anchor
stringlengths 50
3.92k
| positive
stringlengths 55
6.16k
|
|---|---|
Dirac-Born-Infeld actions and Tachyon Monopoles: We investigate magnetic monopole solutions of the non-abelian DBI action
describing 2 coincident non-BPS D9-branes in flat space. Just as in the case of
kink and vortex solitonic tachyon solutions of the full DBI non-BPS actions, as
previously analyzed by Sen, these monopole configurations are singular in the
first instance and require regularization. We discuss a suitable non-abelian
ansatz and show it solves the equations of motion to leading order in the
regularization parameter. Fluctuations are studied and shown to describe a
codimension 3 BPS D6-brane. A formula is derived for its tension. We comment on
the implication to our results from both the trace (Tr) and symmetrized trace
(Str) prescriptions of the non-abelian DBI action of coincident non-BPS
D9-branes. | From Big Crunch To Big Bang - Is It Possible?: We discuss the possibility of a transition from a contracting flat space -
big crunch - to an expanding flat space - big bang. |
On the complete classification of the unitary N=2 minimal superconformal
field theories: Aiming at a complete classification of unitary N=2 minimal models (where the
assumption of space-time supersymmetry has been dropped), it is shown that each
modular invariant candidate of a partition function for such a theory is indeed
the partition function of a minimal model. A family of models constructed via
orbifoldings of either the diagonal model or of the space-time supersymmetric
exceptional models demonstrates that there exists a unitary N=2 minimal model
for every one of the allowed partition functions in the list obtained from
Gannon's work.
Kreuzer and Schellekens' conjecture that all simple current invariants can be
obtained as orbifolds of the diagonal model, even when the extra assumption of
higher-genus modular invariance is dropped, is confirmed in the case of the
unitary N=2 minimal models by simple counting arguments. | Solving all 4-point correlation functions for bosonic open string theory
in the high energy limit: We study the implication of decoupling zero-norm states in the high-energy
limit, for the 26 dimensional bosonic open string theory. Infinitely many
linear relations among 4-point functions are derived algebraically, and their
unique solution is found. Equivalent results are also obtained by taking the
high-energy limit of Virasoro constraints, and as an independent check, we
compute all 4-point functions of 3 tachyons and an arbitrary massive state by
saddle-point approximation. |
Island on codimension-two branes in AdS/dCFT: The previous studies of the island and double holography mainly focus on
codimension-one branes. This paper explores the island on the codimension-two
brane in AdS/dCFT. The codimension-two brane is closely related to conical
singularity, which is very different from the codimension-one brane. We analyze
the mass spectrum of gravitons on the codimension-two brane and find that the
larger the brane tension is, the smaller the gravitational mass is. The
massless mode is forbidden by either the boundary or normalization conditions.
We prove that the first massive gravitational mode is located on the
codimension-two brane; the larger the tension, the better the localization. It
is similar to the case of codimension-one brane and builds an excellent
physical foundation for the study of black hole evolution on codimension-two
branes. We find that the Page curve of eternal black holes can be recovered due
to the island ending on the codimension-two brane. The new feature is that the
extremal surface passing the horizon cannot be defined after some finite time
in the no-island phase. Fortunately, this unusual situation does not affect the
Page curve since it happens after Page time. | Asymptotically Universal Crossover in Perturbation Theory with a Field
Cutoff: We discuss the crossover between the small and large field cutoff (denoted
x_{max}) limits of the perturbative coefficients for a simple integral and the
anharmonic oscillator. We show that in the limit where the order k of the
perturbative coefficient a_k(x_{max}) becomes large and for x_{max} in the
crossover region, a_k(x_{max}) is proportional to the integral from -infinity
to x_{max} of e^{-A(x-x_0(k))^2}dx. The constant A and the function x_0(k) are
determined empirically and compared with exact (for the integral) and
approximate (for the anharmonic oscillator) calculations. We discuss how this
approach could be relevant for the question of interpolation between
renormalization group fixed points. |
A simple strategy for renormalization: QED at one-loop level: We demonstrate our simple strategy for renormalization with QED at one-loop
level, basing on an elaboration of the effective field theory philosophy. No
artificial regularization or deformation of the original theory is introduced
here and hence no manipulation of infinities, ambiguities arise instead of
infinities. Ward identities first come to reduce the number of ambiguities, the
residual ones could in principle be removed by imposing physical boundary
conditions. Renormalization group equations arise as "decoupling theorems" in
the underlying theory perspective. In addition, a technical theorem concerning
routing of external momenta is also presented and illustrated with the
self-energy and vertex function as examples. | Energy trapped Ising model: In this paper we have considered the 3D Ising model perturbed with the energy
operator coupled with a non uniform harmonic potential acting as a trap,
showing that this system satisfies the trap-size scaling behavior. Eventually,
we have computed the correlators $\langle \sigma (z) \sigma (0)\rangle$, $
\langle \epsilon (z) \epsilon (0)\rangle$ and $\langle \sigma (z) \epsilon
(0)\rangle$ near the critical point by means of conformal perturbation theory.
Combining this result with Monte Carlo simulations, we have been able to
estimate the OPE coefficients $C^{\sigma}_{\sigma\epsilon}$,
$C^{\epsilon}_{\sigma\sigma}$ and $C^{\epsilon}_{\epsilon\epsilon}$, finding a
good agreement with the values obtained in [1,2]. |
ADHM Polytopes: We discuss the construction of ADHM data for Yang-Mills instantons with the
symmetries of the regular polytopes in four dimensions. We show that the case
of the pentatope can be studied using a simple modification of the approach
previously developed for platonic data. For the remaining polytopes, we
describe a framework in which the building blocks of the ADHM data correspond
to the edges in the extended Dynkin diagram that arises via the McKay
correspondence. These building blocks are then assembled into ADHM data through
the identification of pairs of commuting representations of the associated
binary polyhedral group. We illustrate our procedure by the construction of
ADHM data associated with the pentatope, the hyperoctahedron and the 24-cell,
with instanton charges 4, 7 and 23, respectively. Furthermore, we show that
within our framework these are the lowest possible charges with these
symmetries. Plots of topological charge densities are presented that confirm
the polytope structure and the relation to JNR instanton data is clarified. | Universality of low-energy scattering in (2+1) dimensions: We prove that, in (2+1) dimensions, the S-wave phase shift, $ \delta_0(k)$, k
being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or
\delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$.
This result is established first in the framework of the Schr\"odinger equation
for a large class of potentials, second for a massive field theory from proved
analyticity and unitarity, and, finally, we look at perturbation theory in
$\phi_3^4$ and study its relation to our non-perturbative result. The
remarkable fact here is that in n-th order the perturbative amplitude diverges
like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln
k)^{-1}$. We show how these two facts can be reconciled. |
Unifying Relations for Scattering Amplitudes: We derive new amplitudes relations revealing a hidden unity among
wide-ranging theories in arbitrary spacetime dimensions. Our results rely on a
set of Lorentz invariant differential operators which transmute physical
tree-level scattering amplitudes into new ones. By transmuting the amplitudes
of gravity coupled to a dilaton and two-form, we generate all the amplitudes of
Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon,
nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates
amplitudes in string theory and its variants. As a corollary, celebrated
aspects of gluon and graviton scattering like color-kinematics duality, the KLT
relations, and the CHY construction are inherited traits of the transmuted
amplitudes. Transmutation recasts the Adler zero as a trivial consequence of
the Weinberg soft theorem and implies new subleading soft theorems for certain
scalar theories. | One-vortex moduli space and Ricci flow: The metric on the moduli space of one abelian Higgs vortex on a surface has a
natural geometrical evolution as the Bradlow parameter, which determines the
vortex size, varies. It is shown by various arguments, and by calculations in
special cases, that this geometrical flow has many similarities to Ricci flow. |
Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1: We point out that the entropy of (near) extremal black holes can be
interpreted as the entanglement entropy of dual conformal quantum mechanics via
AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and
derive this claim from AdS3/CFT2. We also analytically compute the entanglement
entropy in the two dimensional CFT of a free Dirac fermion compactified on a
circle at finite temperature. From this result, we clarify the relation between
the thermal entropy and entanglement entropy, which is essential for the
entanglement interpretation of black hole entropy. | Hamiltonian formulation of SL(3) Ur-KdV equation: We give a unified view of the relation between the $SL(2)$ KdV, the mKdV, and
the Ur-KdV equations through the Fr\'{e}chet derivatives and their inverses.
For this we introduce a new procedure of obtaining the Ur-KdV equation, where
we require that it has no non-local operators. We extend this method to the
$SL(3)$ KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian
structure of Ur-Bsq equationin a simple form. In particular, we explicitly
construct the hamiltonian operator of the Ur-Bsq system which defines the
poisson structure of the system, through the Fr\'{e}chet derivative and its
inverse. |
Physics-to-gauge conversion at black hole horizons: Requiring the presence of a horizon imposes constraints on the physical phase
space. After a careful analysis of dilaton gravity in 2D with boundaries
(including the Schwarzschild and Witten black holes as prominent examples), it
is shown that the classical physical phase space is smaller as compared to the
generic case if horizon constraints are imposed. Conversely, the number of
gauge symmetries is larger for the horizon scenario. In agreement with a recent
conjecture by 't Hooft, we thus find that physical degrees of freedom are
converted into gauge degrees of freedom at a horizon. | Abelian matrix models in two loops: We perform a two-loop calculation of the effective Lagrangian for the
low--energy modes of the quantum mechanical system obtained by dimensional
reduction from 4D, N = 1 supersymmetric QED. The bosonic part of the Lagrangian
describes the motion over moduli space of vector potentials A_i endowed with a
nontrivial conformally flat metric. We determined the coefficient of the
two-loop correction to the metric, which is proportional to 1/A^6. For the
matrix model obtained from Abelian 4D, N = 2 theory, this correction vanishes,
as it should. |
Time evolution of a toy semiholographic glasma: We extend our previous study of a toy model for coupling classical Yang-Mills
equations for describing overoccupied gluons at the saturation scale with a
strongly coupled infrared sector modeled by AdS/CFT. Including propagating
modes in the bulk we find that the Yang-Mills sector loses its initial energy
to a growing black hole in the gravity dual such that there is a conserved
energy-momentum tensor for the total system while entropy grows monotonically.
This involves a numerical AdS simulation with a backreacted boundary source far
from equilibrium. | Entropy Current and Fluid-Gravity Duality in Gauss-Bonnet theory: Working within the approximation of small amplitude expansion, recently an
entropy current has been constructed on the horizons of dynamical black hole
solution in any higher derivative theory of gravity. In this note, we have
dualized this horizon entropy current to a boundary entropy current in an
asymptotically AdS black hole metric with a dual description in terms of
dynamical fluids living on the AdS boundary. This boundary entropy current is
constructed using a set of mapping functions relating each point on the horizon
to a point on the boundary. We have applied our construction to black holes in
Einstein-Gauss-Bonnet theory. We have seen that up to the first order in
derivative expansion, Gauss-Bonnet terms do not add any extra corrections to
fluid entropy as expected. However, at the second order in derivative
expansion, the boundary current will non-trivially depend on how we choose our
horizon to boundary map, which need not be expressible entirely in terms of
fluid variables. So generically, the boundary entropy current generated by
dualizing the horizon current will not admit a fluid dynamical description. |
Exact Consequences of the Trace Anomaly in Four Dimensions: The general form of the stress-tensor three-point function in four dimensions
is obtained by solving the Ward identities for the diffeomorphism and Weyl
symmetries. Several properties of this correlator are discussed, such as the
renormalization and scheme independence and the analogies with the anomalous
chiral triangle. At the critical point, the coefficients a and c of the
four-dimensional trace anomaly are related to two finite, scheme-independent
amplitudes of the three-point function. Off-criticality, the imaginary parts of
these amplitudes satisfy sum rules which express the total
renormalization-group flow of a and c between pairs of critical points.
Although these sum rules are similar to that satisfied by the two-dimensional
central charge, the monotonicity of the flow, i.e. the four-dimensional
analogue of the c-theorem, remains to be proven. | On scrambling, tomperature and superdiffusion in de Sitter space: This paper investigates basic properties of the de Sitter static patch using
simple two-point functions in the probe approximation. We find that de Sitter
equilibrates in a superdiffusive manner, unlike most physical systems which
equilibrate diffusively. We also examine the scrambling time. In de Sitter, the
two-point functions of free fields do not decay for sometime because quanta can
reflect off the pole of the static patch. This suggests a minimum scrambling
time of the order $\log(1/G_N)$, even for perturbations introduced on the
stretched horizon, indicating fast scrambling inside de Sitter static patch. We
also discuss the interplay between thermodynamic temperature and inverse
correlation time, sometimes called "tomperature". |
Gravitational electron-positron scattering: A scattering process with gravitons as an intermediate state is investigated.
To study such a scattering, the Gravitoelectromagnetism theory is considered.
It is a gravitational theory built on the analogy between gravity and
electromagnetism. The complete Lagrangian formulation of the
gravitoelectromagnetic theory includes interactions of gravitons with fermions
and photons that leads us to calculate their scattering amplitudes and
cross-sections. In this context, the gravitational cross-section of the
$e^{-}+e^{+}\longrightarrow\mu^{-}+\mu^{+}$ scattering process is obtained. A
comparison between the electromagnetic and gravitational cross-sections is
made. | Matrix Orientifolding and Models with Four or Eight Supercharges: The conditions under which matrix orientifolding and supersymmetry
transformations commute are known to be stringent. Here we present the cases
possessing four or eight supercharges upon ${\bf Z}_3$ orbifolding followed by
matrix orientifolding. These cases descend from the matrix models with eight
plus eight supercharges. There are fifty in total, which we enumerate. |
Question on the Existence of Gravitational Anomalies: The existence of gravitational anomalies claimed by Alvarez-Gaume and Witten
is examined critically. It is pointed out that they were unaware of the
essential difference between T-product quantities and T*-product quantities.
Field equations and, therefore, the Noether theorem are, in general, violated
in the case of T*-product quantities, that is, those directly calculable from
Feynman integrals. In the 2-dimensional case, it is explicitly confirmed that
the energy-momentum tensor is strictly conserved if the above stated property
of the T*-product quantities is correctly taken into account. The non-existence
of gravitational anomalies is explicitly demonstrated for the BRS-formulated
2-dimensional quantum gravity in the Heisenberg picture. | Blowup formulae in Donaldson-Witten theory and integrable hierarchies: We investigate blowup formulae in Donaldson-Witten theory with gauge group
SU(N), using the theory of hyperelliptic Kleinian functions. We find that the
blowup function is a hyperelliptic sigma-function and we describe an explicit
procedure to expand it in terms of the Casimirs of the gauge group up to
arbitrary order. As a corollary, we obtain a new expression for the contact
terms and we show that the correlation functions involving the exceptional
divisor are governed by the KdV hierarchy. We also show that, for manifolds of
simple type, the blowup function becomes a tau-function for a multisoliton
solution. |
Uniqueness of charged static asymptotically flat black holes in
dynamical Chern-Simons gravity: Making use of the conformal positive energy theorem we prove the uniqueness
of four-dimensional static electrically charged black holes being the solution
of Chern-Simons dynamical gravity equations of motion. We assume that black
hole spacetime contains an asymptotically flat spacelike hypersurface with
compact interior and non-degenerate components of the event horizon. | Increasing Potentials in Non-Abelian and Abelian Gauge Theories: An exact solution for an SU(2) Yang-Mills field coupled to a scalar field is
given. This solution has potentials with a linear and Coulomb part. This may
have some physical importance since many phenomenological QCD studies assume a
linear plus Coulomb potential. Usually the linear potential is motivated with
lattice gauge theory arguments. Here the linear potential is an exact result of
the field equations. We also show that in the Nielsen-Olesen Abelian model
there is an exact solution in the BPS limit which has a Coulomb-like
electromagnetic field and a logarithmically rising scalar field. Both of these
solutions must be cut off from above to avoid infinite field energy. |
Equilibration rates in a strongly coupled nonconformal quark-gluon
plasma: We initiate the study of equilibration rates of strongly coupled quark-gluon
plasmas in the absence of conformal symmetry. We primarily consider a
supersymmetric mass deformation within ${\cal N}=2^{*}$ gauge theory and use
holography to compute quasinormal modes of a variety of scalar operators, as
well as the energy-momentum tensor. In each case, the lowest quasinormal
frequency, which provides an approximate upper bound on the thermalization
time, is proportional to temperature, up to a pre-factor with only a mild
temperature dependence. We find similar behaviour in other holographic plasmas,
where the model contains an additional scale beyond the temperature. Hence, our
study suggests that the thermalization time is generically set by the
temperature, irrespective of any other scales, in strongly coupled gauge
theories. | Hard thermal loops in long wave-length and static external gravitational
fields: We study, in the long wave-length and static limits, the structure of the
n-point graviton functions at high temperature. Using the gauge and Weyl
invariance of the theory, we derive a simple expression for the hard thermal
amplitudes in these two limits. |
On Superpotentials for D-Branes in Gepner Models: A large class of D-branes in Calabi-Yau spaces can be constructed at the
Gepner points using the techniques of boundary conformal field theory. In this
note we develop methods that allow to compute open string amplitudes for such
D-branes. In particular, we present explicit formulas for the products of open
string vertex operators of untwisted A-type branes. As an application we show
that the boundary theories of the quintic associated with the special
Lagrangian submanifolds Im \omega_i z_i = 0 where \omega_i^5=1 possess no
continuous moduli. | BFT Method for Mixed Constrained Systems and Chern-Simons Theory: We show that the BFT embedding method is problematic for mixed systems
(systems possessing both first and second class constraints). The Chern-Simons
theory as an example is worked out in detail. We give two methods to solve the
problem leading to two different types of finite order BFT embedding for
Chern-Simons theory. |
Universal consistent truncation for 6d/7d gauge/gravity duals: Recently, AdS_7 solutions of IIA supergravity have been classified; there are
infinitely many of them, whose expression is known analytically, and with
internal space of S^3 topology. Their field theory duals are six-dimensional
(1,0) SCFT's. In this paper we show that for each of these AdS_7 solutions
there exists a consistent truncation from massive IIA supergravity to minimal
gauged supergravity in seven dimensions. This theory has an SU(2) gauge group,
and a single scalar, whose value is related to a certain distortion of the
internal S^3. This explains the universality observed in recent work on AdS_5
and AdS_4 solutions dual to compactifications of the (1,0) SCFT_6's. Thanks to
previous work on the minimal gauged supergravity, the truncation also implies
the existence of holographic RG-flows connecting those solutions to the AdS_7
vacuum, as well as new classes of IIA AdS_3 solutions. | Some phenomenological aspects of Type IIB/F-theory string
compactifications: This article is the PhD thesis of the author. It is focused on Type II
compactifications because of the potential for the construction of realistic
MSSM-like compactifications. In particular we concentrate in Type IIB
Calabi-Yau orientifolds and its non-perturbative realization: F-theory. These
sort of models, have attracted a lot of attention during recent years due to
their phenomenological interest. The first part is devoted to an introductory
survey of some concepts and aspects of Type II vacua like e.g. the low energy
effective action or soft terms. It is also included a brief presentation of
F-theory stressing the phenomenological interest of local models. In the second
part we present an analysis of the theoretical and phenomenological issues of
modulus dominated SUSY breaking. In addition it is examined its status in
comparison with recent LHC data. Finally, the third part is devoted to the
analysis of flux and instanton effects on local F-theory models. Yukawas and
matter fields wave functions corresponding to these models are calculated. The
results may allow for an understanding of the problem of fermion hierarchies in
the Standard Model. |
Modular Differential Equations with Movable Poles and Admissible RCFT
Characters: Studies of modular linear differential equations (MLDE) for the
classification of rational CFT characters have been limited to the case where
the coefficient functions (in monic form) have no poles, or poles at special
points of moduli space. Here we initiate an exploration of the vast territory
of MLDEs with two characters and any number of poles at arbitrary points of
moduli space. We show how to parametrise the most general equation precisely
and count its parameters. Eliminating logarithmic singularities at all the
poles provides constraint equations for the accessory parameters. By taking
suitable limits, we find recursion relations between solutions for different
numbers of poles. The cases of one and two movable poles are examined in detail
and compared with predictions based on quasi-characters to find complete
agreement. We also comment on the limit of coincident poles. Finally we show
that there exist genuine CFT corresponding to many of the newly-studied cases.
We emphasise that the modular data is an output, rather than an input, of our
approach. | Non-threshold D-brane bound states and black holes with non-zero entropy: We start with BPS-saturated configurations of two (orthogonally) intersecting
M-branes and use the electro-magnetic duality or dimensional reduction along a
boost, in order to obtain new p-brane bound states. In the first case the
resulting configurations are interpreted as BPS-saturated non-threshold bound
states of intersecting p-branes, and in the second case as p-branes
intersecting at angles and their duals. As a by-product we deduce the
enhancement of supersymmetry as the angle approaches zero. We also comment on
the D-brane theory describing these new bound states, and a connection between
the angle and the world-volume gauge fields of the D-brane system. We use these
configurations to find new embeddings of the four and five dimensional black
holes with non-zero entropy, whose entropy now also depends on the angle and
world-volume gauge fields. The corresponding D-brane configuration sheds light
on the microscopic entropy of such black holes. |
N=1 super-Chern-Simons coupled to parity-preserving matter from
Atiyah-Ward space-time: In this letter, we present the Parkes-Siegel formulation for the massive
Abelian $N$$=$$1$ super-{\QED} coupled to a self-dual supermultiplet, by
introducing a chiral multiplier superfield. We show that after carrying out a
suitable dimensional reduction from ($2$$+$$2$) to ($1$$+$$2$) dimensions, and
performing some necessary truncations, the simple supersymmetric extension of
the ${\tau}_{3}$QED$_{1+2}$ coupled to a Chern-Simons term naturally comes out. | Notes On Holomorphic String And Superstring Theory Measures Of Low Genus: It has long been known that in principle, the genus g vacuum amplitude for
bosonic strings or superstrings in 26 or 10 dimensions can be entirely
determined from conditions of holomorphy. Moreover, this has been done in
practice for bosonic strings of low genus. Here we describe in a unified way
how to determine the bosonic string and superstring vacuum amplitude in genus 1
and 2 via holomorphy. The main novelty is the superstring analysis in genus 2,
where we use holomorphy to get a new understanding of some of the results that
previously have been obtained by more explicit calculations. |
Berry phase in the phase space worldline representation: the axial
anomaly and classical kinetic theory: The Berry phase is analyzed for Weyl and Dirac fermions in a phase space
representation of the worldline formalism. Kinetic theories are constructed for
both at a classical level. Whereas the Weyl fermion case reduces in dimension,
resembling a theory in quantum mechanics, the Dirac fermion case takes on a
manifestly Lorentz covariant form. To achieve a classical kinetic theory for
the non-Abelian Dirac fermion Berry phase a spinor construction of Barut and
Zanghi is utilized. The axial anomaly is also studied at a quantum level. It is
found that under an adiabatic approximation, which is necessary for
facilitating a classical kinetic theory, the index of the Dirac operator for
massless fermions vanishes. Even so, similarities of an axial rotation to an
exact non-covariant Berry phase transform are drawn by application of the
Fujikawa method to the Barut and Zanghi spinors on the worldline. | AdS_{d+1} --> AdS_d: Coset methods are used to construct the action describing the dynamics of the
(massive) Nambu-Goldstone scalar degree of freedom associated with the
spontaneous breaking of the isometry group of AdS_{d+1} space to that of an
AdS_d subspace. The resulting action is an SO(2,d) invariant AdS generalization
of the Nambu-Goto action. The vector field theory equivalent action is also
determined. |
Casimir effect between moving branes: We consider a supersymmetric model with a single matter supermultiplet in a
five-dimensional space-time with orbifold compactification along the fifth
dimension. The boundary conditions on the two orbifold planes are chosen in
such a way that supersymmetry remains unbroken on the boundaries. We calculate
the vacuum energy-momentum tensor in a configuration in which the boundary
branes are moving with constant velocity. The results show that the
contribution from fermions cancels that of bosons only in the static limit, but
in general a velocity-dependent Casimir energy arises between the branes. We
relate this effect to the particle production due to the branes motion and
finally we discuss some cosmological consequences. | $\mathcal{N}=2^*$ gauge theory, free fermions on the torus and
Painlevé VI: In this paper we study the extension of Painlev\'e/gauge theory
correspondence to circular quivers by focusing on the special case of $SU(2)$
$\mathcal{N}=2^*$ theory. We show that the Nekrasov-Okounkov partition function
of this gauge theory provides an explicit combinatorial expression and a
Fredholm determinant formula for the tau-function describing isomonodromic
deformations of $SL_2$ flat connections on the one-punctured torus. This is
achieved by reformulating the Riemann-Hilbert problem associated to the latter
in terms of chiral conformal blocks of a free-fermionic algebra. This viewpoint
provides the exact solution of the renormalization group flow of the $SU(2)$
$\mathcal{N}=2^*$ theory on self-dual $\Omega$-background and, in the
Seiberg-Witten limit, an elegant relation between the IR and UV gauge
couplings. |
Dualities for 3d Theories with Tensor Matter: We study dualities for ${\cal N}=2$ 3d Chern-Simons matter theories with
gauge groups U/Sp/O, matter in the two-index tensor representations
(adjoint/symmetric/antisymmetric) in addition to the fundamental
representation, and a superpotential. These dualities are analogous to
Kutasov-Schwimmer-Seiberg dualities in 4d. We test them by computing the
superconformal index and the partition function on $S^3$ for many dual pairs
and find perfect agreement. In some cases we find a simple dual description for
theories with tensor matter and no superpotential, thereby generalizing the
"Duality Appetizer" of Jafferis and Yin to an infinite class of theories. We
also investigate nonperturbative truncation of the chiral ring proposed in the
context of 4d dualities. | Thermodynamic Origin of the Null Energy Condition: We derive the classical null energy condition, understood as a constraint on
the Ricci tensor, from the second law of thermodynamics applied locally to
Bekenstein-Hawking entropy associated with patches of null congruences. The
derivation provides evidence that the null energy condition, which has usually
been regarded as a condition on matter, is fundamentally a property of gravity. |
Weak quasitriangular Quasi-Hopf algebra structure of minimal models: The chiral vertex operators for the minimal models are constructed and used
to define a fusion product of representations. The existence of commutativity
and associativity operations is proved. The matrix elements of the
associativity operations are shown to be given in terms of the 6-j symbols of
the weak quasitriangular quasi-Hopf algebra obtained by truncating $\usl$ at
roots of unity. | N=1 Supersymmetric Quantum Mechanics on a Curved Space: The quantum mechanics of an N=1 supersymmetric dynamical system constrained
to a hypersurface embedded in the higher dimensional Euclidean space is
investigated by using the projection-operator method (POM) of constrained
systems. It is shown that the Hamiltonian obtained by the successive operations
of projection operators contains the additional terms, which are completely
missed when imposing constraints before the quantization. We derive the
conditions the additional terms should satisfy when the N=1 supersymmetry holds
in the resulting system, and present the geometrical interpretations of these
additional terms. |
The Schur Expansion of Characteristic Polynomials and Random Matrices: We develop a new framework to compute the exact correlators of characteristic
polynomials, and their inverses, in random matrix theory. Our results hold for
general potentials and incorporate the effects of an external source. In matrix
model realizations of string theory, these correspond to correlation functions
of exponentiated "(anti-)branes" in a given background of "momentum branes".
Our method relies on expanding the (inverse) determinants in terms of Schur
polynomials, then re-summing their expectation values over the allowed
representations of the symmetric group. Beyond unifying previous, seemingly
disparate calculations, this powerful technique immediately delivers two new
results: 1) the full finite $N$ answer for the correlator of inverse
determinant insertions in the presence of a matrix source, and 2) access to an
interesting, novel regime $M>N$, where the number of inverse determinant
insertions $M$ exceeds the size of the matrix $N$. | Simulating a numerical UV Completion of Quartic Galileons: The Galileon theory is a prototypical effective field theory that
incorporates the Vainshtein screening mechanism--a feature that arises in some
extensions of General Relativity, such as massive gravity. The Vainshtein
effect requires that the theory contain higher order derivative interactions,
which results in Galileons, and theories like them, failing to be technically
well-posed. While this is not a fundamental issue when the theory is correctly
treated as an effective field theory, it nevertheless poses significant
practical problems when numerically simulating this model. These problems can
be tamed using a number of different approaches: introducing an active low-pass
filter and/or constructing a UV completion at the level of the equations of
motion, which controls the high momentum modes. These methods have been tested
on cubic Galileon interactions, and have been shown to reproduce the correct
low-energy behavior. Here we show how the numerical UV-completion method can be
applied to quartic Galileon interactions, and present the first simulations of
the quartic Galileon model using this technique. We demonstrate that our
approach can probe physics in the regime of the effective field theory in which
the quartic term dominates, while successfully reproducing the known results
for cubic interactions. |
On black hole thermodynamics from super Yang-Mills: We consider maximally supersymmetric U(N) Yang-Mills in (1+p)-dimensions for
p < 3. In the 't Hooft large N limit this is conjectured to be dual to N
Dp-branes in the decoupling limit. At low temperatures T << \lambda^{1/(3-p)}
governed by the dimensionful 't Hooft coupling \lambda, supergravity black
holes predict the free energy density goes as ~ N^2 T^{2(7-p)/(5-p)} and the
expectation value of the scalars goes as ~ T^{2/(5-p)}, with dimensions made up
by \lambda. The purpose of this work is to explain the origin of these peculiar
powers of temperature. We argue that these powers naturally arise by requiring
that the low energy moduli of the theory become strongly coupled at low
temperature. As an application, we consider the BMN quantum mechanics that
results from a supersymmetric deformation of the p=0 theory. The black holes
dual to this deformed theory have not yet been constructed, and our analysis
can be used to make an explicit prediction for their thermodynamic behaviour. | A black hole hologram in de Sitter space: In this paper we show that the entropy of de Sitter space with a black hole
in arbitrary dimension can be understood using a modified Cardy-Verlinde
entropy formula. We also comment on the observer dependence of the de Sitter
entropy. |
Orientifold limits of singular $F$-theory vacua: We construct global orientifold limits of singular $F$-theory vacua whose
associated gauge groups are SO(3), SO(5), SO(6), $F_4$, SU(4), and Spin(7). For
each limit we show a universal tadpole relation is satisfied, which is a
homological identity whose dimension-zero component encodes the matching of the
D3 charge between each $F$-theory compactification and its orientifold limit.
While for smooth $F$-theory compactifications which admit global orientifold
limits the contribution to the associated universal tadpole relation comes from
its Chern class, we show that for all singular $F$-theory compactifications
under consideration, the contribution to the universal tadpole relation comes
from its \emph{stringy} Chern class. | Self-dual solutions of 2+1 Einstein gravity with a negative cosmological
constant: All the causally regular geometries obtained from (2+1)-anti-de Sitter space
by identifications by isometries of the form $P \rightarrow (\exp \pi\xi) P$,
where $\xi$ is a self-dual Killing vector of $so(2,2)$, are explicitely
constructed. Their remarkable properties (Killing vectors, Killing spinors) are
listed. These solutions of Einstein gravity with negative cosmological constant
are also invariant under the string duality transformation applied to the
angular translational symmetry $\phi \rightarrow \phi+a$ The analysis is made
particularly convenient through the construction of {\em global} coordinates
adapted to the identifications.} |
$SU(3)_C\times SU(2)_L\times U(1)_Y\left( \times U(1)_X \right)$ as a
symmetry of division algebraic ladder operators: We demonstrate a model which captures certain attractive features of $SU(5)$
theory, while providing a possible escape from proton decay. In this paper we
show how ladder operators arise from the division algebras $\mathbb{R}$,
$\mathbb{C}$, $\mathbb{H}$, and $\mathbb{O}$. From the $SU(n)$ symmetry of
these ladder operators, we then demonstrate a model which has much structural
similarity to Georgi and Glashow's $SU(5)$ grand unified theory. However, in
this case, the transitions leading to proton decay are expected to be blocked,
given that they coincide with presumably forbidden transformations which would
incorrectly mix distinct algebraic actions. As a result, we find that we are
left with $G_{sm} = SU(3)_C\times SU(2)_L\times U(1)_Y / \mathbb{Z}_6$.
Finally, we point out that if $U(n)$ ladder symmetries are used in place of
$SU(n)$, it may then be possible to find this same $G_{sm}=SU(3)_C\times
SU(2)_L\times U(1)_Y / \mathbb{Z}_6$, together with an extra $U(1)_X$ symmetry,
related to $B-L$. | Soft photon radiation and entanglement: We study the entanglement between soft and hard particles produced in generic
scattering processes in QED. The reduced density matrix for the hard particles,
obtained via tracing over the entire spectrum of soft photons, is shown to have
a large eigenvalue, which governs the behavior of the Renyi entropies and of
the non-analytic part of the entanglement entropy at low orders in perturbation
theory. The leading perturbative entanglement entropy is logarithmically IR
divergent. The coefficient of the IR divergence exhibits certain universality
properties, irrespectively of the dressing of the asymptotic charged particles
and the detailed properties of the initial state. In a certain kinematical
limit, the coefficient is proportional to the cusp anomalous dimension in QED.
For Fock basis computations associated with two-electron scattering, we derive
an exact expression for the large eigenvalue of the density matrix in terms of
hard scattering amplitudes, which is valid at any finite order in perturbation
theory. As a result, the IR logarithmic divergences appearing in the
expressions for the Renyi and entanglement entropies persist at any finite
order of the perturbative expansion. To all orders, however, the IR logarithmic
divergences exponentiate, rendering the large eigenvalue of the density matrix
IR finite. The all-orders Renyi entropies (per unit time, per particle flux),
which are shown to be proportional to the total inclusive cross-section in the
initial state, are also free of IR divergences. The entanglement entropy, on
the other hand, retains non-analytic, logarithmic behavior with respect to the
size of the box (which provides the IR cutoff) even to all orders in
perturbation theory. |
AdS$_3$ T-duality and evidence for ${\cal N}=5,6$ superconformal quantum
mechanics: We construct two families of AdS$_2$ vacua in Type IIB Supergravity
performing U(1) and SL(2) T-dualities on the $\text{AdS}_3 \times \text{$
\widehat{\mathbb{CP}}\!\!~^3$} \times $ I solutions to Type IIA recently
reported in arXiv:2304.12207. Depending on the T-duality we operate, we find
two different classes of solutions of the type $\text{AdS}_2 \times \text{$
\widehat{\mathbb{CP}}\!\!~^3$} \times $ I $\times$ I and $\text{AdS}_3 \times
\text{$ \widehat{\mathbb{CP}}\!\!~^3$} \times $ I $\times$ S$^1$. This provides
evidence for more general classes of solutions $\text{AdS}_2 \times \text{$
\widehat{\mathbb{CP}}\!\!~^3$} \times \Sigma $, dual to superconformal quantum
mechanics with ${\cal N}=5,6$ supersymmetry. | The 1.5 Order Formalism does not Generate a Valid BRS Transformation for
Supergravity: The 1.5 order formalism (sometimes called a `trick') is the cornerstone of
modern supergravity. In this paper, the free massive Wess--Zumino theory is
used as a simple toy model to look at the BRS symmetry of the first, second and
1.5 order formalisms. This easily shows that the 1.5 order formalism is flawed
for all theories. The 1.5 algebra naively appears to close. However, when it is
analyzed in detail, in a simple model, where easy calculations are available,
the 1.5 formalism always generates an invalid BRS operator, which is not even
nilpotent. This clearly is also the case for supergravity. It follows that a
revised and completed set of nilpotent first order supergravity transformations
is needed to properly understand 3+1 dimensional supergravity. Such a set seems
easy to write down, by simply adding two more auxiliary fields so that the spin
connection becomes part of a super--YM multiplet. |
Role of switching-on and -off effects in the vacuum instability: We find exact differential mean numbers of fermions and bosons created from
the vacuum due to a composite electric field of special configuration. This
configuration imitates a finite switching-on and -off regime and consists of
fields that switch-on exponentially from the infinitely remote past, remains
constant during a certain interval $T$ and switch-off exponentially to the
infinitely remote future. We show that calculations in the slowly varying field
approximation are completely predictable in the framework of a locally constant
field approximation. Beyond the slowly varying field approximation, we study
effects of fast switching-on and -off in a number of cases when the size of the
dimensionless parameter $\sqrt{eE}T$ is either close or exceeds the threshold
value that determines the transition from a regime sensitive to on-off
parameters to the slowly varying regime for which these effects are secondary. | Dilaton Black Hole Entropy from Entropy Function Formalism: It has been shown that the entropy function formalism is an efficient way to
calculate the entropy of black holes in string theory. We check this formalism
for the extremal charged dilaton black hole. We find the general
four-derivative correction on the black hole entropy from the value of the
entropy function at its extremum point. |
Brane-Antibrane Action from Boundary String Field Theory: In this paper we give the boundary string field theory description of
brane-antibrane systems. From the world-sheet action of brane-antibrane systems
we obtain the tachyon potential and discuss the tachyon condensation exactly.
We also find the world-volume action including the gauge fields. Moreover we
determine RR-couplings exactly for non-BPS branes and brane-antibranes. These
couplings are written by superconnections and correspond to K^1(M) and K^0(M)
for the non-BPS branes and brane-antibranes, respectively. We also show that
Myers terms appear if we include the transverse scalars in the boundary sigma
model action. | Note on Twisted Elliptic Genus of K3 Surface: We discuss the possibility of Mathieu group M24 acting as symmetry group on
the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the
present authors. One way of testing this proposal is to derive the twisted
elliptic genera for all conjugacy classes of M24 so that we can determine the
unique decomposition of expansion coefficients of K3 elliptic genus into
irreducible representations of M24. In this paper we obtain all the hitherto
unknown twisted elliptic genera and find a strong evidence of Mathieu
moonshine. |
Dissipative Axial Inflation: We analyze in detail the background cosmological evolution of a scalar field
coupled to a massless abelian gauge field through an axial term
$\frac{\phi}{f_\gamma} F \tilde{F}$, such as in the case of an axion. Gauge
fields in this case are known to experience tachyonic growth and therefore can
backreact on the background as an effective dissipation into radiation energy
density $\rho_R$, which which can lead to inflation without the need of a flat
potential. We analyze the system, for momenta $k$ smaller than the cutoff
$f_\gamma$, including numerically the backreaction. We consider the evolution
from a given static initial condition and explicitly show that, if $f_\gamma$
is smaller than the field excursion $\phi_0$ by about a factor of at least
${\cal O} (20)$, there is a friction effect which turns on before that the
field can fall down and which can then lead to a very long stage of inflation
with a generic potential. In addition we find superimposed oscillations, which
would get imprinted on any kind of perturbations, scalars and tensors. Such
oscillations have a period of 4-5 efolds and an amplitude which is typically
less than a few percent and decreases linearly with $f_\gamma$. We also stress
that the comoving curvature perturbation on uniform density should be sensitive
to slow-roll parameters related to $\rho_R$ rather than $\dot{\phi}^2/2$,
although we postpone a calculation of the power spectrum and of non-gaussianity
to future work and we simply define and compute suitable slow roll parameters.
Finally we stress that this scenario may be realized in the axion case, if the
coupling $1/f_\gamma$ to U(1) (photons) is much larger than the coupling
$1/f_G$ to non-abelian gauge fields (gluons), since the latter sets the range
of the potential and therefore the maximal allowed $\phi_0\sim f_G$. | Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel
gluing: The correspondence between four-dimensional $\mathcal{N}=2$ superconformal
field theories and vertex operator algebras, when applied to theories of class
$\mathcal{S}$, leads to a rich family of VOAs that have been given the monicker
chiral algebras of class $\mathcal{S}$. A remarkably uniform construction of
these vertex operator algebras has been put forward by Tomoyuki Arakawa in
arXiv:1811.01577. The construction of arXiv:1811.01577 takes as input a choice
of simple Lie algebra $\mathfrak{g}$, and applies equally well regardless of
whether $\mathfrak{g}$ is simply laced or not. In the non-simply laced case,
however, the resulting VOAs do not correspond in any clear way to known
four-dimensional theories. On the other hand, the standard realisation of class
$\mathcal S$ theories involving non-simply laced symmetry algebras requires the
inclusion of outer automorphism twist lines, and this requires a further
development of the approach of arXiv:1811.01577. In this paper, we give an
account of those further developments and propose definitions of most chiral
algebras of class $\mathcal S$ with outer automorphism twist lines. We show
that our definition passes some consistency checks and point out some important
open problems. |
Christ-Lee Model: Augmented Supervariable Approach: We derive the complete set of off-shell nilpotent and absolutely
anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations
for the gauge-invariant Christ-Lee model by exploiting the celebrated
(dual-)horizontality conditions together with the gauge-invariant and
(anti-)co-BRST invariant restrictions within the framework of geometrical
"augmented" supervariable approach to BRST formalism. We show the (anti-) BRST
and (anti-)co-BRST invariances of the Lagrangian in the context of
supervariable approach. We also provide the geometrical origin and capture the
key properties associated with the (anti-)BRST and (anti-)co-BRST symmetry
transformations (and corresponding conserved charges) in terms of the
supervariables and Grassmannian translational generators. | Supersymmetric Spin Glass: The evidently supersymmetric four-dimensional Wess-Zumino model with quenched
disorder is considered at the one-loop level. The infrared fixed points of a
beta-function form the moduli space $M = RP^2$ where two types of phases were
found: with and without replica symmetry. While the former phase possesses only
a trivial fixed point, this point become unstable in the latter phase which may
be interpreted as a spin glass phase. |
Exact results in N=2 gauge theories: We derive exact formulae for the partition function and the expectation
values of Wilson/'t Hooft loops, thus directly checking their S-duality
transformations. We focus on a special class of N=2 gauge theories on S^4 with
fundamental matter. In particular we show that, for a specific choice of the
masses, the matrix model integral defining the gauge theory partition function
localizes around a finite set of critical points where it can be explicitly
evaluated and written in terms of generalized hypergeometric functions. From
the AGT perspective the gauge theory partition function, evaluated with this
choice of masses, is viewed as a four point correlator involving the insertion
of a degenerated field. The well known simplicity of the degenerated correlator
reflects the fact that for these choices of masses only a very restrictive type
of instanton configurations contributes to the gauge theory partition function. | Energy's and amplitudes' positivity: In QFT, the null energy condition (NEC) for a classical field configuration
is usually associated with that configuration's stability against small
perturbations, and with the sub-luminality of these. Here, we exhibit an
effective field theory that allows for stable NEC-violating solutions with
exactly luminal excitations only. The model is the recently introduced
`galileon', or more precisely its conformally invariant version. We show that
the theory's low-energy S-matrix obeys standard positivity as implied by
dispersion relations. However we also show that if the relevant NEC-violating
solution is inside the effective theory, then other (generic) solutions allow
for superluminal signal propagation. While the usual association between
sub-luminality and positivity is not obeyed by our example, that between NEC
and sub-luminality is, albeit in a less direct way than usual. |
The first-order deviation of superpolynomial in an arbitrary
representation from the special polynomial: Like all other knot polynomials, the superpolynomials should be defined in
arbitrary representation R of the gauge group in (refined) Chern-Simons theory.
However, not a single example is yet known of a superpolynomial beyond
symmetric or antisymmetric representations. We consider the expansion of the
superpolynomial around the special polynomial in powers of (q-1) and (t-1) and
suggest a simple formula for the first-order deviation, which is presumably
valid for arbitrary representation. This formula can serve as a crucial lacking
test of various formulas for non-trivial superpolynomials, which will appear in
the literature in the near future. | Property values: By ascribing a complex anticommuting variable $\zeta$ to each basic {\em
property} of a field, it is possible to describe all the fundamental particles
as combinations of only five $\zeta$ and understand the occurrence of particle
generations. An extension of space-time $x$ to include property then specifies
the `where-when and what' of an event and it allows for a generalized
relativity wherein the gauge fields lie in the $x - \zeta$ sector and the Higgs
fields in the $\zeta - \zeta$ sector. |
Self-dual compact gauged baby skyrmions in a continuous medium: We investigate the existence of self-dual configurations in the restricted
gauged baby Skyrme model enlarged with a $Z_2$--symmetry, which introduces a
real scalar field. For such a purpose, we implement the Bogomol'nyi procedure
that provides a lower bound for the energy and the respective self-dual
equations whose solutions saturate such a bound. Aiming to solve the self-dual
equations, we specifically focused on a class of topological structures called
compacton. We obtain the corresponding numerical solutions within two distinct
scenarios, each defined by a scalar field, allowing us to describe different
magnetic media. Finally, we analyze how the compacton profiles change when
immersed in each medium. | SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one
Logarithmic CFT: We show that the SU(2)_0 WZNW model has a hidden OSp(2|2)_{-2} symmetry. Both
these theories are known to have logarithms in their correlation functions. We
also show that, like OSp(2|2)_{-2}, the logarithmic structure present in the
SU(2)_0 model is due to the underlying c=-2 sector. We also demonstrate that
the quantum Hamiltonian reduction of SU(2)_0 leads very directly to the
correlation functions of the c=-2 model. We also discuss some of the novel
boundary effects which can take place in this model. |
Quantum Field Theory in Large N Wonderland: Three Lectures: In these lecture notes, I review how to use large N techniques to solve
quantum field theories in various dimensions. In particular, the case of
N-dimensional quantum mechanics, non-relativistic cold and dense neutron
matter, and scalar field theory in four dimensions are covered. A recurring
theme is that large N solutions are fully non-perturbative, and can be used to
reliably access quantum field theory for parameter regions where weak-coupling
expansions simply fail. | TTbar deformation and the light-cone gauge: The homogeneous inviscid Burgers equation which determines the spectrum of a
TTbar deformed model has a natural interpretation as the condition of the gauge
invariance of the target space-time energy and momentum of a (non-critical)
string theory quantised in a generalised uniform light-cone gauge which depends
on the deformation parameter. As a simple application of the light-cone gauge
interpretation we derive the TTbar deformed Lagrangian for a system of any
number of scalars, fermions and chiral bosons with an arbitrary potential. We
find that the TTbar deformation is driven by the canonical Noether
stress-energy tensor but not the covariant one. |
Observables from the Spinning Eikonal: We study the classical dynamics of spinning particles using scattering
amplitudes and eikonal exponentiation. We show that observables are determined
by a simple algorithm. A wealth of complexity arises in perturbation theory as
positions, momenta and spins must be iteratively corrected at each order. Even
though we restrict ourselves to one-loop computations at quadratic order in
spin, nevertheless we encounter and resolve a number of subtle effects.
Finally, we clarify the links between our work and various other eikonal
approaches to spinning observables. | Classification of kinematical Lie algebras: We summarise the classification of kinematical Lie algebras in arbitrary
dimension and indicate which of the kinematical Lie algebras admit an invariant
inner product. |
The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations: We introduce an extension of the generalised $T\bar{T}$-deformation described
by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We
show that this gives deformations of S-matrices beyond CDD factors, generating
arbitrary functional dependence on momenta. We further derive from basic
principles of statistical mechanics the flow equations for the free energy and
all free energy fluxes. From this follows, without invoking the microscopic
Bethe ansatz or other methods from integrability, that the thermodynamics of
the deformed models are described by the integral equations of the
thermodynamic Bethe-Ansatz, and that the exact average currents take the form
expected from generalised hydrodynamics, both in the classical and quantum
realms. | Holographic incoherent transport in Einstein-Maxwell-dilaton Gravity: Recent progress in the holographic approach makes it more transparent that
each conductivity can be decomposed into the coherent contribution due to
momentum relaxation and the incoherent contribution due to intrinsic current
relaxation. In this paper we investigate this decomposition in the framework of
Einstein-Maxwell-dilaton theory. We derive the perturbation equations, which
are decoupled for a large class of background solutions, and then obtain the
analytic results of conductivity with the slow momentum relaxation in low
frequency approximation, which is consistent with the known results from memory
matrix techniques. |
Overlaps of Partial Neel States and Bethe States: Partial Neel states are generalizations of the ordinary Neel (classical
anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps
of these states with Bethe states. We first identify this overlap with a
partial version of reflecting-boundary domain-wall partition function, and then
derive various determinant representations for off-shell and on-shell Bethe
states. | Bit threads on hypergraphs: Recent work has characterized the various inequalities that entanglement
entropies represented by min-cuts on hypergraphs will satisfy. This collection,
the hypergraph entropy cone, can be seen as a generalization of the holographic
entropy cone which describes the entropies given by both min-cuts on 2-graphs
and those of holographic states in AdS/CFT. In this article we describe a
generalization of bit threads which allows us to describe max multiflows on
hypergraphs. We further comment on its properties and interpretation in
holography. |
Exploring the gravity sector of emergent higher-spin gravity: effective
action and a solution: We elaborate the description of the semi-classical gravity sector of
Yang-Mills matrix models on a covariant quantum FLRW background. The basic
geometric structure is a frame, which arises from the Poisson structure on an
underlying $S^2$ bundle over space-time. The equations of motion for the
associated Weitzenb\"ock torsion obtained in arXiv:2002.02742 are rewritten in
the form of Yang-Mills-type equations for the frame. An effective action is
found which reproduces these equations of motion, which contains an
Einstein-Hilbert term coupled to a dilaton, an axion and a Maxwell-type term
for the dynamical frame. An explicit rotationally invariant solution is found,
which describes a gravitational field coupled to the dilaton. | Indices for 6 dimensional superconformal field theories: We review some recent developments in the 6 dimensional (2, 0) superconformal
field theories, focusing on their BPS spectra in the Coulomb and symmetric
phases computed by various Witten indices. We shall discuss the instanton
partition function of 5d maximal super-Yang-Mills theory, and the 6d
superconformal index. |
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric
AdS$_{\bf 5}$ black holes: We present a holographic derivation of the entropy of supersymmetric
asymptotically AdS$_5$ black holes. We define a BPS limit of black hole
thermodynamics by first focussing on a supersymmetric family of complexified
solutions and then reaching extremality. We show that in this limit the black
hole entropy is the Legendre transform of the on-shell gravitational action
with respect to three chemical potentials subject to a constraint. This
constraint follows from supersymmetry and regularity in the Euclidean bulk
geometry. Further, we calculate, using localization, the exact partition
function of the dual $\mathcal{N}=1$ SCFT on a twisted $S^1\times S^3$ with
complexified chemical potentials obeying this constraint. This defines a
generalization of the supersymmetric Casimir energy, whose Legendre transform
at large $N$ exactly reproduces the Bekenstein-Hawking entropy of the black
hole. | Complexity for link complement States in Chern Simons Theory: We study notions of complexity for link complement states in Chern Simons
theory with compact gauge group $G$. Such states are obtained by the Euclidean
path integral on the complement of $n$-component links inside a 3-manifold
$M_3$. For the Abelian theory at level $k$ we find that a natural set of
fundamental gates exists and one can identify the complexity as differences of
linking numbers modulo $k$. Such linking numbers can be viewed as coordinates
which embeds all link complement states into $\mathbb{Z}_k ^{\otimes n(n-1)/2}$
and the complexity is identified as the distance with respect to a particular
norm. For non-Abelian Chern Simons theories, the situation is much more
complicated. We focus here on torus link states and show that the problem can
be reduced to defining complexity for a single knot complement state. We
suggest a systematic way to choose a set of minimal universal generators for
single knot complement states and then evaluate the complexity using such
generators. A detailed illustration is shown for $SU(2)_k$ Chern Simons theory
and the results can be extended to general compact gauge group. |
Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories: The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare
and dressed BPS monopole operators. We utilise the conformal dimension to
define a fan which, upon intersection with the weight lattice of a GNO-dual
group, gives rise to a collection of semi-groups. It turns out that the unique
Hilbert bases of these semi-groups are a sufficient, finite set of monopole
operators which generate the entire chiral ring. Moreover, the knowledge of the
properties of the minimal generators is enough to compute the Hilbert series
explicitly. The techniques of this paper allow an efficient evaluation of the
Hilbert series for general rank gauge groups. As an application, we provide
various examples for all rank two gauge groups to demonstrate the novel
interpretation. | Deconfinement and Thermodynamics in 5D Holographic Models of QCD: We review 5D holographic approaches to finite temperature QCD. Thermodynamic
properties of the "hard-wall" and the "soft-wall" models are derived. Various
non-realistic features in these models are cured by the set-up of improved
holographic QCD, that we review here. |
Mass Deformations of Unoriented Quiver Theories: We study the interplay between mass deformations and unoriented projections
of super-conformal quiver gauge theories resulting from D3-branes at (toric)
Calabi-Yau singularities. We focus on simple orbifold cases
($\mathbb{C}^3/\mathbb{Z}_3$ and $\mathbb{C}^3/\mathbb{Z}_4$) and their
non-orbifold descendants. This allows us to generalize the construction rules
and clarify points that have been previously overlooked. In particular we spell
out the conditions of anomaly cancellations as well as super-conformal
invariance that typically require the introduction of flavour branes, which in
turn may spoil toric symmetry. Finally, we discuss duality cascades in this
context and the interplay between Seiberg/toric duality and unoriented
projection with (or without) mass deformations. | Background independent exact renormalisation: A geometric formulation of Wilson's exact renormalisation group is presented
based on a gauge invariant ultraviolet regularisation scheme without the
introduction of a background field. This allows for a manifestly background
independent approach to quantum gravity and gauge theories in the continuum.
The regularisation is a geometric variant of Slavnov's scheme consisting of a
modified action, which suppresses high momentum modes, supplemented by
Pauli-Villars determinants in the path integral measure. An exact
renormalisation group flow equation for the Wilsonian effective action is
derived by requiring that the path integral is invariant under a change in the
cutoff scale while preserving quasi-locality. The renormalisation group flow is
defined directly on the space of gauge invariant actions without the need to
fix the gauge. We show that the one-loop beta function in Yang-Mills and the
one-loop divergencies of General Relativity can be calculated without fixing
the gauge. As a first non-perturbative application we find the form of the
Yang-Mills beta function within a simple truncation of the Wilsonian effective
action. |
Color Superconductivity in Holographic SYM Theory: A holographic bottom-up model used in studying the superconducting system is
applied to search for the color superconducting phase of supersymmetric
Yang-Mills theory. We apply the probe analysis of this model to the
supersymmetric Yang-Mills theory in both the confinement and deconfinement
phases. In this analysis, we find the color superconductivity in both phases
when the baryon chemical potential exceeds a certain critical value. This
result implies that, above the critical chemical potential, a color non-singlet
diquark operator, namely the Cooper pair, has its vacuum expectation value even
in the confinement phase. In order to improve this peculiar situation, we
proceed the analysis by taking account of the full back-reaction from the
probe. As a result, the color superconducting phase, which is observed in the
probe approximation, disappears in both the confinement and deconfinement
phases when parameters of the theory are set within their reasonable values. | Marginal Deformations of 3d N=4 Linear Quiver Theories: We study superconformal deformations of the $T_\rho^{\hat\rho}[SU(N)]$
theories of Gaiotto-Hanany-Witten, paying special attention to mixed-branch
operators with both electrically- and magnetically-charged fields. We explain
why all marginal ${\cal N}=2$ operators of an ${\cal N}=4$ CFT$_3$ can be
extracted unambiguously from the superconformal index. Computing the index at
the appropriate order we show that the mixed moduli in
$T_\rho^{\hat\rho}[SU(N)]$ theories are double-string operators transforming in
the (Adjoint, Adjoint) representation of the electric and magnetic flavour
groups, up to some overcounting for quivers with abelian gauge nodes. We
comment on the holographic interpretation of the results, arguing in particular
that gauged supergravities can capture the entire moduli space if, in addition
to the (classical) parameters of the background solution, one takes also into
account the (quantization) moduli of boundary conditions. |
Hidden Simplicity of Gauge Theory Amplitudes: These notes were given as lectures at the CERN Winter School on Supergravity,
Strings and Gauge Theory 2010. We describe the structure of scattering
amplitudes in gauge theories, focussing on the maximally supersymmetric theory
to highlight the hidden symmetries which appear. Using the BCFW recursion
relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory,
and describe how it produces a sum of invariants of a large symmetry algebra.
We review amplitudes in the planar theory beyond tree-level, describing the
connection between amplitudes and Wilson loops, and discuss the implications of
the hidden symmetries. | Holographic complexity is nonlocal: We study the "complexity equals volume" (CV) and "complexity equals action"
(CA) conjectures by examining moments of of time symmetry for $\rm AdS_3$
wormholes having $n$ asymptotic regions and arbitrary (orientable) internal
topology. For either prescription, the complexity relative to $n$ copies of the
$M=0$ BTZ black hole takes the form $\Delta C = \alpha c \chi $, where $c$ is
the central charge and $\chi$ is the Euler character of the bulk time-symmetric
surface. The coefficients $\alpha_V = -4\pi/3$, $\alpha_A = 1/6 $ defined by CV
and CA are independent of both temperature and any moduli controlling the
geometry inside the black hole. Comparing with the known structure of dual CFT
states in the hot wormhole limit, the temperature and moduli independence of
$\alpha_V$, $\alpha_A$ implies that any CFT gate set defining either complexity
cannot be local. In particular, the complexity of an efficient quantum circuit
building local thermofield-double-like entanglement of thermal-sized patches
does not depend on the separation of the patches so entangled. We also comment
on implications of the (positive) sign found for $\alpha_A$, which requires the
associated complexity to decrease when handles are added to our wormhole. |
Scaling Exponents for Lattice Quantum Gravity in Four Dimensions: In this work nonperturbative aspects of quantum gravity are investigated
using the lattice formulation, and some new results are presented for critical
exponents, amplitudes and invariant correlation functions. Values for the
universal scaling dimensions are compared with other nonperturbative approaches
to gravity in four dimensions, and specifically to the conjectured value for
the universal critical exponent $\nu =1 /3$. It is found that the lattice
results are generally consistent with gravitational anti-screening, which would
imply a slow increase in the strength of the gravitational coupling with
distance, and here detailed estimates for exponents and amplitudes
characterizing this slow rise are presented. Furthermore, it is shown that in
the lattice approach (as for gauge theories) the quantum theory is highly
constrained, and eventually by virtue of scaling depends on a rather small set
of physical parameters. Arguments are given in support of the statement that
the fundamental reference scale for the growth of the gravitational coupling
$G$ with distance is represented by the observed scaled cosmological constant
$\lambda$, which in gravity acts as an effective nonperturbative infrared
cutoff. In the vacuum condensate picture a fundamental relationship emerges
between the scale characterizing the running of $G$ at large distances, the
macroscopic scale for the curvature as described by the observed cosmological
constant, and the behavior of invariant gravitational correlation functions at
large distances. Overall, the lattice results suggest that the infrared slow
growth of $G$ with distance should become observable only on very large
distance scales, comparable to $\lambda$. It is hoped that future high
precision satellite experiments will possibly come within reach of this small
quantum correction, as suggested by a vacuum condensate picture of quantum
gravity. | Thermodynamics of a charged hairy black hole in (2+1) dimensions: In this paper we study thermodynamics, statistics and spectroscopic aspects
of a charged black hole with a scalar hair coupled to the gravity in (2+1)
dimensions. We obtained effects of the black hole charge and scalar field on
the thermodynamical and statistical quantities. We find that scalar charge may
increase entropy, temperature and probability, while may decrease black hole
mass, free and internal energy. Also electric charge increases probability and
decreases temperature and internal energy. Also we investigate stability of the
system and find that the thermodynamical stability exists. |
Born-Infeld-AdS black hole phase structure: Landau theory and free
energy landscape approaches: We start with a brief overview of the basic thermodynamic properties of the
Born-Infeld metric in AdS spacetime. Using the concept of the enthalpy
characterizing the total mass of the black hole, in our present paper, we probe
the thermal phase transition structure, the dynamic and kinetic behavior of the
Born-Infeld-AdS black hole. The emergence of the triple point behavior and the
possible ruling out the reentrant phase transition, for a certain parametric
value of the charge on the free energy landscape, we scrutinize the stochastic
dynamics and the kinetic processes. We describe such processes during the black
hole phase transitions in terms of the Landau functional and equivalently by
the Fokker-Planck equation in the context of black hole chemistry.
Our analysis establishes a pertinent bridge between the thermal behavior
among the different states of the Van-der-Waals-like fluids and the
Born-Infeld-AdS black holes phases. To visualize the direct implications of the
Landau functional of the usual Van-der-Waals-like fluids, we consistently
employed the generic Landau formalism for the analysis of the black hole phase
transitions of the Born-Infeld-AdS black holes. We find that such
investigations are worthy of study in implementing the continuous phase
transition behavior during the Hawking radiation. For more details, and in
addition to the exploitation of the Landau functional, we introduce ... | Correspondence Principle in a PP-wave Background: We discuss the correspondence point between a string state and a black hole,
in a pp-wave background, and find that the answer is considerably different
from that in a flat spacetime background. |
Phase Transitions of Correlations in Black Hole Geometries: We study the holographic realization of optimized correlation measures --
measures of quantum correlation that generalize elementary entropic formulas --
in two-dimensional thermal states dual to spacetimes with a black hole horizon.
We consider the symmetric bipartite optimized correlation measures: the
entanglement of purification, Q-correlation, R-correlation, and squashed
entanglement, as well as the mutual information, a non-optimized correlation
measure, and identify the bulk surface configurations realizing their geometric
duals over the parameter space of boundary region sizes and the black hole
radius. This parameter space is divided into phases associated with given
topologies for these bulk surface configurations, and first-order phase
transitions occur as a new topology of bulk surfaces becomes preferred. The
distinct phases can be associated with different degrees of correlation between
the boundary regions and the thermal environment. The Q-correlation has the
richest behavior, with a structure of nested optimizations leading to two
topologically distinct bulk surface configurations being equally valid as
geometric duals at generic points in the phase diagram. | The fate of non-diagonalizable interactions in quasidilaton theory: It has been shown that the spherically symmetric solutions in a subclass of
quasidilaton theory are stable against all degrees of freedom and does not even
exhibit superluminal propagation. These solutions can be found by switching off
scalar-tensor interactions, which can not be removed by a local transformation.
In this paper, we extend the analysis to quasidilaton theory, including
non-diagonalizable scalar-tensor interactions. We show that all solutions
inside the Vainshtein radius are problematic : the scalar mode in massive
graviton suffers from gradient instabilities, the vector mode are infinitely
strongly coupled vector perturbations, or the Vainshtein mechanism is absent. |
Heterotic/$F$-theory Duality and Narasimhan-Seshadri Equivalence: Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry
breaking presents the challenge of achieving the dual $\mathbb{Z}_{2}$-action
on the $F$-theory model in such a way that the $\mathbb{Z}_{2}$-quotient is
Calabi-Yau with an Enriques $\mathrm{GUT}$ surface over which
$SU\left(5\right)_{gauge}$ symmetry is maintained. We propose a new way to
approach this problem by taking advantage of a little-noticed choice in the
application of Narasimhan-Seshadri equivalence between real $E_{8}$-bundles
with Yang-Mills connection and their associated complex holomorphic
$E_{8}^{\mathbb{C}}$-bundles, namely the one given by the real outer
automorphism of $E_{8}^{\mathbb{C}}$ by complex conjugation. The triviality of
the restriction on the compact real form $E_{8}$ allows one to introduce it
into the $\mathbb{Z}_{2}$-action, thereby restoring $E_{8}$- and hence
$SU\left(5\right)_{gauge}$- symmetry on which the Wilson line can be wrapped. | Cohomological gauge theory, quiver matrix models and Donaldson-Thomas
theory: We study the relation between Donaldson-Thomas theory of Calabi-Yau
threefolds and a six-dimensional topological Yang-Mills theory. Our main
example is the topological U(N) gauge theory on flat space in its Coulomb
branch. To evaluate its partition function we use equivariant localization
techniques on its noncommutative deformation. As a result the gauge theory
localizes on noncommutative instantons which can be classified in terms of
N-coloured three-dimensional Young diagrams. We give to these noncommutative
instantons a geometrical description in terms of certain stable framed coherent
sheaves on projective space by using a higher-dimensional generalization of the
ADHM formalism. From this formalism we construct a topological matrix quantum
mechanics which computes an index of BPS states and provides an alternative
approach to the six-dimensional gauge theory. |
G-Structures and Wrapped NS5-Branes: We analyse the geometrical structure of supersymmetric solutions of type II
supergravity of the form R^{1,9-n} x M_n with non-trivial NS flux and dilaton.
Solutions of this type arise naturally as the near-horizon limits of wrapped NS
fivebrane geometries. We concentrate on the case d=7, preserving two or four
supersymmetries, corresponding to branes wrapped on associative or SLAG
three-cycles. Given the existence of Killing spinors, we show that M_7 admits a
G_2-structure or an SU(3)-structure, respectively, of specific type. We also
prove the converse result. We use the existence of these geometric structures
as a new technique to derive some known and new explicit solutions, as well as
a simple theorem implying that we have vanishing NS three-form and constant
dilaton whenever M_7 is compact with no boundary. The analysis extends simply
to other type II examples and also to type I supergravity. | Multiplicity-free $U_q(sl_N)$ 6-j symbols: relations, asymptotics,
symmetries: A closed form expression for multiplicity-free quantum 6-j symbols (MFS) was
proposed in arXiv:1302.5143 for symmetric representations of $U_q(sl_N)$, which
are the simplest class of multiplicity-free representations. In this paper we
rewrite this expression in terms of q-hypergeometric series ${}_4\Phi_3$. We
claim that it is possible to express any MFS through the 6-j symbol for
$U_q(sl_2)$ with a certain factor. It gives us a universal tool for the
extension of various properties of the quantum 6-j symbols for $U_q(sl_2)$ to
the MFS. We demonstrate this idea by deriving the asymptotics of the MFS in
terms of associated tetrahedron for classical algebra $U(sl_N)$.
Next we study MFS symmetries using known hypergeometric identities such as
argument permutations and Sears' transformation. We describe symmetry groups of
MFS. As a result we get new symmetries, which are a generalization of the
tetrahedral symmetries and the Regge symmetries for N = 2. |
Induced Parity Breaking Term in Arbitrary Odd Dimensions at Finite
Temperature: We calculate the exact parity odd part of the effective action
($\Gamma_{odd}^{2d+1}$) for massive Dirac fermions in 2d+1 dimensions at finite
temperature, for a certain class of gauge field configurations. We consider
first Abelian external gauge fields, and then we deal with the case of a
non-Abelian gauge group containing an Abelian U(1) subgroup. For both cases, it
is possible to show that the result depends on topological invariants of the
gauge field configurations, and that the gauge transformation properties of
$\Gamma_{odd}^{2d+1}$ depend only on those invariants and on the winding number
of the gauge transformation. | Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory: We derive a new functional renormalization group equation for Hamiltonian
Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and
ghost propagators are solved under the assumption of ghost dominance within
different diagrammatic approximations. The results are compared to those
obtained in the variational approach and the reliability of the approximations
is discussed. |
A refinement of entanglement entropy and the number of degrees of
freedom: We introduce a "renormalized entanglement entropy" which is intrinsically UV
finite and is most sensitive to the degrees of freedom at the scale of the size
R of the entangled region. We illustrated the power of this construction by
showing that the qualitative behavior of the entanglement entropy for a
non-Fermi liquid can be obtained by simple dimensional analysis. We argue that
the functional dependence of the "renormalized entanglement entropy" on R can
be interpreted as describing the renormalization group flow of the entanglement
entropy with distance scale. The corresponding quantity for a spherical region
in the vacuum, has some particularly interesting properties. For a conformal
field theory, it reduces to the previously proposed central charge in all
dimensions, and for a general quantum field theory, it interpolates between the
central charges of the UV and IR fixed points as R is varied from zero to
infinity. We conjecture that in three (spacetime) dimensions, it is always
non-negative and monotonic, and provides a measure of the number of degrees of
freedom of a system at scale R. In four dimensions, however, we find examples
in which it is neither monotonic nor non-negative. | A fermion-soliton system: self-consistent solutions, vacuum polarization
and charge quantization: An integrable two-dimensional system related to certain fermion-soliton
systems is studied. The self-consistent solutions of a static version of the
system are obtained by using the tau function approach. The self-consistent
solutions appear as an infinite number of topological sectors labeled by $n \in
\IZ_{+}$, such that in each sector the scalar field would evolve continuously
from a trivial configuration to the one with half integer topological charge.
The spinor bound states are found analytically for each topological
configuration of the background scalar field. The bound state energy satisfies
an algebraic equation of degree $2n$, so the study of the energy spectrum finds
a connection to the realm of algebraic geometry. We provide explicit
computations for the topological sectors $n=1,2$. Then, by monitoring the
energy spectrum, including the energy flow of any level across $E_n=0$, we
discuss the vacuum polarization induced by the soliton. It is shown that the
equivalence between the Noether and topological currents and the fact that the
coupling constant is related to the one of the Wess-Zumino-Novikov-Witten
(WZNW) model imply the quantization of the spinor and topological charges.
Moreover, we show that the soliton mass as a function of the boson mass agrees
with the Skyrmes's phenomenological conjecture. Our analytical developments
improve and generalize the recent numerical results in the literature performed
for a closely related model by Shahkarami and Gousheh, JHEP06(2011)116. The
construction of the bound states corresponding to the topological sectors $n
\geq 3$ is briefly outlined. |
Longitudinal Rescaling of Quantum Electrodynamics: We investigate quantum longitudinal rescaling of electrodynamics,
transforming coordinates as $x^{0,3}\to\lambda x^{0,3}$ and $x^{1,2}\to
x^{1,2}$, to one loop. We do this by an aspherical Wilsonian renormalization,
which was applied earlier to pure Yang-Mills theory. We find the anomalous
powers of $\lambda$ in the renormalized couplings. Our result is only valid for
$\lambda \lesssim 1$, because perturbation theory breaks down for $\lambda \ll
1$. | Segmented strings coupled to a B-field: In this paper we study segmented strings in AdS$_3$ coupled to a background
two-form whose field strength is proportional to the volume form. By changing
the coupling, the theory interpolates between the Nambu-Goto string and the
$SL(2)$ Wess-Zumino-Witten model. In terms of the kink momentum vectors, the
action is independent of the coupling and the classical theory reduces to a
single discrete-time Toda-type theory. The WZW model is a singular point in
coupling space where the map into Toda variables degenerates. |
Finite-size correction and bulk hole-excitations for special case of an
open XXZ chain with nondiagonal boundary terms at roots of unity: Using our solution for the open spin-1/2 XXZ quantum spin chain with N spins
and two arbitrary boundary parameters at roots of unity, the central charge and
the conformal dimensions for bulk hole excitations are derived from the 1/N
correction to the energy (Casimir energy). | Hydrodynamics with gauge anomaly: Variational principle and Hamiltonian
formulation: We present a variational principle for relativistic hydrodynamics with
gauge-anomaly terms for a fluid coupled to an Abelian background gauge field.
For this we utilize the Clebsch parametrization of the velocity field. We also
set up the Hamiltonian formulation and the canonical framework for the theory.
While the equations of motion only involve the density and velocity fields,
i.e., the Clebsch potentials only appear in the combination which is the
velocity field, the generators of symmetry transformations (including the
Hamiltonian) depend explicitly on one of the Clebsch potentials, if the
background field is time-dependent. For the special case of time-independent
background fields, this feature is absent. |
Unitarity of Singh-Hagen model in $D$ dimensions: The particle content of the Singh-Hagen model ($SH$) in $D$ dimensions is
revisited. We suggest a complete set of spin-projection operators acting on
totally symmetric rank-3 fields. We give a general expression for the
propagator and determine the coefficients of the $SH$ model confirming previous
results of the literature. Adding totally symmetric source terms we provide an
unitarity analysis in $D$ dimensions. | Cornering Quantum Gravity: After introducing the covariant phase space calculus, Noether's theorems are
discussed, with particular emphasis on Noether's second theorem and the role of
gauge symmetries. This is followed by the enunciation of the theory of
asymptotic symmetries, and later its application to gravity. Specifically, we
review how the BMS group arises as the asymptotic symmetry group of gravity at
null infinity. Symmetries are so powerful and constraining that memory effects
and soft theorems can be derived from them. The lectures end with more recent
developments in the field: the corner proposal as a unified paradigm for
symmetries in gravity, the extended phase space as a resolution to the problem
of charge integrability, and eventually the implications of the corner proposal
on quantum gravity. |
Equilateral Non-Gaussianity and New Physics on the Horizon: We examine the effective theory of single-field inflation in the limit where
the scalar perturbations propagate with a small speed of sound. In this case
the non-linearly realized time-translation symmetry of the Lagrangian implies
large interactions, giving rise to primordial non-Gaussianities. When the
non-Gaussianities are measurable, these interactions will become strongly
coupled unless new physics appears close to the Hubble scale. Due to its
proximity to the Hubble scale, the new physics is not necessarily decoupled
from inflationary observables and can potentially affect the predictions of the
model. To understand the types of corrections that may arise, we construct
weakly-coupled completions of the theory and study their observational
signatures. | On spin 3 interacting with gravity: Recently Boulanger and Leclercq have constructed cubic four derivative
$3-3-2$ vertex for interaction of spin 3 and spin 2 particles. This vertex is
trivially invariant under the gauge transformations of spin 2 field, so it
seemed that it could be expressed in terms of (linearized) Riemann tensor. And
indeed in this paper we managed to reproduce this vertex in the form $R
\partial \Phi \partial \Phi$, where $R$ -- linearized Riemann tensor and $\Phi$
-- completely symmetric third rank tensor. Then we consider deformation of this
vertex to $(A)dS$ space and show that such deformation produce "standard"
gravitational interaction for spin 3 particles (in linear approximation) in
agreement with general construction of Fradkin and Vasiliev. Then we turn to
the massive case and show that the same higher derivative terms allows one to
extend gauge invariant description of massive spin 3 particle from constant
curvature spaces to arbitrary gravitational backgrounds satisfying $R_{\mu\nu}
= 0$. |
Quantum Instabilities of Solitons: We compute the vacuum polarization energies for a couple of soliton models in
one space and one time dimensions. These solitons are mappings that connect
different degenerate vacua. From the considered sample solitons we conjecture
that the vacuum polarization contribution to the total energy leads to
instabilities whenever degenerate vacua with different curvatures in field
space are accessible to the soliton. | Hierarchy problem and the cosmological constant in a five-dimensional
Brans-Dicke brane world model: We discuss a new solution, admitting the existence of dS_{4} branes, in
five-dimensional Brans-Dicke theory. It is shown that, due to a special form of
a bulk scalar field potential, for certain values of the model parameters the
effective cosmological constant can be made small on the brane, where the
hierarchy problem of gravitational interaction is solved. We also discuss new
stabilization mechanism which is based on the use of auxiliary fields. |
New $\text{AdS}_2/\text{CFT}_1$ pairs from $\text{AdS}_3$ and monopole
bubbling: We present general results on generating $\text{AdS}_2$ solutions to Type II
supergravity from $\text{AdS}_3$ solutions via U(1) and SL(2) T-dualities. We
focus on a class of Type IIB solutions with small $\mathcal{N}=4$
supersymmetry, that we show can be embedded into a more general class of
solutions obtained by double analytical continuation from $\text{AdS}_3$
geometries with small $\mathcal{N}=(0,4)$ supersymmetry constructed in the
literature. We then start the analysis of the superconformal quantum mechanics
dual to the $\mathcal{N}=4$ backgrounds focusing on a subclass of
$\text{AdS}_2\times\text{S}^3\times\mathbb{T}^3$ solutions foliated over a
Riemann surface. We show that the associated supersymmetric quantum mechanics
describes monopole bubbling in 4d $\mathcal{N}=2$ supersymmetric gauge theories
living in D3-D7 branes, as previously discussed in the literature. Therefore,
we propose that our solutions provide a geometrical description via holography
of monopole bubbling in 4d $\mathcal{N}=2$ SCFTs. We check our proposal with
the computation of the central charge. | Fermionic pole-skipping in holography: We examine thermal Green's functions of fermionic operators in quantum field
theories with gravity duals. The calculations are performed on the gravity side
using ingoing Eddington-Finkelstein coordinates. We find that at negative
imaginary Matsubara frequencies and special values of the wavenumber, there are
multiple solutions to the bulk equations of motion that are ingoing at the
horizon and thus the boundary Green's function is not uniquely defined. At
these points in Fourier space a line of poles and a line of zeros of the
correlator intersect. We analyze these `pole-skipping' points in
three-dimensional asymptotically anti-de Sitter spacetimes where exact Green's
functions are known. We then generalize the procedure to higher-dimensional
spacetimes. We also discuss the special case of a fermion with half-integer
mass in the BTZ background. We discuss the implications and possible
generalizations of the results. |
The Space-Cone Gauge, Lorentz Invariance and On-Shell Recursion for
One-Loop Yang-Mills amplitudes: Recursion relations are succinctly obtained for $(++... +)$ and $(-++... +)$
amplitudes in the context of the space-cone gauge in QCD. We rely on the
helicity symmetry of the problems to dictate our choices of reference twistors
and the momentum shifts to complexify the amplitudes. Of great importance is
the power of gauge Lorentz invariance, which is enough to determine the soft
factors in the latter cases. | Relativistic Rigid Particles: Classical Tachyons and Quantum Anomalies: Causal rigid particles whose action includes an {\it arbitrary} dependence on
the world-line extrinsic curvature are considered. General classes of solutions
are constructed, including {\it causal tachyonic} ones. The Hamiltonian
formulation is developed in detail except for one degenerate situation for
which only partial results are given and requiring a separate analysis.
However, for otherwise generic rigid particles, the precise specification of
Hamiltonian gauge symmetries is obtained with in particular the identification
of the Teichm$\ddot{\rm u}$ller and modular spaces for these systems. Finally,
canonical quantisation of the generic case is performed paying special
attention to the phase space restriction due to causal propagation. A mixed
Lorentz-gravitational anomaly is found in the commutator of Lorentz boosts with
world-line reparametrisations. The subspace of gauge invariant physical states
is therefore not invariant under Lorentz transformations. Consequences for
rigid strings and membranes are also discussed. |
Scattering amplitudes from a deconstruction of Feynman diagrams: We show how to apply the BCFW recursion relation to Feynman loop integrals
with the help of the Feynman-tree theorem. We deconstruct in this way all
Feynman diagrams in terms of on-shell subamplitudes. Every cut originating from
the Feynman-tree theorem corresponds to an integration over the phase space of
an unobserved particle pair. We argue that we can calculate scattering
amplitudes alternatively by the construction of on-shell and gauge-invariant
subamplitudes. | 6d $\mathcal N=(1,0)$ anomalies on $S^1$ and F-theory implications: We show that the pure gauge anomalies of 6d $\mathcal N=(1,0)$ theories
compactified on a circle are captured by field-dependent Chern-Simons terms
appearing at one-loop in the 5d effective theories. These terms vanish if and
only if anomalies are canceled. In order to obtain this result, it is crucial
to integrate out the massive Kaluza-Klein modes in a way that preserves 6d
Lorentz invariance; the often-used zeta-function regularization is not
sufficient. Since such field-dependent Chern-Simons terms do not arise in the
reduction of M-theory on a threefold, six-dimensional F-theory
compactifications are automatically anomaly free, whenever the M/F-duality can
be used. A perfect match is then found between the 5d $\mathcal N=1$
prepotentials of the classical M-theory reduction and one-loop circle
compactification of an anomaly free theory. Finally, from this potential, we
read off the quantum corrections to the gauge coupling functions. |
Anti-Instability of Complex Ghost: We argue that Lee-Wick's complex ghost appearing in any higher derivative
theory is stable and its asymptotic field exists. It may be more appropriate to
call it ``anti-unstable" in the sense that, the more the ghost `decays' into
lighter ordinary particles, the larger the probability the ghost remains as
itself becomes. This is explicitly shown by analyzing the two-point functions
of the ghost Heisenberg field which is obtained as an exact result in the
$N\rightarrow\infty$ limit in a massive scalar ghost theory with light
$O(N)$-vector scalar matter. The anti-instability is a consequence of the fact
that the poles of the complex ghost propagator are located on the physical
sheet in the complex plane of four-momentum squared. This should be contrasted
to the case of the ordinary unstable particle, whose propagator has no pole on
the physical sheet. | Super-GCA from $\mathcal{N} = (2,2)$ Super-Virasoro: We derive the extended Supersymmetric Galilean Conformal Algebra (SGCA) in
two spacetime dimensions by the method of group contraction on $2d$
$\mathcal{N}=(2,2)$ superconformal algebra. Both the parent and daughter
algebras are infinite-dimensional. We provide the representation theory of the
algebra. We adopt a superspace formalism for the SGCA fields, allowing us to
write them down in a compact notation as components of superfields. We also
discuss correlation functions, short supermultiplets and null states. |
Star Spectroscopy in the Constant B field Background: In this paper we calculate the spectrum of Neumann matrix with zero modes in
the presence of the constant B field in Witten's cubic string field theory. We
find both the continuous spectrum inside $[{-1\over3}, 0)$ and the constraint
on the existence of the discrete spectrum. For generic $\theta$, -1/3 is not in
the discrete spectrum but in the continuous spectrum. For each eigenvalue in
the continuous spectrum there are four twist-definite degenerate eigenvector
except for -1/3 at which the degeneracy is two. However, for each
twist-definite eigenvector the twist parity is opposite among the two spacetime
components. Based upon the result at -1/3 we prove that the ratio of brane
tension to be one as expected. Furthermore, we discuss the factorization of
star algebra in the presence of B field under zero-slope limit and comment on
the implications of our results to the recent proposed map of Witten's star to
Moyal's star. | A Note on Chiral Symmetry Breaking from Intersecting Branes: In this paper, we will consider the chiral symmetry breaking in the
holographic model constructed from the intersecting brane configuration, and
investigate the Nambu-Goldstone bosons associated with this symmetry breaking. |
Spectral sum rules and finite volume partition function in gauge
theories with real and pseudoreal fermions: Based on the chiral symmetry breaking pattern and the corresponding
low-energy effective lagrangian, we determine the fermion mass dependence of
the partition function and derive sum rules for eigenvalues of the QCD Dirac
operator in finite Euclidean volume. Results are given for $N_c = 2$ and for
Yang-Mills theory coupled to several light adjoint Majorana fermions. They
coincide with those derived earlier in the framework of random matrix theory. | Special functions, transcendentals and their numerics: Cyclotomic polylogarithms are reviewed and new results concerning the special
constants that occur are presented. This also allows some comments on previous
literature results using PSLQ. |
On the 6d Origin of Non-invertible Symmetries in 4d: It is well-known that six-dimensional superconformal field theories can be
exploited to unravel interesting features of lower-dimensional theories
obtained via compactifications. In this short note we discuss a new application
of 6d (2,0) theories in constructing 4d theories with Kramers-Wannier-like
non-invertible symmetries. Our methods allow to recover previously known
results, as well as to exhibit infinitely many new examples of four dimensional
theories with "M-ality" defects (arising from operations of order $M$
generalizing dualities). In particular, we obtain examples of order $M=p^k$,
where $p>1$ is a prime number and $k$ is a positive integer. | Conical singularities regularized in warped six-dimensional flux
compactification and their induced brane cosmology: We discuss the regularization of codimension-2 singularities in warped
six-dimensional Einstein-Maxwell axisymmetric models by replacing them by
codimension-1 branes of a ring form, situated around the axis of symmetry.
Further we consider the case of one capped regularized conical brane of
codimension one and study the cosmological evolution which is induced on it as
it moves in between the known {\it static} bulk and cap solutions. We present
the resulting brane Friedmann equation which gives a dominant five-dimensional
$\rho^2$ energy density term at high energies and a term linear to the energy
density at low energies with, however, negative coefficient in the small
four-brane radius limit (i.e. with negative effective Newton's constant) |
Newton versus Coulomb for Kaluza-Klein modes: We consider a set of elementary compactifications of $D+1$ to $D$ spacetime
dimensions on a circle: first for pure general relativity, then in the presence
of a scalar field, first free then with a non minimal coupling to the Ricci
scalar, and finally in the presence of gauge bosons. We compute the tree-level
amplitudes in order to compare some gravitational and non-gravitational
amplitudes. This allows us to recover the known constraints of the $U(1)$,
dilatonic and scalar Weak Gravity Conjectures in some cases, and to show the
interplay of the different interactions. We study the KK modes pair-production
in different dimensions. We also discuss the contribution to some of these
amplitudes of the non-minimal coupling in higher dimensions for scalar fields
to the Ricci scalar. | Commutator Anomaly in Noncommutative Quantum Mechanics: In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative
phase space is given by using a generalized Bopp's shift. Then the anomaly term
of commutator of arbitrary physical observable operators on noncommutative
phase space is obtained. Finally, the basic uncertainty relations for
space-space and space-momentum as well as momentum-momentum operators in
noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary
physical observable operators in NCQM are discussed. |
IIA string instanton corrections to the four-fermion correlator in the
intersection of Del Pezzo surfaces: The Becker-Becker-Strominger formula, describing the string world-sheet
instanton corrections to the four-fermion correlator in the Calabi-Yau
compactified type-IIA superstrings, is calculated in the special case of the
Calabi-Yau threefold realized in the intersection of two Del Pezzo surfaces. We
also derive the selection rules in the supersymmetric GUT of the Pati-Salam
type associated with our construction. | Aspects of Localized Gravity Around the Soft Minima: n-Dimensional pure gravity theory can be obtained as the effective theory of
an n+1 model (with non-compact extra dimension) where general n+1
reparametrization invariance is explicitly broken in the extra dimension. As
was pointed out in the literature, a necessary consistency condition for having
a non-vanishing four dimensional Newton constant is the normalizability in the
extra dimension of the zero mass graviton. This, in turn, implies that gravity
localization is produced around the local minima of a potential in the extra
dimension. We study gravity in the neighborhood of the soft ("thick") local
minima. |
Carroll covariant scalar fields in two dimensions: Conformal Carroll symmetry generically arises on null manifolds and is
important for holography of asymptotically flat spacetimes, generic black hole
horizons and tensionless strings. In this paper, we focus on two dimensional
(2d) null manifolds and hence on the 2d Conformal Carroll or equivalently the
3d Bondi-Metzner-Sachs (BMS) algebra. Using Carroll covariance, we write the
most general free massless Carroll scalar field theory and discover three
inequivalent actions. Of these, two viz. the time-like and space-like actions,
have made their appearance in literature before. We uncover a third that we
call the mixed-derivative theory. As expected, all three theories enjoy
off-shell BMS invariance. Interestingly, we find that the on-shell symmetry of
mixed derivative theory is a single Virasoro algebra instead of the full BMS.
We discuss potential applications to tensionless strings and flat holography. | Extended Hamiltonian Formalism of the Pure Space-Like Axial Gauge
Schwinger Model II: Canonical methods are not sufficient to properly quantize space-like axial
gauges. In this paper, we obtain guiding principles which allow the
construction of an extended Hamiltonian formalism for pure space-like axial
gauge fields. To do so, we clarify the general role residual gauge fields play
in the space-like axial gauge Schwinger model. In all the calculations we fix
the gauge using a rule, $n{\cdot}A=0$, where $n$ is a space-like constant
vector and we refer to its direction as $x_-$. Then, to begin with, we
construct a formulation in which the quantization surface is space-like but not
parallel to the direction of $n$. The quantization surface has a parameter
which allows us to rotate it, but when we do so we keep the direction of the
gauge field fixed. In that formulation we can use canonical methods. We
bosonize the model to simplify the investigation. We find that the
antiderivative, $({\partial}_-)^{-1}$, is ill-defined whatever quantization
coordinates we use as long as the direction of $n$ is space-like. We find that
the physical part of the dipole ghost field includes infrared divergences.
However, we also find that if we introduce residual gauge fields in such a way
that the dipole ghost field satisfies the canonical commutation relations, then
the residual gauge fields are determined so as to regularize the infrared
divergences contained in the physical part. The propagators then take the form
prescribed by Mandelstam and Leibbrandt. We make use of these properties to
develop guiding principles which allow us to construct consistent operator
solutions in the pure space-like case where the quantization surface is
parallel to the direction of $n$ and canonical methods do not suffice. |
``Non chiral'' primary superfields in the AdS_{d+1}/CFT_d correspondence: We consider some long multiplets describing bulk massive excitations of
M-theory two-branes and IIB string three-branes which correspond to ``non
chiral'' primary operators of the boundary OSp(8/4) and SU(2,2/4)
superconformal field theories. Examples of such multiplets are the ``radial''
modes on the branes, including up to spin 4 excitations, which may be then
considered as prototypes of states which are not described by the K-K spectrum
of the corresponding supergravity theories on AdS_4 x S_7 and AdS_5 x S_5
respectively. | A Nonabelian $(1,0)$ Tensor Multiplet Theory in 6D: We construct a general nonabelian (1,0) tensor multiplet theory in six
dimensions. The gauge field of this (1,0) theory is non-dynamical, and the
theory contains a continuous parameter $b$. When $b=1/2$, the (1,0) theory
possesses an extra discrete symmetry enhancing the supersymmetry to (2,0), and
the theory turns out to be identical to the (2,0) theory of Lambert and
Papageorgakis (LP). Upon dimension reduction, we obtain a general ${\cal N}=1$
supersymmetric Yang-Mills theory in five dimensions. The applications of the
theories to D4 and M5-branes are briefly discussed. |
One-Loop Radiative Corrections to the QED Casimir Energy: In this paper, we investigate one-loop radiative corrections to the Casimir
energy in the presence of two perfectly conducting parallel plates for QED
theory within the renormalized perturbation theory. In fact, there are three
contributions for radiative corrections to the Casimir energy, up to order
$\alpha$. Only the two-loop diagram, which is of order $\alpha$, has been
computed by Bordag et. al (1985), approximately. Here, up to this order, we
consider corrections due to two one-loop terms, i.e., photonic and fermionic
loop corrections resulting from renormalized QED Lagrangian, more precisely.
Our results show that only the fermionic loop has a very minor correction and
the correction of photonic loop vanishes. | Role of matter in extended quasidilaton massive gravity: The extended quasidilaton theory is one of the simplest Lorentz-invariant
massive gravity theories which can accommodate a stable self-accelerating
vacuum solution. In this paper we revisit this theory and study the effect of
matter fields. For a matter sector that couples minimally to the physical
metric, we find hints of a Jeans type instability in the IR. In the analogue
k-essence field set-up, this instability manifests itself as an IR ghost for
the scalar field perturbation, but this can be interpreted as a classical
instability that becomes relevant below some momentum scale in terms of matter
density perturbations. We also consider the effect of the background evolution
influenced by matter on the stability of the gravity sector perturbations. In
particular, we address the previous claims of ghost instability in the IR
around the late time attractor. We show that, although the matter-induced
modification of the evolution potentially brings tension to the stability
conditions, one goes beyond the regime of validity of the effective theory well
before the solutions become unstable. We also draw attention to the fact that
the IR stability conditions are also enforced by the existence requirements of
consistent background solutions. |
Perturbative unitarity in quasi-single field inflation: We study implications of perturbative unitarity for quasi-single field
inflation with the inflaton and one massive scalar. Analyzing high energy
scattering, we show that non-Gaussianities with $|f_{\rm NL}|\gtrsim1$ cannot
be realized without turning on interactions which violate unitarity at a high
energy scale. Then, we provide a relation between $f_{\rm NL}$ and the scale of
new physics that is required for UV completion. In particular we find that for
the Hubble scale $H\gtrsim 6\times 10^{9}$ GeV, Planck suppressed operators can
easily generate too large non-Gaussanities and so it is hard to realize
successful quasi-single field inflation without introducing a mechanism to
suppress quantum gravity corrections. Also we generalize the analysis to the
regime where the isocurvature mode is heavy and the inflationary dynamics is
captured by the inflaton effective theory. Requiring perturbative unitarity of
the two-scalar UV models with the inflaton and one heavy scalar, we clarify the
parameter space of the $P(X,\phi)$ model which is UV completable by a single
heavy scalar. | Thermodynamic schemes of charged BTZ-like black holes in arbitrary
dimensions: We investigate thermodynamic schemes of charged BTZ-like black holes in
arbitrary dimensions, namely higher-dimensional charged black holes in which
the electromagnetic sector exhibits the same properties with that of the usual
three-dimensional BTZ solution. We first present the Euclidean on-shell action
in arbitrary dimensions, inserting a radial cutoff. We then extract the
corresponding thermodynamic quantities from the semi-classical partition
function in different ensembles and find that there exist two possible
thermodynamic schemes, with different outcomes. Regarding the traditional
scheme (scheme I), where the length cutoff is identified with the AdS radius,
we show that charged BTZ-like black holes are super-entropic, namely they
violate the reverse isoperimetric inequality conjecture, and their
super-entropicity is strongly connected to a fundamental thermodynamic
instability. This class of solutions is the first demonstration of
super-entropic black holes which possess second-order critical points and,
since thermodynamic instabilities always arise, it is not possible to
physically interpret the corresponding van der Waals critical phenomenon in
this scheme. In the second scheme (II) where the length cutoff is considered as
an independent variable, namely the system respects the conjectured reverse
isoperimetric inequality, we show that the solutions are thermodynamically
stable in an ensemble where the length cutoff is kept fixed, and hence one can
provide an explanation for the van der Waals critical phenomenon. Furthermore,
in order to verify the consistency of the second scheme, we study the
Joule-Thomson expansion and we extract the Joule-Thomson coefficient, the
inversion temperature, the inversion curves, and the isenthalpic curves. The
results indicate that this class of AdS black holes can be considered as
interacting statistical systems. Additionally, ... |
Towards Gravity from the Quantum: We review quantum causal histories starting with their interpretations as a
quantum field theory on a causal set and a quantum geometry. We discuss the
difficulties that background independent theories based on quantum geometry
encounter in deriving general relativity as the low energy limit. We then
suggest that general relativity should be viewed as a strictly effective theory
coming from a fundamental theory with no geometric degrees of freedom. The
basic idea is that an effective theory is characterized by effective coherent
degrees of freedom and their interactions. Having formulated the pre-geometric
background independent theory as a quantum information theoretic processor, we
are able to use the method of noiseless subsystems to extract such coherent
(protected) excitations. We follow the consequences, in particular, the
implications of effective locality and time. | Black Holes, Wormholes, and the Disappearance of Global Charge: One of the paradoxes associated with the theory of the formation and
subsequent Hawking evaporation of a black hole is the disappearance of
conserved global charges. It has long been known that metric fluctuations at
short distances (wormholes) violate global-charge conservation; if global
charges are apparently conserved at ordinary energies, it is only because
wormhole-induced global-charge-violating terms in the low-energy effective
Lagrangian are suppressed by large mass denominators. However, such suppressed
interactions can become important at the high energy densities inside a
collapsing star. We analyze this effect for a simple model of the black-hole
singularity. (Our analysis is totally independent of any detailed theory of
wormhole dynamics; in particular it does not depend on the wormhole theory of
the vanishing of the cosmological constant.) We find that in general all charge
is extinguished before the infalling matter crosses the singularity. No global
charge appears in the outgoing Hawking radiation because it has all gone down
the wormholes. |
Anti-Evaporation of Schwarzschild-de Sitter Black Holes in $F(R)$
gravity: We studied the anti-evaporation of degenerate Schwarzschild-de Sitter black
hole (so-called Nariai space-time) in modified $F(R)$ gravity. The analysis of
perturbations of the Nariai black hole is done with the conclusion that
anti-evaporation may occur in such a theory already on classical level. For
several power-law $F(R)$ gravities which may describe the inflation and/or dark
energy eras we presented the theory parameters bounds for occurrence of
anti-evaporation and conjectured creation of infinite number of horizons. | The Force and Gravity of Events: Local events are characterized by "where", "when" and "what". Just as
(bosonic) spacetime forms the backdrop for location and time, (fermionic)
property space can serve as the backdrop for the attributes of a system. With
such a scenario I shall describe a scheme that is capable of unifying
gravitation and the other forces of nature. The generalized metric contains the
curvature of spacetime and property separately, with the gauge fields linking
the bosonic and fermionic arenas. The super-Ricci scalar can then automatically
yield the spacetime Lagrangian of gravitation and the standard model (plus a
cosmological constant) upon integration over property coordinates. |
Evidence for Negative Stiffness of QCD Strings: QCD strings are color-electric flux tubes between quarks with a finite
thickness and thus a finite curvature stiffness. Contrary to an earlier
rigid-string by Polyakov and Kleinert, and motivated by the properties of a
magnetic flux tubes in type-II superconductors we put forward the hypothesis
that QCD strings have a {\em negative\/ stiffness. We set up a new string model
with this property and show that it is free of the three principal problems of
rigid-strings --- particle states with negative norm, nonexistence of a
lowest-energy state, and wrong high-temperature behavior of string tension ---
thus making it a better candidate for a string description of quark forces than
previous models. | Hypermultiplet effective action: N = 2 superspace approach: In an earlier paper (hep-th/0101127), we developed heat kernel techniques in
N = 2 harmonic superspace for the calculation of the low-energy effective
action of N = 4 SYM theory, which can be considered as the most symmetric N = 2
SYM theory. Here, the results are extended to generic N = 2 SYM theories. This
involves a prescription for computing the variation of the hypermultiplet
effective action. Integrability of this variation allows the hypermultiplet
effective action to be deduced. This prescription permits a very simple
superfield derivation of the perturbative holomorphic prepotential. Explicit
calculations of the prepotential and the leading non-holomorphic correction are
presented. |
Projective Coordinates and Projective Space Limit: The "projective lightcone limit" has been proposed as an alternative
holographic dual of an AdS space. It is a new type of group contraction for a
coset G/H preserving the isometry group G but changing H. In contrast to the
usual group contraction, which changes G preserving the spacetime dimension, it
reduces the dimensions of the spacetime on which G is realized. The obtained
space is a projective space on which the isometry is realized as a linear
fractional transformation. We generalize and apply this limiting procedure to
the "Hopf reduction" and obtain (n-1)-dimensional complex projective space from
(2n-1)-dimensional sphere preserving SU(n) symmetry. | The Cosmology of Massless String Modes: We consider the spacetime dynamics of a gas of closed strings in the context
of General Relativity in a background of arbitrary spatial dimensions. Our
motivation is primarily late time String Gas Cosmology, where such a spacetime
picture has to emerge after the dilaton has stabilized. We find that after
accounting for the thermodynamics of a gas of strings, only string modes which
are massless at the self-dual radius are relevant, and that they lead to a
dynamics which is qualitatively different from that induced by the modes
usually considered in the literature. In the context of an ansatz with three
large spatial dimensions and an arbitrary number of small extra dimensions, we
obtain isotropic stabilization of these extra dimensions at the self-dual
radius. This stabilization occurs for fixed dilaton, and is induced by the
special string states we focus on. The three large dimensions undergo a regular
Friedmann-Robertson-Walker expansion. We also show that this framework for
late-time cosmology is consistent with observational bounds. |
Quantum gravity effects at a black hole horizon: Quantum fluctuations in the background geometry of a black hole are shown to
affect the propagation of matter states falling into the black hole in a
foliation that corresponds to observations purely outside the horizon. A state
that starts as a Minkowski vacuum at past null infinity gets entangled with the
gravity sector, so that close to the horizon it can be represented by a
statistical ensemble of orthogonal states. We construct an operator connecting
the different states and comment on the possible physical meaning of the above
construction. The induced energy-momentum tensor of these states is computed in
the neighbourhood of the horizon, and it is found that energy-momentum
fluctuations become large in the region where the bulk of the Hawking radiation
is produced. The background spacetime as seen by an outside observer may be
drastically altered in this region, and an outside observer should see
significant interactions between the infalling matter and the outgoing Hawking
radiation. The boundary of the region of strong quantum gravitational effects
is given by a time-like hypersurface of constant Schwarzschild radius $r$ one
Planck unit away from the horizon. This boundary hypersurface is an example of
a stretched horizon. | Unity of Superstring Dualities: The effective action for type II string theory compactified on a six torus is
$N=8$ supergravity, which is known to have an $E_{7}$ duality symmetry. We show
that this is broken by quantum effects to a discrete subgroup, $E_7(\Z)$, which
contains both the T-duality group $SO(6,6;\Z)$ and the S-duality group
$SL(2;\Z)$. We present evidence for the conjecture that $E_7(\Z)$ is an exact
\lq U-duality' symmetry of type II string theory. This conjecture requires
certain extreme black hole states to be identified with massive modes of the
fundamental string. The gauge bosons from the Ramond-Ramond sector couple not
to string excitations but to solitons. We discuss similar issues in the context
of toroidal string compactifications to other dimensions, compactifications of
the type II string on $K_3\times T^2$ and compactifications of
eleven-dimensional supermembrane theory. |
Comments on M Theory Dynamics on G2 Holonomy Manifolds: We study the dynamics of M-theory on G2 holonomy manifolds, and consider in
detail the manifolds realized as the quotient of the spin bundle over S^3 by
discrete groups. We analyse, in particular, the class of quotients where the
triality symmetry is broken. We study the structure of the moduli space,
construct its defining equations and show that three different types of
classical geometries are interpolated smoothly. We derive the N=1
superpotentials of M-theory on the quotients and comment on the membrane
instanton physics. Finally, we turn on Wilson lines that break gauge symmetry
and discuss some of the implications. | Exact Description of D-branes via Tachyon Condensation: We examine the fluctuations around a Dp-brane solution in an unstable D-brane
system using boundary states and also boundary string field theory. We show
that the fluctuations correctly reproduce the fields on the Dp-brane. Plugging
these into the action of the unstable D-brane system, we recover not only the
tension and RR charge, but also full effective action of the Dp-brane exactly.
Our method works for general unstable D-brane systems and provides a simple
proof of D-brane descent/ascent relations under the tachyon condensation. In
the lowest dimensional unstable D-brane system, called K-matrix theory,
D-branes are described in terms of operator algebra. We show the equivalence of
the geometric and algebraic descriptions of a D-brane world-volume manifold
using the equivalence between path integral and operator formulation of the
boundary quantum mechanics. As a corollary, the Atiyah-Singer index theorem is
naturally obtained by looking at the coupling to RR-fields. We also generalize
the argument to type I string theory. |
Light-front field theories at finite temperature: We study the question of generalizing light-front field theories to finite
temperature. We show that the naive generalization has serious problems and we
identify the source of the difficulty. We provide a proper generalization of
these theories to finite temperature based on a relativistic description of
thermal field theories, both in the real and the imaginary time formalisms.
Various issues associated with scalar and fermion theories, such as
non-analyticity of self-energy, tensor decomposition are discussed in detail. | On Non-linear Action for Gauged M2-brane: We propose a non-linear extension of U(1) \times U(1) (abelian) ABJM model
including T_{M2} (higher derivative) corrections. The action proposed here is
expected to describe a single M2-brane proving C^4/Z_k target space. The model
includes couplings with the 3-form background in the eleven-dimensional
supergravity which is consistent with the orbifold projection. We show that the
novel higgs mechanism proposed by Mukhi and Papageorgakis does work even in the
presence of higher derivative corrections and couplings with the background
field, giving the correct structure of the Dirac-Born-Infeld action with
Wess-Zumino term for a D2-brane. We also find half BPS solutions in the full
non-linear theory which is interpreted as an another M2-brane intersecting with
the original M2-brane. A possible generalization to U(N) \times U(N) gauge
group is briefly discussed. |
Line Operators in 4d Chern-Simons Theory and Cherkis Bows: We show that the phase spaces of a large family of line operators in 4d
Chern-Simons theory with $\text{GL}_n$ gauge group are given by Cherkis bow
varieties with $n$ crosses. These line operators are characterized by
Hanany-Witten type brane constructions involving D3, D5, and NS5 branes in an
$\Omega$-background. Linking numbers of the five-branes and mass parameters for
the D3 brane theories determine the phase spaces and in special cases they
correspond to vacuum moduli spaces of 3d $\mathcal{N}=4$ quiver theories.
Examples include line operators that conjecturally create T, Q, and L-operators
in integrable spin chains. | Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models: We present a Ward identity for nonlinear sigma models using generalized
nonlinear shift symmetries, without introducing current algebra or coset space.
The Ward identity constrains correlation functions of the sigma model such that
the Adler's zero is guaranteed for $S$-matrix elements, and gives rise to a
subleading single soft theorem that is valid at the quantum level and to all
orders in the Goldstone decay constant. For tree amplitudes, the Ward identity
leads to a novel Berends-Giele recursion relation as well as an explicit form
of the subleading single soft factor. Furthermore, interactions of the cubic
biadjoint scalar theory associated with the single soft limit, which was
previously discovered using the Cachazo-He-Yuan representation of tree
amplitudes, can be seen to emerge from matrix elements of conserved currents
corresponding to the generalized shift symmetry. |
Fermions via spinor-valued one-forms: Spinor-valued one-forms (Rarita-Schwinger fields) are normally used in the
context of supergravity, where they describe spin 3/2 particles (gravitinos).
Indeed, when decomposed into irreducible representations of the Lorentz group
such a field contains both a spin 1/2 and a spin 3/2 component, and the
Rarita-Schwinger Lagrangian is designed to make only the spin 3/2 propagate. We
point out that the opposite construction is also possible, and give a
spinor-valued one-form field Lagrangian that describes a propagating spin 1/2
particle. | Integrable models with twist function and affine Gaudin models: This thesis deals with a class of integrable field theories called models
with twist function. The main examples of such models are integrable non-linear
sigma models, such as the Principal Chiral Model, and their deformations. A
first obtained result is the proof that the so-called Bi-Yang-Baxter model,
which is a two-parameter deformation of the Principal Chiral Model, is also a
model with twist function. It is then shown that inhomogeneous Yang-Baxter type
deformations modify certain global symmetries of the undeformed model into
Poisson-Lie symmetries. Another chapter concerns the construction of an
infinite number of local charges in involution for all integrable sigma models
and their deformations : this result is based on the general formalism shared
by all these models as field theories with twist function.
The second part of the thesis concerns Gaudin models. These are integrable
models associated with Lie algebras. In particular, field theories with twist
function are related to Gaudin models associated with affine Lie algebras. A
standard approach for studying the spectrum of quantum Gaudin models over
finite algebras is the one of Feigin-Frenkel-Reshetikhin. In this thesis,
generalisations of this approach are conjectured, motivated and tested. One of
them deals with the so-called cyclotomic finite Gaudin models. The second one
concerns the Gaudin models associated with affine Lie algebras. |
Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity
Cuts: We propose a systematic way to carry out the method introduced in
hep-th/0410077 for computing certain unitarity cuts of one-loop N=4 amplitudes
of gluons. We observe that the class of cuts for which the method works
involves all next-to-MHV n-gluon one-loop amplitudes of any helicity
configurations. As an application of our systematic procedure, we obtain the
complete seven-gluon one-loop leading-color amplitude
A_{7;1}(1-,2-,3-,4+,5+,6+,7+). | Localized massive excitation of quantum gravity as a dark particle: We construct a static and spherical excited state without singularities in
renormalizable quantum gravity with background-free nature asymptotically. Its
diameter is given by a correlation length of the quantum gravity, longer than
the Planck length by 2 orders of magnitude, and it has a Schwarzschild tail
outside. The quantum gravity dynamics inside is described by employing a
nonperturbative expression of higher-order corrections assumed from a physical
requirement that the dynamics disappear at the edge where it is in strong
coupling. A running coupling constant that is a manifestation of nonlinearity
and nonlocality is managed by approximating it as a mean field that depends on
the radial coordinate. If the mass is several times the Planck mass, we can set
up a system of linearized equations of motion for the gravitational potentials
incorporating the running effect and obtain the excited state as its solution.
It may be a candidate for dark matter, and will give a new perspective on black
hole physics. |
Gauging Cosets: We show how to gauge the set of raising and lowering generators of an
arbitrary Lie algebra. We consider SU(N) as an example. The nilpotency of the
BRST charge requires constraints on the ghosts associated to the raising and
lowering generators. To remove these constraints we add further ghosts and we
need a second BRST charge to obtain nontrivial cohomology. The second BRST
operator yields a group theoretical explanation of the grading encountered in
the covariant quantization of superstrings. | Entanglement entropy in holographic moving mirror and Page curve: We calculate the time evolution of entanglement entropy in two dimensional
conformal field theory with a moving mirror. For a setup modeling Hawking
radiation, we obtain a linear growth of entanglement entropy and show that this
can be interpreted as the production of entangled pairs. For a setup, which
mimics black hole formation and evaporation, we find that the evolution follows
the ideal Page curve. We perform these computations by constructing the gravity
dual of the moving mirror model via holography. We also argue that our
holographic setup provides a concrete model to derive the Page curve for black
hole radiation in the strong coupling regime of gravity. |
Topological Born-Infeld Actions and D-Branes: We propose that the effective field theories of certain wrapped D-branes are
given by topological actions based on Born-Infeld theory. In particular, we
present a Born-Infeld version of the Abelian Donaldson-Witten theory. We then
consider wrapping D3 branes on calibrated submanifolds and for the Calabi-Yau
four-fold case, discuss how the resulting theory could give rise to a
Born-Infeld version of the ampicheiral twisted N=4 super Yang-Mills topological
field theory. | Evidence for a bound on the lifetime of de Sitter space: Recent work has suggested a surprising new upper bound on the lifetime of de
Sitter vacua in string theory. The bound is parametrically longer than the
Hubble time but parametrically shorter than the recurrence time. We investigate
whether the bound is satisfied in a particular class of de Sitter solutions,
the KKLT vacua. Despite the freedom to make the supersymmetry breaking scale
exponentially small, which naively would lead to extremely stable vacua, we
find that the lifetime is always less than about exp(10^(22)) Hubble times, in
agreement with the proposed bound. |
New Spinor Field Realizations of the Non-Critical $W_{3}$ String: We investigate the new spinor field realizations of the $W_{3}$ algebra,
making use of the fact that the $W_{3}$ algebra can be linearized by the
addition of a spin-1 current. We then use these new realizations to build the
nilpotent Becchi-Rouet-Stora--Tyutin (BRST) charges of the spinor non-critical
$W_{3}$ string. | Characters, Coadjoint Orbits and Duistermaat-Heckman Integrals: The asymptotics of characters $\chi_{k\lambda}(\exp(h/k))$ of irreducible
representations of a compact Lie group $G$ for large values of the scaling
factor $k$ are given by Duistermaat-Heckman (DH) integrals over coadjoint
orbits of $G$. This phenomenon generalises to coadjoint orbits of central
extensions of loop groups $\widehat{LG}$ and of diffeomorphisms of the circle
$\widehat{\rm Diff}(S^1)$. We show that the asymptotics of characters of
integrable modules of affine Kac-Moody algebras and of the Virasoro algebra
factorize into a divergent contribution of the standard form and a convergent
contribution which can be interpreted as a formal DH orbital integral.
For some Virasoro modules, our results match the formal DH integrals recently
computed by Stanford and Witten. In this case, the $k$-scaling has the same
origin as the one which gives rise to classical conformal blocks. Furthermore,
we consider reduced spaces of Virasoro coadjoint orbits and we suggest a new
invariant which replaces symplectic volume in the infinite dimensional
situation. We also consider other modules of the Virasoro algebra (in
particular, the modules corresponding to minimal models) and we obtain DH-type
expressions which do not correspond to any Virasoro coadjoint orbits.
We study volume functions $V(x)$ corresponding to formal DH integrals over
coadjoint orbits of the Virasoro algebra. We show that they are related by the
Hankel transform to spectral densities $\rho(E)$ recently studied by Saad,
Shenker and Stanford. |
Non-existence of a dilaton gravity action for the exact string black
hole: We prove that no local diffeomorphism invariant two-dimensional theory of the
metric and the dilaton without higher derivatives can describe the exact string
black hole solution found a decade ago by Dijkgraaf, Verlinde and Verlinde. One
of the key points in this proof is the concept of dilaton-shift invariance. We
present and solve (classically) all dilaton-shift invariant theories of
two-dimensional dilaton gravity. Two such models, resembling the exact string
black hole and generalizing the CGHS model, are discussed explicitly. | Non Abelian Tachyon Kinks: Starting from the action of two coincident non-BPS D9-branes, we investigate
kink configurations of the U(2) matrix tachyon field. We consider both Str and
Tr prescriptions for the trace over gauge indices of the non-BPS action.
Non-abelian tachyon condensation in the theory with Tr prescription, and the
resulting fluctuations about the kink profile, are shown to give rise to a
theory of two coincident BPS D8-branes. This is a natural non-abelian
generalization of Sen's mechanism of tachyon condensation on a single non-BPS
Dp-brane yielding a single BPS brane of codimesion one. By contrast, starting
with the Str gauge trace prescription of the coincident non-BPS D9-brane
action, such a generalization of Sen's mechanism appears problematic. |
The Qubits of Qunivac: We formulate a theory of quantum processes, extend it to a generic quantum
cosmology, formulate a reversible quantum logic for the Quantum Universe As
Computer, or Qunivac. Qunivac has an orthogonal group of cosmic dimensionality.
It has a Clifford algebra of ``cosmonions,'' extending the quaternions to a
cosmological number of anticommuting units. Its qubits obey Clifford-Wilczek
statistics and are associated with unit cosmonions. This makes it relatively
easy to program the Dirac equation on Qunivac in a Lorentz-invariant way.
Qunivac accommodates a field theory and a gauge theory. Its gauge group is
necessarily a quantum group. | Comments on the NSVZ $β$ Functions in Two-dimensional $\mathcal
N=(0,2)$ Supersymmetric Models: The NSVZ $\beta$ functions in two-dimensional $\mathcal N=(0,2)$
supersymmetric models are revisited. We construct and discuss a broad class of
such models using the gauge formulation. All of them represent direct analogs
of four-dimensional ${\mathcal N} =1$ Yang-Mills theories and are free of
anomalies. Following the same line of reasoning as in four dimensions we
distinguish between the holomorphic and canonical coupling constants. This
allows us to derive the exact two-dimensional $\beta$ functions in all models
from the above class. We then compare our results with a few examples which
have been studied previously. |
Frobenius manifolds, Integrable Hierarchies and Minimal Liouville
Gravity: We use the connection between the Frobrenius manifold and the Douglas string
equation to further investigate Minimal Liouville gravity. We search a solution
of the Douglas string equation and simultaneously a proper transformation from
the KdV to the Liouville frame which ensure the fulfilment of the conformal and
fusion selection rules. We find that the desired solution of the string
equation has explicit and simple form in the flat coordinates on the Frobenious
manifold in the general case of (p,q) Minimal Liouville gravity. | Homogeneous Yang-Baxter deformations as undeformed yet twisted models: The homogeneous Yang-Baxter deformation is part of a larger web of integrable
deformations and dualities that recently have been studied with motivations in
integrable $\sigma$-models, solution-generating techniques in supergravity and
Double Field Theory, and possible generalisations of the AdS/CFT
correspondence. The $\sigma$-models obtained by the homogeneous Yang-Baxter
deformation with periodic boundary conditions on the worldsheet are on-shell
equivalent to undeformed models, yet with twisted boundary conditions. While
this has been known for some time, the expression provided so far for the twist
features non-localities (in terms of the degrees of freedom of the deformed
model) that prevent practical calculations, and in particular the construction
of the classical spectral curve. We solve this problem by rewriting the
equation defining the twist in terms of the degrees of freedom of the
undeformed yet twisted model, and we show that we are able to solve it in full
generality. Remarkably, this solution is a local expression. We discuss the
consequences of the twist at the level of the monodromy matrix and of the
classical spectral curve, analysing in particular the concrete examples of
abelian, almost abelian and Jordanian deformations of the Yang-Baxter class. |
Quantum Conformal Gravity: We present the manifestly covariant canonical operator formalism of a Weyl
invariant (or equivalently, a locally scale invariant) gravity whose classical
action consists of the well-known conformal gravity and Weyl invariant
scalar-tensor gravity, on the basis of the Becchi-Rouet-Stora-Tyupin (BRST)
formalism. It is shown that there exists a Poincar${\rm{\acute{e}}}$-like
$\mathit{IOSp}(8|8)$ global symmetry as in Einstein's general relativity, which
should be contrasted to the case of only the Weyl invariant scalar-tensor
gravity where we have a more extended Poincar${\rm{\acute{e}}}$-like
$\mathit{IOSp}(10|10)$ global symmetry. This reduction of the global symmetry
is attributed to the presence of the St\"{u}ckelberg symmetry. | A new insight into BRST anomalies in string theory: Using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky,
we investigate the algebraic structure of anomalies in the Polyakov string
theory that appear as the Schwinger terms in super-commutation relations
between BRST charge and total hamiltonian. We obtain the most general form of
the anomalies in the extended phase space, without any reference to a two
dimensional metric. This pregeometri- cal result, refered to as the genelarized
Virasoro anomaly, independent of the gauge and the regularization under a minor
assumption, is a non-perturbative result, and valid for any space-time
dimension. In a configuration space, in which the two dimensional metric can be
identified, we can geometrize the result without assuming the weak
gravitational field, showing that the most general anomaly exactly exhibits the
Weyl anomaly. |
$D5$-brane type I superstring background fields in terms of type IIB
ones by canonical method and T-duality approach: We consider type IIB superstring theory with embedded $D5$-brane and choose
boundary conditions which preserve half of the initial supersymmetry. In the
canonical approach that we use, boundary conditions are treated as canonical
constraints. The effective theory, obtained from the initial one on the
solution of boundary conditions, has the form of the type I superstring theory
with embedded $D5$-brane. We obtain the expressions for $D5$-brane background
fields of type I theory in terms of the $D5$-brane background fields of type
IIB theory. We show that beside known $\Omega$ even fields, they contain
squares of $\Omega$ odd ones, where $\Omega$ is world-sheet parity
transformation, $\Omega:\sigma\to -\sigma$. We relate result of this paper and
the results of [1] using T-dualities along four directions orthogonal to
$D5$-brane. | Entropy of Contracting Universe in Cyclic Cosmology: Following up a recent proposal \cite{BF} for a cyclic model based on phantom
dark energy, we examine the content of the contracting universe (cu) and its
entropy $S_{cu}$. We find that beyond dark energy the universe contains on
average zero or at most a single photon which if present immediately after
turnaround has infinitesimally energy which subsequently blue shifts to produce
$e^+e^-$ pairs. These statements are independent of the equation of state
$\omega = p/\rho$ of dark energy provided $\omega < -1$. Thus $S_{cu} = 0$ and
if observations confirm $\omega < -1$ the entropy problem is solved. We discuss
the absence of a theoretical lower bound on $\phi = |\omega + 1|$, then
describe an anthropic fine tuning argument that renders unlikely extremely
small $\phi$. The present bound $\phi \lesssim 0.1$ already implies a time
until turnaround of $(t_T - t_0) \gtrsim 100$ Gy. |
The effective two-loop Euler-Heisenberg action for scalar and spinor QED
in a general constant background field: Using the Worldline formalism of QED we compute the two-loop effective action
induced by a charged scalar, respectively spinor particle in a general constant
electromagnetic field. | N=1 Super-$τ_{3}$QED from Atiyah-Ward Space-Time: In this letter, we present the action for the massive super-{\QED}. A pair of
chiral and a pair of anti-chiral superfields with opposite U(1)-charges are
required. We also carry out a dimensional reduction {\it{\`a la}} Scherk from
(2+2) to (1+2) dimensions, and we show that, after suitable truncations are
performed, the supersymmetric extension of the ${\tau}_{3}$QED$_{1+2}$
naturally comes out. |
Angular profile of emission of non-zero spin fields from a
higher-dimensional black hole: Recent works have included the effect of rotation on simulations of black
hole events at the LHC, showing that the angular momentum of the black hole
cannot be ignored and it makes a non-trivial contribution for most of the
lifetime of the black hole. A key consequence of the rotation of the black hole
is that the Hawking radiation is no longer isotropic, making it more difficult
to infer space-time parameters from measurements of the emitted particles. In
this letter we study the angular distribution of the Hawking emission of
non-zero spin particles with specific helicity on the brane. We argue that the
shape of the distribution could be used as a measure of the angular momentum of
the black hole. | Holographic Weyl Anomalies for 4d Defects in 6d SCFTs: In this note, we study $1/4$- and $1/2$-BPS co-dimension two superconformal
defects in the $6d$ $\mathcal{N}=(2,0)$ $A_{N-1}$ SCFT at large $N$ using their
holographic descriptions as solutions of $11d$ supergravity. In this regime, we
are able to compute the defect contribution to the sphere entanglement entropy
and the change in the stress-energy tensor one-point function due to the
presence of the defect using holography. From these quantities, we are then
able to unambiguously compute the values for two of the twenty-nine total Weyl
anomaly coefficients that characterize $4d$ conformal defects in six and higher
dimensions. We are able to demonstrate the consistency of the supergravity
description of the defect theories with the average null energy condition on
the field theory side. For each class of defects that we consider, we also show
that the A-type Weyl anomaly coefficient is non-negative. Lastly, we uncover
and resolve a discrepancy between the on-shell action of the $7d$ $1/4$-BPS
domain wall solutions and that of their $11d$ uplift. |
Testing Closed String Field Theory with Marginal Fields: We study the feasibility of level expansion and test the quartic vertex of
closed string field theory by checking the flatness of the potential in
marginal directions. The tests, which work out correctly, require the
cancellation of two contributions: one from an infinite-level computation with
the cubic vertex and the other from a finite-level computation with the quartic
vertex. The numerical results suggest that the quartic vertex contributions are
comparable or smaller than those of level four fields. | Non-Abelian Magnetic Field and Curvature Effects on Pair Production: We calculate the Schwinger pair production rates in $\mathbb{R}^{3,1}$ as
well as in the positively curved space $S^2 \times \mathbb{R}^{1,1}$ for both
spin-$0$ and spin-$\frac{1}{2}$ particles under the influence of an external
$SU(2) \times U(1)$ gauge field producing an additional uniform non-abelian
magnetic field besides the usual uniform abelian electric field. To this end,
we determine and subsequently make use of the spectrum of the gauged Laplace
and Dirac operators on both the flat and the curved geometries. We find that
there are regimes in which the purely non-abelian and the abelian parts of the
gauge field strength have either a counterplaying or reinforcing role, whose
overall effect may be to enhance or suppress the pair production rates.
Positive curvature tends to enhance the latter for spin-$0$ and suppress it for
spin-$\frac{1}{2}$ fields, while the details of the couplings to the purely
abelian and the non-abelian parts of the magnetic field, which are extracted
from the spectrum of the Laplace and Dirac operators on $S^2$, determine the
cumulative effect on the pair production rates. These features are elaborated
in detail. |
Page Curves for Accelerating Black Holes: The island paradigm for the fine-grained entropy of Hawking radiation is
applied to eternal charged accelerating black holes. In the absence of the
island, the entanglement entropy grows linearly and divergent at late times,
while once the island outside the event horizon is taken into account, the
unitary Page curve is reproduced naturally. The impact of the charge and the
acceleration is investigated at late times. For the Page time and the
scrambling time, they both increase as the acceleration increases, while
decreasing as the charge increases. In particular, neutral black holes have the
largest Page time and scrambling time. It is worth noting that the Page time
and the scrambling time are divergent in the extremal limit, which implies that
islands may be related to the causal structure of spacetime. | M-Theory on S^1/Z_2 : New Facts from a Careful Analysis: We carefully re-examine the issues of solving the modified Bianchi identity,
anomaly cancellations and flux quantization in the S^1/Z_2 orbifold of M-theory
using the boundary-free "upstairs" formalism, avoiding several misconceptions
present in earlier literature. While the solution for the four-form G to the
modified Bianchi identity appears to depend on an arbitrary parameter b, we
show that requiring G to be globally well-defined, i.e. invariant under small
and large gauge and local Lorentz transformations, fixes b=1. This value also
is necessary for a consistent reduction to the heterotic string in the
small-radius limit. Insisting on properly defining all fields on the circle, we
find that there is a previously unnoticed additional contribution to the
anomaly inflow from the eleven-dimensional topological term. Anomaly
cancellation then requires a quadratic relation between b and the combination
lambda^6/kappa^4 of the gauge and gravitational coupling constants lambda and
kappa. This contrasts with previous beliefs that anomaly cancellation would
give a cubic equation for b. We observe that our solution for G automatically
satisfies integer or half-integer flux quantization for the appropriate cycles.
We explicitly write out the anomaly cancelling terms of the heterotic string as
inherited from the M-theory approach. They differ from the usual ones by the
addition of a well-defined local counterterm. We also show how five-branes
enter our analysis. |
Magnetic catalysis in QED_3 at finite temperature: beyond the constant
mass approximation: We solve the Schwinger-Dyson equations for (2+1)-dimensional QED in the
presence of a strong external magnetic field. The calculation is done at finite
temperature and the fermionic self energy is not supposed to be
momentum-independent, which is the usual simplification in such calculations.
The phase diagram in the temperature-magnetic field plane is determined. For
intermediate magnetic fields the critical temperature turns out to have a
square root dependence on the magnetic field, but for very strong magnetic
fields it approaches a B-independent limiting value. | Scattering in Anti-de Sitter Space and Operator Product Expansion: We develop a formalism to evaluate generic scalar exchange diagrams in
AdS_{d+1} relevant for the calculation of four-point functions in AdS/CFT
correspondence. The result may be written as an infinite power series of
functions of cross-ratios. Logarithmic singularities appear in all orders
whenever the dimensions of involved operators satisfy certain relations. We
show that the AdS_{d+1} amplitude can be written in a form recognisable as the
conformal partial wave expansion of a four-point function in CFT_{d} and
identify the spectrum of intermediate operators. We find that, in addition to
the contribution of the scalar operator associated with the exchanged field in
the AdS diagram, there are also contributions of some other operators which may
possibly be identified with two-particle bound states in AdS. The CFT
interpretation also provides a useful way to ``regularize'' the logarithms
appearing in AdS amplitude. |
Aspects of self-dual Yang-Mills and self-dual gravity: In this thesis, we study the all same helicity loop amplitudes in self-dual
Yang-Mills and self-dual gravity. These amplitudes have long been conjectured
to be interpreted as an anomaly and are recently linked to the UV divergence of
two-loop quantum gravity. In the first part of the thesis, we study the loop
amplitudes in self-dual Yang-Mills. We show that the four point one-loop
amplitude can be reduced to a computation of shifts, which strongly suggests a
case for an anomaly interpretation. We next propose a new formula for the
one-loop amplitudes at all multiplicity, in terms of the Berends-Giele currents
connected by an effective propagator. We prove the formula by observing that it
readily implies the correct collinear properties. To demonstrate the validity
of our formula, we do an explicit computation at 3, 4 and 5 points and
reproduce the known results. The region momenta variables play an important
role in our formula and thus it points to both the worldsheet and the momentum
twistor interpretations. In the second part of the thesis, we study the one
loop behaviour of chiral Einstein-Cartan gravity and the one-loop amplitudes in
self-dual gravity. | Ultraviolet properties of Maximal Supergravity: We argue that recent results in string perturbation theory indicate that the
four-graviton amplitude of four-dimensional N=8 supergravity might be
ultraviolet finite up to eight loops. We similarly argue that the h-loop
M-graviton amplitude might be finite for h<7+M/2. |
Effective actions for dual massive (super) p-forms: In $d$ dimensions, the model for a massless $p$-form in curved space is known
to be a reducible gauge theory for $p>1$, and therefore its covariant
quantisation cannot be carried out using the standard Faddeev-Popov scheme.
However, adding a mass term and also introducing a Stueckelberg reformulation
of the resulting $p$-form model, one ends up with an irreducible gauge theory
which can be quantised \`a la Faddeev and Popov. We derive a compact expression
for the massive $p$-form effective action, $\Gamma^{(m)}_p$, in terms of the
functional determinants of Hodge-de Rham operators. We then show that the
effective actions $\Gamma^{(m)}_p$ and $\Gamma^{(m)}_{d-p-1}$ differ by a
topological invariant. This is a generalisation of the known result in the
massless case that the effective actions $\Gamma_p$ and $\Gamma_{d-p-2}$
coincide modulo a topological term. Finally, our analysis is extended to the
case of massive super $p$-forms coupled to background ${\cal N}=1$ supergravity
in four dimensions. Specifically, we study the quantum dynamics of the
following massive super $p$-forms: (i) vector multiplet; (ii) tensor multiplet;
and (iii) three-form multiplet. It is demonstrated that the effective actions
of the massive vector and tensor multiplets coincide. The effective action of
the massive three-form is shown to be a sum of those corresponding to two
massive scalar multiplets, modulo a topological term. | Real Time Propagator in the First Quantised Formalism: We argue that a basic modification must be made to the first quantised
formalism of string theory if the physics of `particle creation' is to be
correctly described. The analogous quantisation of the relativistic particle is
performed, and it is shown that the proper time along the world line must go
both forwards and backwards (in the usual quantisation it only goes forwards).
The matrix propagator of the real time formalism is obtained from the two
directions of proper time. (Talk given at the Thermal Fields Workshop held at
Banff, Canada (August 1993).) |
Gauge Transformation of Double Field Theory for Open String: We combine symmetry structures of ordinary (parallel directions) and dual
(transversal directions) coordinates to construct the Dirac-Born-Infeld (DBI)
theory. The ordinary coordinates are associated with the Neumann boundary
conditions and the dual coordinates are associated with the Dirichlet boundary
conditions. Gauge fields become scalar fields by exchanging the ordinary and
dual coordinates. A gauge transformation of a generalized metric is governed by
the generalized Lie derivative. The gauge transformation of the massless closed
string theory gives the $C$-bracket, but the gauge transformation of the open
string theory gives the $F$-bracket. The $F$-bracket with the strong
constraints is different from the Courant bracket by an exact one-form. This
exact one-form should come from the one-form gauge field. Based on symmetry
point of view, we deduce a suitable action with a non-zero $H$-flux at the
low-energy level. From an equation of motion of the scalar dilaton, it defines
a generalized scalar curvature. Finally, we construct a double sigma model with
a boundary term and show that this model with constraints is classically
equivalent to the ordinary sigma model. | On Production of Excited Kaluza-Klein States in Large Radius
Compactification Scenario: Production of exotic states at LHC is considered in the large radius
compactification scenario. We envisage a five dimensional theory for a scalar
field in five dimensional flat spacetime. It is compactified on a circle,
$S^1$, with radius, $R$. The radius is assumed to be in TeV scale appealing to
LRC hypothesis. The production of Kaluza-Klein states whose masses lie in the
vicinity of TeV range is considered. Instead of appealing to any specific
model, bounds on inelastic cross sections and near forward differental cross
section are derived from the Lehmann-Symanzik-Zimmermann (LSZ) formulation. We
consider decompactified theory should compactification radius be large enough
to unravel the fifth spacial dimension in LHC energy scale. Bounds on cross
sections are also derived for this scenario. We present bounds on inclusive
cross sections for reactions like $a+b\rightarrow c+X$, X being unobserved
states. We plot the bounds as a function of energy and propose that these
bounds might be useful for search of exotic states in LHC experiments like
ATLAS and CMS. |
Borel Summation and Analytic Continuation of the Heat Kernel on
Hyperbolic Space: The heat kernel expansion on even-dimensional hyperbolic spaces is asymptotic
at both short and long times, with interestingly different Borel properties for
these short and long time expansions. Resummations in terms of incomplete gamma
functions provide accurate extrapolations and analytic continuations, relating
the heat kernel to the Schrodinger kernel, and the heat kernel on hyperbolic
space to the heat kernel on spheres. For the diagonal heat kernel there is also
a duality between short and long times which mixes the scalar and spinor heat
kernels. | Traversable wormholes in AdS and bounds on information transfer: We analyze the amount of information that can be sent through the traversable
wormholes of Gao, Jafferis, and Wall. Although we find that the wormhole is
open for a proper time shorter than the Planck time, the transmission of a
signal through the wormhole can sometimes remain within the semiclassical
regime. For black holes with horizons of order the AdS radius, information
cannot be reliably sent through the wormhole. However, black holes with horizon
radius much larger than the AdS radius do allow for the transmission of a
number of quanta of order the horizon area in AdS units. More information can
be sent through the wormhole by increasing the number of light fields
contributing to the negative energy. Our bulk computations agree with a
boundary analysis based on quantum teleportation. |
Celestial Supersymmetry: We discuss supersymmetric Yang-Mills theory coupled to dilatons in the
framework of celestial holography. We show that in the presence of point-like
dilaton sources, the CCFT operators associated with the gauge supermultiplet
acquire a simple, factorized form. They factorize into the holomorphic
(super)current part and the exponential "light" operators of Liouville theory,
in the infinite central charge limit. The current sector exhibits (1,0)
supersymmetry, thus implementing spacetime supersymmetry in CCFT. | Comparative analysis of finite field-dependent BRST transformations: We present a review of our recent study (A. Reshetnyak, IJMPA 29 (2014)
1450128; P. Moshin, A. Reshetnyak, Nucl. Phys. B 888 (2014) 92; Phys. Lett B
739 (2014) 110; IJMPA 29 (2014) 1450159; IJMPA 30 (2015) 1550021; IJMPA 31
(2016) 1650111), in which the concept of finite field-dependent BRST and
BRST-antiBRST transformations for gauge theories was introduced, and their
properties investigated. An algorithm of exact calculation for the Jacobian of
a respective change of variables in the path integral is presented.
Applications to the Yang--Mills theory and Standard Model, in view of infra-red
(Gribov) peculiarities, are discussed. |
W-symmetries on the Homogeneous Space G/U(1)^r: A construction of $W$-symmetries is given only in terms of the nonlocal
fields (parafermions ${\ps}_{\al}$), which take values on the homogeneous space
$G/U(1)^r$, where $G$ is a simply connected compact Lie group manifold (its
accompanying Lie algebra ${\cal G}$ is a simple one of rank $r$). Only certain
restriction of the root set of Lie algebra on which the parafermionic fields
take values are satisfied, then a consistent and non-trivial extension of the
stress momentum tensor may exist. For arbitrary simple-laced algebras, i.e. the
$A-D-E$ cases, a more detailed discussion is given. The OPE of spin three
primary field are calculated, in which a primary field with spin four is
emerging. | Quantum Newtonian Dynamics on a Light Front: We recall the special features of quantum dynamics on a light-front (in an
infinite momentum frame) in string and field theory. The reason this approach
is more effective for string than for fields is stressed: the light-front
dynamics for string is that of a true Newtonian many particle system, since a
string bit has a fixed Newtonian mass. In contrast, each particle of a field
theory has a variable Newtonian mass P^+, so the Newtonian analogy actually
requires an infinite number of species of elementary Newtonian particles. This
complication substantially weakens the value of the Newtonian analogy in
applying light-front dynamics to nonperturbative problems. Motivated by the
fact that conventional field theories can be obtained as infinite tension
limits of string theories, we propose a way to recast field theory as a
standard Newtonian system. We devise and analyze some simple quantum mechanical
systems that display the essence of the proposal, and we discuss prospects for
applying these ideas to large N_c QCD. |
Nonspontaneous Supersymmetry Breaking: A new way of supersymmetry breaking involving a dynamical parameter is
introduced. It is independent of particle phenomenology and gauge groups. The
only requirement is that Lorentz invariance be valid strictly infinitesimally
(i. e. Spin(1,3) be for some values of the parameter replaced by a compact
group G locally isomorphic to Spin(1,3). | Toward Realistic Intersecting D-Brane Models: We provide a pedagogical introduction to a recently studied class of
phenomenologically interesting string models, known as Intersecting D-Brane
Models. The gauge fields of the Standard-Model are localized on D-branes
wrapping certain compact cycles on an underlying geometry, whose intersections
can give rise to chiral fermions. We address the basic issues and also provide
an overview of the recent activity in this field. This article is intended to
serve non-experts with explanations of the fundamental aspects, and also to
provide some orientation for both experts and non-experts in this active field
of string phenomenology. |
Connecting topological strings and spectral theory via non-autonomous
Toda equations: We consider the Topological String/Spectral theory duality on toric
Calabi-Yau threefolds obtained from the resolution of the cone over the
$Y^{N,0}$ singularity. Assuming Kyiv formula, we demonstrate this duality in a
special regime thanks to an underlying connection between spectral determinants
of quantum mirror curves and the non-autonomous (q)-Toda system. We further
exploit this link to connect small and large time expansions in Toda equations.
In particular we provide an explicit expression for their tau functions at
large time in terms of a strong coupling version of irregular $W_N$ conformal
blocks at $c=N-1$. These are related to a special class of multi-cut matrix
models which describe the strong coupling regime of four dimensional,
$\mathcal{N}=2$ $SU(N)$ super Yang-Mills. | Escaping the Interiors of Pure Boundary-State Black Holes: We consider a class of pure black hole microstates and demonstrate that they
can be made escapable by turning on certain double trace deformations in the
CFT. These microstates are dual to BCFT states prepared via a Euclidean path
integral starting from a boundary in Euclidean time. These states are dual to
black holes in the bulk with an End-of-the-World brane; a codimension one
timelike boundary of the spacetime behind the horizon. We show that by tuning
the sign of the coupling of the double trace operator to the boundary
conditions on the brane the deformation injects negative energy into the black
hole causing a time advance for signals behind the horizon. We demonstrate how
the property of escapability in the considered microstates follows immediately
from the traversability of deformed wormholes. We briefly comment on
reconstruction of the black hole interior and state dependence. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.