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NNLO BFKL Pomeron eigenvalue in N=4 SYM: We obtain an analytical expression for the Next-to-Next-to-Leading order of
the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4
using Quantum Spectral Curve (QSC) integrability based method. The result is
verified with more than 60 digits precision using the numerical method
developed by us in a previous paper. As a byproduct we developed a general
analytic method of solving the QSC perturbatively. | hep-th |
Quantum properties of the polytopic action in some simple geometries: The partition function corresponding to the "polytopic" action, a new action
for the gravitational interaction which we have proposed recently, is computed
in the simplest two-dimensional geometries of genus zero and one. The
functional integral over the Liouville field is approximated by an ordinary
integral over the constant zero mode. We study the dependence on both the
coupling constant and the cosmological constant, and compare with recent
scaling results in standard 2D quantum gravity. | hep-th |
On the density of states in a free CFT and finite volume corrections: Results from spectral geometry such as Weyl's formula can be used to relate
the thermodynamic properties of a free massless field to the spatial manifold
on which it is defined. We begin by calculating the free energy in two cases:
manifolds posessing a boundary and spheres. The subextensive contributions
allow us to test the Cardy-Verlinde formula and offer a new perspective on why
it only holds in a free theory if one allows for a change in the overall
coefficient. After this we derive an expression for the density of states that
takes the form of a Taylor series. This series leads to an improvement over
known results when the area of the manifold's boundary is nonzero but much less
than the appropriate power of its volume. | hep-th |
Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds: The problem of computing the anomalous dimensions of a class of (nearly)
half-BPS operators with a large R-charge is reduced to the problem of
diagonalizing a Cuntz oscillator chain. Due to the large dimension of the
operators we consider, non-planar corrections must be summed to correctly
construct the Cuntz oscillator dynamics. These non-planar corrections do not
represent quantum corrections in the dual gravitational theory, but rather,
they account for the backreaction from the heavy operator whose dimension we
study. Non-planar corrections accounting for quantum corrections seem to spoil
integrability, in general. It is interesting to ask if non-planar corrections
that account for the backreaction also spoil integrability. We find a limit in
which our Cuntz chain continues to admit extra conserved charges suggesting
that integrability might survive. | hep-th |
Quantum Background Independence of Closed String Field Theory: We prove local background independence of the complete quantum closed string
field theory using the recursion relations for string vertices and the
existence of connections in CFT theory space. Indeed, with this data we
construct an antibracket preserving map between the state spaces of two nearby
conformal theories taking the corresponding string field measures $d\mu
e^{2S/\hbar}$ into each other. A geometrical construction of the map is
achieved by introducing a Batalin-Vilkovisky (BV) algebra on spaces of Riemann
surfaces, together with a map to the BV algebra of string functionals. The
conditions of background independence show that the field independent terms of
the master action arise from vacuum vertices $\V_{g,0}$, and that the overall
$\hbar$-independent normalization of the string field measure involves the
theory space connection. Our result puts on firm ground the widely believed
statement that string theories built from nearby conformal theories are
different states of the same theory. | hep-th |
An explicit construction of Wakimoto realizations of current algebras: It is known from a work of Feigin and Frenkel that a Wakimoto type,
generalized free field realization of the current algebra $\widehat{\cal G}_k$
can be associated with each parabolic subalgebra ${\cal P}=({\cal G}_0+{\cal
G}_+)$ of the Lie algebra ${\cal G}$, where in the standard case ${\cal G}_0$
is the Cartan and ${\cal P}$ is the Borel subalgebra. In this letter we obtain
an explicit formula for the Wakimoto realization in the general case. Using
Hamiltonian reduction of the WZNW model, we first derive a Poisson bracket
realization of the ${\cal G}$-valued current in terms of symplectic bosons
belonging to ${\cal G}_+$ and a current belonging to ${\cal G}_0$. We then
quantize the formula by determining the correct normal ordering. We also show
that the affine-Sugawara stress-energy tensor takes the expected quadratic form
in the constituents. | hep-th |
Electrified branes: A geometrical form of the supersymmetry conditions for D-branes on arbitrary
type II supersymmetric backgrounds is derived, as well as the associated BPS
bounds. The treatment is general and allows to consider, for instance,
non-static configurations or D-branes supporting a non-vanishing electric flux,
hence completing previous partial results. In particular, our discussion
clarifies how the notion of calibration can be extended in order to be
applicable to the most general supersymmetric configurations. As an
exemplifying preliminary step, the procedure followed is first applied to
fundamental strings. | hep-th |
Simplifying the Tree-level Superstring Massless Five-point Amplitude: We use the pure spinor formalism to obtain the supersymmetric massless
five-point amplitude at tree-level in a streamlined fashion. We also prove the
equivalence of an OPE identity in string theory with a subset of the
Bern-Carrasco-Johansson five-point kinematic relations, and demonstrate how the
remaining BCJ identities follow from the different integration regions over the
open string world-sheet, therefore providing a first principles derivation of
the (supersymmetric) BCJ identities. | hep-th |
Exploring SU(3) Structure Moduli Spaces with Integrable G2 Structures: We study the moduli space of SU(3) structure manifolds X that form the
internal compact spaces in four-dimensional N=1/2 domain wall solutions of
heterotic supergravity with flux. Together with the direction perpendicular to
the four-dimensional domain wall, X forms a non-compact 7-manifold Y with
torsionful G2 structure. We use this G2 embedding to explore how X(t) varies
along paths C(t) in the SU(3) structure moduli space. Our analysis includes the
Bianchi identities which strongly constrain the flow. We show that requiring
that the SU(3) structure torsion is preserved along the path leads to
constraints on the G2 torsion and the embedding of X in Y. Furthermore, we
study flows along which the torsion classes of X go from zero to non-zero
values. In particular, we present evidence that the flow of half-flat SU(3)
structures may contain Calabi-Yau loci, in the presence of non-vanishing
H-flux. | hep-th |
Universality of the Holographic Angular Momentum Cutoff: The AdS/CFT dual description of a peripheral heavy ion collision involves an
asymptotically AdS rotating black hole. The explicitly known black holes of
this kind, with planar event horizon topology [the "KMV$_0$" spacetimes], have
been shown to be unstable when string-theoretic effects are taken into account.
It has been argued that this implies a "holographic" angular momentum cutoff
for peripheral collisions at very high energies. However, the KMV$_0$ black
hole corresponds to a specific velocity distribution in the aftermath of a
peripheral collision, and this distribution is not realistic at all points of
the interaction zone. It could therefore be argued that the angular momentum
cutoff is an artefact of this particular choice of bulk geometry. We
demonstrate that, on the contrary, a Quark-Gluon Plasma with any physically
reasonable internal velocity distribution corresponds to a black hole which is
still unstable, in the same way as the KMV$_0$ spacetime. The angular momentum
cutoff is therefore a universal prediction of the holographic description of
these collisions. | hep-th |
M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory: A self-contained review is given of the matrix model of M-theory. The
introductory part of the review is intended to be accessible to the general
reader. M-theory is an eleven-dimensional quantum theory of gravity which is
believed to underlie all superstring theories. This is the only candidate at
present for a theory of fundamental physics which reconciles gravity and
quantum field theory in a potentially realistic fashion. Evidence for the
existence of M-theory is still only circumstantial---no complete
background-independent formulation of the theory yet exists. Matrix theory was
first developed as a regularized theory of a supersymmetric quantum membrane.
More recently, the theory appeared in a different guise as the discrete
light-cone quantization of M-theory in flat space. These two approaches to
matrix theory are described in detail and compared. It is shown that matrix
theory is a well-defined quantum theory which reduces to a supersymmetric
theory of gravity at low energies. Although the fundamental degrees of freedom
of matrix theory are essentially pointlike, it is shown that higher-dimensional
fluctuating objects (branes) arise through the nonabelian structure of the
matrix degrees of freedom. The problem of formulating matrix theory in a
general space-time background is discussed, and the connections between matrix
theory and other related models are reviewed. | hep-th |
Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex
Models: Boundary conditions compatible with integrability are obtained for two
dimensional models by solving the factorizability equations for the reflection
matrices $K^{\pm}(\theta)$. For the six vertex model the general solution
depending on four arbitrary parameters is found. For the $A_{n-1}$ models all
diagonal solutions are found. The associated integrable magnetic Hamiltonians
are explicitly derived. | hep-th |
Symmetry enhancement in 4d Spin(n) gauge theories and compactification
from 6d: We consider a known sequence of dualities involving $4d$ ${\cal N}=1$
theories with $Spin(n)$ gauge groups and use it to construct a new sequence of
models exhibiting IR symmetry enhancement. Then, motivated by the observed
pattern of IR symmetries we conjecture six-dimensional theories the
compactification of which on a Riemann surface yields the $4d$ sequence of
models along with their symmetry enhancements, and put them to several
consistency checks. | hep-th |
An eight-dimensional approach to G_2 manifolds: We develop a systematic approach to G_2 holonomy manifolds with an
SU(2)xSU(2) isometry using maximal eight-dimensional gauged supergravity to
describe D6-branes wrapped on deformed three-spheres. A quite general metric
ansatz that generalizes the celebrated Bryant-Salamon metric involves nine
functions. We show that only six of them are the independent ones and derive
the general first order system of differential equations that they obey. As a
byproduct of our analysis, we generalize the notion of the twist that relates
the spin and gauge connections in a way that involves non-trivially the scalar
fields. | hep-th |
MHV-Vertices for Gravity Amplitudes: We obtain a CSW-style formalism for calculating graviton scattering
amplitudes and prove its validity through the use of a special type of
BCFW-like parameter shift. The procedure is illustrated with explicit examples. | hep-th |
Yukawa Corrections from Four-Point Functions in Intersecting D6-Brane
Models: We discuss corrections to the Yukawa matrices of the Standard Model (SM)
fermions in intersecting D-brane models due to four-point interactions.
Recently, an intersecting D-brane model has been found where it is possible to
obtain correct masses and mixings for all quarks as well as the tau lepton.
However, the masses for the first two charged leptons come close to the right
values but are not quite correct. Since the electron and muon are quite light,
it is likely that there are additional corrections to their masses which cannot
be neglected. With this in mind, we consider contributions to the SM fermion
mass matrices from four-point interactions. In an explicit model, we show that
it is indeed possible to obtain the SM fermion masses and mixings which are a
better match to those resulting from experimental data extrapolated at the
unification scale when these corrections are included. These corrections may
have broader application to other models. | hep-th |
Quantizing the non-linear graviton: We consider holomorphic Poisson-BF theory on twistor space. Classically, this
describes self-dual Einstein gravity on space-time, but at the quantum level it
is plagued by an anomaly. The anomaly corresponds to the fact that
integrability of the self-dual vacuum Einstein equations does not survive in
self-dual quantum gravity. We compute the anomaly polynomials in the Poisson-BF
theory, as well as in this theory coupled to a holomorphic BF theory on twistor
space describing self-dual Yang-Mills. We show that all anomalies may be
cancelled by further coupling to a twistor field representing a type of axion
on space-time. When the twistor anomalies are cancelled, all $n\geq4$-pt
amplitudes vanish and integrability is restored. | hep-th |
Superconducting Source of the Kerr-Newman Electron: Regular superconducting solution for interior of the Kerr-Newman (KN)
spinning particle is obtained. For parameters of electron it represents a
highly oblated rotating bubble formed by Higgs field which expels the
electromagnetic (em) field and currents from interior to domain wall boundary
of the bubble.
The external em and gravitational fields correspond exactly to Kerr-Newman
solution, while interior of the bubble is flat and forms a `false' vacuum with
zero energy density. Vortex of the KN em field forms a quantum Wilson loop on
the edge of the rotating disk-like bubble. | hep-th |
Area-preserving structure of 2d-gravity: The effective action for 2d-gravity with manifest area-preserving invariance
is obtained in the flat and in the general gravitational background. The
cocyclic properties of the last action are proved, and generalizations on
higher dimensions are discussed. | hep-th |
Electrically Charged Einstein-Born-Infeld Black Holes with Massive
Dilaton: We numerically construct static and spherically symmetric electrically
charged black hole solutions in Einstein-Born-Infeld gravity with massive
dilaton. The numerical solutions show that the dilaton potential allows many
more black hole causal structures than the massless dilaton. We find that
depending on the black hole mass and charge and the dilaton mass the black
holes can have either one, two, or three horizons. The extremal solutions are
also found out. As an interesting peculiarity we note that there are extremal
black holes with an inner horizon and with triply degenerated horizon. | hep-th |
Spontaneous symmetry breakings in the singlet scalar Yukawa model within
the auxiliary field method: The aim of this work is to investigate the occurrence of two different
spontaneous symmetry breakings {at} two levels of the description of
fermion-scalar field model, by means of a set of gap equations and {with} a
background field effective action. For that, we consider the Yukawa model, as a
toy model for interactions between non-massive fermions intermediated by a
self-interacting real scalar field. This model has at stakes two symmetries at
the classical level that, as we know, might be spontaneously or dynamically
broken with mass generation for the particles. The auxiliary field method is
considered and it produces coupled renormalized gap equations. The effective
action is then written with quantum contributions by {the} external background
{field} method. We brought to light how the renormalization procedure affects
the physical gaps, investigate its properties, and discuss the connection
between the auxiliary fields not only to define composite states but also to
compute the effective action. | hep-th |
3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes: We study CFT data of 3-dimensional superconformal field theories (SCFTs)
arising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via
so-called 3d/3d correspondence, central charges of these SCFTs are related to a
$SL(2)$ Chern-Simons (CS) invariant on the 3-manifolds. We give a rigorous
definition of the invariant in terms of resurgence theory and a state-integral
model for the complex CS theory. We numerically evaluate the central charges
for several closed 3-manifolds with small hyperbolic volume. The computation
suggests that the wrapped M5-brane systems give infinitely many discrete SCFTs
with small central charges. We also analyze these `minimal' SCFTs in the eye of
3d $\mathcal{N}=2$ superconformal bootstrap. | hep-th |
Superconformal Quantum Mechanics and the Discrete Light-Cone
Quantisation of N=4 SUSY Yang-Mills: We study the quantum mechanical sigma model arising in the discrete
light-cone quantisation of N=4 supersymmetric Yang-Mills theory. The target
space is a certain torus fibration over a scale-invariant special Kahler
manifold. We show that the expected SU(1,1|4) light-cone superconformal
invariance of the N=4 theory emerges in a limit where the volume of the fibre
goes to zero and give an explicit construction of the generators. The
construction given here yields a large new family of superconformal quantum
mechanical models with SU(1,1|4) invariance. | hep-th |
Geometric Transitions, Flops and Non-Kahler Manifolds: I: We construct a duality cycle which provides a complete supergravity
description of geometric transitions in type II theories via a flop in
M-theory. This cycle connects the different supergravity descriptions before
and after the geometric transitions. Our construction reproduces many of the
known phenomena studied earlier in the literature and allows us to describe
some new and interesting aspects in a simple and elegant fashion. A precise
supergravity description of new torsional manifolds that appear on the type IIA
side with branes and fluxes and the corresponding geometric transition are
obtained. A local description of new G_2 manifolds that are circle fibrations
over non-Kahler manifolds is presented. | hep-th |
Possible Effects of Spacetime Foam in Particle Physics: We present an extension of quantum field theory to the case when the
spacetime topology fluctuates (spacetime foam). In this extension the number of
bosonic fields becomes a variable and the ground state is characterized by a
finite particle number density. It is shown that when the number of fields
remains a constant, the standard field theory is restored. However, in the
complete theory the ground state has a nontrivial properties. In particular, it
produces an increase in the level of quantum fluctuations in the field
potentials and an additional renormalization of masses of particles. We examine
fluctuations of massless fields and show that in the presence of a temperature
(thermal state) these fluctuations has 1/f spectrum. Thus, the main prediction
of the theory is that our universe should be filled with a random
electromagnetic field which should produce an additional 1/f - noise in
electric circuits. | hep-th |
Color Current Induced by Gluon in Background Field Method of QCD: By using the background field method of QCD in a path integral approach, we
derive the equation of motion for the classical chromofield and for the gluon
in a system containing the gluon and the classical chromofield simultaneously.
This inhomogeneous field equation contains a current term, which is the
expectation value of a composite operator including linear, square and cubic
terms of the gluon field. We also derive identities which the current should
obey from the gauge invariance. We calculate the current at the leading order
where the current induced by the gluon is opposite in sign to that induced by
the quark. This is just the feature of the non-Abelian gauge field theory which
has asymptotic freedom. Physically, the induced current can be treated as the
'displacement' current in the polarized vacuum, and its effect is equivalent to
redefining the field and the coupling constant. | hep-th |
Shear viscosity of the $Φ^4$ theory from classical simulation: Shear viscosity of the classical $\Phi^4$ theory is measured using classical
microcanonical simulation. To calculate the Kubo formula, we measure the
energy-momentum tensor correlation function, and apply the Green-Kubo relation.
Being a classical theory, the results depend on the cutoff which should be
chosen in the range of the temperature. Comparison with experimentally
accessible systems is also performed. | hep-th |
Emergent gravity from off-shell energy fixing: Off-shell processes do not preserve the Energy Momentum Tensor (EMT) in QFT.
Fixing the EMT throughout off-shell processes, implies a graviton-like quantum
field to emerge without dynamics. Its dynamics are generated through quantum
corrections. This Fixed Off-Shell Energy Condition (FOSEC) implies the
existence of a linear gravity-like theory, and in special cases the full
Poincar\`e gauge theory. In this work it is shown that imposing the FOSEC in
QFT implies the emergence of a viable quantum theory of gravity. | hep-th |
Non-Minimal Warm Inflation and Perturbations on the Warped DGP Brane
with Modified Induced Gravity: We construct a warm inflation model with inflaton field non-minimally coupled
to induced gravity on a warped DGP brane. We incorporate possible modification
of the induced gravity on the brane in the spirit of $f(R)$-gravity. We study
cosmological perturbations in this setup. In the case of two field inflation
such as warm inflation, usually entropy perturbations are generated. While it
is expected that in the case of one field inflation these perturbations to be
removed, we show that even in the absence of the radiation field, entropy
perturbations are generated in our setup due to non-minimal coupling and
modification of the induced gravity. | hep-th |
Tachyons and the preferred frames: Quantum field theory of space-like particles is investigated in the framework
of absolute causality scheme preserving Lorentz symmetry. It is related to an
appropriate choice of the synchronization procedure (definition of time). In
this formulation existence of field excitations (tachyons) distinguishes an
inertial frame (privileged frame of reference) via spontaneous breaking of the
so called synchronization group. In this scheme relativity principle is broken
but Lorentz symmetry is exactly preserved in agreement with local properties of
the observed world. It is shown that tachyons are associated with unitary
orbits of Poincar\'e mappings induced from $SO(2)$ little group instead of
$SO(2,1)$ one. Therefore the corresponding elementary states are labelled by
helicity. The cases of the helicity $\lambda = 0$ and $\lambda =
\pm\frac{1}{2}$ are investigated in detail and a corresponding consistent field
theory is proposed. In particular, it is shown that the Dirac-like equation
proposed by Chodos et al., inconsistent in the standard formulation of QFT, can
be consistently quantized in the presented framework. This allows us to treat
more seriously possibility that neutrinos might be fermionic tachyons as it is
suggested by experimental data about neutrino masses. | hep-th |
Light-Cone Quantization a of Scalar Field on Time-Dependent Backgrounds: We discuss what is light-cone quantization on a curved spacetime also without
a null Killing vector. Then we consider as an example the light-cone
quantization of a scalar field on a background with a Killing vector and the
connection with the second quantization of the particle in the same background.
It turns out that the proper way to define the light-cone quantization is to
require that the constant light-cone time hypersurface is null or,
equivalently, that the particle Hamiltonian is free of square roots. Moreover,
in order to quantize the scalar theory it is necessary to use not the original
scalar rather a scalar field density, i.e. the Schr\"odinger wave functional
depends on a scalar density and not on the original field. Finally we recover
this result as the second quantization of a particle on the same background,
where it is necessary to add as input the fact that we are dealing with a
scalar density. | hep-th |
Non-BPS D8-branes and Dynamic Domain Walls in Massive IIA Supergravities: We study the D8-branes of the Romans massive IIA supergravity theory using
the coupled supergravity and worldvolume actions. D8 branes can be regarded as
domain walls with the jump in the extrinsic curvature at the brane given by the
Israel matching conditions. We examine the restrictions that these conditions
place on extreme and non-extreme solutions and find that they rule out some of
the supersymmetric solutions given by Bergshoeff {\em et al}. We consider what
happens when the dilaton varies on the worldvolume of the brane, which implies
that the brane is no longer static. We obtain a family of D8-brane solutions
parametrized by a non-extremality term on each side of the brane and the
asymptotic values of the 10-form field. The non-extremality parameters can be
related to the velocity of the brane. We also study 8-brane solutions of a
massive IIA supergravity theory introduced by Howe, Lambert and West. This
theory also admits a 10-form formulation, but the 10-form is not a R-R sector
field and so these 8-branes are not D-branes. | hep-th |
On the Duffin-Kemmer-Petiau Formulation of the Covariant Hamiltonian
Dynamics in Field Theory: We show that the De Donder-Weyl (DW) covariant Hamiltonian field equations of
any field can be written in Duffin-Kemmer-Petiau (DKP) matrix form. As a
consequence, the (modified) DKP beta-matrices (5 X 5 in four space-time
dimensions) are of universal significance for all fields admitting the DW
Hamiltonian formulation, not only for a scalar field, and can be viewed as
field theoretic analogues of the symplectic matrix, leading to the so-called
``k-symplectic'' (k=4) structure. We also briefly discuss what could be viewed
as the covariant Poisson bracket given by beta-matrices and the corresponding
Poisson bracket formulation of DW Hamiltonian field equations. | hep-th |
Black branes on the linear dilaton background: We show that the complete static black p-brane supergravity solution with a
single charge contains two and only two branches with respect to behavior at
infinity in the transverse space. One branch is the standard family of
asymptotically flat black branes, and another is the family of black branes
which asymptotically approach the linear dilaton background with antisymmetric
form flux (LDB). Such configurations were previously obtained in the
near-horizon near-extreme limit of the dilatonic asymptotically flat p-branes,
and used to describe the thermal phase of field theories involved in the DW/QFT
dualities and the thermodynamics of little string theory in the case of the
NS5-brane. Here we show by direct integration of the Einstein equations that
the asymptotically LDB p-branes are indeed exact supergravity solutions, and we
prove a new uniqueness theorem for static p-brane solutions satisfying cosmic
censorship. In the non-dilatonic case, our general non-asymptotically flat
p-branes are uncharged black branes on the background $AdS_{p+2}\times
S^{D-p-2}$ supported by the form flux. We develop the general formalism of
quasilocal quantities for non-asymptotically flat supergravity solutions with
antisymmetric form fields, and show that our solutions satisfy the first law of
theormodynamics. We also suggest a constructive procedure to derive rotating
asymptotically LDB brane solutions. | hep-th |
Born sigma model for branes in exceptional geometry: In double field theory, the physical space has been understood as a subspace
of the doubled space. Recently, the doubled space is defined as the
para-Hermitian manifold and the physical space is realized as a leaf of a
foliation of the doubled space. This construction naturally introduces the
fundamental 2-form, which plays an important role in a reformulation of string
theory known as the Born sigma model. In this paper, we present the Born sigma
model for $p$-branes in M-theory and type IIB theory by extending the
fundamental 2-form into U-duality-covariant $(p+1)$-forms. | hep-th |
Noncommuting Electric Fields and Algebraic Consistency in Noncommutative
Gauge theories: We show that noncommuting electric fields occur naturally in
$\theta$-expanded noncommutative gauge theories. Using this noncommutativity,
which is field dependent, and a hamiltonian generalisation of the
Seiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian
formulations of these theories, is established. A comparison of results in
different descriptions shows that this generalised map acts as canonical
transformation in the physical subspace only. Finally, we apply the hamiltonian
formulation to derive the gauge symmetries of the action. | hep-th |
On the holographic width of flux tubes: We investigate the width of the flux tube between heavy static quark charges.
Using the gauge/gravity duality, we find the properties of the minimal
connected surface related to the width of the bound state. We show that in the
confining phase, the logarithmic broadening predicted by the effective string
description and observed in lattice simulations is a generic property of all
confining backgrounds. We also study the transverse fluctuations of the string
connecting two static quarks in curved backgrounds. Our formalism is applied to
AdS space where we compute the expectation value of the square of transverse
deviations of the string, a quantity related to the width. | hep-th |
Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4: We show that a scalar field conformally coupled to AdS gravity in four
dimensions with a quartic self-interaction can be embedded into M-theory. The
holographic effective potential is exactly calculated, allowing us to study
non-perturbatively the stability of AdS_4 in the presence of the conformally
coupled scalar. It is shown that there exists a one-parameter family of
conformal scalar boundary conditions for which the boundary theory has an
unstable vacuum. In this case, the bulk theory has instanton solutions that
mediate the decay of the AdS_4 space. These results match nicely with the
vacuum structure and the existence of instantons in an effective
three-dimensional boundary model. | hep-th |
D-branes and Discrete Torsion: We show that discrete torsion is implemented in a D-brane world-volume theory
by using a projective representation of the orbifold point group. We study the
example of C^3/Z_2 x Z_2 and show that the resolution of singularities agrees
with that proposed by Vafa and Witten. A new type of fractional brane appears. | hep-th |
On String Junctions in Supersymmetric Gauge Theories: We study junctions consisting of confining strings in N=1 supersymmetric
large N gauge theories by means of the gauge/gravity correspondence. We realize
these junctions as D-brane configurations in infrared geometries of the
Klebanov-Strassler (KS) and the Maldacena-Nunez (MN) solutions. After
discussing kinematics associated with the balance of tensions, we compute the
energies of baryon vertices numerically. In the KS background, baryon vertices
give negative contributions to the energies. The results for the MN background
strongly suggest that the energies of baryon vertices exactly vanish, as in the
case of supersymmetric (p,q)-string junctions. We find that brane
configurations in the MN background have a property similar to the holomorphy
of the M-theory realization of (p,q)-string junctions. With the help of this
property, we analytically prove the vanishing of the energies of baryon
vertices in the MN background. | hep-th |
Fluid-gravity correspondence in the scalar-tensor theory of gravity:
(in)equivalence of Einstein and Jordan frames: The duality of gravitational dynamics (projected on a null hypersurface) and
of fluid dynamics is investigated for the scalar tensor (ST) theory of gravity.
The description of ST gravity, in both Einstein and Jordan frames, is analyzed
from fluid-gravity viewpoint. In the Einstein frame the dynamical equation for
the metric leads to the Damour-Navier-Stokes (DNS) equation with an external
forcing term, coming from the scalar field in ST gravity. In the Jordan frame
the situation is more subtle. We observe that finding the DNS equation in this
frame can lead to two pictures. In one picture, the usual DNS equation is
modified by a Coriolis-like force term, which originates completely from the
presence of a non-minimally coupled scalar field ($\phi$) on the gravity side.
Moreover, the identified fluid variables are no longer conformally equivalent
with those in the Einstein frame. However, this picture is consistent with the
saturation of Kovtun-Son-Starinets (KSS) bound. In the other picture, we find
the standard DNS equation (i.e. without the Coriolis-like force), with the
fluid variables conformally equivalent with those in Einstein frame. But, the
second picture, may not agree with the KSS bound for some values of $\phi$. We
conclude by rewriting the Raychaudhuri equation and the tidal force equation in
terms of the relevant parameters to demonstrate how the expansion scalar and
the shear-tensor evolve in the spacetime. Although, the area law of entropy is
broken in ST gravity, we show that the rewritten form of Raychaudhuri's
equation correctly results in the generalized second law of black hole
thermodynamics. | hep-th |
Novel algebraic structures from the polysymplectic form in field theory: The polysymplectic $(n+1)$-form is introduced as an analogue of the
symplectic form for the De Donder-Weyl polymomentum Hamiltonian formulation of
field theory. The corresponding Poisson brackets on differential forms are
constructed. The analogues of the Poisson algebra are shown to be generalized
(non-commutative and higher-order) Gerstenhaber algebras defined in the text. | hep-th |
Universal Terms of Entanglement Entropy for 6d CFTs: We derive the universal terms of entanglement entropy for 6d CFTs by applying
the holographic and the field theoretical approaches, respectively. Our
formulas are conformal invariant and agree with the results of [34,35].
Remarkably, we find that the holographic and the field theoretical results
match exactly for the $C^2$ and $Ck^2$ terms. Here $C$ and $k$ denote the Weyl
tensor and the extrinsic curvature, respectively. As for the $k^4$ terms, we
meet the splitting problem of the conical metrics. The splitting problem in the
bulk can be fixed by equations of motion. As for the splitting on the boundary,
we assume the general forms and find that there indeed exists suitable
splitting which can make the holographic and the field theoretical $k^4$ terms
match. Since we have much more equations than the free parameters, the match
for $k^4$ terms is non-trivial. | hep-th |
Meromorphic Scaling Flow of N=2 Supersymmetric SU(2) Yang-Mills with
Matter: Beta-functions are derived for the flow of N=2 SUSY SU(2) Yang-Mills in
4-dimensions with massless matter multiplets in the fundamental representation
of the gauge group. The beta-functions represent the flow of the couplings as
the VEV of the Higgs field is lowered and are modular forms of weight -2. They
have the correct asymptotic behaviour at both the strong and weak coupling
fixed points. Corrections to the massless beta-functions when masses are turned
on are discussed. | hep-th |
$T{\overline T}$ deformations and the width of fundamental particles: We provide a simple geometric meaning for deformations of so-called
$T{\overline T}$ type in relativistic and non-relativistic systems.
Deformations by the cross products of energy and momentum currents in
integrable quantum field theories are known to modify the thermodynamic Bethe
ansatz equations by a "CDD factor". In turn, CDD factors may be interpreted as
additional, fixed shifts incurred in scattering processes: a finite width added
to the fundamental particles (or, if negative, to the free space between them).
We suggest that this physical effect is a universal way of understanding
$T{\overline T}$ deformations, both in classical and quantum systems. We first
show this in non-relativistic systems, with particle conservation and
translation invariance, using the deformation formed out of the densities and
currents of particles and momentum. This holds at the level of the equations of
motion, and for any interaction potential, integrable or not. We then argue,
and show by similar techniques in free relativistic particle systems, that
$T\overline T$ deformations of relativistic systems produce the equivalent
phenomenon, accounting for length contractions. We also show that, in both the
relativistic and non-relativistic cases, the width of particles is equivalent
to a state-dependent change of metric, where the distance function discounts
the particles' widths, or counts the additional free space. This generalises
and explains the known field-dependent coordinate change describing $T\overline
T$ deformations. The results connect such deformations with generalised
hydrodynamics, where the relations between scattering shifts, widths of
particles and state-dependent changes of metric have been established. | hep-th |
Towards AdS Distances in String Theory: The AdS Distance Conjecture proposes to assign a notion of distance between
AdS vacua in quantum gravity. We perform some initial developments of this
idea. We first propose more sharply how to define a metric on conformal
variations of AdS through the action. This metric is negative, making the
distance ill-defined, a property relating to the famous conformal factor
problem of quantum gravity. However, in string theory, variations of the AdS
conformal factor are accompanied by variations of the internal dimensions and
of the background flux. We propose an $\textit{action metric}$, which accounts
for all of these variations simultaneously. Accounting for the variations of
the overall volume of the internal dimensions can flip the sign of the action
metric making it positive. This positivity is related to the absence of scale
separation between the internal and external dimensions: the negative external
conformal contribution must be sub-dominant to the positive internal
contribution. We then focus specifically on the families of solutions of
eleven-dimensional supergravity on AdS$_4 \times S^7$ and AdS$_7 \times S^4$.
For these, there is only a single further additional contribution to the action
metric coming from variations of the Freund-Rubin flux. This contribution is
subtle to implement, and the unique prescription we find requires singling out
the radial direction of AdS as special. Adding the flux contribution yields an
overall total action metric which becomes positive for both the AdS$_4$ and
AdS$_7$ families of solutions. The final result is therefore a procedure which
yields a well-defined distance for these families of solutions. | hep-th |
Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills: We conjecture that every rational Yangian invariant in N=4 SYM theory
satisfies a recently introduced notion of cluster adjacency. We provide
evidence for this conjecture by using the Sklyanin Poisson bracket on Gr(4,n)
to check numerous examples. | hep-th |
The black hole/string transition in AdS$_3$ and confining backgrounds: String stars, or Horowitz-Polchinski solutions, are Euclidean string theory
saddles with a normalizable condensate of thermal winding strings. String stars
were suggested as a possible description of stringy (Euclidean) black holes
close to the Hagedorn temperature. In this work, we continue the study
initiated in arXiv:2202.06966 by investigating the thermodynamic properties of
string stars in asymptotically (thermal) anti-de Sitter backgrounds. First, we
discuss the case of AdS$_3$ with mixed RR and NS-NS fluxes (including the pure
NS-NS system) and comment on a possible BTZ/string transition unique to
AdS$_3$. Second, we present new ``winding-string gas'' saddles for confining
holographic backgrounds such as the Witten model, and determine the subleading
correction to their Hagedorn temperature. We speculate a black brane/string
transition in these models and argue for a possible relation to the deconfined
phase of 3+1 dimensional pure Yang-Mills. | hep-th |
Holographic torus correlators in $\text{AdS}_3$ gravity coupled to
scalar field: This paper investigates holographic torus correlators of generic operators at
conformal infinity and a finite cutoff within AdS$_3$ gravity coupled with a
free scalar field. Using a near-boundary analysis and solving the gravitational
boundary value problem, we solve Einstein's equation and calculate mixed
correlators for massless and massive coupled scalar fields. The conformal ward
identity on the torus has been reproduced holographically, which can be
regarded as a consistency check. Further, recurrence relations for a specific
class of higher-point correlators are derived, validating AdS$_3$/CFT$_2$ with
non-trivial boundary topology. While the two-point scalar correlator is
accurately computed on the thermal AdS$_3$ saddle, the higher-point correlators
associated with scalar and stress tensor operators are explored. | hep-th |
Trialities and Exceptional Lie Algebras: DECONSTRUCTING the Magic Square: A construction of the magic square, and hence of exceptional Lie algebras, is
carried out using trialities rather than division algebras. By way of
preparation, a comprehensive discussion of trialities is given, incorporating a
number of novel results and proofs. Many of the techniques are closely related
to, or derived from, ideas which are commonplace in theoretical physics. The
importance of symmetric spaces in the magic square construction is clarified,
allowing the Jacobi property to be verified for each algebra in a uniform and
transparent way, with no detailed calculations required. A variation on the
construction, corresponding to other symmetric spaces, is also given. | hep-th |
Third Order Tree Contributions in the Causal Approach: We consider the general framework of perturbative quantum field theory for
the pure Yang-Mills model developed in [9] and prove that the tree
contributions do not give anomalies. We will provide a more general form of
this gauge invariance property. | hep-th |
W Algebras, W Gravities and their Moduli Spaces: By generalizing the Drinfel'd--Sokolov reduction we construct a large class
of W algebras as reductions of Kac--Moody algebras. Furthermore we construct
actions, invariant under local left and right W transformations, which are the
classical covariant induced actions for W gravity. Talk presented by T. Tjin at
the Trieste Summerschool on strings and related topics. | hep-th |
Lax Operator and superspin chains from 4D CS gauge theory: We study the properties of interacting line defects in the four-dimensional
Chern Simons (CS) gauge theory with invariance given by the $SL\left(
m|n\right) $ super-group family. From this theory, we derive the oscillator
realisation of the Lax operator for superspin chains with $SL(m|n)$ symmetry.
To this end, we investigate the holomorphic property of the bosonic Lax
operator $\mathcal{L}$ and build a differential equation $%
\mathfrak{D}\mathcal{L}=0$ solved by the Costello-Gaioto-Yagi realisation of
$\mathcal{L}$ in the framework of\ the CS theory. We generalize this
construction to the case of gauge super-groups, and develop a Dynkin
super-diagram algorithm to\ deal with the decomposition of the Lie
superalgebras. We obtain the generalisation of the Lax operator describing the
interaction between the electric Wilson super-lines and the magnetic 't Hooft
super-defects. This coupling is given in terms of a mixture of bosonic and
fermionic oscillator degrees of freedom in the phase space of magnetically
charged 't Hooft super-lines. The purely fermionic realisation of the superspin
chain Lax operator is also investigated and it is found to coincide exactly
with the $\mathbb{Z}_{2}$- gradation of Lie superalgebras.\ \newline Keywords:
4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkin
super-diagrams, Superspin chains and integrability, Super- Lax operator. | hep-th |
Is quantum teleportation beyond horizon possible?: We ask whether quantum teleportation from the outside to the inside of a
horizon is possible, using entanglement extracted from a vacuum. We first
calculate analytically, within the perturbation theory, entanglement extracted
from the Minkowski vacuum into a pair of an inertial and an accelerated
Unruh-DeWitt detectors, which are initially in the ground states and interact
with a neutral massless scalar field for an infinitely long time. We find that
entanglement can be extracted, but is "fragile", depending on adiabaticity of
switching of the detectors at the infinite past and future. We then consider
the standard scheme of quantum teleportation utilizing the extracted
entanglement, and find that the standard teleportation is not superior to
channels without entanglement. | hep-th |
Non-local self-healing of Higgs inflation: Higgs inflation is known to be a minimal extension of the Standard Model
allowing for the description of the early Universe inflation. This model is
considered as an effective field theory since it has a relatively low cutoff
scale, thus requiring further extensions to be a valid description of the
reheating phase. We present a novel unified approach to the problem of
unitarization and UV completion of the Higgs inflation model without
introducing new massive degrees of freedom. This approach is based on an
analytic infinite derivative modification of the Higgs field kinetic term. We
construct a unitary non-local UV completion of the original Higgs inflation
model while the inflationary stage is kept stable with respect to quantum
corrections. | hep-th |
Remarks on the thermofield double state in 4D black hole background: Recently it was shown that there is an anomalous singularity of propagators
in spacetimes with horizons for thermal states with non--canonical
temperatures. In this paper we extend these observations to the situation when
the background geometry is given by the four--dimensional Schwarzschild and
Reissner-Nordstr\"om black holes. Namely, we demonstrate that the two-point
function in the free scalar field theory acquires anomalous singularity when
the two points are located on the horizon. This singularity is anomalous in the
sense that the coefficient before the divergent term in the two-point function
differs from the canonical one and depends explicitly on the temperature of the
state. As it was previously shown, it leads to the explosive behavior of the
regularised stress-energy tensor on the horizon when the temperature of the
state does not coincide with the canonical temperature of the horizon. | hep-th |
A selection rule for transitions in PT-symmetric quantum theory: Carl Bender and collaborators have developed a quantum theory governed by
Hamiltonians that are PT-symmetric rather than Hermitian. To implement this
theory, the inner product was redefined to guarantee positive norms of
eigenstates of the Hamiltonian. In the general case, which includes arbitrary
time-dependence in the Hamiltonian, a modification of the Schrodinger equation
is necessary as shown by Gong and Wang to conserve probability. In this paper,
we derive the following selection rule: transitions induced by time dependence
in a PT-symmetric Hamiltonian cannot occur between normalized states of
differing PT-norm. We show three examples of this selection rule in action: two
matrix models and one in the continuum. | hep-th |
Extraction of shear viscosity in stationary states of relativistic
particle systems: Starting from a classical picture of shear viscosity we construct a
stationary velocity gradient in a microscopic parton cascade. Employing the
Navier-Stokes ansatz we extract the shear viscosity coefficient $\eta$. For
elastic isotropic scatterings we find an excellent agreement with the analytic
values. This confirms the applicability of this method. Furthermore for both
elastic and inelastic scatterings with pQCD based cross sections we extract the
shear viscosity coefficient $\eta$ for a pure gluonic system and find a good
agreement with already published calculations. | hep-th |
Spectral properties of the 2D magnetic Weyl-Dirac operator with a
short-range potential: This paper is devoted to the study of the spectral properties of the
Weyl-Dirac or massless Dirac operators, describing the behavior of quantum
quasi-particles in dimension 2 in a homogeneous magnetic field, $B^{\rm ext}$,
perturbed by a chiral-magnetic field, $b^{\rm ind}$, with decay at infinity and
a short-range scalar electric potential, $V$, of the Bessel-Macdonald type.
These operators emerge from the action of a pristine graphene-like QED$_3$
model recently proposed in Eur. Phys. J. B93} (2020) 187. First, we establish
the existence of states in the discrete spectrum of the Weyl-Dirac operators
between the zeroth and the first (degenerate) Landau level assuming that $V=0$.
In sequence, with $V_s \not= 0$, where $V_s$ is an attractive potential
associated with the $s$-wave, which emerges when analyzing the $s$- and
$p$-wave M{\o}ller scattering potentials among the charge carriers in the
pristine graphene-like QED$_3$ model, we provide lower bounds for the sum of
the negative eigenvalues of the operators $|\boldsymbol{\sigma} \cdot
\boldsymbol{p}_{\boldsymbol{A}_\pm}|+ V_s$. Here, $\boldsymbol{\sigma}$ is the
vector of Pauli matrices,
$\boldsymbol{p}_{\boldsymbol{A}_\pm}=\boldsymbol{p}-\boldsymbol{A}_\pm$, with
$\boldsymbol{p}=-i\boldsymbol{\nabla}$ the two-dimensional momentum operator
and $\boldsymbol{A}_\pm$ certain magnetic vector potentials. As a by-product of
this, we have the stability of bipolarons in graphene in the presence of
magnetic fields. | hep-th |
Two Dimensional Horava-Lifshitz Black Hole Solutions: In this paper we address the issue of black hole solutions in
(1+1)-dimensional non-projectable Horava-Lifshitz gravity. We consider several
models by considering different potentials in the scalar matter sector. We also
consider the gravitational collapse of a distribution of pressureless dust
filling a region in one-dimensional space. The time of the collapse can be
faster or slower depending on the parameter $\lambda$ of the theory. | hep-th |
The Black Ring is Unstable: We study non-axisymmetric linearised gravitational perturbations of the
Emparan-Reall black ring using numerical methods. We find an unstable mode
whose onset lies within the "fat" branch of the black ring and continues into
the "thin" branch. Together with previous results using Penrose inequalities
that fat black rings are unstable, this provides numerical evidence that the
entire black ring family is unstable. | hep-th |
Intersecting S-Brane Solutions of D=11 Supergravity: We construct all possible orthogonally intersecting S-brane solutions in
11-dimensions corresponding to standard supersymmetric M-brane intersections.
It is found that the solutions can be obtained by multiplying the brane and the
transverse directions with appropriate powers of two hyperbolic functions of
time. This is the S-brane analog of the ``harmonic function rule''. The
transverse directions can be hyperbolic, flat or spherical. We also discuss
some properties of these solutions. | hep-th |
Confinement interaction in nonlinear generalizations of the
Wick-Cutkosky model: We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky
model. Using an iterative approach and eliminating the mediating field by means
of the covariant Green function we arrive at a Lagrangian density containing
many-point time-nonlocal interaction terms. In low-order approximations of
$\phi^3{+}\phi^4$ theory we obtain the usual two-current interaction as well as
a three-current interaction of a confining type. The same result is obtained
without approximation for a version of the dipole model. The transition to the
Hamiltonian formalism and subsequent canonical quantization is performed with
time non-locality taken into account approximately.
A relativistic three-particle wave equation is derived variationally by using
a three-particle Fock space trial state. The non-relativistic limit of this
equation is obtained and its properties are analyzed and discussed. | hep-th |
One-loop effective potential on hyperbolic manifolds: The one-loop effective potential for a scalar field defined on an ultrastatic
space-time whose spatial part is a compact hyperbolic manifold, is studied
using zeta-function regularization for the one-loop effective action. Other
possible regularizations are discussed in detail. The renormalization group
equations are derived and their connection with the conformal anomaly is
pointed out. The symmetry breaking and the topological mass generation are also
discussed. | hep-th |
Corfu 05 lectures - part I: Strings on curved backgrounds: In these introductory lectures we summarize some basic facts and techniques
about perturbative string theory (sections 1 to 6). These are further developed
(sections 7 and 8) for describing string propagation in the presence of
gravitational or gauge fields. We also remind some solutions of the string
equations of motion, which correspond to remarkable (NS or D) brane
configurations.
A part II by Emilian Dudas will be devoted to orientifold constructions and
applications to string model building. | hep-th |
Deviations from Fermi-Liquid behaviour in (2+1)-dimensional Quantum
Electrodynamics and the normal phase of high-$T_c$ Superconductors: We argue that the gauge-fermion interaction in multiflavour quantum
electrodynamics in $(2 + 1)$-dimensions is responsible for non-fermi liquid
behaviour in the infrared, in the sense of leading to the existence of a
non-trivial (quasi) fixed point that lies between the trivial fixed point (at
infinite momenta) and the region where dynamical symmetry breaking and mass
generation occurs. This quasi-fixed point structure implies slowly varying,
rather than fixed, couplings in the intermediate regime of momenta, a situation
which resembles that of (four-dimensional) `walking technicolour' models of
particle physics. The inclusion of wave-function renormalization yields
marginal $O(1/N)$-corrections to the `bulk' non-fermi liquid behaviour caused
by the gauge interaction in the limit of infinite flavour number. Such
corrections lead to the appearance of modified critical exponents. In
particular, at low temperatures there appear to be logarithmic scaling
violations of the linear resistivity of the system of order $O(1/N)$.
Connection with the anomalous normal-state properties of certain condensed
matter systems relevant for high-temperature superconductivity is briefly
discussed. The relevance of the large (flavour) $N$ expansion to the
fermi-liquid problem is emphasized. As a partial result of our analysis, we
point out the absence of Charge-Density-Wave Instabilities from the effective
low-energy theory, as a consequence of gauge invariance. | hep-th |
Black holes without firewalls: The postulates of black hole complementarity do not imply a firewall for
infalling observers at a black hole horizon. The dynamics of the stretched
horizon, that scrambles and re-emits information, determines whether infalling
observers experience anything out of the ordinary when entering a large black
hole. In particular, there is no firewall if the stretched horizon degrees of
freedom retain information for a time of order the black hole scrambling time. | hep-th |
N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect: It is argued that there are strong similarities between the infra-red physics
of N=2 supersymmetric Yang-Mills and that of the quantum Hall effect, both
systems exhibit a hierarchy of vacua with a sub-group of the modular group
mapping between them. The scaling flow for pure SU(2) N=2 supersymmetric
Yang-Mills in 4-dimensions is re-examined and an earlier suggestion in the
literature, that was singular at strong coupling, is modified to a form that is
well behaved at both weak and strong coupling and describes the crossover in an
analytic fashion. Similarities between the phase diagram and the flow of SUSY
Yang-Mills and that of the quantum Hall effect are then described, with the
Hall conductivity in the latter playing the role of the theta-parameter in the
former. Hall plateaux, with odd denominator filling fractions, are analogous to
fixed points at strong coupling in N=2 SUSY Yang-Mills, where the massless
degrees of freedom carry an odd monopole charge. | hep-th |
Anti-de Sitter space, branes, singletons, superconformal field theories
and all that: There has recently been a revival of interest in anti de-Sitter space (AdS)
brought about by the conjectured duality beteeen physics in the bulk of AdS and
a conformal field theory on the boundary. Since the whole subject of branes,
singletons and superconformal field theories on the AdS boundary was an active
area of research about ten years ago, I begin with a historical review,
including the ``Membrane at the end of the universe'' idea. Next I discuss two
recent papers with Lu and Pope on on $AdS_{5} \times S^{5}$ and on $AdS_{3}
\times S^{3}$, respectively. In each case we note that odd-dimensional spheres
$S^{{2n+1}}$ may be regarded as U(1) bundles over $CP^{n}$ and that this
permits an unconventional ``Hopf''duality along the U(1) fibre. This leads in
particular to the phenomenon of BPS without BPS whereby states which appear to
be non-BPS in one picture are seen to be BPS in the dual picture. | hep-th |
Critical Composite Superconformal String: In the paper the nilpotent conditions of BRST operator for new superconformal
string model were found. This string includes anticommutation $2-d$ fields
additional to the standard Neveu-Schwarz superconformal set which carry quark
quantum numbers. In this case the superconformal symmetry is realized by a
non-linear way. In the superconformal composite string new constraints for 1
and 1/2 conformal dimension should be added to the standard system of Virasoro
superalgebra constraints for 2 and 3/2 conformal dimensions. The number $N$ of
the constraints and numbers $D$ and $D'$ of bosonic and fermionic $2-d$ fields
are connected by a simple relationship $D'/2+D-3N-15=0.$ Also perspectives of
the critical composite superconformal string are discussed. | hep-th |
Heisenberg Groups and Noncommutative Fluxes: We develop a group-theoretical approach to the formulation of generalized
abelian gauge theories, such as those appearing in string theory and M-theory.
We explore several applications of this approach. First, we show that there is
an uncertainty relation which obstructs simultaneous measurement of electric
and magnetic flux when torsion fluxes are included. Next we show how to define
the Hilbert space of a self-dual field. The Hilbert space is Z2-graded and we
show that, in general, self-dual theories (including the RR fields of string
theory) have fermionic sectors. We indicate how rational conformal field
theories associated to the two-dimensional Gaussian model generalize to
(4k+2)-dimensional conformal field theories. When our ideas are applied to the
RR fields of string theory we learn that it is impossible to measure the
K-theory class of a RR field. Only the reduction modulo torsion can be
measured. | hep-th |
The holographic Weyl semi-metal: We present a holographic model of a Weyl semi-metal. We show that upon
varying a mass parameter the model undergoes a quantum phase transition from a
topologically non-trivial state to a trivial one. The order parameter for this
phase transition is the anomalous Hall effect (AHE). We give an interpretation
of the results in terms of a holographic RG flow and compare to a weakly
coupled field theoretical model. Since there are no quasiparticle excitations
in the strongly coupled holographic model the topological phase can not be
bound to notions of topology in momentum space. | hep-th |
On the Topology of the Reduced Classical Configuration Space of Lattice
QCD: We study the topological structure of the quotient of $SU(3)\times SU(3)$ by
diagonal conjugation. This is the simplest nontrivial example for the classical
reduced configuration space of chromodynamics on a spatial lattice in the
Hamiltonian approach. We construct a cell complex structure of the quotient in
such a way that the closures of strata are subcomplexes and we compute the
homology and cohomology groups of the strata and their closures. | hep-th |
Topological Field Theories associated with Three Dimensional
Seiberg-Witten monopoles: Three dimensional topological field theories associated with the three
dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are
presented. These three dimensional monopole equations are obtained by a
dimensional reduction of the four dimensional ones. The starting actions to be
considered are Gaussian types with random auxiliary fields. As the local gauge
symmetries with topological shifts are found to be first stage reducible,
Batalin-Vilkovisky algorithm is suitable for quantization. Then BRST
transformation rules are automatically obtained. Non-trivial observables
associated with Chern classes are obtained from geometric sector and are found
to correspond to those of the topological field theory of Bogomol'nyi
monopoles. | hep-th |
Quantization of the Riemann Zeta-Function and Cosmology: Quantization of the Riemann zeta-function is proposed. We treat the Riemann
zeta-function as a symbol of a pseudodifferential operator and study the
corresponding classical and quantum field theories. This approach is motivated
by the theory of p-adic strings and by recent works on stringy cosmological
models. We show that the Lagrangian for the zeta-function field is equivalent
to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of
the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and
the Langlands program is indicated. The Beilinson conjectures on the values of
L-functions of motives are interpreted as dealing with the cosmological
constant problem. Possible cosmological applications of the zeta-function field
theory are discussed. | hep-th |
Narain to Narnia: We generalize the holographic correspondence between topological gravity
coupled to an abelian Chern-Simons theory in three dimensions and an ensemble
average of Narain's family of massless free bosons in two dimensions,
discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the
correspondence also works for toroidal orbifolds but not for K3 or Calabi-Yau
sigma-models and not always for the minimal models. We conjecture that the
correspondence requires that the central charge is equal to the critical
central charge defined by the asymptotic density of states of the chiral
algebra. For toroidal orbifolds, we extend the holographic correspondence to
correlation functions of twist operators by using topological properties of
rational tangles in the three-dimensional ball, which represent configurations
of vortices associated to a discrete gauge symmetry. | hep-th |
Functional Schroedinger and BRST Quantization of (1+1)--Dimensional
Gravity: We discuss the quantization of pure string--inspired dilaton--gravity in
$(1+1)$--dimensions, and of the same theory coupled to scalar matter. We
perform the quantization using the functional Schroedinger and BRST formalisms.
We find, both for pure gravity and the matter--coupled theory, that the two
quantization procedures give inequivalent ``physical'' results. | hep-th |
Non-Gaussianity in String Cosmology: A Case Study: We study non-gaussianity effects, using the $\delta N$ formalism, in a
multi-field inflationary model consisting of K\"ahler moduli derived from type
IIB string compactification in the large volume limit. The analytical work in
this paper mostly follows the separable potential method developed by Vernizzi
and Wands. The numerical analysis is then used in computing non-gaussianity
beyond slow-roll regime. The possibility of the curvaton scenario is also
discussed. We give the condition for the existence of the curvaton and
calculate the non-guassianity generated by the curvaton decay in the large
volume limit. | hep-th |
Entropy and replica geometry in generic two-dimensional dilaton gravity
theories: We set up a new version of black hole information paradox in an eternal
Narayan black hole, a generic two-dimensional dilaton gravity theory with
non-trivial on-shell bulk action and a product of dimensional reduction from
higher-dimensional AdS black brane, joined to Minkowski bath on both sides. We
also report both similarities as well as important differences between our
model and the famous model of JT gravity coupled with baths. The contradiction
of Hawking's result of entanglement entropy with unitarity is resolved by
including a new saddle in the Euclidean gravitational path integral. As part of
ongoing and developing research, we attempt, and have had partial success, to
explicitly construct the replica wormhole geometry for our model to fully
justify the quantum extremal surface calculations with Euclidean gravitational
path integral, without using holography. | hep-th |
Integrable open-boundary conditions for the supersymmetric t-J model.
The quantum group invariant case: We consider integrable open--boundary conditions for the supersymmetric t--J
model commuting with the number operator $n$ and $S^{z}$. Four families, each
one depending on two arbitrary parameters, are found. We find the relation
between Sklyanin's method of constructing open boundary conditions and the one
for the quantum group invariant case based on Markov traces. The eigenvalue
problem is solved for the new cases by generalizing the Nested Algebraic Bethe
ansatz of the quantum group invariant case (which is obtained as a special
limit). For the quantum group invariant case the Bethe ansatz states are shown
to be highest weights of $spl_{q}(2,1)$. | hep-th |
Distributions of nonsupersymmetric flux vacua: We continue the study of the distribution of nonsupersymmetric flux vacua in
IIb string theory compactified on Calabi-Yau manifolds, as in hep-th/0404116.
We show that the basic structure of this problem is that of finding
eigenvectors of the matrix of second derivatives of the superpotential, and
that many features of the results are determined by features of the generic
ensemble of such matrices, the CI ensemble of Altland and Zirnbauer originating
in mesoscopic physics. We study some simple examples in detail, exhibiting
various factors which can favor low or high scale supersymmetry breaking. | hep-th |
Aspects of holography and rotating AdS black holes: A comparison is made between the thermodynamics of weakly and strongly
coupled Yang-Mills with fixed angular momentum. The free energy of the strongly
coupled Yang-Mills is calculated by using a dual supergravity description
corresponding to a rotating black hole in an Anti de Sitter (AdS) background.
All thermodynamic quantities are shown have the same ratio of 3/4 (independent
of angular momentum) between strong and weak coupling. | hep-th |
Wormhole interaction in 2d Horava-Lifshitz quantum gravity: A lattice regularization for the $2$d projectable Horava-Lifshitz (HL)
quantum gravity is known to be the $2$d causal dynamical triangulations (CDT),
and the $2$d CDT can be generalized so as to include all possible genus
contributions non-perturbatively. We show that in the context of HL gravity,
effects coming from such a non-perturbative sum over topologies can be
successfully taken into account, if we quantize the $2$d projectable HL gravity
with a simple bi-local wormhole interaction. This conference paper is based on
the article, Phys. Lett. B 816 (2021), 136205. | hep-th |
The partition function versus boundary conditions and confinement in the
Yang-Mills theory: We analyse dependence of the partition function on the boundary condition for
the longitudinal component of the electric field strength in gauge field
theories. In a physical gauge the Gauss law constraint may be resolved
explicitly expressing this component via an integral of the physical
transversal variables. In particular, we study quantum electrodynamics with an
external charge and SU(2) gluodynamics. We find that only a charge distribution
slowly decreasing at spatial infinity can produce a nontrivial dependence in
the Abelian theory. However, in gluodynamics for temperatures below some
critical value the partition function acquires a delta-function like dependence
on the boundary condition, which leads to colour confinement. | hep-th |
Code Properties of the Holographic Sierpinski Triangle: We study the holographic quantum error correcting code properties of a
Sierpinski Triangle-shaped boundary subregion in $AdS_4/CFT_3$. Due to existing
no-go theorems in topological quantum error correction regarding fractal noise,
this gives holographic codes a specific advantage over topological codes. We
then further argue that a boundary subregion in the shape of the Sierpinski
gasket in $AdS_5/CFT_4$ does not possess these holographic quantum error
correction properties. | hep-th |
Categorical Pentagon Relations and Koszul Duality: The Kontsevich-Soibelman wall-crossing formula is known to control the
jumping behavior of BPS state counting indices in four-dimensional theories
with $\mathcal{N}=2$ supersymmetry. The formula can take two equivalent forms:
a ``fermionic'' form with nice positivity properties and a ``bosonic'' form
with a clear physical interpretation. In an important class of examples, the
fermionic form of the formula has a mathematical categorification involving PBW
bases for a Cohomological Hall Algebra. The bosonic form lacks an analogous
categorification. We construct an equivalence of chain complexes which
categorifies the simplest example of the bosonic wall-crossing formula: the
bosonic pentagon identity for the quantum dilogarithm. The chain complexes can
be promoted to differential graded algebras which we relate to the PBW bases of
the relevant CoHA by a certain quadratic duality. The equivalence of complexes
then follows from the relation between quadratic duality and Koszul duality. We
argue that this is a special case of a general phenomenon: the bosonic
wall-crossing formulae are categorified to equivalences of $A_\infty$ algebras
which are quadratic dual to PBW presentations of algebras which underlie the
fermionic wall-crossing formulae. We give a partial interpretation of our
differential graded algebras in terms of a holomorphic-topological version of
BPS webs. | hep-th |
Two-dimensional topological field theories as taffy: In this paper we use trivial defects to define global taffy-like operations
on string worldsheets, which preserve the field theory. We fold open and closed
strings on a space X into open strings on products of multiple copies of X, and
perform checks that the "taffy-folded" worldsheets have the same massless
spectra and other properties as the original worldsheets. Such folding tricks
are a standard method in the defects community; the novelty of this paper lies
in deriving mathematical identities to check that e.g. massless spectra are
invariant in topological field theories. We discuss the case of the B model
extensively, and also derive the same identities for string topology, where
they become statements of homotopy invariance. We outline analogous results in
the A model, B-twisted Landau-Ginzburg models, and physical strings. We also
discuss the understanding of the closed string states as the Hochschild
homology of the open string algebra, and outline possible applications to
elliptic genera. | hep-th |
Baby Skyrme model and fermionic zero modes: In this work we investigate some features of the fermionic sector of the
supersymmetric version of the baby Skyrme model. We find that, in the
background of BPS compact Skyrmions, fermionic zero modes are confined to the
defect core. Further, we show that, while three SUSY generators are broken in
the defect core, SUSY is completely restored outside. We study also the effect
of a D-term deformation of the model. Such a deformation allows for the
existence of fermionic zero modes and broken SUSY outside the compact defect. | hep-th |
Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits: We approach the topic of Classical group nilpotent orbits from the
perspective of their moduli spaces, described in terms of Hilbert series and
generating functions. We review the established Higgs and Coulomb branch quiver
theory constructions for A series nilpotent orbits. We present systematic
constructions for BCD series nilpotent orbits on the Higgs branches of quiver
theories defined by canonical partitions; this paper collects earlier work into
a systematic framework, filling in gaps and providing a complete treatment. We
find new Coulomb branch constructions for above minimal nilpotent orbits,
including some based upon twisted affine Dynkin diagrams. We also discuss
aspects of 3d mirror symmetry between these Higgs and Coulomb branch
constructions and explore dualities and other relationships, such as
HyperKahler quotients, between quivers. We analyse all Classical group
nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert
series and the Highest Weight Generating functions for their decompositions
into characters of irreducible representations and/or Hall Littlewood
polynomials. | hep-th |
Renormalisation of φ^4-theory on noncommutative R^4 to all orders: We present the main ideas and techniques of the proof that the
duality-covariant four-dimensional noncommutative \phi^4-model is
renormalisable to all orders. This includes the reformulation as a dynamical
matrix model, the solution of the free theory by orthogonal polynomials as well
as the renormalisation by flow equations involving power-counting theorems for
ribbon graphs drawn on Riemann surfaces. | hep-th |
Anisotropic homogeneous string cosmology with two-loop corrections: The two-loop (order $\alpha'$) $\beta$-function equations, which are
equivalent to the equations of motion of $\alpha'$-corrected string effective
action, are considered for anisotropic homogeneous space-times. These equations
are solved for all Bianchi-type models in two schemes of effective action,
namely $R^2$ and Gauss-Bonnet schemes with zero cosmological constant and then
the metric, dilaton and $B$-field are found at $\alpha'$ perturbative
corrections. | hep-th |
Nuttier Bubbles: We construct new explicit solutions of general relativity from double
analytic continuations of Taub-NUT spacetimes. This generalizes previous
studies of 4-dimensional nutty bubbles. One 5-dimensional locally
asymptotically AdS solution in particular has a special conformal boundary
structure of $AdS_3\times S^1$. We compute its boundary stress tensor and
relate it to the properties of the dual field theory. Interestingly enough, we
also find consistent 6-dimensional bubble solutions that have only one timelike
direction. The existence of such spacetimes with non-trivial topology is
closely related to the existence of the Taub-NUT(-AdS) solutions with more than
one NUT charge. Finally, we begin an investigation of generating new solutions
from Taub-NUT spacetimes and nuttier bubbles. Using the so-called Hopf duality,
we provide new explicit time-dependent backgrounds in six dimensions. | hep-th |
Quantum Field Theory on Fock Projective Space: It is shown that some analog of the ``second quantization'' exists in the
framework of CP(N) theory. I analyse conditions under that ``geometrical
bosons'' may be identified with real physical fields. The compact character of
a state manifold should preserve the quantities of dynamical variables from
divergences. | hep-th |
Classification of N=6 superconformal theories of ABJM type: Studying the supersymmetry enhancement mechanism of Aharony, Bergman,
Jafferis and Maldacena, we find a simple condition on the gauge group
generators for the matter fields. We analyze all possible compact Lie groups
and their representations. The only allowed gauge groups leading to the
manifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x
U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s.
Matter representations are restricted to be the (bi)fundamentals. As a
byproduct we obtain another proof of the complete classification of the three
algebras considered by Bagger and Lambert. | hep-th |
Hidden Symmetries of M Theory: A worldvolume action for membrane is considered to study the target space
local symmetries. We introduce a set of generators of canonical transformations
to exhibit the target space symmetries such as the general coordinate
transformation and the gauge transformation of antisymmetric tensor field.
Similar results are derived for type IIB string with manifestly
S-duality-invariant worldsheet action. | hep-th |
Loop Transfer Matrix and Loop Quantum Mechanics: We extend the previous construction of loop transfer matrix to the case of
nonzero self-intersection coupling constant $\kappa$. The loop generalization
of Fourier transformation allows to diagonalize transfer matrices depending on
symmetric difference of loops and express all eigenvalues of $3d$ loop transfer
matrix through the correlation functions of the corresponding 2d statistical
system. The loop Fourier transformation allows to carry out analogy with
quantum mechanics of point particles, to introduce conjugate loop momentum P
and to define loop quantum mechanics. We also consider transfer matrix on $4d$
lattice which describes propagation of memebranes. This transfer matrix can
also be diagonalized by using generalized Fourier transformation, and all its
eigenvalues are equal to the correlation functions of the corresponding $3d$
statistical system. | hep-th |
IIB matrix model and regularized big bang: The large-$N$ master field of the Lorentzian IIB matrix model can, in
principle, give rise to a particular degenerate metric relevant to a
regularized big bang. The length parameter of this degenerate metric is then
calculated in terms of the IIB-matrix-model length scale. | hep-th |
Footballs, Conical Singularities and the Liouville Equation: We generalize the football shaped extra dimensions scenario to an arbitrary
number of branes. The problem is related to the solution of the Liouville
equation with singularities and explicit solutions are presented for the case
of three branes. The tensions of the branes do not need to be tuned with each
other but only satisfy mild global constraints. | hep-th |
Emergence in Holographic Scenarios for Gravity: 'Holographic' relations between theories have become an important theme in
quantum gravity research. These relations entail that a theory without gravity
is equivalent to a gravitational theory with an extra spatial dimension. The
idea of holography was first proposed in 1993 by Gerard 't Hooft on the basis
of his studies of evaporating black holes. Soon afterwards the holographic
'AdS/CFT' duality was introduced, which since has been intensively studied in
the string theory community and beyond. Recently, Erik Verlinde has proposed
that even Newton's law of gravitation can be related holographically to the
`thermodynamics of information' on screens. We discuss these scenarios, with
special attention to the status of the holographic relation in them and to the
question of whether they make gravity and spacetime emergent. We conclude that
only Verlinde's scheme straightfowardly instantiates emergence. However,
assuming a non-standard interpretation of AdS/CFT may create room for the
emergence of spacetime and gravity there as well. | hep-th |
Unitary Minimal Liouville Gravity and Frobenius Manifolds: We study unitary minimal models coupled to Liouville gravity using Douglas
string equation. Our approach is based on the assumption that there exist an
appropriate solution of the Douglas string equation and some special choice of
the resonance transformation such that necessary selection rules of the minimal
Liouville gravity are satisfied. We use the connection with the Frobenius
manifold structure. We argue that the flat coordinates on the Frobenius
manifold are the most appropriate choice for calculating correlation functions.
We find the appropriate solution of the Douglas string equation and show that
it has simple form in the flat coordinates. Important information is encoded in
the structure constants of the Frobenius algebra. We derive these structure
constants in the canonical coordinates and in the physically relevant domain in
the flat coordinates. We find the leading terms of the resonance transformation
and express the coefficients of the resonance transformation in terms of Jacobi
polynomials. | hep-th |
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