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Gaussian null coordinates, near-horizon geometry and conserved charges
on the horizon of extremal non-dilatonic black $p$-branes: In this paper, we examine the emergence of conserved charges on the horizon
of a particular class of extremal non-dilatonic black $p$-branes (which reduce
to extremal dilatonic black holes in $D=4$ dimensions upon toroidal
compactification) in the presence of a probe massless scalar field in the bulk.
This result is achieved by writing the black $p$-brane geometry in a Gaussian
null coordinate system which allows us to get a non-singular near-horizon
geometry description. We find that the near-horizon geometry is
$AdS_{p+2}\times S^2$ and that the $AdS_{p+2}$ section has an internal
structure which can be seen as a warped product of $AdS_{2}\times S^{p}$ in
Gaussian null coordinates. We show that the bulk scalar field satisfying the
field equations is expanded in terms of non-normalizable and normalizable
modes, which for certain suitable quantization conditions are well-behaved at
the boundary of $AdS_{p+2}$ space. Furthermore, we show that picking the
normalizable modes results in the existence of conserved quantities on the
horizon. We discuss the impact of these conserved quantities in the late time
regime. | Background magnetic field and quantum correlations in the Schwinger
effect: In this work we consider two complex scalar fields distinguished by their
masses coupled to constant background electric and magnetic fields in the
$(3+1)$-dimensional Minkowski spacetime and subsequently investigate a few
measures quantifying the quantum correlations between the created
particle-antiparticle Schwinger pairs. Since the background magnetic field
itself cannot cause the decay of the Minkowski vacuum, our chief motivation
here is to investigate the interplay between the effects due to the electric
and magnetic fields. We start by computing the entanglement entropy for the
vacuum state of a single scalar field. Second, we consider some maximally
entangled states for the two-scalar field system and compute the logarithmic
negativity and the mutual information. Qualitative differences of these results
pertaining to the charge content of the states are emphasised. Based upon these
results, we suggest some possible effects of a background magnetic field on the
degradation of entanglement between states in an accelerated frame, for charged
quantum fields. |
Renormalization Group Approach to Matrix Models and Vector Models: The renormalization group approach is studied for large $N$ models. The
approach of Br\'ezin and Zinn-Justin is explained and examined for matrix
models. The validity of the approach is clarified by using the vector model as
a similar and simpler example. An exact difference equation is obtained which
relates free energies for neighboring values of $N$. The reparametrization
freedom in field space provides infinitely many identities which reduce the
infinite dimensional coupling constant space to that of finite dimensions. The
effective beta functions give exact values for the fixed points and the
susceptibility exponents. A detailed study of the effective renormalization
group flow is presented for cases with up to two coupling constants. We draw
the two-dimensional flow diagram. | Euclidean quantum M5 brane theory on $S^1 \times S^5$: We consider Euclidean quantum M5 brane theory on $S^1\times S^5$. Dimensional
reduction along $S^1$ gives a 5d SYM on $S^5$. We derive this 5d SYM theory
from a classical Lorentzian M5 brane Lagrangian on $S^1 \times S^5$, where
$S^1$ is a timelike circle of radius $T$, by performing a Scherk-Schwarz
reduction along $S^1$ followed by Wick rotation of $T$. |
Quasi-hole solutions in finite noncommutative Maxwell-Chern-Simons
theory: We study Maxwell-Chern-Simons theory in 2 noncommutative spatial dimensions
and 1 temporal dimension. We consider a finite matrix model obtained by adding
a linear boundary field which takes into account boundary fluctuations. The
pure Chern-Simons has been previously shown to be equivalent to the Laughlin
description of the quantum Hall effect. With the addition of the Maxwell term,
we find that there exists a rich spectrum of excitations including solitons
with nontrivial "magnetic flux" and quasi-holes with nontrivial "charges",
which we describe in this article. The magnetic flux corresponds to vorticity
in the fluid fluctuations while the charges correspond to sources of fluid
fluctuations. We find that the quasi-hole solutions exhibit a gap in the
spectrum of allowed charge. | On the solution of the Calogero model and its generalization to the case
of distinguishable particles: The 3-body Calogero problem is solved by separation of variables for
arbitrary exchange statistics. A numerical computation of the 4-body spectrum
is also presented. The results display new features in comparison with the
standard case of bosons and fermions, for instance the energies are not linear
with the interaction parameter $\nu$ and Bethe ansatz as well as Haldane's
statistics are not verified. |
Production of Spin-Two Gauge Bosons: We considered spin-two gauge boson production in the fermion pair
annihilation process and calculated the polarized cross sections for each set
of helicity orientations of initial and final particles. The angular dependence
of these cross sections is compared with the similar annihilation cross
sections in QED with two photons in the final state, with two gluons in QCD and
W-pair in Electroweak theory. | Three-loop color-kinematics duality: A 24-dimensional solution space
induced by new generalized gauge transformations: We obtain full-color three-loop three-point form factors of the stress-tensor
supermultiplet and also of a length-3 half-BPS operator in N=4 SYM based on the
color-kinematics duality and on-shell unitarity. The integrand results are
verified by all planar and non-planar unitarity cuts, and they satisfy the
minimal power-counting of loop momenta and diagrammatic symmetries.
Interestingly, these three-loop solutions, while manifesting all dual Jacobi
relations, contain a large number of free parameters; in particular, there are
24 free parameters for the form factor of stress-tensor supermultiplet. Such
degrees of freedom are due to a new type of generalized gauge transformation
associated with the operator insertion for form factors. We also perform
numerical integration and obtain consistent full-color infrared divergences and
the known planar remainder. The form factors we obtain can be understood as the
N=4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and
are expected to provide the maximally transcendental parts of the latter. |
Equations of motion from Cederwall's pure spinor superspace actions: Using non-minimal pure spinor superspace, Cederwall has constructed
BRST-invariant actions for $D=10$ super-Born-Infeld and $D=11$ supergravity
which are quartic in the superfields. But since the superfields have explicit
dependence on the non-minimal pure spinor variables, it is non-trivial to show
these actions correctly describe super-Born-Infeld and supergravity. In this
paper, we expand solutions to the equations of motion from Cederwall's actions
to leading order around the linearized solutions and show that they correctly
describe the interactions of $D=10$ super-Born-Infeld and $D=11$ supergravity. | Explaining enhanced UV divergence cancellations: We study supergravities with "enhanced UV divergence cancellations". We show
that all these cancellations are explained by a simple dimensional analysis of
nonlinear local supersymmetry (NLS). We also show that in all cases where
E7-type duality was used in the past via vanishing single scalar limit (SSL) to
explain/predict UV cancellations one could have used dimensional analysis of
NLS. The SSL constraints predict in d=4 loop order L less or equal (N-2) for UV
finiteness, dimensional analysis of NLS predicts L less or equal (N-1) for UV
finiteness, including enhanced cases like N=5, L=4. |
Thermodynamics of non-abelian exclusion statistics: The thermodynamic potential of ideal gases described by the simplest
non-abelian statistics is investigated. I show that the potential is the linear
function of the element of the abelian-part statistics matrix. Thus, the
factorizable property in the Haldane (abelian) fractional exclusion shown by
the author [W. H. Huang, Phys. Rev. Lett. 81, 2392 (1998)] is now extended to
the non-abelian case. The complete expansion of the thermodynamic potential is
also given. | Stability of D1-Strings Inside a D3-Brane: Within the tachyon condensation approach, we find that a D(p-2)-brane is
stable inside Dp-branes when the bulk is compactified. It is a codimension-2
soliton of the Dp-brane action with coupling to the bulk (p-1)-form RR field.
We discuss the properties of such solitons. They may appear as detectable
cosmic strings in our universe. |
The ${\cal N}=4$ Coset Model and the Higher Spin Algebra: By computing the operator product expansions between the first two ${\cal
N}=4$ higher spin multiplets in the unitary coset model, the (anti)commutators
of higher spin currents are obtained under the large $(N,k)$ 't Hooft-like
limit. The free field realization with complex bosons and fermions is
presented. The (anti)commutators for generic spins $s_1$ and $s_2$ with
manifest $SO(4)$ symmetry at vanishing 't Hooft-like coupling constant are
completely determined. The structure constants can be written in terms of the
ones in the ${\cal N}=2$ ${\cal W}_{\infty}$ algebra found by Bergshoeff, Pope,
Romans, Sezgin and Shen previously, in addition to the spin-dependent
fractional coefficients and two $SO(4)$ invariant tensors. We also describe the
${\cal N}=4$ higher spin generators, by using the above coset construction
results, for general super spin $s$ in terms of oscillators in the matrix
generalization of $AdS_3$ Vasiliev higher spin theory at nonzero 't Hooft-like
coupling constant. We obtain the ${\cal N}=4$ higher spin algebra for low spins
and present how to determine the structure constants, which depend on the
higher spin algebra parameter, in general, for fixed spins $s_1$ and $s_2$. | Five loop renormalization of $φ^3$ theory with applications to the
Lee-Yang edge singularity and percolation theory: We apply the method of graphical functions that was recently extended to six
dimensions for scalar theories, to $\phi^3$ theory and compute the $\beta$
function, the wave function anomalous dimension as well as the mass anomalous
dimension in the $\overline{\mbox{MS}}$ scheme to five loops. From the results
we derive the corresponding renormalization group functions for the Lee-Yang
edge singularity problem and percolation theory. After determining the
$\varepsilon$ expansions of the respective critical exponents to
$\mathcal{O}(\varepsilon^5)$ we apply recent resummation technology to obtain
improved exponent estimates in 3, 4 and 5 dimensions. These compare favourably
with estimates from fixed dimension numerical techniques and refine the four
loop results. To assist with this comparison we collated a substantial amount
of data from numerical techniques which are included in tables for each
exponent. |
Systematic Implementation of Implicit Regularization for Multi-Loop
Feynman Diagrams: Implicit Regularization (IReg) is a candidate to become an invariant
framework in momentum space to perform Feynman diagram calculations to
arbitrary loop order. In this work we present a systematic implementation of
our method that automatically displays the terms to be subtracted by
Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we
show that the IReg program respects unitarity, locality and Lorentz invariance
and we show that our method is consistent since we are able to display the
divergent content of a multi-loop amplitude in a well defined set of basic
divergent integrals in one loop momentum only which is the essence of IReg.
Moreover, we conjecture that momentum routing invariance in the loops, which
has been shown to be connected with gauge symmetry, is a fundamental symmetry
of any Feynman diagram in a renormalizable quantum field theory. | A Worldsheet Description of Flux Compactifications: We demonstrate how recent developments in string field theory provide a
framework to systematically study type II flux compactifications with
non-trivial Ramond-Ramond profiles. We present an explicit example where
physical observables can be computed order by order in a small parameter which
can be effectively viewed as string coupling constant. We obtain the
corresponding background solution of the string field equations of motions up
to the second order in the expansion. Along the way, we show how the tadpole
cancellations of the string field equations lead to the minimization of the
F-term potential of the low energy supergravity description. String field
action expanded around the obtained background solution furnishes a worldsheet
description of the flux compactifications. |
Induced moduli oscillation by radiation and space expansion in a
higher-dimensional model: We investigate the cosmological expansion of the 3D space in a 6D model
compactified on a sphere, beyond the 4D effective theory analysis. We focus on
a case that the initial temperature is higher than the compactification scale.
In such a case, the pressure for the compact space affects the moduli dynamics
and induces the moduli oscillation even if they are stabilized at the initial
time. Under some plausible assumptions, we derive the explicit expressions for
the 3D scale factor and the moduli background in terms of analytic functions.
Using them, we evaluate the transition times between different cosmological
eras as functions of the model parameters and the initial temperature. | Completely Integrable Equation for the Quantum Correlation Function of
Nonlinear Schrödinger Eqaution: Correlation functions of exactly solvable models can be described by
differential equation [Barough, McCoy, Wu]. In this paper we show that for non
free fermionic case differential equations should be replaced by
integro-differential equations.
We derive an integro-differential equation, which describes time and
temperature dependent correlation function $<\psi(0,0)\psi^\dagger(x,t)>_T$ of
penetrable Bose gas. The integro-differential equation turns out be the
continuum generalization of classical nonlinear Schr\"odinger equation. |
Localization vs holography in $4d$ $\mathcal{N}=2$ quiver theories: We study 4-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories
obtained with an orbifold projection from $\mathcal{N}=4$ SYM, and compute the
2- and 3-point correlation functions among chiral/anti-chiral single-trace
scalar operators and the corresponding structure constants. Exploiting
localization, we map the computation to an interacting matrix model and obtain
expressions for the correlators and the structure constants that are valid for
any value of the 't Hooft coupling in the planar limit of the theory. At strong
coupling, these expressions simplify and allow us to extract the leading
behavior in an analytic way. Finally, using the AdS/CFT correspondence, we
compute the structure constants from the dual supergravity theory and obtain
results that perfectly match the strong-coupling predictions from localization. | Emergence of the Circle in a Statistical Model of Random Cubic Graphs: We consider a formal discretisation of Euclidean quantum gravity defined by a
statistical model of random $3$-regular graphs and making using of the Ollivier
curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows
that the Hausdorff and spectral dimensions of the model approach $1$ in the
joint classical-thermodynamic limit and we argue that the scaling limit of the
model is the circle of radius $r$, $S^1_r$. Given mild kinematic constraints,
these claims can be proven with full mathematical rigour: speaking precisely,
it may be shown that for $3$-regular graphs of girth at least $4$, any sequence
of action minimising configurations converges in the sense of Gromov-Hausdorff
to $S^1_r$. We also present strong evidence for the existence of a second-order
phase transition through an analysis of finite size effects. This --
essentially solvable -- toy model of emergent one-dimensional geometry is meant
as a controllable paradigm for the nonperturbative definition of random flat
surfaces. |
Manifolds of G_2 Holonomy from N=4 Sigma Model: Using two dimensional (2D) N=4 sigma model, with $U(1)^r$ gauge symmetry, and
introducing the ADE Cartan matrices as gauge matrix charges, we build " toric"
hyper-Kahler eight real dimensional manifolds X_8. Dividing by one toric
geometry circle action of X_8 manifolds, we present examples describing
quotients $X_7={X_8\over U(1)}$ of G_2 holonomy. In particular, for the A_r
Cartan matrix, the quotient space is a cone on a $ {S^2}$ bundle over r
intersecting $\bf WCP^2_{(1,2,1)}$ projective spaces according to the A_r
Dynkin diagram. | On the Origin of Gravity and the Laws of Newton: Starting from first principles and general assumptions Newton's law of
gravitation is shown to arise naturally and unavoidably in a theory in which
space is emergent through a holographic scenario. Gravity is explained as an
entropic force caused by changes in the information associated with the
positions of material bodies. A relativistic generalization of the presented
arguments directly leads to the Einstein equations. When space is emergent even
Newton's law of inertia needs to be explained. The equivalence principle leads
us to conclude that it is actually this law of inertia whose origin is
entropic. |
Semi-classical unitarity in 3-dimensional higher-spin gravity for
non-principal embeddings: Higher-spin gravity in three dimensions is efficiently formulated as a
Chern-Simons gauge-theory, typically with gauge algebra sl(N)+sl(N). The
classical and quantum properties of the higher-spin theory depend crucially on
the embedding into the full gauge algebra of the sl(2)+sl(2) factor associated
with gravity. It has been argued previously that non-principal embeddings do
not allow for a semi-classical limit (large values of the central charge)
consistent with unitarity. In this work we show that it is possible to
circumvent these conclusions. Based upon the Feigin-Semikhatov generalization
of the Polyakov-Bershadsky algebra, we construct infinite families of unitary
higher-spin gravity theories at certain rational values of the Chern-Simons
level that allow arbitrarily large values of the central charge up to c = N/4 -
1/8 - O(1/N), thereby confirming a recent speculation by us 1209.2860. | A Multitrace Approach to Noncommutative Φ_2^4: In this article we provide a multitrace analysis of the theory of
noncommutative $\Phi^4$ in two dimensions on the fuzzy sphere ${\bf
S}^2_{N,\Omega}$, and on the Moyal-Weyl plane ${\bf R}^{2}_{\theta, \Omega}$,
with a non-zero harmonic oscillator term added. The doubletrace matrix model
symmetric under $M\longrightarrow -M$ is solved in closed form. An analytical
prediction for the disordered-to-non-uniform-ordered phase transition and an
estimation of the triple point, from the termination point of the critical
boundary, are derived and compared with previous Monte Carlo measurement. |
A Note On Intrinsic Regularization Method: There exist certain intrinsic relations between the ultraviolet divergent
graphs and the convergent ones at the same loop order in renormalizable quantum
field theories. Whereupon we may establish a new method, the intrinsic
regularization method, to regulate those divergent graphs. In this note, we
present a proposal, the inserter proposal, to the method. The $\phi^4$ theory
and QED at the one loop order are dealt with in some detail. Inserters in the
standard model are given. Some applications to SUSY-models are also made at the
one loop order. | Notes about equivalence between Sine-Gordon theory (free fermion point)
and the free fermion theory: The space of local integrals of motion for the Sine-Gordon theory (the free
fermion point) and the theory of free fermions in the light cone coordinates is
investigated. Some important differences between the spaces of local integrals
of motion of these theories are obtained. The equivalence is broken on the
level of the integrals of motion between bosonic and fermionic theories (in the
free fermion point). The integrals of motion are constracted without Quantum
Inverse Scattering Method (QISM)and the additional quantum integrals of motion
are obtaned. So the QISM is not absolutely complete. |
Matrix Factorizations for Local F-Theory Models: I use matrix factorizations to describe branes at simple singularities as
they appear in elliptic fibrations of local F-theory models. Each node of the
corresponding Dynkin diagrams of the ADE-type singularities is associated with
one indecomposable matrix factorization which can be deformed into one or more
factorizations of lower rank. Branes with internal fluxes arise naturally as
bound states of the indecomposable factorizations. Describing branes in such a
way avoids the need to resolve singularities and encodes information which is
neglected in conventional F-theory treatments. This paper aims to show how
branes arising in local F-theory models around simple singularities can be
described in this framework. | Analytic derivation of dual gluons and monopoles from SU(2) lattice
Yang-Mills theory. II. Spin foam representation: In this series of three papers, we generalize the derivation of dual photons
and monopoles by Polyakov, and Banks, Myerson and Kogut, to obtain
approximative models of SU(2) lattice gauge theory. Our approach is based on
stationary phase approximations.
In this second article, we start from the spin foam representation of
3-dimensional SU(2) lattice gauge theory. By extending an earlier work of
Diakonov and Petrov, we approximate the expectation value of a Wilson loop by a
path integral over a dual gluon field and monopole-like degrees of freedom. The
action contains the tree-level Coulomb interaction and a nonlinear coupling
between dual gluons, monopoles and current. |
Perturbative Prepotential and Monodromies in N=2 Heterotic Superstring: We discuss the prepotential describing the effective field theory of N=2
heterotic superstring models. At the one loop-level the prepotential develops
logarithmic singularities due to the appearance of charged massless states at
particular surfaces in the moduli space of vector multiplets. These
singularities modify the classical duality symmetry group which now becomes a
representation of the fundamental group of the moduli space minus the singular
surfaces. For the simplest two-moduli case, this fundamental group turns out to
be a certain braid group and we determine the resulting full duality
transformations of the prepotential, which are exact in perturbation theory. | A comment on bosonization in $d \geq 2$ dimensions: We discuss recent results on bosonization in $d \geq 2$ space-time dimensions
by giving a very simple derivation for the bosonic representation of the
original free fermionic model both in the abelian and non-abelian cases. We
carefully analyse the issue of symmetries in the resulting bosonic model as
well as the recipes for bosonization of fermion currents |
Representations of a quantum-deformed Lorentz algebra, Clebsch-Gordan
map, and Fenchel-Nielsen representation of quantum complex flat connections
at level-$k$: A family of infinite-dimensional irreducible $\star$-representations on
$\mathcal{H}\simeq L^2(\mathbb{R})\otimes\mathbb{C}^k$ is defined for a
quantum-deformed Lorentz algebra $U_\mathbf{q}(sl_2)\otimes
U_{\tilde{\mathbf{q}}}(sl_2)$, where $\mathbf{q}=\exp[\frac{2\pi i}{k}(1+b^2)]$
and $\tilde{\mathbf{q}}=\exp[\frac{2\pi i}{k}(1+b^{-2})]$ with
$k\in\mathbb{Z}_+$ and $|b|=1$. The representations are constructed with the
irreducible representation of quantum torus algebra at level-$k$, which is
developed from the quantization of $\mathrm{SL}(2,\mathbb{C})$ Chern-Simons
theory. We study the Clebsch-Gordan decomposition of the tensor product
representation, and we show that it reduces to the same problem as
diagonalizing the complex Fenchel-Nielson length operators in quantizing
$\mathrm{SL}(2,\mathbb{C})$ flat connections on 4-holed sphere. Finally, the
spectral decomposition of the complex Fenchel-Nielson length operators results
in the direct-integral representation of the Hilbert space $\mathcal{H}$, which
we call the Fenchel-Nielson representation. | Internal symmetry in Poincare gauge gravity: We find a large internal symmetry within 4-dimensional Poincare gauge theory.
In the Riemann-Cartan geometry of Poincare gauge theory the field equation and
geodesics are invariant under projective transformation, just as in affine
geometry. However, in the Riemann-Cartan case the torsion and nonmetricity
tensors change. By generalizing the Riemann-Cartan geometry to allow both
torsion and nonmetricity while maintaining local Lorentz symmetry the
difference of the antisymmetric part of the nonmetricity Q and the torsion T is
a projectively invariant linear combination $S = T - Q$ with the same symmetry
as torsion. The structure equations may be written entirely in terms of S and
the corresponding Riemann-Cartan curvature. The new description of the geometry
has manifest projective and Lorentz symmetries, and vanishing nonmetricity.
Torsion, S and Q lie in the vector space of vector-valued 2-forms. Within the
extended geometry we define rotations with axis in the direction of S. These
rotate both torsion and nonmetricity while leaving S invariant. In n dimensions
and (p, q) signature this gives a large internal symmetry. The four dimensional
case acquires SO(11,9) or Spin(11,9) internal symmetry, sufficient for the
Standard Model. The most general action up to linearity in second derivatives
of the solder form now includes combinations quadratic in torsion and
nonmetricity, torsion-nonmetricity couplings, and the Einstein-Hilbert action.
Imposing projective invariance reduces this to dependence on S and curvature
alone. The new internal symmetry decouples from gravity in agreement with the
Coleman-Mandula theorem. |
The Angular Momentum Operator in the Dirac Equation: The Dirac equation in spherically symmetric fields is separated in two
different tetrad frames. One is the standard cartesian (fixed) frame and the
second one is the diagonal (rotating) frame. After separating variables in the
Dirac equation in spherical coordinates, and solving the corresponding
eingenvalues equations associated with the angular operators, we obtain that
the spinor solution in the rotating frame can be expressed in terms of Jacobi
polynomials, and it is related to the standard spherical harmonics, which are
the basis solution of the angular momentum in the Cartesian tetrad, by a
similarity transformation. | Inequivalent Quantizations of Gauge Theories: It is known that the quantization of a system defined on a topologically
non-trivial configuration space is ambiguous in that many inequivalent quantum
systems are possible. This is the case for multiply connected spaces as well as
for coset spaces. Recently, a new framework for these inequivalent
quantizations approach has been proposed by McMullan and Tsutsui, which is
based on a generalized Dirac approach. We employ this framework for the
quantization of the Yang-Mills theory in the simplest fashion. The resulting
inequivalent quantum sectors are labelled by quantized non-dynamical
topological charges. |
Deformation of Schild String: We attempt to construct new superstring actions with a $D$-plet of Majorana
fermions $\psi^{\cal B}_A$, where ${\cal B}$ is the $D$ dimensional space-time
index and $A$ is the two dimensional spinor index, by deforming the Schild
action. As a result, we propose three kinds of actions: the first is invariant
under N=1 (the world-sheet) supersymmetry transformation and the
area-preserving diffeomorphism. The second contains the Yukawa type
interaction. The last possesses some non-locality because of bilinear terms of
$\psi^{\cal B}_A$. The reasons why completing a Schild type superstring action
with $\psi^{\cal B}_A$ is difficult are finally discussed. | Stability Issues for w < -1 Dark Energy: Precision cosmological data hint that a dark energy with equation of state $w
= P/\rho < -1$ and hence dubious stability is viable. Here we discuss for any
$w$ nucleation from $\Lambda > 0$ to $\Lambda = 0$ in a first-order phase
transition. The critical radius is argued to be at least of galactic size and
the corresponding nucleation rate is glacial, thus underwriting the dark
energy's stability and rendering remote any microscopic effect. |
Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories: We demonstrate electric-magnetic duality in N=1 supersymmetric non-Abelian
gauge theories in four dimensions by presenting two different gauge theories
(different gauge groups and quark representations) leading to the same
non-trivial long distance physics. The quarks and gluons of one theory can be
interpreted as solitons (non-Abelian magnetic monopoles) of the elementary
fields of the other theory. The weak coupling region of one theory is mapped to
a strong coupling region of the other. When one of the theories is Higgsed by
an expectation value of a squark, the other theory is confined. Massless
glueballs, baryons and Abelian magnetic monopoles in the confining description
are the weakly coupled elementary quarks (i.e.\ solitons of the confined
quarks) in the dual Higgs description. | The General 3-Graviton Vertex ($TTT$) of Conformal Field Theories in
Momentum Space in $d=4$: We present a study of the correlation function of three stress-energy tensors
in $d$ dimensions using free field theory realizations, and compare them to the
exact solutions of their conformal Ward identities (CWI's) obtained by a
general approach in momentum space. The identification of the corresponding
form factors is performed within a reconstruction method, based on the
identification of the transverse traceless components $(A_i)$ of the same
correlator. The solutions of the primary CWI' s are found by exploiting the
universality of the Fuchsian indices of the conformal operators and a
re-arrangement of the corresponding inhomogenous hypergeometric systems. We
confirm the number of constants in the solution of the primary CWI's of
previous analysis. In our comparison with perturbation theory, we discuss
scalar, fermion and spin 1 exchanges at 1-loop in dimensional regularization.
Explicit checks in $d=3$ and $d=5$ prove the consistency of this
correspondence. By matching the 3 constants of the CFT solution with the 3 free
field theory sectors available in d=4, the general solutions of the conformal
constraints is expressed just in terms of ordinary scalar 2- and 3-point
functions $(B_0,C_0)$. We show how the renormalized $d=4$ TTT vertex separates
naturally into the sum of a traceless and an anomaly part, the latter
determined by the anomaly functional and generated by the renormalization of
the correlator in dimensional regularization. The result confirms the emergence
of anomaly poles and effective massless exchanges as a specific signature of
conformal anomalies in momentum space, directly connected to the
renormalization of the corresponding gravitational vertices, generalizing the
behaviour found for the $TJJ$ vertex in previous works. |
Sign of BPS index for ${\cal N}=4$ dyons: In this paper we argue how the sign changes on an average for the positive
weight mock modular forms associated with the ${\cal N}=4$ type II string black
holes compactified on orbifolds of $K3\times T^2$. The orbifolds of order $N$
act with $g'\in[M_{23}]$ an order $N$ symplectic orbifold on $K3$ and a $1/N$
shift in one of the circles of the torus $T^2$. We expand the inverse Siegel
modular forms of subgroups of $Sp_2(\mathbb{Z})$ for the magnetic charge
$P^2=2$ in terms of mock Jacobi forms and Appell Lerch sums. We analyze the
average growth of the coefficients of these mock modular forms after theta
decomposition and removing inverse eta products. In particular we remove the
contribution of the fundamental string which rightfully dominates the growth of
the positive weight modular forms after the first few coefficients and ensures
the positivity of the helicity trace index $-B_6$. Using numerics and limits of
divisor sum function we predict the sign of these mock modular forms. We also
observe that the cusp forms associated with the non-geometric orbifolds of $K3$
can only contribute for sign changes up to the first few terms hence their
contribution can be neglected for large electric charges. | Are Textures Natural?: We make the simple observation that, because of global symmetry violating
higher-dimension operators expected to be induced by Planck-scale physics,
textures are generically much too short-lived to be of use for large-scale
structure formation. |
Representations of Super Yangian: We present in detail the classification of the finite dimensional irreducible
representations of the super Yangian associated with the Lie superalgebra
$gl(1|1)$. | Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries
and BPS States: We propose a graph-based approach to 5d superconformal field theories (SCFTs)
based on their realization as M-theory compactifications on singular elliptic
Calabi--Yau threefolds. Field-theoretically, these 5d SCFTs descend from 6d
$\mathcal{N}=(1,0)$ SCFTs by circle compactification and mass deformations. We
derive a description of these theories in terms of graphs, so-called Combined
Fiber Diagrams, which encode salient features of the partially resolved
Calabi--Yau geometry, and provides a combinatorial way of characterizing all 5d
SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly
capture strongly coupled data of the 5d SCFTs, such as the superconformal
flavor symmetry, BPS states, and mass deformations. The capabilities of this
approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The
full potential, however, becomes apparent when applied to theories with higher
rank. Starting with the higher rank conformal matter theories in 6d, we are led
to the discovery of previously unknown flavor symmetry enhancements and new 5d
SCFTs. |
Emergence of AdS geometry in the simulated tempering algorithm: In our previous work [1], we introduced to an arbitrary Markov chain Monte
Carlo algorithm a distance between configurations. This measures the difficulty
of transition from one configuration to the other, and enables us to
investigate the relaxation of probability distribution from a geometrical point
of view. In this paper, we investigate the geometry of stochastic systems whose
equilibrium distributions are highly multimodal with a large number of
degenerate vacua. Implementing the simulated tempering algorithm to such a
system, we show that an asymptotically Euclidean anti-de Sitter geometry
emerges with a horizon in the extended configuration space when the tempering
parameter is optimized such that distances get minimized. | Rational Lax operators and their quantization: We investigate the construction of the quantum commuting hamiltonians for the
Gaudin integrable model. We prove that [Tr L^k(z), Tr L^m(u) ]=0, for k,m < 4 .
However this naive receipt of quantization of classically commuting
hamiltonians fails in general, for example we prove that [Tr L^4(z), Tr L^2(u)
] \ne 0. We investigate in details the case of the one spin Gaudin model with
the magnetic field also known as the model obtained by the "argument shift
method". Mathematically speaking this method gives maximal Poisson commutative
subalgebras in the symmetric algebra S(gl(N)). We show that such subalgebras
can be lifted to U(gl(N)), simply considering Tr L(z)^k, k\le N for N<5. For
N=6 this method fails: [Tr L_{MF}(z)^6, L_{MF}(u)^3]\ne 0 . All the proofs are
based on the explicit calculations using r-matrix technique. We also propose
the general receipt to find the commutation formula for powers of Lax operator.
For small power exponents we find the complete commutation relations between
powers of Lax operators. |
Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories: We study the defect groups of $D_p^b(G)$ theories using geometric engineering
and BPS quivers. In the simple case when $b=h^\vee (G)$, we use the BPS quivers
of the theory to see that the defect group is compatible with a known
Maruyoshi-Song flow. To extend to the case where $b\neq h^\vee (G)$, we use a
similar Maruyoshi-Song flow to conjecture that the defect groups of $D_p^b(G)$
theories are given by those of $G^{(b)}[k]$ theories. In the cases of $G=A_n,
\;E_6, \;E_8$ we cross check our result by calculating the BPS quivers of the
$G^{(b)}[k]$ theories and looking at the cokernel of their intersection matrix. | Skyrme-Faddeev model from 5d super-Yang-Mills: We consider 5d Yang-Mills-Higgs theory with a compact ADE-type gauge group
$G$ and one adjoint scalar field on $\mathbb{R}^{3,1}\times\mathbb{R}_+$, where
$\mathbb{R}_+=[0,\infty)$ is the half-line. The maximally supersymmetric
extension of this model, with five adjoint scalars, appears after a reduction
of 6d ${\cal N}{=}\,(2,0)$ superconformal field theory on
$\mathbb{R}^{3,1}\times\mathbb{R}_+\times S^1$ along the circle $S^1$. We show
that in the low-energy limit, when momenta along $\mathbb{R}^{3,1}$ are much
smaller than along $\mathbb{R}_+$, the 5d Yang-Mills-Higgs theory reduces to a
nonlinear sigma model on $\mathbb{R}^{3,1}$ with a coset $G/H$ as its target
space. Here $H$ is a closed subgroup of $G$ determined by the Higgs-field
asymptotics at infinity. The 4d sigma model describes an infinite tower of
interacting fields, and in the infrared it is dominated by the standard
two-derivative kinetic term and the four-derivative Skyrme-Faddeev term. |
Principal Realization for the extended affine Lie algebra of type $sl_2$
with coordinates in a simple quantum torus with two generators: We construct an irreducible representation for the extended affine algebra of
type $sl_2$ with coordinates in a quantum torus. We explicitly give formulas
using vertex operators similar to those found in the theory of the infinite
rank affine algebra $A_{\infty}$. | Circuit Complexity From Cosmological Islands: Recently in various theoretical works, path-breaking progress has been made
in recovering the well-known Page Curve of an evaporating black hole with
Quantum Extremal Islands, proposed to solve the long-standing black hole
information loss problem related to the unitarity issue. Motivated by this
concept, in this paper, we study cosmological circuit complexity in the
presence (or absence) of Quantum Extremal Islands in the negative (or positive)
Cosmological Constant with radiation in the background of
Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) space-time i.e the presence
and absence of islands in anti-de Sitter and the de Sitter spacetime having
SO(2, 3) and SO(1, 4) isometries respectively. Without using any explicit
details of any gravity model, we study the behaviour of the circuit complexity
function with respect to the dynamical cosmological solution for the scale
factors for the above-mentioned two situations in FLRW space-time using
squeezed state formalism. By studying the cosmological circuit complexity,
Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the
squeezed state, in different parameter spaces, we conclude the non-universality
of these measures. Their remarkably different features in the different
parameter spaces suggest their dependence on the parameters of the model under
consideration. |
Three-Family $SO(10)$ Grand Unification in String Theory: The construction of a supersymmetric $SO(10)$ grand unification with 5
left-handed and 2 right-handed families in the four-dimensional heterotic
string theory is presented. The model has one $SO(10)$ adjoint Higgs field. The
$SO(10)$ current algebra is realized at level 3. | Non-local conservation laws and flow equations for supersymmetric
integrable hierarchies: An infinite series of Grassmann-odd and Grassmann-even flow equations is
defined for a class of supersymmetric integrable hierarchies associated with
loop superalgebras. All these flows commute with the mutually commuting bosonic
ones originally considered to define these hierarchies and, hence, provide
extra fermionic and bosonic symmetries that include the built-in N=1
supersymmetry transformation. The corresponding non-local conserved quantities
are also constructed. As an example, the particular case of the principal
supersymmetric hierarchies associated with the affine superalgebras with a
fermionic simple root system is discussed in detail. |
Self-interaction effects on screening in three-dimensional QED: We have shown that self interaction effects in massive quantum
electrodynamics can lead to the formation of bound states of quark antiquark
pairs. A current-current fermion coupling term is introduced, which induces a
well in the potential energy profile. Explicit expressions of the effective
potential and renormalized parameters are provided. | Euclidean Twistor Unification: Taking Euclidean signature space-time with its local Spin(4)=SU(2)xSU(2)
group of space-time symmetries as fundamental, one can consistently gauge one
SU(2) factor to get a chiral spin connection formulation of general relativity,
the other to get part of the Standard Model gauge fields. Reconstructing a
Lorentz signature theory requires introducing a degree of freedom specifying
the imaginary time direction, which will play the role of the Higgs field.
To make sense of this one needs to work with twistor geometry, which provides
tautological spinor degrees of freedom and a framework for relating by analytic
continuation spinors in Minkowski and Euclidean space-time. It also provides
internal U(1) and SU(3) symmetries as well as a simple construction of the
degrees of freedom of a Standard Model generation of matter fields. In this
proposal the theory is naturally defined on projective twistor space rather
than the usual space-time, so will require further development of a gauge
theory and spinor field quantization formalism in that context. |
On the Picard-Fuchs Equations for Massive N=2 Seiberg-Witten Theories: A new method to obtain the Picard-Fuchs equations of effective, N=2
supersymmetric gauge theories with massive matter hypermultiplets in the
fundamental representation is presented. It generalises a previously described
method to derive the Picard-Fuchs equations of both pure super Yang-Mills and
supersymmetric gauge theories with massless matter hypermultiplets. The
techniques developed are well suited to symbolic computer calculations. | Conformality and Gauge Coupling Unification: It has been recently proposed to embed the standard model in a conformal
gauge theory to resolve the hierarchy problem, and to avoid assuming either
grand unification or low-energy supersymmetry. By model building based on
string-field duality we show how to maintain the successful prediction of an
electroweak mixing angle with $sin^2\theta \simeq 0.231$ in conformal gauge
theories with three chiral families. |
Comments on $SO/Sp$ Gauge Theories from Brane Configurations with an O6
Plane: We use the M theory approach in the presence of an orientifold O6 plane to
understand some aspects of the moduli space of vacua for N=1 supersymmetric
$SO(N_c)/Sp(N_c)$ gauge theories in four dimensions. By exploiting some general
properties of the O6 orientifold, we reproduce some results obtained previously
with an orientifold O4 plane when the flavor group arises from the worldvolume
dynamics of D6 branes. By using semi-infinite D4 branes instead of D6 branes,
we derive the most general form of the rotated curve describing the moduli
space of vacua for N=1 supersymmetric gauge theory with massive matter. | Symmetry decomposition of relative entropies in conformal field theory: We consider the symmetry resolution of relative entropies in the 1+1
dimensional free massless compact boson conformal field theory (CFT) which
presents an internal $U(1)$ symmetry. We calculate various symmetry resolved
R\'enyi relative entropies between one interval reduced density matrices of CFT
primary states using the replica method. By taking the replica limit, the
symmetry resolved relative entropy can be obtained. We also take the XX spin
chain model as a concrete lattice realization of this CFT to perform numerical
computation. The CFT predictions are tested against exact numerical
calculations finding perfect agreement. |
M-theory Superstrata and the MSW String: The low-energy description of wrapped M5 branes in compactifications of
M-theory on a Calabi-Yau threefold times a circle is given by a conformal field
theory studied by Maldacena, Strominger and Witten and known as the MSW CFT.
Taking the threefold to be T$^6$ or K3xT$^2$, we construct a map between a
sub-sector of this CFT and a sub-sector of the D1-D5 CFT. We demonstrate this
map by considering a set of D1-D5 CFT states that have smooth horizonless bulk
duals, and explicitly constructing the supergravity solutions dual to the
corresponding states of the MSW CFT. We thus obtain the largest known class of
solutions dual to MSW CFT microstates, and demonstrate that five-dimensional
ungauged supergravity admits much larger families of smooth horizonless
solutions than previously known. | The Casimir effect in string theory: We discuss the Casimir effect in heterotic string theory. This is done by
considering a Z_2 twist acting on one external compact direction and three
internal coordinates. The hyperplanes fixed by the orbifold generator G realize
the two infinite parallel plates. For the latter to behave as "conducting
material", we implement in a modular invariant way the projection (1-G)/2 on
the spectrum running in the vacuum-to-vacuum amplitude at one-loop. Hence, the
relevant projector to account for the Casimir effect is orthogonal to that
commonly used in string orbifold models, which is (1+G)/2. We find that this
setup yields the same net force acting on the plates in the context of quantum
field theory and string theory. However, when supersymmetry is not present from
the onset, finiteness of the resultant force in field theory is reached by
adding formally infinite forces acting on either side of each plate, while in
string theory both contributions are finite. On the contrary, when
supersymmetry is spontaneously broken a la Scherk-Schwarz, finiteness of each
contribution is fulfilled in field and string theory. |
Charting Class ${\cal S}_k$ Territory: We extend the investigation of the recently introduced class ${\cal S}_k$ of
4d $\mathcal{N}=1$ SCFTs, by considering a large family of quiver gauge
theories within it, which we denote $\mathcal{S}^1_k$. These theories admit a
realization in terms of $\mathbb{Z}_k$ orbifolds of Type IIA configurations of
D4-branes stretched among relatively rotated sets of NS-branes. This fact
permits a systematic investigation of the full family, which exhibits new
features such as non-trivial anomalous dimensions differing from free field
values and novel ways of gluing theories. We relate these ingredients to
properties of compactification of the 6d (1,0) superconformal ${\cal T}_N^k$
theories on spheres with different kinds of punctures. We describe the
structure of dualities in this class of theories upon exchange of punctures,
including transformations that correspond to Seiberg dualities, and exploit the
computation of the superconformal index to check the invariance of the theories
under them. | Open Wilson Lines and Chiral Condensates in Thermal Holographic QCD: We investigate various aspects of a proposal by Aharony and Kutasov
arXiv:0803.3547 [hep-th] for the gravity dual of an open Wilson line in the
Sakai-Sugimoto model or its non-compact version. In particular, we use their
proposal to determine the effect of finite temperature, as well as background
electric and magnetic fields, on the chiral symmetry breaking order parameter.
We also generalize their prescription to more complicated worldsheets and
identify the operators dual to such worldsheets. |
Noncommutativity of the Moving D2-brane Worldvolume: In this paper we study the noncommutativity of a moving membrane with
background fields. The open string variables are analyzed. Some scaling limits
are studied. The equivalence of the magnetic and electric noncommutativities is
investigated. The conditions for equivalence of noncommutativity of the T-dual
theory in the rest frame and noncommutativity of the original theory in the
moving frame are obtained. | Mirror Symmetry of Calabi-Yau Supermanifolds: We study super Landau-Ginzburg mirrors of the weighted projective superspace
WCP^{3|2} which is a Calabi-Yau supermanifold and appeared in
hep-th/0312171(Witten) in the topological B-model. One of them is an elliptic
fibration over the complex plane whose coordinate is given in terms of two
bosonic and two fermionic variables as well as Kahler parameter of WCP^{3|2}.
The other is some patch of a degree 3 Calabi-Yau hypersurface in CP^2 fibered
by the complex plane whose coordinate depends on both above four variables and
Kahler parameter but its dependence behaves quite differently. |
Higher codimension braneworlds from intersecting branes: We study the matching conditions of intersecting brane worlds in Lovelock
gravity in arbitrary dimension. We show that intersecting various codimension 1
and/or codimension 2 branes one can find solutions that represent
energy-momentum densities localized in the intersection, providing thus the
first examples of infinitesimally thin higher codimension braneworlds that are
free of singularities and where the backreaction of the brane in the background
is fully taken into account. | Fermions with a bounded and discrete mass spectrum: A mechanism for determining fermion masses in four spacetime dimensions is
presented, which uses a scalar-field domain wall extending in a fifth spacelike
dimension and a special choice of Yukawa coupling constants. A bounded and
discrete fermion mass spectrum is obtained analytically for spinors localized
in the fifth dimension. These particular mass values depend on a combination of
the absolute value of the Yukawa coupling constant and the parameters of the
scalar potential. A similar mechanism for a finite mass spectrum may apply to
$(1+1)$--dimensional fermions relevant to condensed matter physics. |
The $N=2$ super $W_4$ algebra and its associated generalized KdV
hierarchies: We construct the $N=2$ super $W_4$ algebra as a certain reduction of the
second Gel'fand-Dikii bracket on the dual of the Lie superalgebra of $N=1$
super pseudo-differential operators. The algebra is put in manifestly $N=2$
supersymmetric form in terms of three $N=2$ superfields $\Phi_i(X)$, with
$\Phi_1$ being the $N=2$ energy momentum tensor and $\Phi_2$ and $\Phi_3$ being
conformal spin $2$ and $3$ superfields respectively. A search for integrable
hierarchies of the generalized KdV variety with this algebra as Hamiltonian
structure gives three solutions, exactly the same number as for the $W_2$
(super KdV) and $W_3$ (super Boussinesq) cases. | New Regulators for Quantum Field Theories with Compactified Extra
Dimensions. I: Fundamentals: In this paper, we propose two new regulators for quantum field theories in
spacetimes with compactified extra dimensions. We refer to these regulators as
the ``extended hard cutoff'' (EHC) and ``extended dimensional regularization''
(EDR). Although based on traditional four-dimensional regulators, the key new
feature of these higher-dimensional regulators is that they are specifically
designed to handle mixed spacetimes in which some dimensions are infinitely
large and others are compactified. Moreover, unlike most other regulators which
have been used in the extra-dimension literature, these regulators are designed
to respect the original higher-dimensional Lorentz and gauge symmetries that
exist prior to compactification, and not merely the four-dimensional symmetries
which remain afterward. This distinction is particularly relevant for
calculations of the physics of the excited Kaluza-Klein modes themselves, and
not merely their radiative effects on zero modes. By respecting the full
higher-dimensional symmetries, our regulators avoid the introduction of
spurious terms which would not have been easy to disentangle from the physical
effects of compactification. As part of our work, we also derive a number of
ancillary results. For example, we demonstrate that in a gauge-invariant
theory, analogues of the Ward-Takahashi identity hold not only for the usual
zero-mode (four-dimensional) photons, but for all excited Kaluza-Klein photons
as well. |
Black Holes in Magnetic Monopoles with a Dark Halo: We study a spontaneously broken Einstein-Yang-Mills-Higgs model coupled via a
Higgs portal to an uncharged scalar $\chi$. We present a phase diagram of
self-gravitating solutions showing that, depending on the choice of parameters
of the $\chi$ scalar potential and the Higgs portal coupling constant $
\gamma$, one can identify different regions: If $\gamma$ is sufficiently small
a $\chi$ halo is created around the monopole core which in turn surrounds a
black-hole. For larger values of $\gamma$ no halo exists and the solution is
just a black hole-monopole one. When the horizon radius grows and becomes
larger than the monopole radius solely a black hole solution exists. Because of
the presence of the $\chi$ scalar a bound for the Higgs potential coupling
constant exists and when it is not satisfied, the vacuum is unstable and no
non-trivial solution exists. We briefly comment on a possible connection of our
results with those found in recent dark matter axion models. | Screening and confinement in large N_f QCD_2 and in N=1 SYM_2: The screening nature of the potential between external quarks in massless
$SU(N_c)$ $QCD_2$ is derived using an expansion in $N_f$- the number of
flavors. Applying the same method to the massive model, we find a confining
potential. We consider the N=1 super Yang Mills theory, reveal certain
problematic aspects of its bosonized version and show the associated screening
behavior by applying a point splitting method to the scalar current. |
Three-dimensional Noncommutative Gravity: We formulate noncommutative three-dimensional (3d) gravity by making use of
its connection with 3d Chern-Simons theory. In the Euclidean sector, we
consider the particular example of topology $T^2 \times R$ and show that the 3d
black hole solves the noncommutative equations. We then consider the black hole
on a constant U(1) background and show that the black hole charges (mass and
angular momentum) are modified by the presence of this background. | Quantum Riemann surfaces, 2D gravity and the geometrical origin of
minimal models: Based on a recent paper by Takhtajan, we propose a formulation of 2D quantum
gravity whose basic object is the Liouville action on the Riemann sphere
$\Sigma_{0,m+n}$ with both parabolic and elliptic points. The identification of
the classical limit of the conformal Ward identity with the Fuchsian projective
connection on $\Sigma_{0,m+n}$ implies a relation between conformal weights and
ramification indices. This formulation works for arbitrary $d$ and admits a
standard representation only for $d\le 1$. Furthermore, it turns out that the
integerness of the ramification number constrains $d=1-24/(n^2-1)$ that for
$n=2m+1$ coincides with the unitary minimal series of CFT. |
Asymmetric CFTs arising at the IR fixed points of RG flows: We construct a generalization of the cyclic $\lambda$-deformed models of
\cite{Georgiou:2017oly} by relaxing the requirement that all the WZW models
should have the same level $k$. Our theories are integrable and flow from a
single UV point to different IR fixed points depending on the different
orderings of the WZW levels $k_i$. First we calculate the Zamolodchikov's
C-function for these models as exact functions of the deformation parameters.
Subsequently, we fully characterize each of the IR conformal field theories.
Although the corresponding left and right sectors have different symmetries,
realized as products of current and coset-type symmetries, the associated
central charges are precisely equal, in agreement with the valuesobtained from
the C-function. | An N=2 Superconformal Fixed Point with E_6 Global Symmetry: We obtain the elliptic curve corresponding to an $N=2$ superconformal field
theory which has an $E_6$ global symmetry at the strong coupling point
$\tau=e^{\pi i/3}$. We also find the Seiberg-Witten differential $\lambda_{SW}$
for this theory. This differential has 27 poles corresponding to the
fundamental representation of $E_6$. The complex conjugate representation has
its poles on the other sheet. We also show that the $E_6$ curve reduces to the
$D_4$ curve of Seiberg and Witten. Finally, we compute the monodromies and use
these to compute BPS masses in an $F$-Theory compactification. |
N=4 Supersymmetric Gauge Theory in the Derivative Expansion: Maximally supersymmetric gauge theories have experienced renewed interest due
to the AdS/CFT correspondence and its conjectured S-duality. These gauge
theories possess a large amount of symmetry and have quasi-integrable
properties. We derive the amplitudes in the derivative expansion of the
spontaneously broken examples and perform all loop integrations. The S-matrix
is found via an algebraic recursion and at each order is SL(2,Z) invariant. | Remark About T-duality of Dp-Branes: This note is devoted to the analysis of T-duality of Dp-brane when we perform
T-duality along directions that are transverse to world-volume of Dp-brane. |
Supersymmetry and Bosonization in Three Dimensions: We discuss on the possible existence of a supersymmetric invariance in purely
fermionic planar systems and its relation to the fermion-boson mapping in
three-dimensional quantum field theory. We consider, as a very simple example,
the bosonization of free massive fermions and show that, under certain
conditions on the masses, this model displays a supersymmetric-like invariance
in the low energy regime. We construct the purely fermionic expression for the
supercurrent and the non-linear supersymmetry transformation laws. We argue
that the supersymmetry is absent in the limit of massless fermions where the
bosonized theory is non-local. | Krylov complexity of density matrix operators: Quantifying complexity in quantum systems has witnessed a surge of interest
in recent years, with Krylov-based measures such as Krylov complexity ($C_K$)
and Spread complexity ($C_S$) gaining prominence. In this study, we investigate
their interplay by considering the complexity of states represented by density
matrix operators. After setting up the problem, we analyze a handful of
analytical and numerical examples spanning generic two-dimensional Hilbert
spaces, qubit states, quantum harmonic oscillators, and random matrix theories,
uncovering insightful relationships. For generic pure states, our analysis
reveals two key findings: (I) a correspondence between moment-generating
functions (of Lanczos coefficients) and survival amplitudes, and (II) an
early-time equivalence between $C_K$ and $2C_S$. Furthermore, for maximally
entangled pure states, we find that the moment-generating function of $C_K$
becomes the Spectral Form Factor and, at late-times, $C_K$ is simply related to
$NC_S$ for $N\geq2$ within the $N$-dimensional Hilbert space. Notably, we
confirm that $C_K = 2C_S$ holds across all times when $N=2$. Through the lens
of random matrix theories, we also discuss deviations between complexities at
intermediate times and highlight subtleties in the averaging approach at the
level of the survival amplitude. |
Schwinger-Dyson Equation for Supersymmetric Yang-Mills Theory: We study our Schwinger-Dyson equation as well as the large $N_{c}$ loop
equation for supersymmetric Yang-Mills theory in four dimensions by the N=1
superspace Wilson-loop variable. We are successful in deriving a new manifestly
supersymmetric form in which a loop splitting and joining are represented by a
manifestly supersymmetric as well as supergauge invariant operation in
superspace. This is found to be a natural extension from the abelian case. We
solve the equation to leading order in perturbation theory or equivalently in
the linearized approximation, obtaining a desirable nontrivial answer. The
super Wilson-loop variable can be represented as the system of one-dimensional
fermion along the loop coupled minimally to the original theory. One-loop
renormalization of the one-point Wilson-loop average is explicitly carried out,
exploiting this property. The picture of string dynamics obtained is briefly
discussed. | Quantum soliton scattering manifolds: We consider the quantum multisoliton scattering problem. For BPS theories one
truncates the full field theory to the moduli space, a finite dimensional
manifold of energy minimising field configurations, and studies the quantum
mechanical problem on this. Non-BPS theories -- the generic case -- have no
such obvious truncation. We define a quantum soliton scattering manifold as a
configuration space which satisfies asymptotic completeness and respects the
underlying classical dynamics of slow moving solitons. Having done this, we
present a new method to construct such manifolds. In the BPS case the dimension
of the $n$-soliton moduli space $\mathcal{M}_n$ is $n$ multiplied by the
dimension of $\mathcal{M}_1$. We show that this scaling is not necessarily
valid for scattering manifolds in non-BPS theories, and argue that it is false
for the Skyrme and baby-Skyrme models. In these models, we show that a relative
phase difference can generate a relative size difference during a soliton
collision. Asymptotically, these are zero and non-zero modes respectively and
this new mechanism softens the dichotomy between such modes. Using this
discovery, we then show that all previous truncations of the 2-Skyrmion
configuration space are unsuitable for the quantum scattering problem as they
have the wrong dimension. This gives credence to recent numerical work which
suggests that the low-energy configuration space is 14-dimensional (rather than
12-dimensional, as previously thought). We suggest some ways to construct a
suitable manifold for the 2-Skyrmion problem, and discuss applications of our
new definition and construction for general soliton theories. |
What We Don't Know about BTZ Black Hole Entropy: With the recent discovery that many aspects of black hole thermodynamics can
be effectively reduced to problems in three spacetime dimensions, it has become
increasingly important to understand the ``statistical mechanics'' of the
(2+1)-dimensional black hole of Banados, Teitelboim, and Zanelli (BTZ). Several
conformal field theoretic derivations of the BTZ entropy exist, but none is
completely satisfactory, and many questions remain open: there is no consensus
as to what fields provide the relevant degrees of freedom or where these
excitations live. In this paper, I review some of the unresolved problems and
suggest avenues for their solution. | Generalised Scherk-Schwarz reductions from gauged supergravity: A procedure is described to construct generalised Scherk-Schwarz uplifts of
gauged supergravities. The internal manifold, fluxes, and consistent truncation
Ansatz are all derived from the embedding tensor of the lower-dimensional
theory. We first describe the procedure to construct generalised Leibniz
parallelisable spaces where the vector components of the frame are embedded in
the adjoint representation of the gauge group, as specified by the embedding
tensor. This allows us to recover the generalised Scherk-Schwarz reductions
known in the literature and to prove a no-go result for the uplift of
$\omega$-deformed SO(p,q) gauged maximal supergravities. We then extend the
construction to arbitrary generalised Leibniz parallelisable spaces, which turn
out to be torus fibrations over manifolds in the class above. |
Discrete torsion orbifolds and D-branes II: The consistency of the orbifold action on open strings between D-branes in
orbifold theories with and without discrete torsion is analysed carefully. For
the example of the C^3/Z_2 x Z_2 theory, it is found that the consistency of
the orbifold action requires that the D-brane spectrum contains branes that
give rise to a conventional representation of the orbifold group as well as
branes for which the representation is projective. It is also shown how the
results generalise to the orbifolds C^3/Z_N x Z_N for which a number of novel
features arise. In particular, the N>2 theories with minimal discrete torsion
have non-BPS branes charged under twisted R-R potentials that couple to none of
the (known) BPS branes. | Lie 3-Algebra Non-Abelian (2,0) Theory in Loop Space: It is believed that the multiple M5-branes are described by the non-abelian
(2,0) theory and have the non-local structure. In this note we investigate the
non-abelian (2,0) theory in loop space which incorporates the non-local
property. All fields will be formulated as loop fields and the two-form
potential becomes a part of connection. We make an ansatz for field
supersymmetry transformation with a help of Lie 3-algebra and examine the
closure condition of the transformation to find the field equations. However,
the closure conditions lead to several complex terms and we have not yet found
a simple form for some constrain field equations. In particular, we present the
clear scheme and several detailed calculations in each step. Many useful
$\Gamma$ matrix algebras are derived in the appendix. |
Brane structure and metastable graviton in five-dimensional model with
(non)canonical scalar field: The appearance of inner brane structure is an interesting issue in domain
wall {brane model}. Because such structure usually leads to quasilocalized
modes of various kinds of bulk fields. In this paper, we construct a domain
wall brane model by using a scalar field $\phi$, which couples to its kinetic
term. The inner brane structure emerges as the scalar-kinetic coupling
increases. With such brane structure, we show that it is possible to obtain
gravity resonant modes in both tensor and scalar sectors. The number of the
resonant modes depends on the vacuum expectation value of $\phi$ and the form
of scalar-kinetic coupling. The correspondence between our model and the
canonical one is also discussed. The noncanonical and canonical background
scalar fields are connected by an integral equation, while the warp factor
remains the same. Via this correspondence, the canonical and noncanonical
models share the same linear perturbation spectrum. So the gravity resonances
{obtained} in the noncanonical frame can also be obtained in the standard
model. However, due to the inequivalence between the corresponding background
scalar solutions, the localization condition for the left-chiral fermion zero
mode can be largely different in different frames. Our estimate shows that the
magnitude of the Yukawa coupling in the noncanonical frame might be hundreds
times larger than the one in the canonical frame, if one demands the
localization of the left-chiral fermion zero mode as well as the appearance of
a few gravity resonance modes. | U(N) Gauged N=2 Supergravity and Partial Breaking of Local N=2
Supersymmetry: We study a minimal model of U(N) gauged N=2 supergravity with one
hypermultiplet parametrizing SO(4,1)/SO(4) quaternionic manifold. Local N=2
supersymmetry is known to be spontaneously broken to N=1 in the Higgs phase of
U(1)_{graviphoton} \times U(1). Several properties are obtained of this model
in the vacuum of unbroken SU(N) gauge group. In particular, we derive mass
spectrum analogous to the rigid counterpart and put the entire effective
potential on this vacuum in the standard superpotential form of N=1
supergravity. |
Reduced tensor network formulation for non-Abelian gauge theories in
arbitrary dimensions: Formulating non-Abelian gauge theories as a tensor network is known to be
challenging due to the internal degrees of freedom that result in the
degeneracy in the singular value spectrum. In two dimensions, it is
straightforward to 'trace out' these degrees of freedom with the use of
character expansion, giving a reduced tensor network where the degeneracy
associated with the internal symmetry is eliminated. In this work, we show that
such an index loop also exists in higher dimensions in the form of a closed
tensor network we call the 'armillary sphere'. This allows us to completely
eliminate the matrix indices and reduce the overall size of the tensors in the
same way as is possible in two dimensions. This formulation allows us to
include significantly more representations with the same tensor size, thus
making it possible to reach a greater level of numerical accuracy in the tensor
renormalization group computations. | Open string models with Scherk-Schwarz SUSY breaking and localized
anomalies: We study examples of chiral four-dimensional IIB orientifolds with
Scherk--Schwarz supersymmetry breaking, based on freely acting orbifolds. We
construct a new Z3xZ3' model, containing only D9-branes, and rederive from a
more geometric perspective the known Z6'xZ2' model, containing D9, D5 and \bar
D 5 branes. The cancellation of anomalies in these models is then studied
locally in the internal space. These are found to cancel through an interesting
generalization of the Green--Schwarz mechanism involving twisted Ramond--Ramond
axions and 4-forms. The effect of the latter amounts to local counterterms from
a low-energy effective field theory point of view. We also point out that the
number of spontaneously broken U(1) gauge fields is in general greater than
what expected from a four-dimensional analysis of anomalies. |
Four Dimensional $\mathbf{\mathcal{N}=4}$ SYM and the Swampland: We consider supergravity theories with 16 supercharges in Minkowski space
with dimensions $d>3$. We argue that there is an upper bound on the number of
massless modes in such theories depending on $d$. In particular we show that
the rank of the gauge symmetry group $G$ in $d$ dimensions is bounded by
$r_G\leq 26-d$. This in particular demonstrates that 4 dimensional ${\cal N}=4$
SYM theories with rank bigger than 22, despite being consistent and indeed
finite before coupling to gravity, cannot be consistently coupled to ${\cal
N}=4$ supergravity in Minkowski space and belong to the swampland. Our argument
is based on the swampland conditions of completeness of spectrum of defects as
well as a strong form of the distance conjecture and relies on unitarity as
well as supersymmetry of the worldsheet theory of BPS strings. The results are
compatible with known string constructions and provide further evidence for the
string lamppost principle (SLP): that string theory lamppost seems to capture
${\it all}$ consistent quantum gravitational theories. | An Action for F-theory: $\mathrm{SL}(2) \times \mathbb{R}^+$ Exceptional
Field Theory: We construct the 12-dimensional exceptional field theory associated to the
group $\mathrm{SL}(2) \times \mathbb{R}^+$ . Demanding the closure of the
algebra of local symmetries leads to a constraint, known as the section
condition, that must be imposed on all fields. This constraint has two
inequivalent solutions, one giving rise to 11-dimensional supergravity and the
other leading to F-theory. Thus $\mathrm{SL}(2) \times \mathbb{R}^+$
exceptional field theory contains both F-theory and M-theory in a single
12-dimensional formalism. |
Bosonic Partition Functions at Nonzero (Imaginary) Chemical Potential: We consider bosonic random matrix partition functions at nonzero chemical
potential and compare the chiral condensate, the baryon number density and the
baryon number susceptibility to the result of the corresponding fermionic
partition function. We find that as long as results are finite, the phase
transition of the fermionic theory persists in the bosonic theory. However, in
case that bosonic partition function diverges and has to be regularized, the
phase transition of the fermionic theory does not occur in the bosonic theory,
and the bosonic theory is always in the broken phase. | Non-commutative Holographic QCD and Jet Quenching Parameter: Using gauge/gravity duality, we compute jet quenching parameter in confined
and deconfined phases of noncommutative Sakai-Sugimoto model. In the confined
phase jet quenching parameter is zero and noncommutativity does not affect it.
In deconfined phase we find that the leading correction is negative i.e. it
reduces the magnitude of the jet quenching parameter as compared to its value
in commutative background. Moreover it is seen that the effect of leading
correction is more pronounced at high temperatures |
Four Kahler Moduli Stabilisation in type IIB Orientifolds with K3-fibred
Calabi-Yau threefold compactification: We present a concrete and consistent procedure to generate one kind of
non-perturbative superpotential, including the gaugino condensation corrections
and poly-instanton corrections, in type IIB orientifold compactification with
four Kahler Moduli. Then we use this kind of superpotential as well as the
alphaprime-corrections to Kahler potential to fix all of the four Kahler moduli
on a general Calabi-Yau manifold with typical K3-fibred volume form. In our
construction, the considered Calabi-Yau threefolds are K3-fibred and admit at
least one del Pezzo surface and one W-surface. Searching through all existing
four dimensional reflexive lattice polytopes, we find 23 of them fulfilling all
the requirements. | Tensor amplitudes for partial wave analysis of $ψ
\toΔ\barΔ$ within helicity frame: We have derived the tensor amplitudes for partial wave analysis of
$\psi\to\Delta\bar{\Delta}$, $\Delta \to p \pi$ within the helicity frame, as
well as the amplitudes for the other decay sequences with same final states.
These formulae are practical for the experiments measuring $\psi$ decaying into
$p \bar{p}\pi^+ \pi^-$ final states, such as BESIII with its recently collected
huge $J/\psi$ and $\psi(2S)$ data samples. |
An excursion into the string spectrum: We propose a covariant technique to excavate physical bosonic string states
by entire trajectories rather than individually. The approach is based on Howe
duality: the string's spacetime Lorentz algebra commutes with a certain
inductive limit of $sp(\bullet)$, with the Virasoro constraints forming a
subalgebra of the Howe dual algebra $sp(\bullet)$. There are then infinitely
many simple trajectories of states, which are lowest-weight representations of
$sp(\bullet)$ and hence of the Virasoro algebra. Deeper trajectories are
recurrences of the simple ones and can be probed by suitable
trajectory-shifting operators built out of the Howe dual algebra generators. We
illustrate the formalism with a number of subleading trajectories and compute a
sample of tree-level amplitudes. | Tunneling from a Minkowski vacuum to an AdS vacuum: A new thin-wall
regime: Using numerical and analytic methods, we study quantum tunneling from a
Minkowski false vacuum to an anti-de Sitter true vacuum. Scanning the parameter
space of theories with quartic and non-polynomial potentials, we find that for
any given potential tunneling is completely quenched if gravitational effects
are made sufficiently strong. For potentials where $\epsilon$, the energy
density difference between the vacua, is small compared to the barrier height,
this occurs in the thin-wall regime studied by Coleman and De Luccia. However,
we find that other potentials, possibly with $\epsilon$ much greater than the
barrier height, produce a new type of thin-wall bounce when gravitational
effects become strong. We show that the critical curve that bounds the region
in parameter space where the false vacuum is stable can be found by a
computationally simple overshoot/undershoot argument. We discuss the treatment
of boundary terms in the bounce calculation and show that, with proper
regularization, one obtains an identical finite result for the tunneling
exponent regardless of whether or not these are included. Finally, we briefly
discuss the extension of our results to transitions between anti-de Sitter
vacua. |
Non-Kaehler String Backgrounds and their Five Torsion Classes: We discuss the mathematical properties of six--dimensional non--K\"ahler
manifolds which occur in the context of ${\cal N}=1$ supersymmetric heterotic
and type IIA string compactifications with non--vanishing background H--field.
The intrinsic torsion of the associated SU(3) structures falls into five
different classes. For heterotic compactifications we present an explicit
dictionary between the supersymmetry conditions and these five torsion classes.
We show that the non--Ricci flat Iwasawa manifold solves the supersymmetry
conditions with non--zero H--field, so that it is a consistent heterotic
supersymmetric groundstate. | Superspace Formulation of 4D Higher Spin Gauge Theory: Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so
far have been formulated as constrained systems of differential forms living in
a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory
in superspace, leaving the internal twistor space intact. Remarkably, the
superspace constraints have the same form as those defining the theory in
ordinary spacetime. This construction generalizes straightforwardly to higher
spin gauge theories N>1 supersymmetry. |
Complete construction of magical, symmetric and homogeneous N=2
supergravities as double copies of gauge theories: We show that scattering amplitudes in magical, symmetric or homogeneous N=2
Maxwell-Einstein supergravities can be obtained as double copies of two gauge
theories, using the framework of color/kinematics duality. The left-hand-copy
is N=2 super-Yang-Mills theory coupled to a hypermultiplet, whereas the
right-hand-copy is a non-supersymmetric theory that can be identified as the
dimensional reduction of a D-dimensional Yang-Mills theory coupled to P
fermions. For generic D and P, the double copy gives homogeneous
supergravities. For P=1 and D=7,8,10,14, it gives the magical supergravities.
We compute explicit amplitudes, discuss their soft limit and study the
UV-behavior at one loop. | Unitary S Matrices With Long-Range Correlations and the Quantum Black
Hole: We propose an S matrix approach to the quantum black hole in which causality,
unitarity and their interrelation play a prominent role. Assuming the 't Hooft
S matrix ansatz for a gravitating region surrounded by an asymptotically flat
space-time we find a non-local transformation which changes the standard
causality requirement but is a symmetry of the unitarity condition of the S
matrix. This new S matrix then implies correlations between the in and out
states of the theory with the involvement of a third entity which in the case
of a quantum black hole, we argue is the horizon S matrix. Such correlations
are thus linked to preserving the unitarity of the S matrix and to the fact
that entangling unitary operators are nonlocal. The analysis is performed
within the Bogoliubov S matrix framework by considering a spacetime consisting
of causal complements with a boundary in between. No particular metric or
lagrangian dynamics need be invoked even to obtain an evolution equation for
the full S matrix. Constraints imposed by the new causality requirement and
implications for the effectiveness of field theoretical descriptions and for
complementarity are also discussed. We find that the tension between
information preservation and complementarity may be resolved provided the full
quantum gravity theory either through symmetries or fine tuning forbids the
occurrence of closed time like curves of information flow. Then, even if
causality is violated near the horizon at any intermediate stage, a standard
causal ordering may be preserved for the observer away from the horizon. In the
context of the black hole, the novelty of our formulation is that it appears
well suited to understand unitarity at any intermediate stage of black hole
evaporation. Moreover, it is applicable generally to all theories with long
range correlations including the final state projection models. |
Stability, Causality, and Lorentz and CPT Violation: Stability and causality are investigated for quantum field theories
incorporating Lorentz and CPT violation. Explicit calculations in the quadratic
sector of a general renormalizable lagrangian for a massive fermion reveal that
no difficulty arises for low energies if the parameters controlling the
breaking are small, but for high energies either energy positivity or
microcausality is violated in some observer frame. However, this can be avoided
if the lagrangian is the sub-Planck limit of a nonlocal theory with spontaneous
Lorentz and CPT violation. Our analysis supports the stability and causality of
the Lorentz- and CPT-violating standard-model extension that would emerge at
low energies from spontaneous breaking in a realistic string theory. | Canonical Description of T-duality for Fundamental String and D1-Brane
and Double Wick Rotation: We study T-duality transformations in canonical formalism for Nambu-Gotto
action. Then we investigate the relation between world-sheet double Wick
rotation and sequence of target space T-dualities and Wick rotation in case of
fundamental string and D1-brane. |
Noncommutative Coordinates Invariant under Rotations and Lorentz
Transformations: Dynamics with noncommutative coordinates invariant under three dimensional
rotations or, if time is included, under Lorentz transformations is developed.
These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)
respectively. The noncommutativity is governed by a mass parameter $M$. The
principal results are: (i) a modification of the Heisenberg algebra for
distances smaller than 1/M, (ii) a lower limit, 1/M, on the localizability of
wave packets, (iii) discrete eigenvalues of coordinate operator in timelike
directions, and (iv) an upper limit, $M$, on the mass for which free field
equations have solutions. Possible restrictions on small black holes is
discussed. | QCD_3 Vacum Wave Function: We investigate quantum chromodynamics in 2+1 dimensions ($\rm{QCD}_3$) using
the Hamiltonian lattice field theory approach. The long wavelength structure of
the ground state, which is closely related to the confinement phenomenon, is
analyzed and its vacuum wave function is evaluated by means of the recently
developed truncated eigenvalue equation method. The third order estimations
show nice scaling for the physical quantities. |
Topological Terms and the Misner String Entropy: The method of topological renormalization in anti-de Sitter (AdS) gravity
consists in adding to the action a topological term which renders it finite,
defining at the same time a well-posed variational problem. Here, we use this
prescription to work out the thermodynamics of asymptotically locally anti-de
Sitter (AlAdS) spacetimes, focusing on the physical properties of the Misner
strings of both the Taub-NUT-AdS and Taub-Bolt-AdS solutions. We compute the
contribution of the Misner string to the entropy by treating on the same
footing the AdS and AlAdS sectors. As topological renormalization is found to
correctly account for the physical quantities in the parity preserving sector
of the theory, we then investigate the holographic consequences of adding also
the Chern-Pontryagin topological invariant to the bulk action; in particular,
we discuss the emergence of the parity-odd contribution in the boundary stress
tensor. | Dirac fermions in strong electric field and quantum transport in
graphene: Our previous results on the nonperturbative calculations of the mean current
and of the energy-momentum tensor in QED with the T-constant electric field are
generalized to arbitrary dimensions. The renormalized mean values are found;
the vacuum polarization and particle creation contributions to these mean
values are isolated in the large T-limit, the vacuum polarization contributions
being related to the one-loop effective Euler-Heisenberg Lagrangian.
Peculiarities in odd dimensions are considered in detail. We adapt general
results obtained in 2+1 dimensions to the conditions which are realized in the
Dirac model for graphene. We study the quantum electronic and energy transport
in the graphene at low carrier density and low temperatures when quantum
interference effects are important. Our description of the quantum transport in
the graphene is based on the so-called generalized Furry picture in QED where
the strong external field is taken into account nonperturbatively; this
approach is not restricted to a semiclassical approximation for carriers and
does not use any statistical assumtions inherent in the Boltzmann transport
theory. In addition, we consider the evolution of the mean electromagnetic
field in the graphene, taking into account the backreaction of the matter field
to the applied external field. We find solutions of the corresponding
Dirac-Maxwell set of equations and with their help we calculate the effective
mean electromagnetic field and effective mean values of the current and the
energy-momentum tensor. The nonlinear and linear I-V characteristics
experimentally observed in both low and high mobility graphene samples is quite
well explained in the framework of the proposed approach, their peculiarities
being essentially due to the carrier creation from the vacuum by the applied
electric field. |
Teichmüller parameters for multiple BTZ black hole spacetime: We investigate the Teichm\"{u}ller parameters for a Euclidean multiple BTZ
black hole spacetime. To induce a complex structure in the asymptotic boundary
of such a spacetime, we consider the limit in which two black holes are at a
large distance from each other. In this limit, we can approximately determine
the period matrix (i.e., the Teichm\"{u}ller parameters) for the spacetime
boundary by using a pinching parameter. The Teichm\"{u}ller parameters are
essential in describing the partition function for the boundary conformal field
theory (CFT). We provide an interpretation of the partition function for the
genus two extremal boundary CFT proposed by Gaiotto and Yin that it is relevant
to double BTZ black hole spacetime. | A gauged baby Skyrme model and a novel BPS bound: The baby Skyrme model is a well-known nonlinear field theory supporting
topological solitons in two space dimensions. Its action functional consists of
a potential term, a kinetic term quadratic in derivatives (the "nonlinear sigma
model term") and the Skyrme term quartic in first derivatives. The limiting
case of vanishing sigma model term (the so-called BPS baby Skyrme model) is
known to support exact soliton solutions saturating a BPS bound which exists
for this model. Further, the BPS model has infinitely many symmetries and
conservation laws. Recently it was found that the gauged version of the BPS
baby Skyrme model with gauge group U(1) and the usual Maxwell term, too, has a
BPS bound and BPS solutions saturating this bound. This BPS bound is determined
by a superpotential which has to obey a superpotential equation, in close
analogy to the situation in supergravity. Further, the BPS bound and the
corresponding BPS solitons only may exist for potentials such that the
superpotential equation has a global solution. We also briefly describe some
properties of soliton solutions. |
Decay of massive scalar hair in the background of a dilaton gravity
black hole: We invesigate analytically both the intermediate and late-time behaviour of
the massive scalar field in the background of static spherically symmetric
black hole solution in dilaton gravity with arbitrary coupling constant. The
intermediate asymptotic behaviour of scalar field depends on the field's
parameter mass as well as the multiple number l. On its turn, the late-time
behaviour has the power law decay rate independent on coupling constant in the
theory under consideration. | A proposal for the Yang-Mills vacuum and mass gap: I examine a set of Feynman rules, and the resulting effective action, that
were proposed in order to incorporate the constraint of Gauss's law in the
perturbation expansion of gauge field theories. A set of solutions for the
Lagrangian and Hamiltonian equations of motion in Minkowski space-time, as well
as their stability, are investigated. A discussion of the Euclidean action,
confinement, and the strong-CP problem is also included. The properties and
symmetries of the perturbative and the confining vacuum are explored, as well
as the possible transitions between them, and the relations with
phenomenological models of the strong interactions. |
Near Horizon Geometry of Warped Black Holes in Generalized Minimal
Massive Gravity: We consider spacelike warped AdS$_{3}$ black hole metric in Boyer-Lindquist
coordinate system. We present a coordinates transformation so that it maps
metric in Boyer-Lindquist coordinates to the one in Gaussian null coordinates.
Then we introduce new fall-off conditions near the horizon of non-extremal
warped black holes. We study the near horizon symmetry algebra of such
solutions in the context of Generalized minimal massive gravity. Similar to the
black flower solutions, also we obtain the Heisenberg algebra as the near
horizon symmetry algebra of the warped black flower solutions. We show that the
vacuum state and all descendants of the vacuum have the same energy. Thus these
zero energy excitations on the horizon appear as soft hairs on the warped black
hole. | On the covariance of the Dirac-Born-Infeld-Myers action: A covariant version of the non-abelian Dirac-Born-Infeld-Myers action is
presented. The non-abelian degrees of freedom are incorporated by adjoining to
the (bosonic) worldvolume of the brane a number of anticommuting fermionic
directions corresponding to boundary fermions in the string picture. The
proposed action treats these variables as classical but can be given a matrix
interpretation if a suitable quantisation prescription is adopted. After
gauge-fixing and quantisation of the fermions, the action is shown to be in
agreement with the Myers action derived from T-duality. It is also shown that
the requirement of covariance in the above sense leads to a modified WZ term
which also agrees with the one proposed by Myers. |
Superstratum Symbiosis: Superstrata are smooth horizonless microstate geometries for the
supersymmetric D1-D5-P black hole in type IIB supergravity. In the CFT,
'superstratum states' are defined to be the component of the supergraviton gas
that is obtained by breaking the CFT into '$|00\rangle$-strands' and acting on
each strand with the 'small,' anomaly-free superconformal generators. We show
that the recently-constructed supercharged superstrata represent a final and
crucial component for the construction of the supergravity dual of a generic
superstratum state and how the supergravity solution faithfully represents all
the coherent superstratum states of the CFT. For the supergravity alone, this
shows that generic superstrata do indeed fluctuate as functions of three
independent variables. Smoothness of the complete supergravity solution also
involves 'coiffuring constraints' at second-order in the fluctuations and we
describe how these lead to new predictions for three-point functions in the
dual CFT. We use a hybrid of the original and supercharged superstrata to
construct families of single-mode superstrata that still have free moduli after
one has fixed the asymptotic charges of the system. We also study scalar wave
perturbations in a particular family of such solutions and show that the mass
gap depends on the free moduli. This can have interesting implications for
superstrata at non-zero temperature. | Knots and Matrix Models: We consider a matrix model with d matrices NxN and show that in the limit of
large N and d=0 the model describes the knot diagrams. The same limit in matrix
string theory is also discussed. We speculate that a prototypical M(atrix)
without matrix theory exists in void. |
Finite mass gravitating Yang monopoles: We show that gravity cures the infra-red divergence of the Yang monopole when
a proper definition of conserved quantities in curved backgrounds is used, i.e.
the gravitating Yang monopole in cosmological Einstein theory has a finite mass
in generic even dimensions (including time). In addition, we find exact
Yang-monopole type solutions in the cosmological
Einstein-Gauss-Bonnet-Yang-Mills theory and briefly discuss their properties. | Nonuniqueness of the C operator in PT-symmetric quantum mechanics: The C operator in PT-symmetric quantum mechanics satisfies a system of three
simultaneous algebraic operator equations, $C^2=1$, $[C,PT]=0$, and $[C,H]=0$.
These equations are difficult to solve exactly, so perturbative methods have
been used in the past to calculate C. The usual approach has been to express
the Hamiltonian as $H=H_0+\epsilon H_1$, and to seek a solution for C in the
form $C=e^Q P$, where $Q=Q(q,p)$ is odd in the momentum p, even in the
coordinate q, and has a perturbation expansion of the form $Q=\epsilon
Q_1+\epsilon^3 Q_3+\epsilon^5 Q_5+\ldots$. [In previous work it has always been
assumed that the coefficients of even powers of $\epsilon$ in this expansion
would be absent because their presence would violate the condition that
$Q(p,q)$ is odd in p.] In an earlier paper it was argued that the C operator is
not unique because the perturbation coefficient $Q_1$ is nonunique. Here, the
nonuniqueness of C is demonstrated at a more fundamental level: It is shown
that the perturbation expansion for Q actually has the more general form
$Q=Q_0+\epsilon Q_1+\epsilon^2 Q_2+\ldots$ in which {\it all} powers and not
just odd powers of $\epsilon$ appear. For the case in which $H_0$ is the
harmonic-oscillator Hamiltonian, $Q_0$ is calculated exactly and in closed form
and it is shown explicitly to be nonunique. The results are verified by using
powerful summation procedures based on analytic continuation. It is also shown
how to calculate the higher coefficients in the perturbation series for Q. |
Hydrodynamic and Non-hydrodynamic Excitations in Kinetic Theory -- A
Numerical Analysis in Scalar Field Theory: Viscous hydrodynamics serves as a successful mesoscopic description of the
Quark-Gluon Plasma produced in relativistic heavy-ion collisions. In order to
investigate, how such an effective description emerges from the underlying
microscopic dynamics we calculate the hydrodynamic and non-hydrodynamic modes
of linear response in the sound channel from a first-principle calculation in
kinetic theory. We do this with a new approach wherein we discretize the
collision kernel to directly calculate eigenvalues and eigenmodes of the
evolution operator. This allows us to study the Green's functions at any point
in the complex frequency space. Our study focuses on scalar theory with quartic
interaction and we find that the analytic structure of Green's functions in the
complex plane is far more complicated than just poles or cuts which is a first
step towards an equivalent study in QCD kinetic theory. | Hilbert Spaces for Nonrelativistic and Relativistic "Free" Plektons
(Particles with Braid Group Statistics): Using the theory of fibre bundles, we provide several equivalent intrinsic
descriptions for the Hilbert spaces of $n$ ``free'' nonrelativistic and
relativistic plektons in two space dimensions. These spaces carry a ray
representation of the Galilei group and a unitary representation of the
Poincar\'{e} group respectively. In the relativistic case we also discuss the
situation where the braid group is replaced by the ribbon braid group. |
On the BFFT quantization of first order systems: By using the field-antifield formalism, we show that the method of Batalin,
Fradkin, Fradkina and Tyutin to convert Hamiltonian systems submitted to second
class constraints introduces compensating fields which do not belong to the
BRST cohomology at ghost number one. This assures that the gauge symmetries
which arise from the BFFT procedure are not obstructed at quantum level. An
example where massive electrodynamics is coupled to chiral fermions is
considered. We solve the quantum master equation for the model and show that
the respective counterterm has a decisive role in extracting anomalous
expectation values associated with the divergence of the Noether chiral
current. | Virasoro constraints for Kontsevich-Hurwitz partition function: M.Kazarian and S.Lando found a 1-parametric interpolation between Kontsevich
and Hurwitz partition functions, which entirely lies within the space of KP
tau-functions. V.Bouchard and M.Marino suggested that this interpolation
satisfies some deformed Virasoro constraints. However, they described the
constraints in a somewhat sophisticated form of AMM-Eynard equations for the
rather involved Lambert spectral curve. Here we present the relevant family of
Virasoro constraints explicitly. They differ from the conventional continuous
Virasoro constraints in the simplest possible way: by a constant shift u^2/24
of the L_{-1} operator, where u is an interpolation parameter between
Kontsevich and Hurwitz models. This trivial modification of the string equation
gives rise to the entire deformation which is a conjugation of the Virasoro
constraints L_m -> U L_m U^{-1} and "twists" the partition function, Z_{KH}= U
Z_K. The conjugation U is expressed through the previously unnoticed operators
which annihilate the quasiclassical (planar) free energy of the Kontsevich
model, but do not belong to the symmetry group GL(\infty) of the universal
Grassmannian. |
Boltzmann Equation for Relativistic Neutral Scalar Field in
Non-equilibrium Thermo Field Dynamics: A relativistic neutral scalar field is investigated on the basis of the
Schwinger-Dyson equation in the non-equilibrium thermo field dynamics. A time
evolution equation for a distribution function is obtained from a
diagonalization condition for the Schwinger-Dyson equation. An explicit
expression of the time evolution equation is calculated in the $\lambda\phi^4$
interaction model at the 2-loop level. The Boltzmann equation is derived for
the relativistic scalar field. We set a simple initial condition and
numerically solve the Boltzmann equation and show the time evolution of the
distribution function and the relaxation time. | Three-dimensional de Sitter holography and bulk correlators at late time: We propose an explicitly calculable example of holography on 3-dimensional de
Sitter space by providing a prescription to analytic continue a higher-spin
holography on 3-dimensional anti-de Sitter space. Applying the de Sitter
holography, we explicitly compute bulk correlation functions on 3-dimensional
de Sitter space at late time in a higher-spin gravity. These expressions are
consistent with recent analysis based on bulk Feynman diagrams. Our explicit
computations reveal how holographic computations could provide fruitful
information. |
The vacuum polarization around an axionic stringy black hole: We consider the effect of vacuum polarization around the horizon of a 4
dimensional axionic stringy black hole. In the extreme degenerate limit
($Q_a=M$), the lower limit on the black hole mass for avoiding the polarization
of the surrounding medium is $M\gg (10^{-15}\div 10^{-11})m_p$ ($m_p$ is the
proton mass), according to the assumed value of the axion mass ($m_a\simeq
(10^{-3}\div 10^{-6})~eV$). In this case, there are no upper bounds on the mass
due to the absence of the thermal radiation by the black hole. In the
nondegenerate (classically unstable) limit ($Q_a<M$), the black hole always
polarizes the surrounding vacuum, unless the effective cosmological constant of
the effective stringy action diverges. | Dual PT-Symmetric Quantum Field Theories: Some quantum field theories described by non-Hermitian Hamiltonians are
investigated. It is shown that for the case of a free fermion field theory with
a $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the
mass parameter this symmetry may be either broken or unbroken. When the $\cal
PT$ symmetry is unbroken, the spectrum of the quantum field theory is real. For
the $\cal PT$-symmetric version of the massive Thirring model in
two-dimensional space-time, which is dual to the $\cal PT$-symmetric scalar
Sine-Gordon model, an exact construction of the $\cal C$ operator is given. It
is shown that the $\cal PT$-symmetric massive Thirring and Sine-Gordon models
are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon
models with appropriately shifted masses. |
Mutual information between thermo-field doubles and disconnected
holographic boundaries: We use mutual information as a measure of the entanglement between 'physical'
and thermo-field double degrees of freedom in field theories at finite
temperature. We compute this "thermo-mutual information" in simple toy models:
a quantum mechanics two-site spin chain, a two dimensional massless fermion,
and a two dimensional holographic system. In holographic systems, the
thermo-mutual information is related to minimal surfaces connecting the two
disconnected boundaries of an eternal black hole. We derive a number of salient
features of this thermo-mutual information, including that it is UV finite,
positive definite and bounded from above by the standard mutual information for
the thermal ensemble. We relate the construction of the reduced density
matrices used to define the thermo-mutual information to the Schwinger-Keldysh
formalism, ensuring that all our objects are well defined in Euclidean and
Lorentzian signature. | Renormalization of Hamiltonians: A matrix model of an asymptotically free theory with a bound state is solved
using a perturbative similarity renormalization group for hamiltonians. An
effective hamiltonian with a small width, calculated including the first three
terms in the perturbative expansion, is projected on a small set of effective
basis states. The resulting small hamiltonian matrix is diagonalized and the
exact bound state energy is obtained with accuracy of order 10%. Then, a brief
description and an elementary illustration are given for a related light-front
Fock space operator method which aims at carrying out analogous steps for
hamiltonians of QCD and other theories. |
Non-confinement in Three Dimensional Supersymmetric Yang-Mills Theory: The role of instantons in three dimensional N=2 supersymmetric SU(2)
Yang-Mills theory is studied, especially in relation to the issue of
confinement. The instanton-induced low energy effective action is derived by
extending the dilute gas approximation to the super-moduli space of instantons.
Following Polyakov's description of confinement in compact U(1) gauge theory,
it is argued that there is no confinement in N=2 supersymmetric Yang-Mills
theory. | M-branes on U-folds: We give a preliminary discussion of how the addition of extra coordinates in
M-theory, which together with the original ones parametrise a U-fold, can serve
as a tool for formulating brane dynamics with manifest U-duality. The redundant
degrees of freedom are removed by generalised self-duality constraints or
calibration conditions made possible by the algebraic structure of U-duality.
This is the written version of an invited talk at the 7th International
Workshop "Supersymmetries and Quantum Symmetries", Dubna, July 30-August 4,
2007. |
Quantizing Strings in de Sitter Space: We quantize a string in the de Sitter background, and we find that the mass
spectrum is modified by a term which is quadratic in oscillating numbers, and
also proportional to the square of the Hubble constant. | Superstring 'ending' on super-D9-brane: a supersymmetric action
functional for the coupled brane system: A supersymmetric action functional describing the interaction of the
fundamental superstring with the D=10, type IIB Dirichlet super-9-brane is
presented. A set of supersymmetric equations for the coupled system is obtained
from the action principle. It is found that the interaction of the string
endpoints with the super-D9-brane gauge field requires some restrictions for
the image of the gauge field strength. When those restrictions are not imposed,
the equations imply the absence of the endpoints, and the equations coincide
either with the ones of the free super-D9-brane or with the ones for the free
closed type IIB superstring. Different phases of the coupled system are
described. A generalization to an arbitrary system of intersecting branes is
discussed. |
Simple Stringy Dynamical SUSY Breaking: We present simple string models which dynamically break supersymmetry without
non-Abelian gauge dynamics. The Fayet model, the Polonyi model, and the
O'Raifeartaigh model each arise from D-branes at a specific type of
singularity. D-brane instanton effects generate the requisite exponentially
small scale of supersymmetry breaking. | Swampland Constraints on the SymTFT of Supergravity: We consider string/M-theory reductions on a compact space $X=X^\text{loc}
\cup X^\circ$, where $X^\text{loc}$ contains the singular locus, and $X^\circ$
its complement. For the resulting supergravity theories, we construct a
suitable Symmetry Topological Field Theory (SymTFT) associated with the
boundary $\partial X^\text{loc} \coprod \partial X^\circ$. We propose that
boundary conditions for different BPS branes wrapping the same boundary cycles
must be correlated for the SymTFT to yield an absolute theory consistent with
quantum gravity. Using heterotic/M-theory duality, this constraint can be
translated into a field theoretic statement, which restricts the global
structure of $d\geq 7$, $\mathcal{N}=1$ supergravity theories to reproduce
precisely the landscape of untwisted toroidal heterotic compactifications.
Furthermore, for 6d $(2,0)$ theories, we utilize a subtle interplay between
gauged 0-, 2-, and 4-form symmetries to provide a bottom-up explanation of the
correlated boundary conditions in K3 compactifications of type IIB. |
Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model: We study the effect of non-Gaussian average over the random couplings in a
complex version of the celebrated Sachdev-Ye-Kitaev (SYK) model. Using a
Polchinski-like equation and random tensor Gaussian universality, we show that
the effect of this non-Gaussian averaging leads to a modification of the
variance of the Gaussian distribution of couplings at leading order in N. We
then derive the form of the effective action to all orders. An explicit
computation of the modification of the variance in the case of a quartic
perturbation is performed for both the complex SYK model mentioned above and
the SYK generalization proposed in D. Gross and V. Rosenhaus, JHEP 1702 (2017)
093. | Superspace conformal field theory: Conformal sigma models and WZW models on coset superspaces provide important
examples of logarithmic conformal field theories. They possess many
applications to problems in string and condensed matter theory. We review
recent results and developments, including the general construction of WZW
models on type I supergroups, the classification of conformal sigma models and
their embedding into string theory. |
Euclidean wormholes, baby universes, and their impact on particle
physics and cosmology: The euclidean path integral remains, in spite of its familiar problems, an
important approach to quantum gravity. One of its most striking and obscure
features is the appearance of gravitational instantons or wormholes. These
renormalize all terms in the Lagrangian and cause a number of puzzles or even
deep inconsistencies, related to the possibility of nucleation of "baby
universes". In this review, we revisit the early controversies surrounding
these issues as well as some of the more recent discussions of the
phenomenological relevance of gravitational instantons. In particular,
wormholes are expected to break the shift symmetries of axions or Goldstone
bosons non-perturbatively. This can be relevant to large-field inflation and
connects to arguments made on the basis of the Weak Gravity or Swampland
conjectures. It can also affect Goldstone bosons which are of physical interest
in the context of the strong CP problem or as dark matter. | Supersymmetric 3-branes on smooth ALE manifolds with flux: We construct a new family of classical BPS solutions of type IIB supergravity
describing 3-branes transverse to a 6-dimensional space with topology R^2*ALE.
They are characterized by a non-trivial flux of the supergravity 2-forms
through the homology 2-cycles of a generic smooth ALE manifold. Our solutions
have two Killing spinors and thus preserve N=2 supersymmetry. They are
expressed in terms of a quasi harmonic function H (the ``warp factor''), whose
properties we study in the case of the simplest ALE, namely the Eguchi-Hanson
manifold. The equation for H is identified as an instance of the confluent Heun
equation. We write explicit power series solutions and solve the recurrence
relation for the coefficients, discussing also the relevant asymptotic
expansions. While, as in all such N=2 solutions, supergravity breaks down near
the brane, the smoothing out of the vacuum geometry has the effect that the
warp factor is regular in a region near the cycle. We interpret the behavior of
the warp factor as describing a three-brane charge ``smeared'' over the cycle
and consider the asymptotic form of the geometry in that region, showing that
conformal invariance is broken even when the complex type IIB 3-form field
strength is assumed to vanish. We conclude with a discussion of the basic
features of the gauge theory dual. |
A Universal Pattern in Quantum Gravity at Infinite Distance: Quantum gravitational effects become significant at a cut-off species scale
that can be much lower than the Planck scale whenever we get a parametrically
large number of fields becoming light. This is expected to occur at any
perturbative limit of an effective field theory coupled to gravity, or
equivalently, at any infinite distance limit in the field space of the quantum
gravity completion. In this note, we present a universal pattern that links the
asymptotic variation rates in field space of the quantum gravity cut-off
$\Lambda_{\text{sp}}$ and the characteristic mass of the lightest tower of
states $m$: $\frac{\vec\nabla m}{m} \cdot\frac{\vec\nabla \Lambda_{\rm sp}}{
\Lambda_{\rm sp}}=\frac1{d-2}$, where $d$ is the spacetime dimension. This
restriction can be used to make more precise several Swampland criteria that
constrain the effective field theories that can be consistently coupled to
quantum gravity. | Scalar tachyons in the de Sitter universe: We provide a construction of a class of local and de Sitter covariant
tachyonic quantum fields which exist for discrete negative values of the
squared mass parameter and which have no Minkowskian counterpart. These quantum
fields satisfy an anomalous non-homogeneous Klein-Gordon equation. The anomaly
is a covariant field which can be used to select the physical subspace (of
finite codimension) where the homogeneous tachyonic field equation holds in the
usual form. We show that the model is local and de Sitter invariant on the
physical space. Our construction also sheds new light on the massless minimally
coupled field, which is a special instance of it. |
Constraining ${\cal N}=1$ supergravity inflationary framework with
non-minimal Kähler operators: In this paper we will illustrate how to constrain unavoidable K\"ahler
corrections for ${\cal N}=1$ supergravity (SUGRA) inflation from the recent
Planck data. We will show that the non-renormalizable K\"ahler operators will
induce in general non-minimal kinetic term for the inflaton field, and two
types of SUGRA corrections in the potential - the Hubble-induced mass
($c_{H}$), and the Hubble-induced A-term ($a_{H}$) correction. The entire SUGRA
inflationary framework can now be constrained from (i) the speed of sound,
$c_s$, and (ii) from the upper bound on the tensor to scalar ratio,
$r_{\star}$. We will illustrate this by considering a heavy scalar degree of
freedom at a scale, $M_s$, and a light inflationary field which is responsible
for a slow-roll inflation. We will compute the corrections to the kinetic term
and the potential for the light field explicitly. As an example, we will
consider a visible sector inflationary model of inflation where inflation
occurs at the point of inflection, which can match the density perturbations
for the cosmic microwave background radiation, and also explain why the
universe is filled with the Standard Model degrees of freedom. We will scan the
parameter space of the non-renormalizable K\"ahler operators, which we find
them to be order ${\cal O}(1)$, consistent with physical arguments. While the
scale of heavy physics is found to be bounded by the tensor-to scalar ratio,
and the speed of sound, $ {\cal O}(10^{11}\leq M_s\leq 10^{16}) $GeV, for
$0.02\leq c_s\leq 1$ and $10^{-22}\leq r_\star \leq 0.12$. | A BRST Analysis of $W$-symmetries: We perform a classical BRST analysis of the symmetries corresponding to a
generic $w_N$-algebra. An essential feature of our method is that we write the
$w_N$-algebra in a special basis such that the algebra manifestly has a
``nested'' set of subalgebras $v_N^N \subset v_N^{N-1} \subset \dots \subset
v_N^2 \equiv w_N$ where the subalgebra $v_N^i\ (i=2, \dots ,N)$ consists of
generators of spin $s=\{i,i+1,\dots ,N\}$, respectively. In the new basis the
BRST charge can be written as a ``nested'' sum of $N-1$ nilpotent BRST charges.
In view of potential applications to (critical and/or non-critical) $W$-string
theories we discuss the quantum extension of our results. In particular, we
present the quantum BRST-operator for the $W_4$-algebra in the new basis. For
both critical and non-critical $W$-strings we apply our results to discuss the
relation with minimal models. |
Characterizing 4-string contact interaction using machine learning: The geometry of 4-string contact interaction of closed string field theory is
characterized using machine learning. We obtain Strebel quadratic differentials
on 4-punctured spheres as a neural network by performing unsupervised learning
with a custom-built loss function. This allows us to solve for local
coordinates and compute their associated mapping radii numerically. We also
train a neural network distinguishing vertex from Feynman region. As a check,
4-tachyon contact term in the tachyon potential is computed and a good
agreement with the results in the literature is observed. We argue that our
algorithm is manifestly independent of number of punctures and scaling it to
characterize the geometry of $n$-string contact interaction is feasible. | Effective action for the order parameter of the deconfinement transition
of Yang-Mills theories: The effective action for the Polyakov loop serving as an order parameter for
deconfinement is obtained in one-loop approximation to second order in a
derivative expansion. The calculation is performed in $d\geq 4$ dimensions,
mostly referring to the gauge group SU(2). The resulting effective action is
only capable of describing a deconfinement phase transition for
$d>d_{\text{cr}}\simeq 7.42$. Since, particularly in $d=4$, the system is
strongly governed by infrared effects, it is demonstrated that an additional
infrared scale such as an effective gluon mass can change the physical
properties of the system drastically, leading to a model with a deconfinement
phase transition. |
Rigid Surface Operators: Surface operators in gauge theory are analogous to Wilson and 't Hooft line
operators except that they are supported on a two-dimensional surface rather
than a one-dimensional curve. In a previous paper, we constructed a certain
class of half-BPS surface operators in N=4 super Yang-Mills theory, and
determined how they transform under S-duality. Those surface operators depend
on a relatively large number of freely adjustable parameters. In the present
paper, we consider the opposite case of half-BPS surface operators that are
``rigid'' in the sense that they do not depend on any parameters at all. We
present some simple constructions of rigid half-BPS surface operators and
attempt to determine how they transform under duality. This attempt is only
partially successful, suggesting that our constructions are not the whole
story. The partial match suggests interesting connections with quantization. We
discuss some possible refinements and some string theory constructions which
might lead to a more complete picture. | General Relativity from Causality: We study large families of theories of interacting spin 2 particles from the
point of view of causality. Although it is often stated that there is a unique
Lorentz invariant effective theory of massless spin 2, namely general
relativity, other theories that utilize higher derivative interactions do in
fact exist. These theories are distinct from general relativity, as they permit
any number of species of spin 2 particles, are described by a much larger set
of parameters, and are not constrained to satisfy the equivalence principle. We
consider the leading spin 2 couplings to scalars, fermions, and vectors, and
systematically study signal propagation in all these other families of
theories. We find that most interactions directly lead to superluminal
propagation of either a spin 2 particle or a matter particle, and interactions
that are subluminal generate other interactions that are superluminal. Hence,
such theories of interacting multiple spin 2 species have superluminality, and
by extension, acausality. This is radically different to the special case of
general relativity with a single species of minimally coupled spin 2, which
leads to subluminal propagation from sources satisfying the null energy
condition. This pathology persists even if the spin 2 field is massive. We
compare these findings to the analogous case of spin 1 theories, where higher
derivative interactions can be causal. This makes the spin 2 case very special,
and suggests that multiple species of spin 2 is forbidden, leading us to
general relativity as essentially the unique internally consistent effective
theory of spin 2. |
Generalized Dirac monopoles in non-Abelian Kaluza-Klein theories: A method is proposed for generalizing the Euclidean Taub-NUT space, regarded
as the appropriate background of the Dirac magnetic monopole, to non-Abelian
Kaluza-Klein theories involving potentials of generalized monopoles. Usual
geometrical methods combined with a recent theory of the induced
representations governing the Taub-NUT isometries lead to a general conjecture
where the potentials of the generalized monopoles of any dimensions can be
defined in the base manifolds of suitable principal fiber bundles. Moreover, in
this way one finds that apart from the monopole models which are of a
space-like type, there exists a new type of time-like models that can not be
interpreted as monopoles. The space-like models are studied pointing out that
the monopole fields strength are particular solutions the Yang-Mills equations
with central symmetry producing the standard flux of $4\pi$ through the
two-dimensional spheres surrounding the monopole. Examples are given of
manifolds with Einstein metrics carrying SU(2) monopoles. | Categorical Tinkertoys for N=2 Gauge Theories: In view of classification of the quiver 4d N=2 supersymmetric gauge theories,
we discuss the characterization of the quivers with superpotential (Q,W)
associated to a N=2 QFT which, in some corner of its parameter space, looks
like a gauge theory with gauge group G. The basic idea is that the Abelian
category rep(Q,W) of (finite-dimensional) representations of the Jacobian
algebra $\mathbb{C} Q/(\partial W)$ should enjoy what we call the Ringel
property of type G; in particular, rep(Q,W) should contain a universal
`generic' subcategory, which depends only on the gauge group G, capturing the
universality of the gauge sector. There is a family of 'light' subcategories
$\mathscr{L}_\lambda\subset rep(Q,W)$, indexed by points $\lambda\in N$, where
$N$ is a projective variety whose irreducible components are copies of
$\mathbb{P}^1$ in one--to--one correspondence with the simple factors of G.
In particular, for a Gaiotto theory there is one such family of
subcategories, $\mathscr{L}_{\lambda\in N}$, for each maximal degeneration of
the corresponding surface $\Sigma$, and the index variety $N$ may be identified
with the degenerate Gaiotto surface itself: generic light subcategories
correspond to cylinders, while closed-point subcategories to `fixtures'
(spheres with three punctures of various kinds) and higher-order
generalizations. The rules for `gluing' categories are more general that the
geometric gluing of surfaces, allowing for a few additional exceptional N=2
theories which are not of the Gaiotto class. |
Hamiltonian formalism of Minimal Massive Gravity: We study the three-dimensional Minimal Massive Gravity (MMG) in the
Hamiltonian formalism. Canonical expressions for the asymptotic conserved
charges are derived by defining the canonical gauge generators. Specifically,
the construction of asymptotic structure of MMG requires to introduce suitable
boundary conditions. For instance, the application of this procedure is done
for the BTZ black hole as a solution to the MMG field equations. The related
conserved charges give the energy and angular momentum of the BTZ black hole.
We also show that the Poisson bracket algebra of the improved canonical gauge
generators produces an asymptotic gauge group which includes two separable
versions of Virasoro algebras. Finally, we calculate the entropy of black hole
from Cardy formula using the parameters of the boundary conformal field theory
and show the result is consistent with the value obtained from Smarr one. | Quantum BRST operators in the extended BRST-anti-BRST formalism: The quantum BRST-anti-BRST operators are explicitely derived and the
consequences related to correlation functions are investigated. The connection
with the standard formalism and the loopwise expansions for quantum operators
and anomalies in Sp(2) approach are analyzed. |
Spectral action with zeta function regularization: In this paper we propose a novel definition of the bosonic spectral action
using zeta function regularization, in order to address the issues of
renormalizability and spectral dimensions. We compare the zeta spectral action
with the usual (cutoff based) spectral action and discuss its origin,
predictive power, stressing the importance of the issue of the three
dimensionful fundamental constants, namely the cosmological constant, the Higgs
vacuum expectation value, and the gravitational constant. We emphasize the
fundamental role of the neutrino Majorana mass term for the structure of the
bosonic action. | Multi-flavor massless QED$_2$ at finite densities via Lefschetz thimbles: We consider multi-flavor massless $(1+1)$-dimensional QED with chemical
potentials at finite spatial length and the zero-temperature limit. Its sign
problem is solved using the mean-field calculation with complex saddle points. |
Entanglement Entropy of Nontrivial States: We study the entanglement entropy arising from coherent states and
one--particle states. We show that it is possible to define a finite
entanglement entropy by subtracting the vacuum entropy from that of the
considered states, when the unobserved region is the same. | Shock Waves and the Vacuum Structure of Gauge Theories: In Yang-Mills theory massless point sources lead naturally to shock-wave
configurations. Their magnetic counterparts endow the vacuum of the
four-dimensional compact abelian model with a Coulomb-gas behaviour whose
physical implications are briefly discussed. (Contribution to ``Quark
Confinement and the Hadron Spectrum'', Como 20-24 June 1994. Revised version.) |
On the Boundary Conformal Field Theory Approach to Symmetry-Resolved
Entanglement: We study the symmetry resolution of the entanglement entropy of an interval
in two-dimensional conformal field theories (CFTs), by relating the bipartition
to the geometry of an annulus with conformal boundary conditions. In the
presence of extended symmetries such as Kac-Moody type current algebrae,
symmetry resolution is possible only if the boundary conditions on the annulus
preserve part of the symmetry group, i.e. if the factorization map associated
with the spatial bipartition is compatible with the symmetry in question. The
partition function of the boundary CFT (BCFT) is then decomposed in terms of
the characters of the irreducible representations of the symmetry group
preserved by the boundary conditions. We demonstrate that this decomposition
already provides the symmetry resolution of the entanglement spectrum of the
corresponding bipartition. Considering the various terms of the partition
function associated with the same representation, or charge sector, the
symmetry-resolved R\'enyi entropies can be derived to all orders in the UV
cutoff expansion without the need to compute the charged moments. We apply this
idea to the theory of a free massless boson with $U(1)$, $\mathbb{R}$ and
$\mathbb{Z}_2$ symmetry. | Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and
Non-Abelian T Dualities: We present a large class of new backgrounds that are solutions of type IIB
supergravity with a warped AdS${}_5$ factor, non-trivial axion-dilaton,
$B$-field and three-form Ramond-Ramond flux but yet have no five-form flux. We
obtain these solutions and many of their variations by judiciously applying
non-Abelian and Abelian T-dualities, as well as coordinate shifts to
AdS${}_5\times X_5$ IIB supergravity solutions with $X_5=S^5, T^{1,1},
Y^{p,q}$. We address a number of issues pertaining to charge quantization in
the context of non-Abelian T-duality. We comment on some properties of the
expected dual super conformal field theories by studying their CFT central
charge holographically. We also use the structure of the supergravity Page
charges, central charges and some probe branes to infer aspects of the dual
super conformal field theories. |
On Finiteness of 2- and 3-point Functions and the Renormalisation Group: Two and three point functions of composite operators are analysed with regard
to (logarithmically) divergent contact terms. Using the renormalisation group
of dimensional regularisation it is established that the divergences are
governed by the anomalous dimensions of the operators and the leading
UV-behaviour of the $1/\epsilon$-coefficient. Explicit examples are given by
the $<G^2G^2>$-, $<\Theta \Theta>$-trace of the energy momentum tensor) and
$<\bar q q \bar q q>$- correlators in QCD-like theories. The former two are
convergent when all orders are taken into account but divergent at each order
in perturbation theory implying that the latter and the the $\epsilon \to 0$
limit do not generally commute. Finite correlation functions obey unsubtracted
dispersion relations which is of importance when they are directly related to
physical observables. As a byproduct the $R^2$-anomaly is extended to NNLO
($O(\alpha^5)$) using a recent $<G^2G^2>$-computation. | Anomalies of non-invertible self-duality symmetries: fractionalization
and gauging: We study anomalies of non-invertible duality symmetries in both 2d and 4d,
employing the tool of the Symmetry TFT. In the 2d case we rephrase the known
obstruction theory for the Tambara-Yamagami fusion category in a way easily
generalizable to higher dimensions. In both cases we find two obstructions to
gauging duality defects. The first obstruction requires the existence of a
duality-invariant Lagrangian algebra in a certain Dijkgraaf-Witten theory in
one dimension more. In particular, intrinsically non-invertible (a.k.a. group
theoretical) duality symmetries are necessarily anomalous. The second
obstruction requires the vanishing of a pure anomaly for the invertible duality
symmetry. This however depends on further data. In 2d this is specified by a
choice of equivariantization for the duality-invariant Lagrangian algebra. We
propose and verify that this is equivalent to a choice of symmetry
fractionalization for the invertible duality symmetry. The latter formulation
has a natural generalization to 4d and allows us to give a compact
characterization of the anomaly. We comment on various possible applications of
our results to self-dual theories. |
Thermodynamics of accelerating AdS$_4$ black holes from the covariant
phase space: We study the charges and first law of thermodynamics for accelerating,
non-rotating black holes with dyonic charges in AdS$_4$ using the covariant
phase space formalism. In order to apply the formalism to these solutions
(which are asymptotically locally AdS and admit a non-smooth conformal boundary
$\mathscr{I}$) we make two key improvements: 1) We relax the requirement to
impose Dirichlet boundary conditions and demand merely a well-posed variational
problem. 2) We keep careful track of the codimension-2 corner term induced by
the holographic counterterms, a necessary requirement due to the presence of
"cosmic strings" piercing $\mathscr{I}$. Using these improvements we are able
to match the holographic Noether charges to the Wald Hamiltonians of the
covariant phase space and derive the first law of black hole thermodynamics
with the correct "thermodynamic length" terms arising from the strings. We
investigate the relationship between the charges imposed by supersymmetry and
show that our first law can be consistently applied to various classes of
non-supersymmetric solutions for which the cross-sections of the horizon are
spindles. | Singularities in massive conformal gravity: We study the quantum effects of big bang and black hole singularities on
massive conformal gravity. We do this by analyzing the behavior of the on-shell
effective action of the theory at these singularities. The result is that such
singularities are harmless in MCG because the on-shell effective action of the
theory does not diverge at them. |
The volume of the black hole interior at late times: Understanding the fate of semi-classical black hole solutions at very late
times is one of the most important open questions in quantum gravity. In this
paper, we provide a path integral definition of the volume of the black hole
interior and study it at arbitrarily late times for black holes in various
models of two-dimensional gravity. Because of a novel universal cancellation
between the contributions of the semi-classical black hole spectrum and some of
its non-perturbative corrections, we find that, after a linear growth at early
times, the length of the interior saturates at a time, and towards a value,
that is exponentially large in the entropy of the black hole. This provides a
non-perturbative confirmation of the complexity equals volume proposal since
complexity is also expected to plateau at the same value and at the same time. | Non-compact Calabi--Yau Manifolds and Localized Gravity: We study localization of gravity in flat space in superstring theory. We find
that an induced Einstein-Hilbert term can be generated only in four dimensions,
when the bulk is a non-compact Calabi-Yau threefold with non-vanishing Euler
number. The origin of this term is traced to R^4 couplings in ten dimensions.
Moreover, its size can be made much larger than the ten-dimensional
gravitational Planck scale by tuning the string coupling to be very small or
the Euler number to be very large. We also study the width of the localization
and discuss the problems for constructing realistic string models with no
compact extra dimensions. |
Recent Developments in Line Bundle Cohomology and Applications to String
Phenomenology: Vector bundle cohomology represents a key ingredient for string
phenomenology, being associated with the massless spectrum arising in string
compactifications on smooth compact manifolds. Although standard algorithmic
techniques exist for performing cohomology calculations, they are laborious and
ill-suited for scanning over large sets of string compactifications to find
those most relevant to particle physics. In this article we review some recent
progress in deriving closed-form expressions for line bundle cohomology and
discuss some applications to string phenomenology. | MGD-decoupled black holes, anisotropic fluids and holographic
entanglement entropy: The holographic entanglement entropy (HEE) is investigated for a black hole
under the minimal geometric deformation (MGD) procedure, created by
gravitational decoupling via an anisotropic fluid, in an AdS/CFT on the brane
setup. The respective HEE corrections are computed and confronted to the
corresponding corrections for both the standard MGD black holes and the
Schwarzschild ones. |
Trace anomaly for non-relativistic fermions: We study the coupling of a 2+1 dimensional non-relativistic spin 1/2 fermion
to a curved Newton-Cartan geometry, using null reduction from an
extra-dimensional relativistic Dirac action in curved spacetime. We analyze
Weyl invariance in detail: we show that at the classical level it is preserved
in an arbitrary curved background, whereas at the quantum level it is broken by
anomalies. We compute the trace anomaly using the Heat Kernel method and we
show that the anomaly coefficients a, c are proportional to the relativistic
ones for a Dirac fermion in 3+1 dimensions. As for the previously studied
scalar case, these coefficents are proportional to 1/m, where m is the
non-relativistic mass of the particle. | The Toric SO(10) F-Theory Landscape: Supergravity theories in more than four dimensions with grand unified gauge
symmetries are an important intermediate step towards the ultraviolet
completion of the Standard Model in string theory. Using toric geometry, we
classify and analyze six-dimensional F-theory vacua with gauge group SO(10)
taking into account Mordell-Weil U(1) and discrete gauge factors. We determine
the full matter spectrum of these models, including charged and neutral SO(10)
singlets. Based solely on the geometry, we compute all matter multiplicities
and confirm the cancellation of gauge and gravitational anomalies independent
of the base space. Particular emphasis is put on symmetry enhancements at the
loci of matter fields and to the frequent appearance of superconformal points.
They are linked to non-toric K\"ahler deformations which contribute to the
counting of degrees of freedom. We compute the anomaly coefficients for these
theories as well by using a base-independent blow-up procedure and
superconformal matter transitions. Finally, we identify six-dimensional
supergravity models which can yield the Standard Model with high-scale
supersymmetry by further compactification to four dimensions in an Abelian flux
background. |
No Scalar-Haired Cauchy Horizon Theorem in Einstein-Maxwell-Horndeski
Theories: Recently, a no inner (Cauchy) horizon theorem for static black holes with
non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories.
In this paper, we extend the theorem to the static black holes in
Einstein-Maxwell-Horndeski theories. We study the black hole interior geometry
for some exact solutions and find that the spacetime has a (space-like)
curvature singularity where the black hole mass gets an extremum and the
Hawking temperature vanishes. We discuss further extensions of the theorem,
including general Horndeski theories from disformal transformations. | Simulated Annealing for Topological Solitons: The search for solutions of field theories allowing for topological solitons
requires that we find the field configuration with the lowest energy in a given
sector of topological charge. The standard approach is based on the numerical
solution of the static Euler-Lagrange differential equation following from the
field energy. As an alternative, we propose to use a simulated annealing
algorithm to minimize the energy functional directly. We have applied simulated
annealing to several nonlinear classical field theories: the sine-Gordon model
in one dimension, the baby Skyrme model in two dimensions and the nuclear
Skyrme model in three dimensions. We describe in detail the implementation of
the simulated annealing algorithm, present our results and get independent
confirmation of the studies which have used standard minimization techniques. |
$T\bar{T}$ deformation of random matrices: We define and study the $T\bar{T}$ deformation of a random matrix model,
showing a consistent definition requires the inclusion of both the perturbative
and non-perturbative solutions to the flow equation. The deformed model is well
defined for arbitrary values of the coupling, exhibiting a phase transition for
the critical value in which the spectrum complexifies. The transition is
between a single and a double-cut phase, typically third order and in the same
universality class as the Gross-Witten transition in lattice gauge theory. The
$T\bar{T}$ deformation of a double scaled model is more subtle and complicated,
and we are not able to give a compelling definition, although we discuss
obstacles and possible alternatives. Preliminary comparisons with finite
cut-off Jackiw-Teitelboim gravity are presented. | Negative modes of Coleman-de Luccia and black hole bubbles: We study the negative modes of gravitational instantons representing vacuum
decay in asymptotically flat space-time. We consider two different vacuum decay
scenarios: the Coleman-de Luccia $\mathrm{O}(4)$-symmetric bubble, and
$\mathrm{O}(3) \times \mathbb{R}$ instantons with a static black hole. In spite
of the similarities between the models, we find qualitatively different
behaviours. In the $\mathrm{O}(4)$-symmetric case, the number of negative modes
is known to be either one or infinite, depending on the sign of the kinetic
term in the quadratic action. In contrast, solving the mode equation
numerically for the static black hole instanton, we find only one negative mode
with the kinetic term always positive outside the event horizon. The absence of
additional negative modes supports the interpretation of these solutions as
giving the tunnelling rate for false vacuum decay seeded by microscopic black
holes. |
Field Theories Without a Holographic Dual: In applying the gauge-gravity duality to the quark-gluon plasma, one models
the plasma using a particular kind of field theory with specified values of the
temperature, magnetic field, and so forth. One then assumes that the bulk, an
asymptotically AdS black hole spacetime with properties chosen to match those
of the boundary field theory, can be embedded in string theory. But this is not
always the case: there are field theories with no bulk dual. The question is
whether these theories might include those used to study the actual plasmas
produced at such facilities as the RHIC experiment or the relevant experiments
at the LHC. We argue that, \emph{provided} that due care is taken to include
the effects of the angular momentum associated with the magnetic fields
experienced by the plasmas produced by peripheral collisions, the existence of
the dual can be established for the RHIC plasmas. In the case of the LHC
plasmas, the situation is much more doubtful. | SU3 isoscalar factors: A summary of the properties of the Wigner Clebsch-Gordan coefficients and
isoscalar factors for the group SU3 in the SU2$\otimes$U1 decomposition is
presented. The outer degeneracy problem is discussed in detail with a proof of
a conjecture (Braunschweig's) which has been the basis of previous work on the
SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar
factors are produced, along with an algorithm which allows numerical
determination of the factors from the recursion relations. The algorithm
produces isoscalar factors which share all the symmetry properties under
permutation of states and conjugation which are familiar from the SU2 case. The
full set of symmetry properties for the SU3 Wigner-Clebsch-Gordan coefficients
and isoscalar factors are displayed. |
Scalar Casimir effect in a high-dimensional cosmic dispiration spacetime: In this paper we present a complete and detailed analysis of the calculation
of both the Wightman function and the vacuum expectation value of the
energy-momentum tensor that arise from quantum vacuum fluctuations of massive
and massless scalar fields in the cosmic dispiration spacetime, which is formed
by the combination of two topological defects: a cosmic string and a screw
dislocation. This spacetime is obtained in the framework of the Einstein-Cartan
theory of gravity and is considered to be a chiral space-like cosmic string.
For completeness we perform the calculation in a high-dimensional spacetime,
with flat extra dimensions. We found closed expressions for the the
energy-momentum tensor and, in particular, in (3+1)-dimensions, we compare our
results with existing previous ones in the literature for the massless scalar
field case. | On the Road Towards the Quantum Geometer's Universe: An Introduction to
Four-Dimensional Supersymmetric Quantum Field Theories: This brief set of notes presents a modest introduction to the basic features
entering the construction of supersymmetric quantum field theories in
four-dimensional Minkowski spacetime, building a bridge from similar lectures
presented at a previous Workshop of this series, and reaching only at the
doorstep of the full edifice of such theories. |
Divergences of the scalar sector of quadratic gravity: The divergences coming from a particular sector of gravitational fluctuations
around a generic background in general theories of quadratic gravity are
analyzed. They can be summarized in a particular type of scalar model, whose
properties are analyzed. | Note About Canonical Description of T-duality Along Light-Like Isometry: In this short note we analyze canonical description of T-duality along
light-like isometry. We show that T-duality of relativistic string theory on
this background leads to non-relativistic string theory action on T-dual
background. |
An $α'$-complete theory of cosmology and its tensionless limit: We explore the exactly duality invariant higher-derivative extension of
double field theory due to Hohm, Siegel and Zwiebach (HSZ) specialized to
cosmological backgrounds. Despite featuring a finite number of derivatives in
its original formulation, this theory encodes infinitely many $\alpha'$
corrections for metric, B-field and dilaton, which are obtained upon
integrating out certain extra fields. We perform a cosmological reduction with
fields depending only on time and show consistency of this truncation. We
compute the $\alpha'^4$ coefficients of the general cosmological
classification. As a possible model for how to deal with all $\alpha'$
corrections in string theory we give a two-derivative reformulation in which
the extra fields are kept. The corresponding Friedmann equations are then
ordinary second order differential equations that capture all $\alpha'$
corrections. We explore the tensionless limit $\alpha'\rightarrow \infty$,
which features string frame de Sitter vacua, and we set up perturbation theory
in $\frac{1}{\alpha'}$. | Four Dimensional Gravitational Backgrounds Based on N=4 c=4
Superconformal Systems: We propose two new realizations of the N=4, $\hat{c}=4$ superconformal system
based on the compact and non-compact versions of parafermionic algebras. The
target space interpretation of these systems is given in terms of
four-dimensional target spaces with non-trivial metric and topology different
from the previously known four-dimensional semi-wormhole realization. The
proposed $\hat{c}=4$ systems can be used as a building block to construct
perturbatively stable superstring solutions with covariantized target space
supersymmetry around non-trivial gravitational and dilaton backgrounds. |
Holographic principle in spacetimes with extra spatial dimensions: F. Scardigli and R. Casadio have considered uncertainty principles which take
into account the role of gravity and possible existence of extra spatial
dimensions. They have argued that the predicted number of degrees of freedom
enclosed in a given spatial volume matches the holographic counting only for
one of the available generalization and without extra dimensions. Taking into
account the additional inevitable source of uncertainty in distance
measurement, which is missed in their approach, we show that the holographic
properties of the proposed uncertainty principle is recovered in the models
with extra spatial dimensions. | Causality in 3D Massive Gravity Theories: We study the constraints coming from local causality requirement in various
$2+1$ dimensional dynamical theories of gravity. In topologically massive
gravity, with a single parity non-invariant massive degree of freedom, and in
new massive gravity, with two massive spin-$2$ degrees of freedom, causality
and unitarity are compatible with each other and both require the Newton's
constant to be negative. In their extensions, such as the Born-Infeld gravity
and the minimal massive gravity the situation is similar and quite different
from their higher dimensional counterparts, such as quadratic (e.g.,
Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in
conflict. We study the problem both in asymptotically flat and asymptotically
anti-de Sitter spaces. |
Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal
Models: In this paper, we pursue our analysis of the W-infinity symmetry of the
low-energy edge excitations of incompressible quantum Hall fluids. These
excitations are described by (1+1)-dimensional effective field theories, which
are built by representations of the W-infinity algebra. Generic W-infinity
theories predict many more fluids than the few, stable ones found in
experiments. Here we identify a particular class of W-infinity theories, the
minimal models, which are made of degenerate representations only - a familiar
construction in conformal field theory. The W-infinity minimal models exist for
specific values of the fractional conductivity, which nicely fit the
experimental data and match the results of the Jain hierarchy of quantum Hall
fluids. We thus obtain a new hierarchical construction, which is based uniquely
on the concept of quantum incompressible fluid and is independent of Jain's
approach and hypotheses. Furthermore, a surprising non-Abelian structure is
found in the W-infinity minimal models: they possess neutral quark-like
excitations with SU(m) quantum numbers and non-Abelian fractional statistics.
The physical electron is made of anyon and quark excitations. We discuss some
properties of these neutral excitations which could be seen in experiments and
numerical simulations. | Quasitriangular WZW model: A dynamical system is canonically associated to every Drinfeld double of any
affine Kac-Moody group. The choice of the affine Lu-Weinstein-Soibelman double
gives a smooth one-parameter deformation of the standard WZW model. In
particular, the worldsheet and the target of the classical version of the
deformed theory are the ordinary smooth manifolds. The quasitriangular WZW
model is exactly solvable and it admits the chiral decomposition.Its classical
action is not invariant with respect to the left and right action of the loop
group, however it satisfies the weaker condition of the Poisson-Lie symmetry.
The structure of the deformed WZW model is characterized by several ordinary
and dynamical r-matrices with spectral parameter. They describe the q-deformed
current algebras, they enter the definition of q-primary fields and they
characterize the quasitriangular exchange (braiding) relations. Remarkably, the
symplectic structure of the deformed chiral WZW theory is cocharacterized by
the same elliptic dynamical r-matrix that appears in the Bernard generalization
of the Knizhnik-Zamolodchikov equation, with q entering the modular parameter
of the Jacobi theta functions. This reveals a tantalizing connection between
the classical q-deformed WZW model and the quantum standard WZW theory on
elliptic curves and opens the way for the systematic use of the dynamical Hopf
algebroids in the rational q-conformal field theory. |
Generalised Scale Invariant Theories: We present the most general actions of a single scalar field and two scalar
fields coupled to gravity, consistent with second order field equations in four
dimensions, possessing local scale invariance. We apply two different methods
to arrive at our results. One method, Ricci gauging, was known to the
literature and we find this to produce the same result for the case of one
scalar field as a more efficient method presented here. However, we also find
our more efficient method to be much more general when we consider two scalar
fields. Locally scale invariant actions are also presented for theories with
more than two scalar fields coupled to gravity and we explain how one could
construct the most general actions for any number of scalar fields. Our
generalised scale invariant actions have obvious applications to early universe
cosmology, and include, for example, the Bezrukov-Shaposhnikov action as a
subset. | Effective Action Approach for Preheating: We present a semiclassical non-perturbative approach for calculating the
preheating process at the end of inflation. Our method involves integrating out
the decayed particles within the path integral framework and subsequently
determining world-line instanton solutions in the effective action. This
enables us to obtain the effective action of the inflaton, with its imaginary
part linked to the phenomenon of particle creation driven by coherent inflaton
field oscillations. Additionally, we utilize the Bogoliubov transformation to
investigate the evolution of particle density within the medium after multiple
inflaton oscillations. We apply our approach to various final state particles,
including scalar fields, tachyonic fields, and gauge fields. The
non-perturbative approach provides analytical results for preheating that are
in accord with previous methods. |
TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT: We consider high spin, $s$, long twist, $L$, planar operators (asymptotic
Bethe Ansatz) of strong ${\cal N}=4$ SYM. Precisely, we compute the minimal
anomalous dimensions for large 't Hooft coupling $\lambda$ to the lowest order
of the (string) scaling variable $\ell \sim L/ (\ln \mathcal{S}
\sqrt{\lambda})$ with GKP string size $\sim\ln \mathcal{S}\equiv 2 \ln
(s/\sqrt{\lambda})$. At the leading order $(\ln \mathcal{S}) \cdot \ell ^2 $,
we can confirm the O(6) non-linear sigma model description for this bulk term,
without boundary term $(\ln \mathcal{S})^0$. Going further, we derive,
extending the O(6) regime, the exact effect of the size finiteness. In
particular, we compute, at all loops, the first Casimir correction $\ell ^0/\ln
\mathcal{S}$ (in terms of the infinite size O(6) NLSM), which reveals only one
massless mode (out of five), as predictable once the O(6) description has been
extended. Consequently, upon comparing with string theory expansion, at one
loop our findings agree for large twist, while reveal for negligible twist,
already at this order, the appearance of wrapping. At two loops, as well as for
next loops and orders, we can produce predictions, which may guide future
string computations. | Type IIA Moduli Stabilization: We demonstrate that flux compactifications of type IIA string theory can
classically stabilize all geometric moduli. For a particular orientifold
background, we explicitly construct an infinite family of supersymmetric vacua
with all moduli stabilized at arbitrarily large volume, weak coupling, and
small negative cosmological constant. We obtain these solutions from both
ten-dimensional and four-dimensional perspectives. For more general
backgrounds, we study the equations for supersymmetric vacua coming from the
effective superpotential and show that all geometric moduli can be stabilized
by fluxes. We comment on the resulting picture of statistics on the landscape
of vacua. |
Dynamical analysis of the cosmology of mass-varying massive gravity: We study cosmological evolutions of the generalized model of nonlinear
massive gravity in which the graviton mass is given by a rolling scalar field
and is varying along time. By performing dynamical analysis, we derive the
critical points of this system and study their stabilities. These critical
points can be classified into two categories depending on whether they are
identical with the traditional ones obtained in General Relativity. We discuss
the cosmological implication of relevant critical points. | The Scale of Inflation in the Landscape: We determine the frequency of regions of small-field inflation in the Wigner
landscape as an approximation to random supergravities/type IIB flux
compactifications. We show that small-field inflation occurs exponentially more
often than large-field inflation The power of primordial gravitational waves
from inflation is generically tied to the scale of inflation. For small-field
models this is below observational reach. However, we find small-field
inflation to be dominated by the highest inflationary energy scales compatible
with a sub-Planckian field range. Hence, we expect a typical tensor-to-scalar
ratio $r\sim {\cal O}(10^{-3})$ currently undetectable in upcoming CMB
measurements. |
The four-loop six-gluon NMHV ratio function: We use the hexagon function bootstrap to compute the ratio function which
characterizes the next-to-maximally-helicity-violating (NMHV) six-point
amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory at four loops. A
powerful constraint comes from dual superconformal invariance, in the form of a
$\bar{Q}$ differential equation, which heavily constrains the first derivatives
of the transcendental functions entering the ratio function. At four loops, it
leaves only a 34-parameter space of functions. Constraints from the collinear
limits, and from the multi-Regge limit at the leading-logarithmic (LL) and
next-to-leading-logarithmic (NLL) order, suffice to fix these parameters and
obtain a unique result. We test the result against multi-Regge predictions at
NNLL and N$^3$LL, and against predictions from the operator product expansion
involving one and two flux-tube excitations; all cross-checks are satisfied. We
study the analytical and numerical behavior of the parity-even and parity-odd
parts on various lines and surfaces traversing the three-dimensional space of
cross ratios. As part of this program, we characterize all irreducible hexagon
functions through weight eight in terms of their coproduct. We also provide
representations of the ratio function in particular kinematic regions in terms
of multiple polylogarithms. | Deformation of BF theories, Topological Open Membrane and A
Generalization of The Star Deformation: We consider a deformation of the BF theory in any dimension by means of the
antifield BRST formalism. Possible consistent interaction terms for the action
and the gauge symmetries are analyzed and we find a new class of topological
gauge theories. Deformations of the world volume BF theory are considered as
possible deformations of the topological open membrane. Therefore if we
consider these theories on open membranes, we obtain noncommutative structures
of the boundaries of open membranes, and we propose a generalization of the
path integral representation of the star deformation. |
Four dimensional supersymmetric Yang-Mills quantum mechanics with three
colors: The $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(2)$ and
$SU(3)$ gauge symmetry groups is studied. A numerical method to find finite
matrix representation of the Hamiltonian is presented in detail. It is used to
find spectrum of the theory. In the $SU(2)$ case there are bound states in all
channels with definite total number of fermions and angular momentum. For 2,3,4
fermions continuous and discrete spectra coexist in the same range of energies.
These results are confirmation of earlier studies. With $SU(3)$ gauge group,
the continuous spectrum is moved to sectors with more fermions. Supersymmetry
generators are used to identify supermultiplets and determine the level of
restoration of supersymmetry for a finite cutoff. For both theories, with
$SU(2)$ and $SU(3)$ symmetry, wavefunctions are studied and different behavior
of bound and scattering states is observed. | Where does Cosmological Perturbation Theory Break Down?: We apply the effective field theory approach to the coupled metric-inflaton
system, in order to investigate the impact of higher dimension operators on the
spectrum of scalar and tensor perturbations in the short-wavelength regime. In
both cases, effective corrections at tree-level become important when the
Hubble parameter is of the order of the Planck mass, or when the physical wave
number of a cosmological perturbation mode approaches the square of the Planck
mass divided by the Hubble constant. Thus, the cut-off length below which
conventional cosmological perturbation theory does not apply is likely to be
much smaller than the Planck length. This has implications for the
observability of "trans-Planckian" effects in the spectrum of primordial
perturbations. |
Holographic Scattering Amplitudes: Inspired by ancient astronomy, we propose a holographic description of
perturbative scattering amplitudes, as integrals over a `celestial sphere'.
Since Lorentz invariance, local interactions, and particle propagations all
take place in a four-dimensional space-time, it is not trivial to accommodate
them in a lower-dimensional `celestial sphere'. The details of this task will
be discussed step by step, resulting in the Cachazo-He-Yuan (CHY) and similar
scattering amplitudes, thereby providing them with a holographic non-string
interpretation. | New dimer integrable systems and defects in five dimensional gauge
theory: We study the relation between the quantum integrable systems derived from the
dimer graphs and five dimensional $\mathcal{N}=1$ supersymmetric gauge theories
on $S^1 \times \mathbb{R}^4$. We construct integrable systems based on new
dimer graphs obtained from modification of hexagon dimer diagram. We study the
gauge theories in correspondence to the newly proposed integrable systems. By
examining three types of defects -- a line defect, a canonical co-dimensional
two defect and a monodromy defect -- in five-dimensional gauge theory with
$\mathcal{N}=1$ supersymmetry and
$\Omega_{\varepsilon_1,\varepsilon_2}$-background. We identify, in the
$\varepsilon_2 \to 0$ limit, the canonical co-dimensional two defect satisfying
the Baxter T-Q equation of the generalized $A$-type dimer integrable system,
and the monodromy defect as its common eigenstate of the commuting
Hamiltonians, with the eigenvalues being the expectation value of the BPS
Wilson loop in the anti-symmetric representation of the bulk gauge group. |
Topological structure of the vortex solution in Jackiw-Pi model: By using $\phi$ -mapping method, we discuss the topological structure of the
self-duality solution in Jackiw-Pi model in terms of gauge potential
decomposition. We set up relationship between Chern-Simons vortices solution
and topological number which is determined by Hopf index and and Brouwer
degree. We also give the quantization of flux in the case. Then, we study the
angular momentum of the vortex, it can be expressed in terms of the flux. | Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R): We derive the action and symmetries of the bosonic sector of non-Lorentzian
IIB supergravity by taking the non-relativistic string limit. We find that the
bosonic field content is extended by a Lagrange multiplier that implements a
restriction on the Ramond-Ramond fluxes. We show that the SL(2,R)
transformation rules of non-Lorentzian IIB supergravity form a novel, nonlinear
polynomial realization. Using classical invariant theory of polynomial
equations and binary forms, we will develop a general formalism describing the
polynomial realization of SL(2,R) and apply it to the special case of
non-Lorentzian IIB supergravity. Using the same formalism, we classify all the
relevant SL(2,R) invariants. Invoking other bosonic symmetries, such as the
local boost and dilatation symmetry, we show how the bosonic part of the
non-Lorentzian IIB supergravity action is formed uniquely from these SL(2,R)
invariants. This work also points towards the concept of a non-Lorentzian
bootstrap, where bosonic symmetries in non-Lorentzian supergravity are used to
bootstrap the bosonic dynamics in Lorentzian supergravity, without considering
the fermions. |
Discrete analogs of the Darboux-Egoroff metrics: Discrete analogs of the Darboux-Egoroff metrics are considered. It is shown
that the corresponding lattices in the Euclidean space are described by
discrete analogs of the Lame equations. It is proved that up to a gauge
transformation these equations are necessary and sufficient for discrete
analogs of rotation coefficients to exist. Explicit examples of the
Darboux-Egoroff lattices are constructed by means of algebro-geometric methods. | Gauge fixing and metric independence in topological quantum theories: We consider topological gauge theories in three dimensions which are defined
by metric independent lagrangians. It has been claimed that the functional
integration necessarily depends nontrivially on the gauge-fixing metric. We
demonstrate that the partition function and the mean values of the gauge
invariant observables do not really depend on the gauge-fixing metric. |
A Brief History of the Stringy Instanton: The arcane ADHM construction of Yang-Mills instantons can be very naturally
understood in the framework of D-brane dynamics in string theory. In this
point-of-view, the mysterious auxiliary symmetry of the ADHM construction
arises as a gauge symmetry and the instantons are modified at short distances
where string effects become important. By decoupling the stringy effects, one
can recover all the instanton formalism, including the all-important volume
form on the instanton moduli space. We describe applications of the instanton
calculus to the AdS/CFT correspondence and higher derivative terms in the
D3-brane effective action. In these applications, there is an interesting
relation between instanton partition functions, the Euler characteristic of
instanton moduli space and modular symmetry. We also describe how it is now
possible to do multi-instanton calculations in gauge theory and we resolve an
old puzzle involving the gluino condensate in supersymmetric QCD. | Classical and Thermodynamic Stability of Black Branes: It is argued that many non-extremal black branes exhibit a classical
Gregory-Laflamme instability if, and only if, they are locally
thermodynamically unstable. For some black branes, the Gregory-Laflamme
instability must therefore disappear near extremality. For the black $p$-branes
of the type II supergravity theories, the Gregory-Laflamme instability
disappears near extremality for $p=1,2,4$ but persists all the way down to
extremality for $p=5,6$ (the black D3-brane is not covered by the analysis of
this paper). This implies that the instability also vanishes for the
near-extremal black M2 and M5-brane solutions. |
Casimir operators induced by Maurer-Cartan equations: It is shown that for inhomogeneous Lie algebras
$\frak{g}=\frak{s}\overrightarrow{\oplus}_{\Lambda}(\dim \Lambda)L_{1}$
satisfying the condition $\mathcal{N}(\frak{g})=1$, the only Casimir operator
can be explicitly constructed from the Maurer-Cartan equations by means of
wedge products. It is shown that this constraint imposes sharp bounds for the
dimension of the representation $R$. The procedure is generalized to compute
also the rational invariant of some Lie algebras. | Crosscap States in Integrable Field Theories and Spin Chains: We study crosscap states in integrable field theories and spin chains in 1+1
dimensions. We derive an exact formula for overlaps between the crosscap state
and any excited state in integrable field theories with diagonal scattering. We
then compute the crosscap entropy, i.e. the overlap for the ground state, in
some examples. In the examples we analyzed, the result turns out to decrease
monotonically along the renormalization group flow except in cases where the
discrete symmetry is spontaneously broken in the infrared. We next introduce
crosscap states in integrable spin chains, and obtain determinant expressions
for the overlaps with energy eigenstates. These states are long-range entangled
and their entanglement entropy grows linearly until the size of the subregion
reaches half the system size. This property is reminiscent of pure-state black
holes in holography and makes them interesting for use as initial conditions of
quantum quench. As side results, we propose a generalization of Zamolodchikov's
staircase model to flows between D-series minimal models, and discuss the
relation to fermionic minimal models and the GSO projection. |
Factorization of colored knot polynomials at roots of unity: From analysis of a big variety of different knots we conclude that at q which
is an root of unity, q^{2m}=1, HOMFLY polynomials in symmetric representations
[r] satisfy recursion identity: H_{r+m} = H_r H_m for any A, which is a
generalization of the property H_r = (H_1)^r for special polynomials at q=1. We
conjecture a natural generalization to arbitrary representation R, which,
however, is checked only for torus knots. Next, Kashaev polynomial, which
arises from H_R at q=exp(i\pi/|R|), turns equal to the special polynomial with
A substituted by A^|R|, provided R is a single-hook representations (e.g.
arbitrary symmetric) -- what provides a q-A dual to the similar property of
Alexander polynomial. All this implies non-trivial relations for the
coefficients of the differential expansions, which are believed to provide
reasonable coordinates in the space of knots -- existence of such universal
relations means that these variables are still not unconstrained. | $G_2$ Holonomy, Taubes' Construction of Seiberg-Witten Invariants and
Superconducting Vortices: Using a reformulation of topological ${\cal N}=2$ QFT's in M-theory setup,
where QFT is realized via M5 branes wrapping co-associative cycles in a $G_2$
manifold constructed from the space of self-dual 2-forms over $X^4$, we show
that superconducting vortices are mapped to M2 branes stretched between M5
branes. This setup provides a physical explanation of Taubes' construction of
the Seiberg-Witten invariants when $X^4$ is symplectic and the superconducting
vortices are realized as pseudo-holomorphic curves. This setup is general
enough to realize topological QFT's arising from ${\cal N}=2$ QFT's from all
Gaiotto theories on arbitrary 4-manifolds. |
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