain the constant
higher-order correction to the entropy due to the Gauss-Bonnet term.
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Smearing orientifolds in flux compactifications can be OK: We present explicit examples of supergravity solutions corresponding to
backreacting localised (non-intersecting) O6 planes in flux reductions of
massive IIA supergravity and address some criticism towards the very existence
of such solutions. We verify in detail how the smeared orientifold solution
becomes a good approximation to the localised solution in the large volume/weak
coupling limit, as expected. We also find an exotic solution where prior to
backreaction the internal space has a boundary and when backreaction is
included the boundary disappears and the space closes off. The exotic example
is however outside of the supergravity approximation everywhere.
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The Rest-Frame Instant Form of Relativistic Perfect Fluids and of
Non-Dissipative Elastic Materials: For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave an
action principle depending only on their Lagrange coordinates $\alpha^i(x)$
without Clebsch potentials. After a reformulation on arbitrary spacelike
hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant
form of these perfect fluids is given. Their Hamiltonian invariant mass can be
given in closed form for the dust and the photon gas. The action for the
coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids
are studied on the rest-frame Wigner hyperplane. It is also shown that the same
formalism can be applied to non-dissipative relativistic elastic materials
described in terms of Lagrangian coordinates.
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Mass-deformed M2 branes in Stenzel space: We obtain finite-temperature M2 black branes in 11-dimensional supergravity,
in a $G_4$-flux background whose self-dual part approaches a solution of
Cveti\v{c}, Gibbons, L\"u, and Pope, based upon Stenzel's family of Ricci-flat
K\"ahler deformed cones. Our solutions are asymptotically $AdS_4$ times a
7-dimensional Stiefel manifold $V_{5,2}$, and the branes are ``smeared'' to
retain $SO(5)$ symmetry in the internal space. The solutions represent a mass
deformation of the corresponding dual $CFT_3$, whose full description is at
this time only partially-understood. We investigate the possibility of a
confinement/de-confinement phase transition analogous to the $AdS_5 \times S^5$
case, and a possible Gregory-Laflamme type instability which could lead to
polarised brane solutions which break $SO(5)$. We discuss possible consequences
for AdS/CFT and the KKLT cosmological uplift mechanism.
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Wormhole solutions to Horava gravity: We present wormhole solutions to Horava non-relativistic gravity theory in
vacuum. We show that, if the parameter $\lambda$ is set to one, transversable
wormholes connecting two asymptotically de Sitter or anti-de Sitter regions
exist. In the case of arbitrary $\lambda$, the asymptotic regions have a more
complicated metric with constant curvature. We also show that, when the
detailed balance condition is violated softly, tranversable and asymptotically
Minkowski, de Sitter or anti-de Sitter wormholes exist.
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Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra: We review the study of Hopf algebras, classical and quantum R-matrices,
infinite-dimensional Yangian symmetries and their representations in the
context of integrability for the N=4 vs AdS5xS5 correspondence.
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The Quantum Symmetry of Rational Field Theories: The quantum symmetry of a rational quantum field theory is a finite-
dimensional multi-matrix algebra. Its representation category, which determines
the fusion rules and braid group representations of superselection sectors, is
a braided monoidal C^*-category. Various properties of such algebraic
structures are described, and some ideas concerning the classification
programme are outlined. (Invited talk given at the III. International
Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta,
Ukraine, June 1993. To appear in Teor.Mat.Fiz.)
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Cyclic monodromy matrices for sl(n) trigonometric R-matrices: The algebra of monodromy matrices for sl(n) trigonometric R-matrices is
studied. It is shown that a generic finite-dimensional polynomial irreducible
representation of this algebra is equivalent to a tensor product of
L-operators. Cocommutativity of representations is discussed. A special class
of representations - factorizable representations is introduced and
intertwiners for cocommuting factorizable representations are written through
the Boltzmann weights of the sl(n) chiral Potts model.
Let us consider an algebra generated by noncommutative entries of the matrix
$T(u)$ satisfying the famous bilinear relation originated from the quantum
inverse scattering method: $R(\la-\mu)T(\la)T(\mu)=T(\mu)T(\la) R(\la-\mu)$
where $R(\la)$ is R-matrix. For historical reasons this algebra is called the
algebra of monodromy matrices. If $\g$ is a simple finite-dimensional Lie
algebra and $R(\la)$ is $\g$-invariant R-matrix the algebra of monodromy
matrices after a proper specialization gives the Yangian $Y(\g)$ introduced by
Drinfeld. If $R(\la)$ is corresponding trigonometric R-matrix this algebra is
closely connected with $U_q(\g)$ and $U_q(\hat\g)$ at zero level. If $R(\la)$
is $sl(2)$ elliptic R-matrix the algebra of monodromy matrices gives rise to
Sklyanin's algebra.
In this paper we shall study algebras of monodromy matrices for $sl(n)$
trigonometric R-matrices at roots of 1. Finite-dimensional cyclic irreducible
polynomial representations and their intertwiners are discussed.
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Synchrotron radiation from a charge moving along a helix around a
dielectric cylinder: In this paper we investigate the radiation emitted by a charged particle
moving along a helical orbit around a dielectric cylinder immersed into a
homogeneous medium. Formulae are derived for the electromagnetic potentials,
electric and magnetic fields, and for the spectral-angular distribution of the
radiation in the exterior medium. It is shown that under the Cherenkov
condition for dielectric permittivity of the cylinder and the velocity of the
particle image on the cylinder surface, strong narrow peaks appear in the
angular distribution for the number of quanta radiated on a given harmonic. At
these peaks the radiated energy exceeds the corresponding quantity for a
homogeneous medium by several dozens of times. Simple analytic estimates are
given for the heights and widths of these peaks. The results of numerical
calculations for the angular distribution of the radiated quanta are presented
and they are compared with the corresponding quantities for the radiation from
a charge moving along a helical trajectory inside a dielectric cylinder.
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(Non-)Anomalous D-brane and O-plane couplings: the normal bundle: The direct string computation of anomalous D-brane and orientifold plane
couplings is extended to include the curvature of the normal bundle. The
normalization of these terms is fixed unambiguously. New, non-anomalous
gravitational couplings are found.
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Universal Axion Backreaction in Flux Compactifications: We study the backreaction effect of a large axion field excursion on the
saxion partner residing in the same $\mathcal{N}=1$ multiplet. Such
configurations are relevant in attempts to realize axion monodromy inflation in
string compactifications. We work in the complex structure moduli sector of
Calabi-Yau fourfold compactifications of F-theory with four-form fluxes, which
covers many of the known Type II orientifold flux compactifications. Noting
that axions can only arise near the boundary of the moduli space, the powerful
results of asymptotic Hodge theory provide an ideal set of tools to draw
general conclusions without the need to focus on specific geometric examples.
We find that the boundary structure engraves a remarkable pattern in all
possible scalar potentials generated by background fluxes. By studying the
Newton polygons of the extremization conditions of all allowed scalar
potentials and realizing the backreaction effects as Puiseux expansions, we
find that this pattern forces a universal backreaction behavior of the large
axion field on its saxion partner.
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Hiding Charge in a Wormhole: Existence of wormholes can lead to a host of new effects like Misner-Wheeler
"charge without charge" effect, where without being generated by any source an
electric flux arrives from one "universe" and flows into the other "universe".
Here we show the existence of an intriguing opposite possibility. Namely, a
charged object (a charged lightlike brane in our case) sitting at the wormhole
"throat" expels all the flux it produces into just one of the "universes",
which turns out to be of compactified ("tube-like") nature. An outside observer
in the non-compact "universe" detects, therefore, a neutral object. This
charge-hiding effect takes place in a gravity/gauge-field system
self-consistently interacting with a charged lightlike brane as a matter
source, where the gauge field subsystem is of a special non-linear form
containing a square-root of the Maxwell term and which previously has been
shown to produce a QCD-like confining gauge field dynamics in flat space-time.
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A Note on the Relation between Different Forms of Superparticle
Dynamics': A formulation of $D\is 10$ superparticle dynamics is given that contain
space-time and twistor variables. The set of constraints is entirely first
class, and gauge conditions may be imposed that reduces the system to a
Casalbuoni-Brink-Schwarz superparticle, a spinning particle or a twistor
particle.
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Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications: We study the large volume limit of the scalar potential in Calabi-Yau flux
compactifications of type IIB string theory. Under general circumstances there
exists a limit in which the potential approaches zero from below, with an
associated non-supersymmetric AdS minimum at exponentially large volume. Both
this and its de Sitter uplift are tachyon-free, thereby fixing all Kahler and
complex structure moduli, which has been difficult to achieve in the KKLT
scenario. Also, for the class of vacua described in this paper, the gravitino
mass is independent of the flux discretuum, whereas the ratio of the string
scale to the 4d Planck scale is hierarchically small but flux dependent. The
inclusion of alpha' corrections plays a crucial role in the structure of the
potential. We illustrate these ideas through explicit computations for a
particular Calabi-Yau manifold.
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On Non Commutative Calabi-Yau Hypersurfaces: Using the algebraic geometry method of Berenstein et al (hep-th/0005087), we
reconsider the derivation of the non commutative quintic algebra
${\mathcal{A}}_{nc}(5)$ and derive new representations by choosing different
sets of Calabi-Yau charges ${C_{i}^{a}}$. Next we extend these results to
higher $d$ complex dimension non commutative Calabi-Yau hypersurface algebras
${\mathcal{A}}_{nc}(d+2)$. We derive and solve the set of constraint eqs
carrying the non commutative structure in terms of Calabi-Yau charges and
discrete torsion. Finally we construct the representations of
${\mathcal{A}}_{nc}(d+2) $ preserving manifestly the Calabi-Yau condition $
\sum_{i}C_{i}^{a}=0$ and give comments on the non commutative subalgebras.
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Canonical Quantization of Massive Symmetric Rank-Two Tensor in String
Theory: The canonical quantization of a massive symmetric rank-two tensor in string
theory, which contains two Stueckelberg fields, was studied. As a preliminary
study, we performed a canonical quantization of the Proca model to describe a
massive vector particle that shares common properties with the massive
symmetric rank-two tensor model. By performing a canonical analysis of the
Lagrangian, which describes the symmetric rank-two tensor, obtained by Siegel
and Zwiebach (SZ) from string field theory, we deduced that the Lagrangian
possesses only first class constraints that generate local gauge
transformation. By explicit calculations, we show that the massive symmetric
rank-two tensor theory is gauge invariant only in the critical dimension of
open bosonic string theory, i.e., $d=26$. This emphasizes that the origin of
local symmetry is the nilpotency of the Becchi-Rouet-Stora-Tyutin (BRST)
operator, which is valid only in the critical dimension. For a particular gauge
imposed on the Stueckelberg fields, the gauge-invariant Lagrangian of the SZ
model reduces to the Fierz-Pauli Lagrangian of a massive spin-two particle.
Thus, the Fierz-Pauli Lagrangian is a gauge-fixed version of the
gauge-invariant Lagrangian for a massive symmetric rank-two tensor. By noting
that the Fierz-Pauli Lagrangian is not suitable for studying massive spin-two
particles with small masses, we propose the transverse-traceless (TT) gauge to
quantize the SZ model as an alternative gauge condition. In the TT gauge, the
two Stueckelberg fields can be decoupled from the symmetric rank-two tensor and
integrated trivially. The massive spin-two particle can be described by the SZ
model in the TT gauge, where the propagator of the massive spin-two particle
has a well-defined massless limit.
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Classical instability in Lovelock gravity: We introduce a simple method for the investigation of the classical stability
of static solutions with a horizon in Lovelock gravity. The method is
applicable to the investigation of high angular momentum instabilities, similar
to those found by Dotti and Gleiser for Gauss-Bonnet black holes. The method
does not require the knowledge of the explicit analytic form of the black hole
solution. In this paper we apply our method to a case where the explicit
solution is known and show that it identifies correctly the resulting unstable
modes.
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When Black Holes Meet Kaluza-Klein Bubbles: We explore the physical consequences of a recently discovered class of exact
solutions to five dimensional Kaluza-Klein theory. We find a number of
surprising features including: (1) In the presence of a Kaluza-Klein bubble,
there are arbitrarily large black holes with topology S^3. (2) In the presence
of a black hole or a black string, there are expanding bubbles (with de Sitter
geometry) which never reach null infinity. (3) A bubble can hold two black
holes of arbitrary size in static equilibrium. In particular, two large black
holes can be close together without merging to form a single black hole.
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Holomorphic Yukawa Couplings in Heterotic String Theory: We develop techniques, based on differential geometry, to compute holomorphic
Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds
defined as complete intersections in projective spaces. It is shown explicitly
how these techniques relate to algebraic methods for computing holomorphic
Yukawa couplings. We apply our methods to various examples and evaluate the
holomorphic Yukawa couplings explicitly as functions of the complex structure
moduli. It is shown that the rank of the Yukawa matrix can decrease at specific
loci in complex structure moduli space. In particular, we compute the up Yukawa
coupling and the singlet-Higgs-lepton trilinear coupling in the heterotic
standard model described in arXiv:1404.2767
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Type I integrable defects and finite-gap solutions for KdV and
sine-Gordon models: The main purpose of this paper is to extend results, which have been obtained
previously to describe the classical scattering of solitons with integrable
defects of type I, to include the much larger and intricate collection of
finite-gap solutions defined in terms of generalised theta functions. In this
context, it is generally not feasible to adopt a direct approach, via ansatze
for the fields to either side of the defect tuned to satisfy the defect sewing
conditions. Rather, essential use is made of the fact that the defect sewing
conditions themselves are intimately related to Backlund transformations in
order to set up a strategy to enable the calculation of the field on one side
by suitably transforming the field on the other side. The method is implemented
using Darboux transformations and illustrated in detail for the sine-Gordon and
KdV models. An exception, treatable by both methods, indirect and direct, is
provided by the genus 1 solutions. These can be expressed in terms of Jacobi
elliptic functions, which satisfy a number of useful identities of relevance to
this problem. There are new features to the solutions obtained in the
finite-gap context but, in all cases, if a (multi)soliton limit is taken within
the finite-gap solutions previously known results are recovered.
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D-brane Spectra of Nonsupersymmetric, Asymmetric Orbifolds and
Nonperturbative Contributions to the Cosmological Constant: We study nonperturbative aspects of asymmetric orbifolds of type IIA,
focussing on models that allow a dual perturbative heterotic description. In
particular we derive the boundary states that describe the nonsupersymmetric
D-branes of the untwisted sector and their zero mode spectra. These we use to
demonstrate, how some special non BPS multiplets are identified under the
duality map, and give some indications, how the mismatch of bosons and fermions
in the perturbative heterotic spectrum is to be interpreted in terms of the
nonperturbative degrees of freedom on the type IIA side.
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Father time. II. A physical basis behind Feynman's idea of antiparticles
moving backward in time, and an extension of the CPT theorem to include
non-local gauge fields: It has been demonstrated in a recent paper (Mod.Phys.Lett. A13, 1265 (1998);
hep-th/9902020) that the existence of a non-thermodynamic arrow of time at the
atomic level is a fundamental requirement for conservation of energy in
matter-radiation interaction. Since the universe consists of two things only
--- energy and massive matter --- we argue that as a consequence of this
earlier result, particles and antiparticles must necessarily move in opposite
directions in time. Our result further indicates that the CPT theorem can be
extended to cover non-local gauge fields.
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Multi-Instantons and Maldacena's Conjecture: We examine certain n-point functions G_n in {\cal N}=4 supersymmetric SU(N)
gauge theory at the conformal point. In the large-N limit, we are able to sum
all leading-order multi-instanton contributions exactly. We find compelling
evidence for Maldacena's conjecture: (1) The large-N k-instanton collective
coordinate space has the geometry of AdS_5 x S^5. (2) In exact agreement with
type IIB superstring calculations, at the k-instanton level, $G_n = \sqrt{N}
g^8 k^{n-7/2} e^{-8\pi^2 k/g^2}\sum_{d|k} d^{-2} \times F_n(x_1,...,x_n)$,
where F_n is identical to a convolution of n bulk-to-boundary SUGRA
propagators.
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The Mass, Normalization and Late Time behavior of the Tachyon Field: We study the dynamics of the tachyon field $T$. We derive the mass of the
tachyon as the pole of the propagator which does not coincide with the standard
mass given in the literature in terms of the second derivative of $V(T)$ or
$Log[V(T)]$. We determine the transformation of the tachyon in order to have a
canonical scalar field $\phi$. This transformation reduces to the one obtained
for small $\dot T$ but it is also valid for large values of $\dot T$. This is
specially interesting for the study of dark energy where $\dot T\simeq 1$. We
also show that the normalized tachyon field $\phi$ is constrained to the
interval $T_2\leq T \leq T_1$ where $T_1,T_2$ are zeros of the original
potential $V(T)$. This results shows that the field $\phi$ does not know of the
unboundedness of $V(T)$, as suggested for bosonic open string tachyons. Finally
we study the late time behavior of tachyon field using the L'H\^{o}pital rule.
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Entropy function and attractors for AdS black holes: We apply Sen's entropy formalism to the study of the near horizon geometry
and the entropy of asymptotically AdS black holes in gauged supergravities. In
particular, we consider non-supersymmetric electrically charged black holes
with AdS_2 xS^{d-2} horizons in U(1)^4 and U(1)^3 gauged supergravities in d=4
and d=5 dimensions, respectively. We study several cases including
static/rotating, BPS and non-BPS black holes in Einstein as well as in
Gauss-Bonnet gravity. In all examples, the near horizon geometry and black hole
entropy are derived by extremizing the entropy function and are given entirely
in terms of the gauge coupling, the electric charges and the angular momentum
of the black hole.
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Amplitudes at Infinity: We investigate the asymptotically large loop-momentum behavior of multi-loop
amplitudes in maximally supersymmetric quantum field theories in four
dimensions. We check residue-theorem identities among color-dressed leading
singularities in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to
demonstrate the absence of poles at infinity of all MHV amplitudes through
three loops. Considering the same test for $\mathcal{N}=8$ supergravity leads
us to discover that this theory does support non-vanishing residues at infinity
starting at two loops, and the degree of these poles grow arbitrarily with
multiplicity. This causes a tension between simultaneously manifesting
ultraviolet finiteness---which would be automatic in a representation obtained
by color-kinematic duality---and gauge invariance---which would follow from
unitarity-based methods.
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On 1D, N = 4 Supersymmetric SYK-Type Models (I): Proposals are made to describe 1D, N = 4 supersymmetrical systems that extend
SYK models by compactifying from 4D, N = 1 supersymmetric Lagrangians involving
chiral, vector, and tensor supermultiplets. Quartic fermionic vertices are
generated via integrals over the whole superspace, while 2(q-1)-point fermionic
vertices are generated via superpotentials. The coupling constants in the
superfield Lagrangians are arbitrary, and can be chosen to be Gaussian random.
In that case, these 1D, N = 4 supersymmetric SYK models would exhibit
Wishart-Laguerre randomness, which share the same feature among other 1D
supersymmetric SYK models in literature. One difference with 1D, N = 1 and N =
2 models though, is our models contain dynamical bosons, but this is consistent
with other 1D, N = 4 and 2D, N = 2 models in literature. Added conjectures on
duality and possible mirror symmetry realizations on these models is noted.
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Forcing Free Fields: The momentum of a free massive particle, invariant under translation, thereby
realizes a trivial representation of the translation group. By allowing
nontrivial reps of translations, momentum changes with translation, a recipe
for force. Here the procedure is applied to the conventional construction of a
free quantum field using spacetime symmetries, yielding a more general field
with the free field as a special case. It is shown that a particle described by
the quantum field follows the classical trajectories of a massive charged
particle in electromagnetic and gravitational fields.
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The μ- term in Effective Supergravity Theories: The Higgs mixing term coefficient $\mu_{eff}$ is calculated in the scalar
potential in supergravity theories with string origin, in a model independent
approach. A general low energy effective expression is derived, where new
contributions are included which depend on the modular weights $q_{1,2}$ of the
Higgs superfields, the moduli and derivative terms. We find that in a class of
models obtained in the case of compactifications of the heterotic superstring,
the derivative terms are identically zero. Further, the total $\mu_{eff}$-term
vanishes identically if the sum of the two modular weights $q_1+q_2$ is equal
to two. Subleading $\mu$- corrections, in the presence of intermediate gauge
symmetries predicted in viable string scenarios, are also discussed.
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Deconstructing Superconductivity: We present a dimensionally deconstructed model of an s-wave holographic
superconductor. The 2+1 dimensional model includes multiple charged Cooper pair
fields and neutral exciton fields that have interactions governed by hidden
local symmetries. We derive AdS/CFT-like relations for the current and charge
density in the model, and we analyze properties of the Cooper pair condensates
and the complex conductivity.
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Bubble instability of mIIA on $\mathrm{AdS}_4\times S^6$: We consider compactifications of massive IIA supergravity on a six-sphere.
This setup is known to give rise to non-supersymmetric AdS$_4$ vacua preserving
SO$(7)$ as well as G$_2$ residual symmetry. Both solutions have a round $S^6$
metric and are supported by the Romans' mass and internal $F_6$ flux. While the
SO$(7)$ invariant vacuum is known to be perturbatively unstable, the G$_2$
invariant one has been found to have a fully stable Kaluza-Klein spectrum.
Moreover, it has been shown to be protected against brane-jet instabilities.
Motivated by these results, we study possible bubbling solutions connected to
the G$_2$ vacuum, representing non-perturbative instabilities of the latter. We
indeed find an instability channel represented by the nucleation of a bubble of
nothing dressed up with a homogeneous D2 brane charge distribution in the
internal space. Our solution generalizes to the case where $S^6$ is replaced by
any six-dimensional nearly-K\"ahler manifold.
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An entanglement asymmetry study of black hole radiation: Hawking discovery that black holes can evaporate through radiation emission
has posed a number of questions that with time became fundamental hallmarks for
a quantum theory of gravity. The most famous one is likely the information
paradox, which finds an elegant explanation in the Page argument suggesting
that a black hole and its radiation can be effectively represented by a random
state of qubits. Leveraging the same assumption, we ponder the extent to which
a black hole may display emergent symmetries, employing the entanglement
asymmetry as a modern, information-based indicator of symmetry breaking. We
find that for a random state devoid of any symmetry, a $U(1)$ symmetry emerges
and it is exact in the thermodynamic limit before the Page time. At the Page
time, the entanglement asymmetry shows a finite jump to a large value. Our
findings imply that the emitted radiation is symmetric up to the Page time and
then undergoes a sharp transition. Conversely the black hole is symmetric only
after the Page time.
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Unconventional conformal invariance of maximal depth partially massless
fields on $dS_{4}$ and its relation to complex partially massless SUSY: Deser and Waldron have shown that maximal depth partially massless theories
of higher (integer) spin on four-dimensional de Sitter spacetime ($dS_{4}$)
possess infinitesimal symmetries generated by the conformal Killing vectors of
$dS_{4}$. However, it was later shown by Barnich, Bekaer, and Grigoriev that
these theories are not invariant under the conformal algebra $so(4,2)$. To get
some insight into these seemingly contradicting results we write down the full
set of infinitesimal transformations of the fields generated by the fifteen
conformal Killing vectors of $dS_{4}$. In particular, although the
transformations generated by the ten dS Killing vectors are well-known, the
transformations generated by the five non-Killing conformal Killing vectors
were absent from the literature, and we show that they have an `unconventional'
form. In the spin-2 case, we show that the field equations and the action are
invariant under the unconventional conformal transformations. For spin-$s >2$,
the invariance is demonstrated only at the level of the field equations. For
all spins $s \geq 2$, we reproduce the result that the symmetry algebra does
not close on $so(4,2)$. This is due to the appearance of new higher-derivative
symmetry transformations in the commutator of two unconventional
transformations. Our results concerning the closure of the full symmetry
algebra are inconclusive. Then we shift focus to the question of supersymmetry
on $dS_{4}$ and our objective is twofold. First, we uncover a non-interacting
supermultiplet that consists of a complex partially massless spin-2 field and a
complex spin-3/2 field. Second, we showcase the appearance of the
unconventional conformal symmetries in the bosonic subalgebra of our
supermultiplet. The bosonic subalgebra is neither $so(4,1)$ nor $so(4,2)$,
while its closure is currently an open question.
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Warping and F-term uplifting: We analyse the effective supergravity model of a warped compactification with
matter on D3 and D7-branes. We find that the main effect of the warp factor is
to modify the F-terms while leaving the D-terms invariant. Hence warped models
with moduli stabilisation and a small positive cosmological constant resulting
from a large warping can only be achieved with an almost vanishing D-term and a
F-term uplifting. By studying string-motivated examples with gaugino
condensation on magnetised D7-branes, we find that even with a vanishing
D-term, it is difficult to achieve a Minkowski minimum for reasonable parameter
choices. When coupled to an ISS sector the AdS vacua is uplifted, resulting in
a small gravitino mass for a warp factor of order 10^-5.
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Hamiltonian approach to QCD in Coulomb gauge: From the vacuum to finite
temperatures: The variational Hamiltonian approach to QCD in Coulomb gauge is reviewed and
the essential results obtained in recent years are summarized. First the
results for the vacuum sector are discussed, with a special emphasis on the
mechansim of confinement and chiral symmetry breaking. Then the deconfinement
phase transition is described by introducing temperature in the Hamiltonian
approach via compactification of one spatial dimension. The effective action
for the Polyakov loop is calculated and the order of the phase transition as
well as the critical temperatures are obtained for the color group SU(2) and
SU(3). In both cases, our predictions are in good agreement with lattice
calculations.
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Equations of fluid mechanics with N=1 Schrodinger supersymmetry: Equations of fluid mechanics with N=1 Schrodinger supersymmetry are
formulated within the method of nonlinear realizations of Lie groups.
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Scale Vs. Conformal Invariance in the AdS/CFT Correspondence: We present two examples of non-trivial field theories which are scale
invariant, but not conformally invariant. This is done by placing certain field
theories, which are conformally invariant in flat space, onto curved
backgrounds of a specific type. We define this using the AdS/CFT
correspondence, which relates the physics of gravity in asymptotically Anti-de
Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one
dimension fewer. The AdS rotating (Kerr) black holes in five and seven
dimensions provide us with the examples, since by the correspondence we are
able to define and compute the action and stress tensor of four and six
dimensional field theories residing on rotating Einstein universes, using the
``boundary counterterm'' method. The rotation breaks conformal but not scale
invariance. The AdS/CFT framework is therefore a natural arena for generating
such examples of non-trivial scale invariant theories which are not conformally
invariant.
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Null orbifolds in AdS, Time Dependence and Holography: We study M/D-branes in a null-brane background. By taking a near horizon
limit, one is left with cosmological models in the corresponding Poincar\'e
patches. To deal with their usual horizons, we either extend these models to
global AdS or remain in the Poincar\'e patch and apply a T-duality
transformation whenever the effective radius of the compact dimension
associated with the null-brane probes distances smaller than the string scale.
The first scenario gives rise to null orbifolds in AdS spaces, which are
described in detail. Their conformal boundaries are singular. The second has a
dual gauge theory description in terms of Super Yang-Mills in the null-brane
background. The latter is a good candidate for a non-perturbative definition of
string theory in a time-dependent background.
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Open-Closed String Field Theory in the Background B-Field: In this paper, we study open-closed string field theory in the background
B-field in the so-called alpha=p^{+} formulation. The string field theory in
the infrared gives noncommutative gauge theory in the open string sector. Since
this theory includes closed string fields as dynamical variables, we can obtain
another string field theory in the same background through the condensation of
closed string fields, whose low-energy effective action does not show the
noncommutativity of spacetime. Although we have two string field theories in
the same background, we show that these theories are equivalent. In fact, we
give the unitary transformation from string fields in one of them to string
fields in the other.
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Additional Equations Derived from the Ryder Postulates in the
(1/2,0)+(0,1/2) Representation of the Lorentz Group: Developing recently proposed constructions for the description of particles
in the $(1/2,0)\oplus (0,1/2)$ representation space, we derive the second-order
equations. The similar ones were proposed in the sixties and the seventies in
order to understand the nature of various mass and spin states in the
representations of the $O(4,2)$ group. We give some additional insights into
this problem. The used procedure can be generalized for {\it arbitrary} number
of lepton families.
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Causality constraints on corrections to Einstein gravity: We study constraints from causality and unitarity on $2\to2$ graviton
scattering in four-dimensional weakly-coupled effective field theories.
Together, causality and unitarity imply dispersion relations that connect
low-energy observables to high-energy data. Using such dispersion relations, we
derive two-sided bounds on gravitational Wilson coefficients in terms of the
mass $M$ of new higher-spin states. Our bounds imply that gravitational
interactions must shut off uniformly in the limit $G \to 0$, and prove the
scaling with $M$ expected from dimensional analysis (up to an infrared
logarithm). We speculate that causality, together with the non-observation of
gravitationally-coupled higher spin states at colliders, severely restricts
modifications to Einstein gravity that could be probed by experiments in the
near future.
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Quantum mechanical path integrals in the first quantised approach to
quantum field theory: Perturbative quantum field theory usually uses second quantisation and
Feynman diagrams. The worldline formalism provides an alternative approach
based on first quantised particle path integrals, similar in spirit to string
perturbation theory. Here we review the history, main features and present
applications of the formalism. Our emphasis is on recent developments such as
the path integral representation of open fermion lines, the description of
colour using auxiliary worldline fields, incorporation of higher spin, and
extension of the formalism to non-commutative space.
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Boundary Effects in 2+1 Dimensional Maxwell-Chern-Simons Theory: The boundary effects in the screening of an applied magnetic field in a
finite temperature 2+1 dimensional model of charged fermions minimally coupled
to Maxwell and Chern-Simons fields are investigated. It is found that in a
sample with only one boundary -a half-plane- a total Meissner effect takes
place, while in a sample with two boundaries -an infinite strip- the external
magnetic field partially penetrates the material.
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Characteristic numbers of crepant resolutions of Weierstrass models: We compute characteristic numbers of crepant resolutions of Weierstrass
models corresponding to elliptically fibered fourfolds $Y$ dual in F-theory to
a gauge theory with gauge group $G$. In contrast to the case of fivefolds,
Chern and Pontryagin numbers of fourfolds are invariant under crepant
birational maps. It follows that Chern and Pontryagin numbers are independent
on a choice of a crepant resolution. We present the results for the Euler
characteristic, the holomorphic genera, the Todd-genus, the $L$-genus, the
$\hat{A}$-genus, and the curvature invariant $X_8$ that appears in M-theory. We
also show that certain characteristic classes are independent on the choice of
the Kodaria fiber characterizing the group $G$. That is the case of $\int_Y
c_1^2 c_2$, the arithmetic genus, and the $\hat{A}$-genus. Thus, it is enough
to know $\int_Y c_2^2$ and the Euler characteristic $\chi(Y)$ to determine all
the Chern numbers of an elliptically fibered fourfold. We consider the cases of
$G=$ SU($n$) for ($n=2,3,4,5,6,7$), USp($4$), Spin($7$), Spin($8$), Spin($10$),
G$_2$, F$_4$, E$_6$, E$_7$, or E$_8$.
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Addendum to the paper "Combinatorics of the modular group II: the
Kontsevich integrals": Addendum to the paper Combinatorics of the Modular Group II The Kontsevich
integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)
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Derivations and noncommutative differential calculus II: We characterize the derivation $d:A\to \Omega^1_{\der}(A)$ by a universal
property introducing a new class of bimodules.
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Massive Ray-Singer Torsion and Path Integrals: Zero modes are an essential part of topological field theories, but they are
frequently also an obstacle to the explicit evaluation of the associated path
integrals. In order to address this issue in the case of Ray-Singer Torsion,
which appears in various topological gauge theories, we introduce a massive
variant of the Ray-Singer Torsion which involves determinants of the twisted
Laplacian with mass but without zero modes. This has the advantage of allowing
one to explicitly keep track of the zero mode dependence of the theory. We
establish a number of general properties of this massive Ray-Singer Torsion.
For product manifolds $M=N \times S^1$ and mapping tori one is able to
interpret the mass term as a flat $\mathbb{R}_{+}$ connection and one can
represent the massive Ray-Singer Torsion as the path integral of a Schwarz type
topological gauge theory. Using path integral techniques, with a judicious
choice of an algebraic gauge fixing condition and a change of variables which
leaves one with a free action, we can evaluate the torsion in closed form. We
discuss a number of applications, including an explicit calculation of the
Ray-Singer Torsion on $S^1$ for $G=PSL(2,R)$ and a path integral derivation of
a generalisation of a formula of Fried for the torsion of finite order mapping
tori.
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Static Solution of the General Relativistic Nonlinear $σ$-Model
Equation: The nonlinear $\sigma$-model is considered to be useful in describing hadrons
(Skyrmions) in low energy hadron physics and the approximate behavior of the
global texture. Here we investigate the properties of the static solution of
the nonlinear $\sigma$-model equation coupled with gravity. As in the case
where gravity is ignored, there is still no scale parameter that determines the
size of the static solution and the winding number of the solution is $1/2$.
The geometry of the spatial hyperspace in the asymptotic region of large $r$ is
explicitly shown to be that of a flat space with some missing solid angle.
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RNS model from a new angle for strings charged under the Maximal Gauge
Symmetry of the Standard model: We consider the RNS model from a new angle. The longitudinal and time
components of the world-sheet fermions add a $U(1)$ charge to a state. Unlike
the gauginos, the ground state fermions in the open string sector are complex;
spinor representations of $SU(3)_C\otimes SU(2)_L\otimes U(1)_{Y_W}$.
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Exact Effective action for (1+1)-dimensional fermions in an Abelian
background at finite temperature and chemical potential: In this paper we study the effects of a nonzero chemical potential in the
effective action for massless fermions in (1+1) dimensions in an abelian gauge
field background at finite temperature. We calculate the n-point function and
show that the structure of the amplitudes corresponds to a generalization of
the structure noted earlier in a calculation without a chemical potential (the
associated integrals carry the dependence on the chemical potential). Our
calculation shows that the chiral anomaly is unaffected by the presence of a
chemical potential at finite temperature. However, unlike the earlier
calculation (in the absence of a chemical potential) odd point functions do not
vanish. We trace this to the fact that in the presence of a chemical potential
the generalized charge conjugation symmetry of the theory allows for such
amplitudes. In fact, we find that all the even point functions are even
functions of the chemical potential while the odd point functions are odd
functions of it which is consistent with this generalized charge conjugation
symmetry. We show that the origin of the structure of the amplitudes is best
seen from a formulation of the theory in terms of left and right handed
spinors. The calculations are also much simpler in this formulation and it
clarifies many other aspects of the theory.
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From Navier-Stokes To Einstein: We show by explicit construction that for every solution of the
incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely
associated "dual" solution of the vacuum Einstein equations in $p+2$
dimensions. The dual geometry has an intrinsically flat timelike boundary
segment $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of
the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$
becomes highly accelerated. The near-horizon expansion in gravity is shown to
be mathematically equivalent to the hydrodynamic expansion in fluid dynamics,
and the Einstein equation reduces to the incompressible Navier-Stokes equation.
For $p=2$, we show that the full dual geometry is algebraically special Petrov
type II. The construction is a mathematically precise realization of
suggestions of a holographic duality relating fluids and horizons which began
with the membrane paradigm in the 70's and resurfaced recently in studies of
the AdS/CFT correspondence.
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The Poincare mass operator in terms of a hyperbolic algebra: The Poincare mass operator can be represented in terms of a Cl(3,0) Clifford
algebra. With this representation the quadratic Dirac equation and the Maxwell
equations can be derived from the same mathematical structure.
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Anti de Sitter Gravity from BF-Chern-Simons-Higgs Theories: It is shown that an action inspired from a BF and Chern-Simons model, based
on the $AdS_4$ isometry group SO(3, 2), with the inclusion of a Higgs potential
term, furnishes the MacDowell-Mansouri-Chamseddine-West action for gravity,
with a Gauss-Bonnet and cosmological constant term. The $AdS_4$ space is a
natural vacuum of the theory. Using Vasiliev's procedure to construct higher
spin massless fields in AdS spaces and a suitable star product, we discuss the
preliminary steps to construct the corresponding higher-spin action in $AdS_4$
space representing the higher spin extension of this model. Brief remarks on
Noncommutative Gravity are made.
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On Central Charges and Hamiltonians for 0-brane dynamics: We consider general properties of central charges of zero branes and
associated duality invariants, in view of their double role, on the bulk and on
the world volume (quantum-mechanical) theory. A detailed study of the BPS
condition for the mass spectrum arising from toroidal compactifications is
given for 1/2, 1/4 and 1/8 BPS states in any dimensions. As a byproduct, we
retreive the U-duality invariant conditions on the charge (zero mode) spectrum
and the orbit classification of BPS states preserving different fractions of
supersymmetry. The BPS condition for 0-branes in theories with 16
supersymmetries in any dimension is also discussed.
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Hermitian analyticity versus Real analyticity in two-dimensional
factorised S-matrix theories: The constraints implied by analyticity in two-dimensional factorised S-matrix
theories are reviewed. Whenever the theory is not time-reversal invariant, it
is argued that the familiar condition of `Real analyticity' for the S-matrix
amplitudes has to be superseded by a different one known as `Hermitian
analyticity'. Examples are provided of integrable quantum field theories whose
(diagonal) two-particle S-matrix amplitudes are Hermitian analytic but not Real
analytic. It is also shown that Hermitian analyticity is consistent with the
bootstrap equations and that it ensures the equivalence between the notion of
unitarity in the quantum group approach to factorised S-matrices and the
genuine unitarity of the S-matrix.
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One-loop divergences of effective action in $6D,\, {\cal N}=(1,0)$
supersymmetric four-derivative gauge theory: We consider $6D, {\cal N}=(1,0)$ supersymmetric four-derivative model of the
gauge multiplet interacting with the hypermultiplet. We calculate the off-shell
one-loop divergent contributions to the effective action of the model using the
background field method in harmonic superspace.
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Initial Conditions and the Structure of the Singularity in Pre-Big-Bang
Cosmology: We propose a picture, within the pre-big-bang approach, in which the universe
emerges from a bath of plane gravitational and dilatonic waves. The waves
interact gravitationally breaking the exact plane symmetry and lead generically
to gravitational collapse resulting in a singularity with the Kasner-like
structure. The analytic relations between the Kasner exponents and the initial
data are explicitly evaluated and it is shown that pre-big-bang inflation may
occur within a dense set of initial data. Finally, we argue that plane waves
carry zero gravitational entropy and thus are, from a thermodynamical point of
view, good candidates for the universe to emerge from.
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Making Non-Associative Algebra Associative: Based on results about open string correlation functions, a nonassociative
algebra was proposed in a recent paper for D-branes in a background with
nonvanishing $H$. We show that our associative algebra obtained by quantizing
the endpoints of an open string in an earlier work can also be used to
reproduce the same correlation functions. The novelty of this algebra is that
functions on the D-brane do not form a closed algebra. This poses a problem to
define gauge transformations on such noncommutative spaces. We propose a
resolution by generalizing the description of gauge transformations which
naturally involves global symmetries. This can be understood in the context of
matrix theory.
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S-duality and Strong Coupling Behavior of Large N Gauge Theories with
N=4 Supersymmetry: We analyze the strong coupling behavior of the large N gauge theories in
4-dimensions with N=4 supersymmetry by making use of S-duality. We show that at
large values of the coupling constant $\lambda=g_{YM}^2N$ the j-th non-planar
amplitude $f_j(\lambda) (j=0,1,2 ...)$ behaves as $f_j(\lambda)\approx
\lambda^j$. Implication of this behavior is discussed in connection with the
supergravity theory on $AdS_5\times S^5$ suggested by the CFT/AdS
correspondence. S-duality of the gauge theory corresponds to the duality
between the closed and open string loop expansions in the gravity/string
theory.
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Noncommutative Yang-Mills and Noncommutative Relativity: A Bridge Over
Trouble Water: Connes' view at Yang-Mills theories is reviewed with special emphasis on the
gauge invariant scalar product. This landscape is shown to contain Chamseddine
and Connes' noncommutative extension of general relativity restricted to flat
space-time, if the top mass is between 172 and 204 GeV. Then the Higgs mass is
between 188 and 201 GeV.
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An exact evaluation of the Casimir energy in two planar models: The method of images is used to calculate the Casimir energy in Euclidean
space with Dirichlet boundary conditions for two planar models, namely: i. the
non-relativistic Landau problem for a charged particle of mass m for which -
irrespective of the sign of the charge - the energy is negative, and ii. the
model of a real, massive, noninteracting relativistic scalar field theory in 2
+ 1 dimensions, for which the Casimir energy density is non-negative and is
expressed in terms of the Lerch transcendent xxx and the polylogarithm xxx with
0 < xxx < 1 and n = 2, 3.
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Twistfield Perturbations of Vertex Operators in the Z_2-Orbifold Model: We apply Kadanoff's theory of marginal deformations of conformal field
theories to twistfield deformations of Z_2 orbifold models in K3 moduli space.
These deformations lead away from the Z_2 orbifold sub-moduli-space and hence
help to explore conformal field theories which have not yet been understood. In
particular, we calculate the deformation of the conformal dimensions of vertex
operators for p^2<1 in second order perturbation theory.
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On finiteness of Type IIB compactifications: Magnetized branes on
elliptic Calabi-Yau threefolds: The string landscape satisfies interesting finiteness properties imposed by
supersymmetry and string-theoretical consistency conditions. We study N=1
supersymmetric compactifications of Type IIB string theory on smooth
elliptically fibered Calabi-Yau threefolds at large volume with magnetized
D9-branes and D5-branes. We prove that supersymmetry and tadpole cancellation
conditions imply that there is a finite number of such configurations. In
particular, we derive an explicitly computable bound on the number of magnetic
flux quanta, as well as the number of D5-branes, which is independent of the
continuous moduli of the setup. The proof applies if a number of easy to check
geometric conditions of the twofold base are met. We show that these geometric
conditions are satisfied for the almost Fano twofold bases given by each toric
variety associated to a reflexive two-dimensional polytope as well as by the
generic del Pezzo surfaces dP_n with n=0,...,8. Physically, this finiteness
proof shows that there exist a finite collection of four-dimensional gauge
groups and chiral matter spectra in the 4D supergravity theories realized by
these compactifications. As a by-product we explicitly construct all generators
of the Kaehler cones of dP_n and work out their relation to representation
theory.
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Non-Relativistic AdS Branes and Newton-Hooke Superalgebra: We examine a non-relativistic limit of D-branes in AdS_5xS^5 and M-branes in
AdS_{4/7}xS^{7/4}. First, Newton-Hooke superalgebras for the AdS branes are
derived from AdSxS superalgebras as Inonu-Wigner contractions. It is shown that
the directions along which the AdS-brane worldvolume extends are restricted by
requiring that the isometry on the AdS-brane worldvolume and the Lorentz
symmetry in the transverse space naturally extend to the super-isometry. We
also derive Newton-Hooke superalgebras for pp-wave branes and show that the
directions along which a brane worldvolume extends are restricted. Then the
Wess-Zumino terms of the AdS branes are derived by using the
Chevalley-Eilenberg cohomology on the super-AdSxS algebra, and the
non-relativistic limit of the AdS-brane actions is considered. We show that the
consistent limit is possible for the following branes: Dp (even,even) for p=1
mod 4 and Dp (odd,odd) for p=3 mod 4 in AdS_5xS^5, and M2 (0,3), M2 (2,1), M5
(1,5) and M5 (3,3) in AdS_{4}xS^{7} and S^{4}xAdS_{7}. We furthermore present
non-relativistic actions for the AdS branes.
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Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude: The Type II Superstring amplitude to 1-loop order is given by an integral of
$\vartheta$-functions over the moduli space of tori, which diverges for real
momenta. We construct the analytic continuation which renders this amplitude
well defined and finite, and we find the expected poles and cuts in the complex
momentum plane.
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An Exact Black Hole Entropy Bound: We show that a Rademacher expansion can be used to establish an exact bound
for the entropy of black holes within a conformal field theory framework. This
convergent expansion includes all subleading corrections to the
Bekenstein-Hawking term.
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On the Ultraviolet Divergence in QED: The well-known physical equivalence drawn from hole theory is applied in this
article. The author suggests to replace, in the part of Feynman diagram which
cannot be fixed by experiments, each fermion field operator, and hence fermion
propagator, by pairs of equivalent fermion field operators and propagators. The
formulation of this article thus yields additional terms which reveal
characteristic effects that have not been explored previously; such
characteristic effects lead to the appearence of logarithmic running terms and
that finite radiative corrections are directly obtained in calculations.
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On the moduli space curvature at infinity: We analyse the scalar curvature of the vector multiplet moduli space
$\mathcal{M}^{\rm VM}_X$ of type IIA string theory compactified on a
Calabi--Yau manifold $X$. While the volume of $\mathcal{M}^{\rm VM}_X$ is known
to be finite, cases have been found where the scalar curvature diverges
positively along trajectories of infinite distance. We classify the asymptotic
behaviour of the scalar curvature for all large volume limits within
$\mathcal{M}^{\rm VM}_X$, for any choice of $X$, and provide the source of the
divergence both in geometric and physical terms. Geometrically, there are
effective divisors whose volumes do not vary along the limit. Physically, the
EFT subsector associated to such divisors is decoupled from gravity along the
limit, and defines a rigid $\mathcal{N}=2$ field theory with a non-vanishing
moduli space curvature $R_{\rm rigid}$. We propose that the relation between
scalar curvature divergences and field theories that can be decoupled from
gravity is a common trait of moduli spaces compatible with quantum gravity.
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Hamiltonian analysis for Lifshitz type Fields: Using the Dirac Method, we study the Hamiltonian consistency for three field
theories. First we study the electrodynamics a la Ho\v{r}ava and we show that
this system is consistent for an arbitrary dynamical exponent $z.$ Second, we
study a Lifshitz type electrodynamics, which was proposed in [1]. For this last
system we found that the canonical momentum and the electrical field are
related through a Proca type Green function, however this system is consistent.
In addition, we show that the anisotropic Yang-Mills theory with dynamical
exponent $z=2$ is consistent. Finally, we study a generalized anisotropic
Yang-Mills theory and we show that this last system is consistent too.
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N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal
deformations: We continue to investigate the $\mathcal{N}=1$ deformations of
four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) labeled
by a nilpotent element of the flavor symmetry. This triggers a renormalization
group (RG) flow to an $\mathcal{N}=1$ SCFT. We systematically analyze all
possible deformations of this type for certain classes of $\mathcal{N}=2$
SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the $E_6$
SCFT. We find a number of examples where the amount of supersymmetry gets
enhanced to $\mathcal{N}=2$ at the end point of the RG flow. Most notably, we
find that the $SU(N)$ and $Sp(N)$ conformal SQCDs can be deformed to flow to
the Argyres-Douglas (AD) theories of type $(A_1, D_{2N-1})$ and $(A_1, D_{2N})$
respectively. This RG flow therefore allows us to compute the full
superconformal index of the $(A_1,D_N)$ class of AD theories. Moreover, we find
an infrared duality between $\mathcal{N}=1$ theories where the fixed point is
described by an $\mathcal{N}=2$ AD theory. We observe that the classes of
examples that exhibit supersymmetry enhancement saturate certain bounds for the
central charges implied by the associated two-dimensional chiral algebra.
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Einstein-Cartan gravity, matter, and scale-invariant generalization: We study gravity coupled to scalar and fermion fields in the Einstein-Cartan
framework. We discuss the most general form of the action that contains terms
of mass dimension not bigger than four, leaving out only contributions
quadratic in curvature. By resolving the theory explicitly for torsion, we
arrive at an equivalent metric theory containing additional six-dimensional
operators. This lays the groundwork for cosmological studies of the theory. We
also perform the same analysis for a no-scale scenario in which the Planck mass
is eliminated at the cost of adding an extra scalar degree of freedom. Finally,
we outline phenomenological implications of the resulting theories, in
particular to inflation and dark matter production.
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On the Short Distance Behavior of the Critical Ising Model Perturbed by
a Magnetic Field: We apply here a recently developed approach to compute the short distance
corrections to scaling for the correlators of all primary operators of the
critical two dimensional Ising model in a magnetic field. The essence of the
method is the fact that if one deals with O.P.E. Wilson coefficients instead of
correlators, all order I.R. safe formulas can be obtained for the perturbative
expansion with respect to magnetic field. This approach yields in a natural way
the expected fractional powers of the magnetic field, that are clearly absent
in the naive perturbative expression for correlators. The technique of the
Mellin transform have been used to compute the I.R. behavior of the regularized
integrals. As a corollary of our results, by comparing the existing numerical
data for the lattice model we give an estimate of the Vacuum Expectation Value
of the energy operator, left unfixed by usual nonperturbative approaches
(Thermodynamic Bethe Ansatz).
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A holographic critical point: We numerically construct a family of five-dimensional black holes exhibiting
a line of first-order phase transitions terminating at a critical point at
finite chemical potential and temperature. These black holes are constructed so
that the equation of state and baryon susceptibilities approximately match QCD
lattice data at vanishing chemical potential. The critical endpoint in the
particular model we consider has temperature 143 MeV and chemical potential 783
MeV. Critical exponents are calculated, with results that are consistent with
mean-field scaling relations.
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The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2)
gauged supergravities in six dimensions: We obtain necessary and sufficient conditions for a supersymmetric field
configuration in the N=(1,0) U(1) or SU(2) gauged supergravities in six
dimensions, and impose the field equations on this general ansatz. It is found
that any supersymmetric solution is associated to an $SU(2)\ltimes
\mathbb{R}^4$ structure. The structure is characterized by a null Killing
vector which induces a natural 2+4 split of the six dimensional spacetime. A
suitable combination of the field equations implies that the scalar curvature
of the four dimensional Riemannian part, referred to as the base, obeys a
second order differential equation. Bosonic fluxes introduce torsion terms that
deform the $SU(2)\ltimes\mathbb{R}^4$ structure away from a covariantly
constant one. The most general structure can be classified in terms of its
intrinsic torsion. For a large class of solutions the gauge field strengths
admit a simple geometrical interpretation: in the U(1) theory the base is
K\"{a}hler, and the gauge field strength is the Ricci form; in the SU(2)
theory, the gauge field strengths are identified with the curvatures of the
left hand spin bundle of the base. We employ our general ansatz to construct
new supersymmetric solutions; we show that the U(1) theory admits a symmetric
Cahen-Wallach$_4\times S^2$ solution together with a compactifying pp-wave. The
SU(2) theory admits a black string, whose near horizon limit is $AdS_3\times
S_3$. We also obtain the Yang-Mills analogue of the Salam-Sezgin solution of
the U(1) theory, namely $R^{1,2}\times S^3$, where the $S^3$ is supported by a
sphaleron. Finally we obtain the additional constraints implied by enhanced
supersymmetry, and discuss Penrose limits in the theories.
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S-Duality and Helicity Amplitudes: We examine interacting Abelian theories at low energies and show that
holomorphically normalized photon helicity amplitudes transform into dual
amplitudes under SL(2,Z) as modular forms with weights that depend on the
number of positive and negative helicity photons and on the number of internal
photon lines. Moreover, canonically normalized helicity amplitudes transform by
a phase, so that even though the amplitudes are not duality invariant, their
squares are duality invariant. We explicitly verify the duality transformation
at one loop by comparing the amplitudes in the case of an electron and the dyon
that is its SL(2,Z) image, and extend the invariance of squared amplitudes
order by order in perturbation theory. We demonstrate that S-duality is
property of all low-energy effective Abelian theories with electric and/or
magnetic charges and see how the duality generically breaks down at high
energies.
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Renormalisability of non-homogeneous T-dualised sigma-models: The quantum equivalence between sigma-models and their non-abelian T-dualised
partners is examined for a large class of four dimensional non-homogeneous and
quasi-Einstein metrics with an isometry group SU(2) times U(1). We prove that
the one-loop renormalisability of the initial torsionless sigma-models is
equivalent to the one-loop renormalisability of the T-dualised torsionful
model. For a subclass of Kahler original metrics, the dual partners are still
Kahler (with torsion).
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Vortices and domain walls in a Chern-Simons theory with magnetic moment
interaction: We study the structure and properties of vortices in a recently proposed
Abelian Maxwell-Chern-Simons model in $2 +1 $ dimensions. The model which is
described by gauge field interacting with a complex scalar field, includes two
parity and time violating terms: the Chern-Simons and the anomalous magnetic
terms. Self-dual relativistic vortices are discussed in detail. We also find
one dimensional soliton solutions of the domain wall type. The vortices are
correctly described by the domain wall solutions in the large flux limit.
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On Chebyshev Wells: Periods, Deformations, and Resurgence: We study the geometry and mechanics (both classical and quantum) of potential
wells described by squares of Chebyshev polynomials. We show that in a small
neighbourhood of the locus cut out by them in the space of hyperelliptic
curves, these systems exhibit low-orders/low-orders resurgence, where
perturbative fluctuations about the vacuum determine perturbative fluctuations
about non-perturbative saddles.
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Electric Chern-Simons term, enlarged exotic Galilei symmetry and
noncommutative plane: The extended exotic planar model for a charged particle is constructed. It
includes a Chern-Simons-like term for a dynamical electric field, but produces
usual equations of motion for the particle in background constant uniform
electric and magnetic fields. The electric Chern-Simons term is responsible for
the non-commutativity of the boost generators in the ten-dimensional enlarged
exotic Galilei symmetry algebra of the extended system. The model admits two
reduction schemes by the integrals of motion, one of which reproduces the usual
formulation for the charged particle in external constant electric and magnetic
fields with associated field-deformed Galilei symmetry, whose commuting boost
generators are identified with the nonlocal in time Noether charges reduced
on-shell. Another reduction scheme, in which electric field transmutes into the
commuting space translation generators, extracts from the model a free particle
on the noncommutative plane described by the two-fold centrally extended
Galilei group of the non-relativistic anyons.
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Bell violation in $2\rightarrow 2$ scattering in photon, gluon and
graviton EFTs: In this paper, we explore Bell inequality violation for $2\rightarrow2$
scattering in Effective Field Theories (EFTs) of photons, gluons, and
gravitons. Using the CGLMP Bell parameter ($I_2$), we show that, starting from
an appropriate initial non-product state, the Bell inequality can always be
violated in the final state (i.e.,$I_2 >2$) at least for some scattering angle.
For an initial product state, we demonstrate that abelian gauge theories behave
qualitatively differently than non-abelian gauge theories (or Gravity) from the
point of view of Bell violation in the final state: in the non-abelian case,
Bell violation ($I_2>2$) is never possible within the validity of EFTs for
weakly coupled UV completions. Interestingly, we also find that, for a
maximally entangled initial state, scattering can reduce the degree of
entanglement only for CP-violating theories. Thus Bell violation in
$2\rightarrow2$ scattering can, in principle, be used to classify CP conserving
vs violating theories.
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Greybody factors for a minimally coupled massless scalar field in
Einstein-Born-Infeld dilaton spacetime: We have analyzed in detail the propagation of a minimally coupled massless
scalar field in the gravitational background of a four-dimensional
Einstein-Born-Infeld dilaton charged black hole. We have obtained analytical
expressions for the absorption cross section as well as for the decay rate for
the scalar field in the aforementioned spacetime, and we have shown graphically
its behavior for different values of the free parameters of the theory.
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Quantum Group Symmetries in Conformal Field Theory: Quantum groups play the role of hidden symmetries of some two-dimensional
field theories. We discuss how they appear in this role in the
Wess-Zumino-Witten model of conformal field theory.
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More AdS_3 correlators: We compute three-point functions for the $SL(2,\mathbb R)$-WZNW model. After
reviewing the case of the two-point correlator, we compute spectral flow
preserving and nonpreserving correlation functions in the space-time picture
involving three vertex operators carrying an arbitrary amount of spectral flow.
When only one or two insertions have nontrivial spectral flow numbers, the
method we employ allows us to find expressions without any constraint on the
spin values. Unlike these cases, the same procedure restrains the possible spin
configurations when three vertices belong to nonzero spectral flow sectors. We
perform several consistency checks on our results. In particular, we verify
that they are in complete agreement with previously computed correlators
involving states carrying a single unit of spectral flow.
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On the effective potential for Horava-Lifshitz-like theories with the
arbitrary critical exponent: We calculate the one-loop effective potential for Horava-Lifshitz-like QED
and Yukawa-like theory for arbitrary values of the critical exponent and the
space-time dimension.
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Maxwell Chern Simons Theory in a Geometric Representation: We quantize the Maxwell Chern Simons theory in a geometric representation
that generalizes the Abelian Loop Representation of Maxwell theory. We find
that in the physical sector, the model can be seen as the theory of a massles
scalar field with a topological interaction that enforces the wave functional
to be multivalued. This feature allows to relate the Maxwell Chern Simons
theory with the quantum mechanics of particles interacting through a Chern
Simons field
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AdS/CFT Correspondence, Critical Strings and Stochastic Quantization: We show that dilaton beta-function equation in the brane-like sigma-model
(regarded as NSR analogue of string theory on $AdS_5\times{S^5}$) has the form
of stochastic Langevin equation with non-Markovian noise. The worldsheet cutoff
is identified with stochastic time and the $V_5$-operator plays the role of the
noise. We derive the Fokker-Planck equation associated with this stochastic
process and show that the Hamiltonian of the $AdS_5$ supergravity defines the
distribution satisfying this Fokker-Planck equation. This means that the
dynamical compactification of flat ten-dimensional space-time on
$AdS_5\times{S^5}$ occurs as a result of the non-Markovian stochastic process,
generated by the $V_5$-operator noise. This provides us with an insight into
relation between holography principle and the concept of stochastic
quantization from the point of view of critical string theory.
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Chiral Dynamics in Weak, Intermediate, and Strong Coupling QED in Two
Dimensions: N flavor QED in two dimensions is reduced to a quantum mechanics problem with
N degrees of freedom for which the potential is determined by the ground state
of the problem itself. The chiral condensate is determined at all values of
temperature, fermion masses, and the $\theta$ parameter. In the single flavor
case, the anomalous mass (m) dependence of the chiral condensate at
$\theta=\pi$ at low temperature is found. The critical value is given by $m_c
\sim .437 e/\sqrt{\pi}$.
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Nonlinear supersymmetry in the quantum Calogero model: It is long known that the rational Calogero model describing n identical
particles on a line with inverse-square mutual interaction potential is quantum
superintegrable. We review the (nonlinear) algebra of the conserved quantum
charges and the intertwiners which relate the Liouville charges at couplings g
and g+1. For integer values of g, these intertwiners give rise to additional
conserved charges commuting with all Liouville charges and known since the
1990s. We give a direct construction of such a charge, the unique one being
totally antisymmetric under particle permutations. It is of order
n(n-1)(2g-1)/2 in the momenta and squares to a polynomial in the Liouville
charges. With a natural Z_2 grading, this charge extends the algebra of
conserved charges to a nonlinear supersymmetric one. We provide explicit
expressions for intertwiners, charges and their algebra in the cases of two,
three and four particles.
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Rolling down to D-brane and tachyon matter: We investigate the spatially inhomogeneous decay of an unstable D-brane and
construct an asymptotic solution which describes a codimension one D-brane and
the tachyon matter in boundary string field theory. In this solution, the
tachyon matter exists around the lower-dimensional D-brane.
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F-term Stabilization of Odd Axions in LARGE Volume Scenario: In the context of the LARGE volume scenario, stabilization of axionic moduli
is revisited. This includes both even and odd axions with their scalar
potential being generated by F-term contributions via various tree-level and
non-perturbative effects like fluxed E3-brane instantons and fluxed
poly-instantons. In all the cases, we estimate the decay constants and masses
of the axions involved.
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Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on
K3: We investigate certain fixed points in the boundary conformal field theory
representation of type IIA D-branes on Gepner points of K3. They correspond
geometrically to degenerate brane configurations, and physically lead to
enhanced gauge symmetries on the world-volume. Non-abelian gauge groups arise
if the stabilizer group of the fixed points is realized projectively, which is
similar to D-branes on orbifolds with discrete torsion. Moreover, the fixed
point boundary states can be resolved into several irreducible components.
These correspond to bound states at threshold and can be viewed as (non-locally
free) sub-sheaves of semi-stable sheaves. Thus, the BCFT fixed points appear to
carry two-fold geometrical information: on the one hand they probe the boundary
of the instanton moduli space on K3, on the other hand they probe discrete
torsion in D-geometry.
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Ekpyrotic Reheating and Fate of Inflaton: It is shown that perturbative reheating can reach a sufficiently high
temperature with small or negligible inflaton decay rate provided that the
inflaton potential becomes negative after inflation. In our model, inflaton and
dark energy field are two independent scalar fields, and, depending on the mass
of the inflaton and its coupling to matter fields, there is a possibility that
the remaining inflaton after reheating can become a dark matter candidate.
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Sfermions and gauginos in a Lorentz-violating theory: In Lorentz-violating supergravity, sfermions have spin 1/2 and other unusual
properties. If the dark matter consists of such particles, there is a natural
explanation for the apparent absence of cusps and other small scale structure:
The Lorentz-violating dark matter is cold because of the large particle mass,
but still moves at nearly the speed of light. Although the R-parity of a
sfermion, gaugino, or gravitino is +1 in the present theory, these particles
have an "S-parity'' which implies that the LSP is stable and that they are
produced in pairs. On the other hand, they can be clearly distinguished from
the superpartners of standard supersymmetry by their highly unconventional
properties.
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Non-local Lagrangian Mechanics: Noether theorem and Hamiltonian
formalism: We study Lagrangian systems with a finite number of degrees of freedom that
are non-local in time. We obtain an extension of Noether theorem and Noether
identities to this kind of Lagrangians. A Hamiltonian formalism is then set up
for this systems. $n$-order local Lagrangians can be treated as a particular
case and the standard results for them are recovered. The method is then
applied to several other cases, namely two examples of non-local oscillators
and the p-adic particle.
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Holographic Bubbles with Jecco: Expanding, Collapsing and Critical: Cosmological phase transitions can proceed via the nucleation of bubbles that
subsequently expand and collide. The resulting gravitational wave spectrum
depends crucially on the properties of these bubbles. We extend our previous
holographic work on planar bubbles to circular bubbles in a strongly-coupled,
non-Abelian, four-dimensional gauge theory. This extension brings about two new
physical properties. First, the existence of a critical bubble, which we
determine. Second, the bubble profile at late times exhibits a richer
self-similar structure, which we verify. These results require a new 3+1
evolution code called Jecco that solves the Einstein equations in the
characteristic formulation in asymptotically AdS spaces. Jecco is written in
the Julia programming language and is freely available. We present an outline
of the code and the tests performed to assess its robustness and performance.
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Open group transformations: Open groups whose generators are in arbitrary involutions may be quantized
within a ghost extended framework in terms of a nilpotent BFV-BRST charge
operator. Previously we have shown that generalized quantum Maurer-Cartan
equations for arbitrary open groups may be extracted from the quantum
connection operators and that they also follow from a simple quantum master
equation involving an extended nilpotent BFV-BRST charge and a master charge.
Here we give further details of these results. In addition we establish the
general structure of the solutions of the quantum master equation. We also
construct an extended formulation whose properties are determined by the
extended BRST charge in the master equation.
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Analyticity and Crossing Symmetry of Superstring Loop Amplitudes: Bros, Epstein and Glaser proved crossing symmetry of the S-matrix of a theory
without massless fields by using certain analyticity properties of the
off-shell momentum space Green's function in the complex momentum plane. The
latter properties follow from representing the momentum space Green's function
as Fourier transform of the position space Green's function, satisfying certain
properties implied by the underlying local quantum field theory. We prove the
same analyticity properties of the momentum space Green's functions in
superstring field theory by directly working with the momentum space Feynman
rules even though the corresponding properties of the position space Green's
function are not known. Our result is valid to all orders in perturbation
theory, but requires, as usual, explicitly subtracting / regulating the
non-analyticities associated with massless particles. These results can also be
used to prove other general analyticity properties of the S-matrix of
superstring theory.
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Fusion rules and macroscopic loops from discretized approach to
two-dimensional gravity: We investigate the multi-loop correlators and the multi-point functions for
all of the scaling operators in unitary minimal conformal models coupled to
two-dimensional gravity from the two-matrix model. We show that simple fusion
rules for these scaling operators exist, and these are summarized in a compact
form as fusion rules for loops. We clarify the role of the boundary operators
and discuss its connection to how loops touch each other. We derive a general
formula for the n-resolvent correlators, and point out the structure similar to
the crossing symmetry of underlying conformal field theory. We discuss the
connection of the boundary conditions of the loop correlators to the touching
of loops for the case of the four-loop correlators.
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Noncommutative relativistic particles: We present a relativistic formulation of noncommutative mechanics were the
object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent
quantity. Its canonical conjugate momentum is also introduced, what permits to
obtain an explicit form for the generators of the Lorentz group in the
noncommutative case. The theory, which is invariant under reparametrization,
generalizes recent nonrelativistic results. Free noncommutative bosonic
particles satisfy an extended Klein-Gordon equation depending on two
parameters.
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Minimal models of field theories: SDYM and SDGR: There exists a natural $L_\infty$-algebra or $Q$-manifold that can be
associated to any (gauge) field theory. Perturbatively, it can be obtained by
reducing the $L_\infty$-algebra behind the jet space BV-BRST formulation to its
minimal model. We explicitly construct the minimal models of self-dual
Yang-Mills and self-dual gravity theories, which also represents their
equations of motion as Free Differential Algebras. The minimal model regains
all relevant information about the field theory, e.g. actions, charges,
anomalies, can be understood in terms of the corresponding $Q$-cohomology.
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Time-Dependent Hartree-Fock Solution of Gross-Neveu models: Twisted Kink
Constituents of Baryons and Breathers: We find the general solution to the time-dependent Hartree-Fock problem for
the Gross-Neveu models, with both discrete (GN2) and continuous (NJL2) chiral
symmetry. We find new multi-baryon, multi-breather and twisted breather
solutions, and show that all GN2 baryons and breathers are composed of
constituent twisted kinks of the NJL2 model.
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BMS modular covariance and structure constants: Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs
algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein
gravity in 3d asymptotically flat spacetimes. When defined on a torus, these
field theories come equipped with a modified modular structure. We use the
modular covariance of the BMS torus two-point function to develop formulae for
different three-point structure constants of the field theory. These structure
constants indicate that BMSFTs follow the eigenstate thermalization hypothesis,
albeit with some interesting changes to usual 2d CFTs. The singularity
structures of the structure constants contain information on perturbations of
cosmological horizons in 3d asymptotically flat spacetimes, which we show can
also be obtained as a limit of BTZ quasinormal modes.
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Tensor Perturbations from Bounce Inflation Scenario in f(Q) Gravity: In this paper, we construct a bounce inflation cosmological scenario in the
framework of the modified symmetric teleparallel gravity, namely f(Q) theory,
and investigate the tensor perturbations therein. As is well-known, the tensor
perturbations generated in the very early Universe (inflation and pre-inflation
regions) can account for the primordial gravitational waves (PGWs) that are to
be detected by the next generation of GW experiments. We discuss the stability
condition of the tensor perturbations in the bounce inflation process and
investigate in detail the evolution of the perturbation variable. The general
form of the tensor power spectrum is obtained both for large as well as small
scale modes. As a result, we show for both kinds of modes (short or long
wavelength modes), and the tensor spectrum may get a positive tilt in the
parametric range where the tensor perturbation proves to be stable -- this
interestingly hints an enhancement of gravitational waves' amplitude in the
background of the f(Q) bounce-inflation scenario. Moreover, we study the
LQC-like scenario as a specific case of our model, in which, the primordial
tensor power spectrum turns out to be nearly scale-invariant on both small and
large scales.
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Gravitons as super-strong interacting particles, and low-energy quantum
gravity: It is shown by the author that if gravitons are super-strong interacting
particles and the low-temperature graviton background exists, the basic
cosmological conjecture about the Dopplerian nature of redshifts may be false.
In this case, a full magnitude of cosmological redshift would be caused by
interactions of photons with gravitons. A new dimensional constant which
characterizes one act of interaction is introduced and estimated. Non-forehead
collisions with gravitons will lead to a very specific additional relaxation of
any photonic flux. It gives a possibility of another interpretation of
supernovae 1a data - without any kinematics. Of course, all of these facts may
implicate a necessity to change the standard cosmological paradigm. Some
features of a new paradigm are discussed here, too. A quantum mechanism of
classical gravity based on an existence of this sea of gravitons is described
for the Newtonian limit. This mechanism needs graviton pairing and "an atomic
structure" of matter for working it, and leads to the time asymmetry. If the
considered quantum mechanism of classical gravity is realized in the nature,
than an existence of black holes contradicts to Einstein's equivalence
principle. It is shown that in this approach the two fundamental constants -
Hubble's and Newton's ones - should be connected between themselves. The
theoretical value of the Hubble constant is computed. In this approach, every
massive body would be decelerated due to collisions with gravitons that may be
connected with the Pioneer 10 anomaly. It is shown that the predicted and
observed values of deceleration are in good agreement. Some unsolved problems
are discussed, so as possibilities to verify some conjectures in laser-based
experiments.
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"Double-trace" Deformations, Boundary Conditions and Spacetime
Singularities: Double-trace deformations of the AdS/CFT duality result in a new perturbation
expansion for string theory, based on a non-local worldsheet. We discuss some
aspects of the deformation in the low energy gravity approximation, where it
appears as a change in the boundary condition of fields. We relate unique
features of the boundary of AdS to the worldsheet becoming non-local, and
conjecture that non-local worldsheet actions may be generic in other classes of
backgrounds.
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On Solvable Time-Dependent Model and Rolling Closed String Tachyon: We investigate the SL(2,R)/U(1) WZW model with level 0<k<2 as a solvable
time-dependent background in string theory. This model is expected to be dual
to the one describing a rolling closed string tachyon with a time-like linear
dilaton. We examine its exact metric and minisuperspace wave functions. Two
point functions and the one-loop vacuum amplitude are computed and their
relation to the closed string emission is discussed. Comparing with the results
from the minisuperspace approximation, we find a physical interpretation of our
choice to continue the Euclidean model into the Lorentzian one. Three point
functions are also examined.
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Gauge Field Improvement,Form-Scalar Duality and Conformal Invariance: The problem of maintaining scale and conformal invariance in Maxwell and
general N-form gauge theories away from their critical dimension d=2(N+1) is
analyzed.We first exhibit the underlying group-theoretical clash between
locality,gauge,Lorentz and conformal invariance require- ments. "Improved"
traceless stress tensors are then constructed;each violates one of the above
criteria.However,when d=N+2,there is a duality equivalence between N-form
models and massless scalars.Here we show that conformal invariance is not
lost,by constructing a quasilocal gauge invariant improved stress tensor.The
correlators of the scalar theory are then reproduced,including the latter's
trace anomaly.
|
Topologically Massive Gauge Theory with O(2) Symmetry: We discuss the structure of the vacua in $O(2)$ topologically massive gauge
theory on a torus. Since $O(2)$ has two connected components, there are four
classical vacua. The different vacua impose different boundary conditions on
the gauge potentials. We also discuss the non-perturbative transitions between
the vacua induced by vortices of the theory.
|
Smallest Dirac Eigenvalue Distribution from Random Matrix Theory: We derive the hole probability and the distribution of the smallest
eigenvalue of chiral hermitian random matrices corresponding to Dirac operators
coupled to massive quarks in QCD. They are expressed in terms of the QCD
partition function in the mesoscopic regime. Their universality is explicitly
related to that of the microscopic massive Bessel kernel.
|
Analytical Bethe Ansatz for Quantum-Algebra-Invariant Spin Chains: We have recently constructed a large class of open quantum spin chains which
have quantum-algebra symmetry and which are integrable. We show here that these
models can be exactly solved using a generalization of the analytical Bethe
Ansatz (BA) method. In particular, we determine in this way the spectrum of the
transfer matrices of the $U_q [(su(2)]$-invariant spin chains associated with
$A^{(1)}_1$ and $A^{(2)}_2$ in the fundamental representation. The
quantum-algebra invariance of these models plays an essential role in obtaining
these results. The BA equations for these open chains are ``doubled'' with
respect to the BA equations for the corresponding closed chains.
|
Self-Duality, Ramond-Ramond Fields, and K-Theory: Just as D-brane charge of Type IIA and Type IIB superstrings is classified,
respectively, by K^1(X) and K(X), Ramond-Ramond fields in these theories are
classified, respectively, by K(X) and K^1(X). By analyzing a recent proposal
for how to interpret quantum self-duality of RR fields, we show that the Dirac
quantization formula for the RR p-forms, when properly formulated, receives
corrections that reflect curvature, lower brane charges, and an anomaly of
D-brane world-volume fermions. The K-theory framework is important here,
because the term involving the fermion anomaly cannot be naturally expressed in
terms of cohomology and differential forms.
|
Gukov-Pei-Putrov-Vafa conjecture for $SU(N)/\mathbb{Z}_m$: In our earlier work, we studied the $\hat{Z}$-invariant(or homological
blocks) for $SO(3)$ gauge group and we found it to be same as
$\hat{Z}^{SU(2)}$. This motivated us to study the $\hat{Z}$-invariant for
quotient groups $SU(N)/\mathbb{Z}_m$, where $m$ is some divisor of $N$.
Interestingly, we find that $\hat{Z}$-invariant is independent of $m$.
|
$1/N$ correction in holographic Wilson loop from quantum gravity: We study $1/N$ corrections to a Wilson loop in holographic duality. Extending
the AdS/CFT correspondence beyond the large $N$ limit is an important but a
subtle issue, as it needs quantum gravity corrections in the gravity side. To
find a physical property of the quantum corrected geometry of near-horizon
black 0-branes previously obtained by Hyakutake, we evaluate a Euclidean string
worldsheet hanging down in the geometry, which corresponds to a rectangular
Wilson loop in the $SU(N)$ quantum mechanics with 16 supercharges at a finite
temperature with finite $N$. We find that the potential energy defined by the
Wilson loop increases due to the $1/N$ correction, therefore the quantum
gravity correction weakens the gravitational attraction.
|
On the Instanton Contributions to the Masses and Couplings of $E_6$
Singlets: We consider the gauge neutral matter in the low--energy effective action for
string theory compactification on a \cym\ with $(2,2)$ world--sheet
supersymmetry. At the classical level these states (the \sing's of $E_6$)
correspond to the cohomology group $H^1(\M,{\rm End}\>T)$. We examine the first
order contribution of instantons to the mass matrix of these particles. In
principle, these corrections depend on the \K\ parameters $t_i$ through factors
of the form $e^{2\p i t_i}$ and also depend on the complex structure
parameters. For simplicity we consider in greatest detail the quintic threefold
$\cp4[5]$. It follows on general grounds that the total mass is often, and
perhaps always, zero. The contribution of individual instantons is however
nonzero and the contribution of a given instanton may develop poles associated
with instantons coalescing for certain values of the complex structure. This
can happen when the underlying \cym\ is smooth. Hence these poles must cancel
between the coalescing instantons in order that the superpotential be finite.
We examine also the \Y\ couplings involving neutral matter \ysing\ and neutral
and charged fields \ymix, which have been little investigated even though they
are of phenomenological interest. We study the general conditions under which
these couplings vanish classically. We also calculate the first--order
world--sheet instanton correction to these couplings and argue that these also
vanish.
|
The Conformal Limit of Inflation in the Era of CMB Polarimetry: We argue that the non-detection of primordial tensor modes has taught us a
great deal about the primordial universe. In single-field slow-roll inflation,
the current upper bound on the tensor-to-scalar ratio, $r < 0.07$ $(95 \%
~CL)$, implies that the Hubble slow-roll parameters obey $\varepsilon \ll
\eta$, and therefore establishes the existence of a new hierarchy. We dub this
regime the conformal limit of (slow-roll) inflation, and show that it includes
Starobinsky-like inflation as well as all viable single-field models with a
sub-Planckian field excursion. In this limit, all primordial correlators are
constrained by the full conformal group to leading non-trivial order in
slow-roll. This fixes the power spectrum and the full bispectrum, and leads to
the "conformal" shape of non-Gaussianity. The size of non-Gaussianity is
related to the running of the spectral index by a consistency condition, and
therefore it is expected to be small. In passing, we clarify the role of
boundary terms in the $\zeta$ action, the order to which constraint equations
need to be solved, and re-derive our results using the Wheeler-deWitt
formalism.
|
The role of singular spinor fields in a torsional gravity,
Lorentz-violating, framework: In this work, we consider a generalization of quantum electrodynamics
including Lorentz violation and torsional-gravity, in the context of general
spinor fields as classified in the Lounesto scheme. Singular spinor fields will
be shown to be less sensitive to the Lorentz violation, as far as couplings
between the spinor bilinear covariants and torsion are regarded. In addition,
we prove that flagpole spinor fields do not admit minimal coupling to the
torsion. In general, mass dimension four couplings are deeply affected when
singular flagpole spinors are considered, instead of the usual Dirac spinors.
We also construct a mapping between spinors in the covariant framework and
spinors in Lorentz symmetry breaking scenarios, showing how one may
transliterate spinors of different classes between the two cases. Specific
examples concerning the mapping of Dirac spinor fields in Lorentz violating
scenarios into flagpole and flag-dipole spinors with full Lorentz invariance
(including the cases of Weyl and Majorana spinors) are worked out.
|
A Small Deformation of a Simple Theory: We study an interesting relevant deformation of the simplest interacting N=2
SCFT---the original Argyres-Douglas (AD) theory. We argue that, although this
deformation is not strictly speaking Banks-Zaks like (certain operator
dimensions change macroscopically), there are senses in which it constitutes a
mild deformation of the parent AD theory: the exact change in the "a" anomaly
is small and is essentially saturated at one loop. Moreover, contributions from
IR operators that have a simple description in the UV theory reproduce a
particular limit of the IR index to a remarkably high order. These results lead
us to conclude that the IR theory is an interacting N=1 SCFT with particularly
small "a" and "c" central charges and that this theory sheds some interesting
light on the spectrum of its AD parent.
|
Hopf algebra of graphs and the RG equations: We study the renormalization group equations following from the Hopf algebra
of graphs. Vertex functions are treated as vectors in dual to the Hopf algebra
space. The RG equations on such vertex functions are equivalent to RG equations
on individual Feynman integrals. The solution to the RG equations may be
represented as an exponent of the beta-function. We explicitly show that the
exponent of the one-loop beta function enables one to find the coefficients in
front of the leading logarithms for individual Feynman integrals. The same
results are obtained in parquet approximation.
|
BMS in Cosmology: Symmetries play an interesting role in cosmology. They are useful in
characterizing the cosmological perturbations generated during inflation and
lead to consistency relations involving the soft limit of the statistical
correlators of large-scale structure dark matter and galaxies overdensities. On
the other hand, in observational cosmology the carriers of the information
about these large-scale statistical distributions are light rays traveling on
null geodesics. Motivated by this simple consideration, we study the structure
of null infinity and the associated BMS symmetry in a cosmological setting. For
decelerating Friedmann-Robertson-Walker backgrounds, for which future null
infinity exists, we find that the BMS transformations which leaves the
asymptotic metric invariant to leading order. Contrary to the asymptotic flat
case, the BMS transformations in cosmology generate Goldstone modes
corresponding to both scalar and tensor degrees of freedom which may exist at
null infinity and perturb the asymptotic data. Therefore, BMS transformations
generate physically inequivalent vacua as they populate the universe at null
infinity with these physical degrees of freedom. We also discuss the
gravitational memory effect when cosmological expansion is taken into account.
In this case, there are extra contribution to the gravitational memory due to
the tail of the retarded Green functions which are supported not only on the
light-cone, but also in its interior. The gravitational memory effect can be
understood also from an asymptotic point of view as a transition among
cosmological BMS-related vacua.
|
Dressed Minimal Surfaces in AdS$_4$: We apply an arbitrary number of dressing transformations to a static minimal
surface in AdS(4). Interestingly, a single dressing transformation, with the
simplest dressing factor, interrelates the latter to solutions of the Euclidean
non linear sigma model in dS(3). We present an expression for the area element
of the dressed minimal surface in terms of that of the initial one and comment
on the boundary region of the dressed surface. Finally, we apply the above
formalism to the elliptic minimal surfaces and obtain new ones.
|
Families index theorem in supersymmetric WZW model and twisted K-theory:
The SU(2) case: The construction of twisted K-theory classes on a compact Lie group is
reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The
Quillen superconnection is introduced for a family of supercharges parametrized
by a compact Lie group and the Chern character is explicitly computed in the
case of SU(2). For large euclidean time, the character form is localized on a
D-brane.
|
On Limit Cycles in Supersymmetric Theories: Contrary to popular belief conformality does not require zero beta functions.
This follows from the work of Jack and Osborn, and examples in
non-supersymmetric theories were recently found by some of us. In this note we
show that such examples are absent in unitary N=1 supersymmetric
four-dimensional field theories. More specifically, we show to all orders in
perturbation theory that the beta-function vector field of such theories does
not admit limit cycles. A corollary of our result is that unitary N=1
supersymmetric four-dimensional theories cannot be superscale-invariant without
being superconformal.
|
Density matrix of a quantum field in a particle-creating background: We consider the time evolution of a quantized field in backgrounds that
violate the vacuum stability (particle-creating backgrounds). Our aim is to
study the exact form of the final quantum state (the density operator at a
final instant of time) that has emerged from a given arbitrary initial state
(from a given arbitrary density operator at the initial time instant) in the
course of the evolution. We find a generating functional that allows us to have
the density operators for any initial state. Averaging over states of a
subsystem of antiparticles (particles), we obtain explicit forms for reduced
density operators for subsystems of particles (antiparticles). Studying
one-particle correlation functions, we establish a one-to-one correspondence
between these functions and the reduced density operators. It is shown that in
the general case a presence of bosons (e.g. gluons) in an initial state
increases the creation rate of the same kind of bosons. We discuss the question
(and its relation to the initial stage of quark-gluon plasma formation) whether
a thermal form of one-particle distribution can appear even if the final state
of the complete system is not a thermal equilibrium. In this respect, we
discuss some cases when a pair creation by an electric-like field can mimic a
one-particle thermal distribution. We apply our technics to some QFT problems
in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric,
and metric. In particular, we study the time and temperature behavior of mean
numbers of created particles provided switching on and off effects of the
external field are negligible. It is shown that at high temperatures and in
slowly varying electric fields the rate of particle creation is essentially
time-dependent.
|
A note on generalized electrodynamics: The generalized Maxwell equations with arbitrary gauge parameter are
considered in the $11\times 11$-matrix form. The gauge invariance of such a
model is broken due to the presence of a scalar field. The canonical and
symmetrical Belinfante energy-momentum tensors are found. The dilatation
current is obtained and we demonstrate that the theory possesses the dilatation
symmetry. The matrix Schr\"{o}dinger form of equations is derived. The
non-minimal interaction in curved space-time is introduced and equations are
considered in Friedmann - Robertson - Walker background. We obtain some
solutions of equations for the vector field.
|
Quantum theory, thermal gradients and the curved Euclidean space: The Euclidean space, obtained by the analytical continuation of time, to an
imaginary time, is used to model thermal systems. In this work, it is taken a
step further to systems with spatial thermal variation, by developing an
equivalence between the spatial variation of temperature in a thermal bath and
the curvature of the Euclidean space. The variation in temperature is recast as
a variation in the metric, leading to a curved Euclidean space. The equivalence
is substantiated by analyzing the Polyakov loop, the partition function and the
periodicity of the correlation function. The bulk thermodynamic properties like
the energy, entropy and the Helmholtz free energy are calculated from the
partition function, for small metric perturbations, for a neutral scalar field.
The Dirac equation for an external Dirac spinor, traversing in a thermal bath
with spatial thermal gradients, is solved in the curved Euclidean space. The
fundamental behavior exhibited by the Dirac spinor eigenstate, may provide a
possible mechanism to validate the theory, at a more basal level, than
examining only bulk thermodynamic properties. Furthermore, in order to verify
the equivalence at the level of classical mechanics, the geodesic equation is
analyzed in a classical backdrop. The mathematical apparatus is borrowed from
the physics of quantum theory in a gravity-induced space-time curvature. As
spatial thermal variations are obtainable at QCD or QED energies, it may be
feasible for the proposed formulation to be validated experimentally.
|
Gauge Theoretic Formulation of Dilatonic Gravity Coupled to Particles: We discuss the formulation of the CGHS model in terms of a topological BF
theory coupled to particles carrying non-Abelian charge.
|
Toward Bound-State Approach to Strangeness in Holographic QCD: An approach to realize a hyperon as a bound-state of a two-flavor baryon and
a kaon is considered in the context of the Sakai-Sugimoto model of holographic
QCD, which approach has been known in the Skyrme model as the bound-state
approach to strangeness. As a simple case of study, pseudo-scalar kaon is
considered as fluctuation around a baryon. In this case, strongly-bound
hyperon-states are absent, different from the case of the Skyrme model.
Observed is a weak bound-state which would correspond to \Lambda(1405).
|
What can we learn from Knizhnik--Zamolodchikov Equations?: We discuss structural similarities between Knizhnik--Zamolodchikov equations
(in fact, their simplest version needed to introduce the Drinfeld associator)
and Dyson--Schwinger equations. We emphasize that the latter allow for a
filtration by co-radical degree using quasi-shuffle products and the lower
central series filtration of the Lie algebra of Feynman graphs. This clarifies
how they are a generalization of the KZ equations. This is a starting point for
a algebraic organization of the next-to...-to leading log expansion which has
been worked out in collaboration with Olaf Krueger and which will be given
elsewhere [1,2].
|
Dynamical equivalence, commutation relations and noncommutative geometry: We revisit Wigner's question about the admissible commutation relations for
coordinate and velocity operators given their equations of motion (EOM). In
more general terms we want to consider the question of how to quantize
dynamically equivalent Hamiltonian structures. A unique answer can presumably
be given in those cases, where we have a dynamical symmetry. In this case
arbitrary deformations of the symmetry algebra should be dynamically
equivalent. We illustrate this for the linear as well as the singular
1d-oscillator. In the case of nonlinear EOM quantum corrections have to be
taken into account. We present some examples thereof New phenomena arise in
case of more then one degree of freedom, where sometimes the interaction can be
described either by the Hamiltonian or by nonstandard commutation relations.
This may induce a noncommutative geometry (for example the 2d-oscillator in a
constant magnetic field). Also some related results from nonrelativistic
quantum field theory applied to solid state physics are briefly discussed
within this framework
|
Zero-mode wave functions by localized gauge fluxes: We study chiral zero-mode wave functions on blow-up manifolds of $T^2/Z_N$
orbifolds with both bulk and localized magnetic flux backgrounds. We introduce
a singular gauge transformation in order to remove $Z_N$ phases for $Z_N$
twisted boundary condition of matter fields. We compute wave functions of not
only bulk zero modes but also localized modes at the orbifold singular points,
which correspond to new zero modes induced by localized flux. By studying their
Yukawa couplings, it turns out that only three patterns of Yukawa couplings are
allowed. Our theory has a specific coupling selection rule.
|
New Vacua of Gauged N=8 Supergravity: We analyze a particular SU(2) invariant sector of the scalar manifold of
gauged N=8 supergravity in five dimensions, and find all the critical points of
the potential within this sector. The critical points give rise to Anti-de
Sitter vacua, and preserve at least an SU(2) gauge symmetry. Consistent
truncation implies that these solutions correspond to Anti-de Sitter
compactifications of IIB supergravity, and hence to possible near-horizon
geometries of 3-branes. Thus we find new conformal phases of softly broken N=4
Yang--Mills theory. One of the critical points preserves N=2 supersymmetry in
the bulk and is therefore completely stable, and corresponds to an N=1
superconformal fixed point of the Yang--Mills theory. The corresponding
renormalization group flow from the N=4 point has c_{IR}/c_{UV} = 27/32. We
also discuss the ten-dimensional geometries corresponding to these critical
points.
|
Renormalisability of the SU(n) Gauge Theory with Massive Gauge Bosons: The problem of renormalisability of the SU(n) theory with massive gauge
bosons is reinverstigated in the present work. We expound that the quantization
under the Lorentz condition caused by the mass term of the gauge fields leads
to a ghost action which is the same as that of the usual SU(n) Yang-Mills
theory in the Landau gauge. Furthermore, we clarify that the mass term of the
gauge fields cause no additional complexity to the Slavnov-Taylor identity of
the generating functional for the regular vertex functions and does not change
the equations satisfied by the divergent part of this generating functional.
Finally, we prove that the renormalisability of the theory can be deduced from
the renormalisability of the Yang-Mills theory.
|
On Parasupersymmetries in Relativistic Coulomb Problem for the Modified
Stueckelberg Equation: This paper presents a first example of parasupersymmetric relativistic
quantum-mechanical model with non-oscillator-like interaction: the Coulomb
problem for the modified Stueckelberg equation, describing a relativistic
massive spin-1 particle in the electromagnetic field of a point charge.
|
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