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On Yangian-invariant regularisation of deformed on-shell diagrams in N=4
super-Yang-Mills theory: We investigate Yangian invariance of deformed on-shell diagrams with D=4, N=4
superconformal symmetry. We find that invariance implies a direct relationship
between the deformation parameters and the permutation associated to the
on-shell graph. We analyse the connection with deformations of scattering
amplitudes in N=4 super-Yang-Mills theory and the possibility of using the
deformation parameters as a regulator preserving Yangian invariance. A study of
higher-point tree and loop graphs suggests that manifest Yangian invariance of
the amplitude requires trivial deformation parameters. | On quantum group symmetry and Bethe ansatz for the asymmetric twin spin
chain with integrable boundary: Motivated by a study of the crossing symmetry of the `gemini' representation
of the affine Hecke algebra we give a construction for crossing tensor space
representations of ordinary Hecke algebras. These representations build
solutions to the Yang--Baxter equation satisfying the crossing condition (that
is, integrable quantum spin chains). We show that every crossing representation
of the Temperley--Lieb algebra appears in this construction, and in particular
that this construction builds new representations. We extend these to new
representations of the blob algebra, which build new solutions to the Boundary
Yang--Baxter equation (i.e. open spin chains with integrable boundary
conditions).
We prove that the open spin chain Hamiltonian derived from Sklyanin's
commuting transfer matrix using such a solution can always be expressed as the
representation of an element of the blob algebra, and determine this element.
We determine the representation theory (irreducible content) of the new
representations and hence show that all such Hamiltonians have the same
spectrum up to multiplicity, for any given value of the algebraic boundary
parameter. (A corollary is that our models have the same spectrum as the open
XXZ chain with nondiagonal boundary -- despite differing from this model in
having reference states.) Using this multiplicity data, and other ideas, we
investigate the underlying quantum group symmetry of the new Hamiltonians. We
derive the form of the spectrum and the Bethe ansatz equations. |
A BMS-invariant free scalar model: The BMS (Bondi-van der Burg-Metzner-Sachs) symmetry arises as the asymptotic
symmetry of flat spacetime at null infinity. In particular, the BMS algebra for
three dimensional flat spacetime (BMS$_3$) is generated by the super-rotation
generators which form a Virasoro sub-algebra with central charge $c_L$,
together with mutually-commuting super-translation generators. The
super-rotation and super-translation generators have non-trivial commutation
relations with another central charge $c_M$. In this paper, we study a free
scalar theory in two dimensions exhibiting BMS$_3$ symmetry, which can also be
understood as the ultra-relativistic limit of a free scalar CFT$_2$. Upon
canonical quantization on the highest weight vacuum, the central charges are
found to be $c_L=2$ and $c_M=0$. Because of the vanishing central charge
$c_M=0$, the theory features novel properties: there exist primary states which
form a multiplet, and the Hilbert space can be organized by an enlarged version
of BMS modules dubbed the staggered modules. We further calculate correlation
functions and the torus partition function, the later of which is also shown
explicitly to be modular invariant. | Spontaneous Symmetry Breaking in Gauge Theories: a Historical Survey: The personal and scientific history of the discovery of spontaneous symmetry
breaking in gauge theories is outlined and its scientific content is reviewed |
Heterotic phase transitions and singularities of the gauge dyonic string: Heterotic strings on $R^6 \times K3$ generically appear to undergo some
interesting new phase transition at that value of the string coupling for which
the one of the six-dimensional gauge field kinetic energies changes sign. An
exception is the $E_8 \times E_8$ string with equal instanton numbers in the
two $E_8$'s, which admits a heterotic/heterotic self-duality. In this paper, we
generalize the dyonic string solution of the six-dimensional heterotic string
to include non-trivial gauge field configurations corresponding to self-dual
Yang-Mills instantons in the four transverse dimensions. We find that vacua
which undergo a phase transition always admit a string solution exhibiting a
naked singularity, whereas for vacua admitting a self-duality the solution is
always regular. When there is a phase transition, there exists a choice of
instanton numbers for which the dyonic string is tensionless and
quasi-anti-self-dual at that critical value of the coupling. For an infinite
subset of the other choices of instanton number, the string will also be
tensionless, but all at larger values of the coupling. | Survey of the Tachyonic Lump in Bosonic String Field Theory: We study some properties of the tachyonic lumps in the level truncation
scheme of bosonic cubic string field theory. We find that several gauges work
well and that the size of the lump as well as its tension is approximately
independent of these gauge choices at level (2,4). We also examine the
fluctuation spectrum around the lump solution, and find that a tachyon with
m^2=-0.96 and some massive scalars appear on the lump world-volume. This result
strongly supports the conjecture that a codimension 1 lump solution is
identified with a D-brane of one lower dimension within the framework of
bosonic cubic string field theory. |
Closed time like curve and the energy condition in 2+1 dimensional
gravity: We consider gravity in 2+1 dimensions in presence of extended stationary
sources with rotational symmetry. We prove by direct use of Einstein's
equations that if i) the energy momentum tensor satisfies the weak energy
condition, ii) the universe is open (conical at space infinity), iii) there are
no CTC at space infinity, then there are no CTC at all. | Conformal 3-point functions and the Lorentzian OPE in momentum space: In conformal field theory in Minkowski momentum space, the 3-point
correlation functions of local operators are completely fixed by symmetry.
Using Ward identities together with the existence of a Lorentzian operator
product expansion (OPE), we show that the Wightman function of three scalar
operators is a double hypergeometric series of the Appell $F_4$ type. We extend
this simple closed-form expression to the case of two scalar operators and one
traceless symmetric tensor with arbitrary spin. Time-ordered and
partially-time-ordered products are constructed in a similar fashion and their
relation with the Wightman function is discussed. |
General fluctuations of the type II pure spinor string on curved
backgrounds: The general fluctuations, in the form of vertex operators, for the type II
superstring in the pure spinor formalism are considered. We review the
construction of these vertex operators in flat space-time. We then review the
type II superstrings in curved background in the pure spinor formalism to
finally construct the vertex operators on a generic type II supergravity
background. | CANONICAL NONABELIAN DUAL TRANSFORMATIONS IN SUPERSYMMETRIC FIELD
THEORIES: A generating functional $F$ is found for a canonical nonabelian dual
transformation which maps the supersymmetric chiral O(4) $\sigma$-model to an
equivalent supersymmetric extension of the dual $\sigma$-model. This $F$
produces a mapping between the classical phase spaces of the two theories in
which the bosonic (coordinate) fields transform nonlocally, the fermions
undergo a local tangent space chiral rotation, and all currents (fermionic and
bosonic) mix locally. Purely bosonic curvature-free currents of the chiral
model become a {\em symphysis} of purely bosonic and fermion bilinear currents
of the dual theory. The corresponding transformation functional $T$ which
relates wavefunctions in the two quantum theories is argued to be {\em exactly}
given by $T=\exp(iF)$. |
On the Protected Spectrum of the Minimal Argyres-Douglas Theory: Despite the power of supersymmetry, finding exact closed-form expressions for
the protected operator spectra of interacting superconformal field theories
(SCFTs) is difficult. In this paper, we take a step towards a solution for the
"simplest" interacting 4D $\mathcal{N}=2$ SCFT: the minimal Argyres-Douglas
(MAD) theory. We present two results that go beyond the well-understood Coulomb
branch and Schur sectors. First, we find the exact closed-form spectrum of
multiplets containing operators that are chiral with respect to any
$\mathcal{N}=1\subset\mathcal{N}=2$ superconformal subalgebra. We argue that
this "full" chiral sector (FCS) is as simple as allowed by unitarity for a
theory with a Coulomb branch and that, up to a rescaling of $U(1)_r$ quantum
numbers and the vanishing of a finite number of states, the MAD FCS is
isospectral to the FCS of the free $\mathcal{N}=2$ Abelian gauge theory. In the
language of superconformal representation theory, this leaves only the spectrum
of the poorly understood $\bar{\mathcal{C}}_{R,r(j,\bar j)}$ multiplets to be
determined. Our second result sheds light on these observables: we find an
exact closed-form answer for the number of $\bar{\mathcal{C}}_{0,r(j,0)}$
multiplets, for any $r$ and $j$, in the MAD theory. We argue that this
sub-sector is also as simple as allowed by unitarity for a theory with a
Coulomb branch and that there is a natural map to the corresponding sector of
the free $\mathcal{N}=2$ Abelian gauge theory. These results motivate a
conjecture on the full local operator algebra of the MAD theory. | Quantum Gravity via Random Triangulations of R^4 and Gravitons as
Goldstone Bosons of SL(4)/O(4): A model of random triangulations of a domain in $R^{(4)}$ is presented. The
global symmetries of the model include SL(4) transformations and translations.
If a stable microscopic scale exists for some range of parameters, the model
should be in a translation invariant phase where SL(4) is spontaneously broken
to O(4). In that phase, SL(4) Ward identities imply that the correlation length
in the spin two channel of a symmetric tensor field is infinite. Consequently,
it may be possible to identify the continuum limit of four dimensional Quantum
Gravity with points inside that phase. |
Fuzzy Classical Dynamics as a Paradigm for Emerging Lorentz Geometries: We show that the classical equations of motion for a particle on three
dimensional fuzzy space and on the fuzzy sphere are underpinned by a natural
Lorentz geometry. From this geometric perspective, the equations of motion
generally correspond to forced geodesic motion, but for an appropriate choice
of noncommutative dynamics, the force is purely noncommutative in origin and
the underpinning Lorentz geometry some standard space-time with, in general,
non-commutatuve corrections to the metric. For these choices of the
noncommutative dynamics the commutative limit therefore corresponds to geodesic
motion on this standard space-time. We identify these Lorentz geometries to be
a Minkowski metric on $\mathbb{R}^4$ and $\mathbb{R} \times S ^2$ in the cases
of a free particle on three dimensional fuzzy space ($\mathbb{R}^3_\star$) and
the fuzzy sphere ($S^2_\star$), respectively. We also demonstrate the
equivalence of the on-shell dynamics of $S^2_\star$ and a relativistic charged
particle on the commutative sphere coupled to the background magnetic field of
a Dirac monopole. | SU(3) Yang-Mills Hamiltonian in the flux-tube gauge: Strong coupling
expansion and glueball dynamics: It is shown that the formulation of the SU(3) Yang-Mills quantum Hamiltonian
in the "flux-tube gauge" $A_{a1}=0$ for all a=1,2,4,5,6,7 and $A_{a2}=0$ for
all a=5,7 allows for a systematic and practical strong coupling expansion of
the Hamiltonian in $\lambda\equiv g^{-2/3}$, equivalent to an expansion in the
number of spatial derivatives. Introducing an infinite spatial lattice with box
length a, the "free part" is the sum of Hamiltonians of Yang-Mills quantum
mechanics of constant fields for each box, and the "interaction terms" contain
higher and higher number of spatial derivatives connecting different boxes. The
Faddeev-Popov operator, its determinant and inverse, are rather simple, but
show a highly non-trivial periodic structure of six Gribov-horizons separating
six Weyl-chambers. The energy eigensystem of the gauge reduced Hamiltonian of
SU(3) Yang-Mills mechanics of spatially constant fields can be calculated in
principle with arbitrary high precision using the orthonormal basis of all
solutions of the corresponding harmonic oscillator problem, which turn out to
be made of orthogonal polynomials of the 45 components of eight irreducible
symmetric spatial tensors. First results for the low-energy glueball spectrum
are obtained which substantially improve those by Weisz and Ziemann using the
constrained approach. Thus, the gauge reduced approach using the flux-tube
gauge proposed here, is expected to enable one to obtain valuable
non-perturbative information about low-energy glueball dynamics, using
perturbation theory in $\lambda$. |
A class of non-geometric M-theory compactification backgrounds: We study a particular class of supersymmetric M-theory eight-dimensional
non-geometric compactification backgrounds to three-dimensional Minkowski
space-time, proving that the global space of the non-geometric compactification
is still a differentiable manifold, although with very different geometric and
topological properties with respect to the corresponding standard M-theory
compactification background: it is a compact complex manifold admitting a
K\"ahler covering with deck transformations acting by holomorphic homotheties
with respect to the K\"ahler metric. We show that this class of non-geometric
compactifications evade the Maldacena-Nu\~nez no-go theorem by means of a
mechanism originally developed by Mario Garc\'ia-Fern\'andez and the author for
Heterotic Supergravity, and thus do not require $l_{P}$-corrections to allow
for a non-trivial warp factor or four-form flux. We obtain an explicit
compactification background on a complex Hopf four-fold that solves all the
equations of motion of the theory. We also show that this class of
non-geometric compactification backgrounds is equipped with a holomorphic
principal torus fibration over a projective K\"ahler base as well as a
codimension-one foliation with nearly-parallel $G_{2}$-leaves, making thus
contact with the work of M. Babalic and C. Lazaroiu on the foliation structure
of the most general M-theory supersymmetric compactifications. | On the Infrared Limit of Unconstrained SU(2) Yang-Mills Theory: The variables appropriate for the infrared limit of unconstrained SU(2)
Yang-Mills field theory are obtained in the Hamiltonian formalism. It is shown
how in the infrared limit an effective nonlinear sigma model type Lagrangian
can be derived which out of the six physical fields involves only one of three
scalar fields and two rotational fields summarized in a unit vector. Its
possible relation to the effective Lagrangian proposed recently by Faddeev and
Niemi is discussed. |
Flat JT Gravity and the BMS-Schwarzian: We consider Minkowskian Jackiw-Teitelboim (JT) gravity in Bondi gauge at
finite temperature, with non-zero vacuum energy. Its asymptotic symmetries span
an extension of the warped Virasoro group, dubbed "BMS$_2$", which we
investigate in detail. In particular, we show that this extension has a single
coadjoint orbit when central charges are real and non-zero. The ensuing
BMS-Schwarzian action has no saddle points, and only coincides with the
boundary action functional of flat JT gravity up to a crucial dilatonic
zero-mode that ensures the existence of a well-defined bulk variational
principle. We evaluate the corresponding gravitational partition function,
which turns out to be one-loop exact precisely thanks to the presence of such a
zero-mode. | Thermoelectric Transport Coefficients from Charged Solv and Nil Black
Holes: In the present work we study charged black hole solutions of the
Einstein-Maxwell action that have Thurston geometries on its near horizon
region. In particular we find solutions with charged Solv and Nil geometry
horizons. We also find Nil black holes with hyperscaling violation. For all our
solutions we compute the thermoelectric DC transport coefficients of the
corresponding dual field theory. We find that the Solv and Nil black holes
without hyperscaling violation are dual to metals while those with hyperscaling
violation are dual to insulators. |
Communication protocols and QECCs from the perspective of TQFT, Part I:
Constructing LOCC protocols and QECCs from TQFTs: Topological quantum field theories (TQFTs) provide a general,
minimal-assumption language for describing quantum-state preparation and
measurement. They therefore provide a general language in which to express
multi-agent communication protocols, e.g. local operations, classical
communication (LOCC) protocols. Here we construct LOCC protocols using TQFT,
and show that LOCC protocols generically induce quantum error-correcting codes
(QECCs). Using multi-observer scenarios described by quantum Darwinism and
Bell/EPR experiments as examples, we show how these LOCC-induced QECCs
effectively convert entanglement into classical redundancy. In the accompanying
Part II, we show that such QECCs can be regarded as implementing, or inducing
the emergence of, spacetimes on the boundaries between interacting systems. We
investigate this connection between inter-agent communication and spacetime
using BF and Chern-Simons theories, and then using topological M-theory. | Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory: We show that the simplest non commutative renormalizable field theory, the
$\phi^4$ model on four dimensional Moyal space with harmonic potential is
asymptotically safe to all orders in perturbation theory |
Q-balls in Non-Minimally Coupled Palatini Inflation and their
Implications for Cosmology: We demonstrate the existence of Q-balls in non-minimally coupled inflation
models with a complex inflaton in the Palatini formulation of gravity. We show
that there exist Q-ball solutions which are compatible with inflation and we
derive a window in the inflaton mass squared for which this is the case. In
particular, we confirm the existence of Q-ball solutions with $\phi \sim
10^{17}-10^{18}$ GeV, consistent with the range of field values following the
end of slow-roll Palatini inflation. We study the Q-balls and their properties
both numerically and in an analytical approximation. The existence of such
Q-balls suggests that the complex inflaton condensate can fragment into
Q-balls, and that there may be an analogous process for the case of a real
inflaton with fragmentation to neutral oscillons. We discuss the possible
post-inflationary cosmology following the formation of Q-balls, including an
early Q-ball matter domination (eMD) period and the effects of this on the
reheating dynamics of the model, gravitational wave signatures which may be
detectable in future experiments, and the possibility that Q-balls could lead
to the formation of primordial black holes (PBHs). In particular, we show that
Palatini Q-balls with field strengths typical of inflaton condensate
fragmentation can directly form black holes with masses around 500 kg or more
when the self-coupling is $\lambda = 0.1$, resulting in very low (less than 100
GeV) reheating temperatures from black hole decay, with smaller black hole
masses and larger reheating temperatures possible for smaller values of
$\lambda$. Q-ball dark matter from non-minimally coupled Palatini inflation may
also be a direction for future work. | Fields in nonaffine bundles. IV. Harmonious non-Abelian currents in
string defects: This article continues the study of the category of harmonious field models
that was recently introduced as a kinetically non-linear generalisation of the
well known harmonic category of multiscalar fields over a supporting brane
wordsheet in a target space with a curved Riemannian metric. Like the perfectly
harmonious case of which a familiar example is provided by ordinary barotropic
perfect fluids, another important subcategory is the simply harmonious case,
for which it is shown that as well as ``wiggle'' modes of the underlying brane
world sheet, and sound type longitudinal modes, there will also be transverse
shake modes that propagate at the speed of light. Models of this type are shown
to arise from a non-Abelian generalisation of the Witten mechanism for
conducting string formation by ordinary scalar fields with a suitable quartic
self coupling term in the action. |
Cosmological Theories From $SO(2,2)/SO(2)\times SO(1,1)$: We herein set forth intrinsically four-dimensional string solutions and
analyze some of its properties. The solutions are constructed as gauged WZW
models of the coset $SO(2,2)/SO(2)\times SO(1,1)$. We recover backgrounds
having metric and antisymmetric tensors, dilaton fields and two electromagnetic
fields. The theories describe anisotropically expanding and static universes
for some time values. | Phase Structure and Compactness: In order to study the influence of compactness on low-energy properties, we
compare the phase structures of the compact and non-compact two-dimensional
multi-frequency sine-Gordon models. It is shown that the high-energy scaling of
the compact and non-compact models coincides, but their low-energy behaviors
differ. The critical frequency $\beta^2 = 8\pi$ at which the sine-Gordon model
undergoes a topological phase transition is found to be unaffected by the
compactness of the field since it is determined by high-energy scaling laws.
However, the compact two-frequency sine-Gordon model has first and second order
phase transitions determined by the low-energy scaling: we show that these are
absent in the non-compact model. |
Borcherds-Kac-Moody Symmetry of N=4 Dyons: We consider compactifications of heterotic string theory to four dimensions
on CHL orbifolds of the type T^6 /Z_N with 16 supersymmetries. The exact
partition functions of the quarter-BPS dyons in these models are given in terms
of genus-two Siegel modular forms. Only the N=1,2,3 models satisfy a certain
finiteness condition, and in these cases one can identify a Borcherds-Kac-Moody
superalgebra underlying the symmetry structure of the dyon spectrum. We
identify the real roots, and find that the corresponding Cartan matrices
exhaust a known classification. We show that the Siegel modular form satisfies
the Weyl denominator identity of the algebra, which enables the determination
of all root multiplicities. Furthermore, the Weyl group determines the
structure of wall-crossings and the attractor flows of the theory. For N> 4, no
such interpretation appears to be possible. | Planar QED at finite temperature and density: Hall conductivity, Berry's
phases and minimal conductivity of graphene: We study 1-loop effects for massless Dirac fields in two spatial dimensions,
coupled to homogeneous electromagnetic backgrounds, both at zero and at finite
temperature and density. In the case of a purely magnetic field, we analyze the
relationship between the invariance of the theory under large gauge
transformations, the appearance of Chern-Simons terms and of different Berry's
phases. In the case of a purely electric background field, we show that the
effective Lagrangian is independent of the chemical potential and of the
temperature. More interesting: we show that the minimal conductivity, as
predicted by the quantum field theory, is the right multiple of the
conductivity quantum and is, thus, consistent with the value measured for
graphene, with no extra factor of pi in the denominator. |
One-dimensional holographic superconductor from AdS_3/CFT_2
correspondence: We obtain a holographical description of a superconductor by using the d=2
case of the AdS_{d+1}/CFT_d correspondence. The gravity system is a
(2+1)-dimensional AdS black hole coupled to a Maxwell field and charged scalar.
The dual (1+1)-dimensional superconductor will be strongly correlated. The
characteristic exponents for vector perturbations at the boundary degenerate,
which implies that d=2 is a critical dimension and the Green's function needs
to be regularized. In the normal phase, the current-current correlation
function and the conductivity can be analytically solved at zero chemical
potential. The dc conductivity can be analytically solved at finite chemical
potential. When we add a scalar hair to the black hole, a charged condensate
happens at low temperatures. We compare our results with higher-dimensional
cases. | Supersymmetric Consistent Truncations of IIB on T(1,1): We study consistent Kaluza-Klein reductions of type IIB supergravity on
T(1,1) down to five-dimensions. We find that the most general reduction
containing singlets under the global SU(2)xSU(2) symmetry of T(1,1) is N=4
gauged supergravity coupled to three vector multiplets with a particular
gauging due to topological and geometric flux. Key to this reduction is several
modes which have not been considered before in the literature and our
construction allows us to easily show that the Papadopoulos - Tseytlin ansatz
for IIB solutions on T(1,1) is a consistent truncation. This explicit reduction
provides an organizing principle for the linearized spectrum around the warped
deformed conifold as well as the baryonic branch and should have applications
to the physics of flux compactifications with warped throats. |
Generalized entropy function for Schwarzschild and non-extremal black
holes in string theory: This paper has been withdrawn by the author due to a crucial error | Contrast data mining for the MSSM from strings: We apply techniques from data mining to the heterotic orbifold landscape in
order to identify new MSSM-like string models. To do so, so-called contrast
patterns are uncovered that help to distinguish between areas in the landscape
that contain MSSM-like models and the rest of the landscape. First, we develop
these patterns in the well-known $\mathbb{Z}_6$-II orbifold geometry and then
we generalize them to all other $\mathbb{Z}_N$ orbifold geometries. Our
contrast patterns have a clear physical interpretation and are easy to check
for a given string model. Hence, they can be used to scale down the potentially
interesting area in the landscape, which significantly enhances the search for
MSSM-like models. Thus, by deploying the knowledge gain from contrast mining
into a new search algorithm we create many novel MSSM-like models, especially
in corners of the landscape that were hardly accessible by the conventional
search algorithm, for example, MSSM-like $\mathbb{Z}_6$-II models with
$\Delta(54)$ flavor symmetry. |
Gradient flow and the Wilsonian renormalization group flow: The gradient flow is the evolution of fields and physical quantities along a
dimensionful parameter~$t$, the flow time. We give a simple argument that
relates this gradient flow and the Wilsonian renormalization group (RG) flow.
We then illustrate the Wilsonian RG flow on the basis of the gradient flow in
two examples that possess an infrared fixed point, the 4D many-flavor gauge
theory and the 3D $O(N)$ linear sigma model. | Resolving spacetime singularities in flux compactifications & KKLT: In flux compactifications of type IIB string theory with D3 and seven-branes,
the negative induced D3 charge localized on seven-branes leads to an apparently
pathological profile of the metric sufficiently close to the source. With the
volume modulus stabilized in a KKLT de Sitter vacuum this pathological region
takes over a significant part of the entire compactification, threatening to
spoil the KKLT effective field theory. In this paper we employ the
Seiberg-Witten solution of pure $SU(N)$ super Yang-Mills theory to argue that
wrapped seven-branes can be thought of as bound states of more microscopic
exotic branes. We argue that the low-energy worldvolume dynamics of a stack of
$n$ such exotic branes is given by the $(A_1,A_{n-1})$ Argyres-Douglas theory.
Moreover, the splitting of the perturbative (in $\alpha'$) seven-brane into its
constituent branes at the non-perturbative level resolves the apparently
pathological region close to the seven-brane and replaces it with a region of
$\mathcal{O}(1)$ Einstein frame volume. While this region generically takes up
an $\mathcal{O}(1)$ fraction of the compactification in a KKLT de Sitter vacuum
we argue that a small flux superpotential \textit{dynamically} ensures that the
4d effective field theory of KKLT remains valid nevertheless. |
Global Spacetime Structure of Compactified Inflationary Universe: We investigate the global spacetime structure of torus de Sitter universe,
which is exact de Sitter space with torus identification based on the flat
chart. We show that past incomplete null geodesics in torus de Sitter universe
are locally extendible. Then we give an extension of torus de Sitter universe
so that at least one of the past incomplete null geodesics in the original
spacetime becomes complete. However we find that extended torus de Sitter
universe has two ill behaviors. The first one is a closed causal curve. The
second one is so called quasi regular singularity, which means that there is no
global, consistent extension of spacetime where all curves become complete,
nevertheless each curve is locally extensible. | Nambu and the Ising Model: In 2021, to mark the occasion of 2021 was Y\^oichir\^o Nambu's birth
centenary, we engaged in writing a historical/scientific description of his
most incisive papers. Nambu was the humblest genius we have known, and we
expected to find some of his great but forgotten insights. We found one,
written in 1947: ``A Note on the Eigenvalue Problem in Crystal Statistics",
where he formulates and solves the $(N\times N)$ Ising model in a
$2N$-dimensional Hilbert space |
Open effective theory of scalar field in rotating plasma: We study the effective dynamics of an open scalar field interacting with a
strongly-coupled two-dimensional rotating CFT plasma. The effective theory is
determined by the real-time correlation functions of the thermal plasma. We
employ holographic Schwinger-Keldysh path integral techniques to compute the
effective theory. The quadratic effective theory computed using holography
leads to the linear Langevin dynamics with rotation. The noise and dissipation
terms in this equation get related by the fluctuation-dissipation relation in
presence of chemical potential due to angular momentum. We further compute
higher order terms in the effective theory of the open scalar field. At quartic
order, we explicitly compute the coefficient functions that appear in front of
various terms in the effective action in the limit when the background plasma
is slowly rotating. The higher order effective theory has a description in
terms of the non-linear Langevin equation with non-Gaussianity in the thermal
noise. | Non-perturbative Methods in Supersymmetric Theories: The aim of these notes is to provide a short introduction to supersymmetric
theories: supersymmetric quantum mechanics, Wess-Zumino models and
supersymmetric gauge theories. A particular emphasis is put on the underlying
structures and non-perturbative effects in N=1, N=2 and N=4 Yang-Mills
theories. (Extended version of lectures given at the TROISIEME CYCLE DE LA
PHYSIQUE EN SUISSE ROMANDE) |
A New Approach to Scale Symmetry Breaking and Confinement: Scale invariant theories which contain (in $4-D$) a four index field strength
are considered. The integration of the equations of motion of these $4-index$
field strength gives rise to scale symmetry breaking. The phenomena of mass
generation and confinement are possible consequences of this. | New angles on D-branes: A low-energy background field solution is presented which describes several
D-membranes oriented at angles with respect to one another. The mass and charge
densities for this configuration are computed and found to saturate the BPS
bound, implying the preservation of one-quarter of the supersymmetries.
T-duality is exploited to construct new solutions with nontrivial angles from
the basic one. |
Small Kinetic Mixing in String Theory: Kinetic mixing between gauge fields of different $U(1)$ factors is a
well-studied phenomenon in 4d EFT. In string compactifications with $U(1)$s
from sequestered D-brane sectors, kinetic mixing becomes a key target for the
UV prediction of a phenomenologically important EFT operator. Surprisingly, in
many cases kinetic mixing is absent due to a non-trivial cancellation. In
particular, D3-D3 kinetic mixing in type-IIB vanishes while D3-anti-D3 mixing
does not. This follows both from exact CFT calculations on tori as well as from
a leading-order 10d supergravity analysis, where the key cancellation is
between the $C_2$ and $B_2$ contribution. We take the latter approach, which is
the only one available in realistic Calabi-Yau settings, to a higher level of
precision by including sub-leading terms of the brane action and allowing for
non-vanishing $C_0$. The exact cancellation persists, which we argue to be the
result of $SL(2,\mathbb{R})$ self-duality. We note that a $B_2C_2$ term on the
D3-brane, which is often missing in the recent literature, is essential to
obtain the correct zero result. Finally, allowing for
$SL(2,\mathbb{R})$-breaking fluxes, kinetic mixing between D3-branes arises at
a volume-suppressed level. We provide basic explicit formulae, both for kinetic
as well as magnetic mixing, leaving the study of phenomenologically relevant,
more complex situations for the future. We also note that describing our result
in 4d supergravity appears to require higher-derivative terms - an issue which
deserves further study. | Correlations in Hawking radiation and the infall problem: It is sometimes believed that small quantum gravity effects can encode
information as `delicate correlations' in Hawking radiation, thus saving
unitarity while maintaining a semiclassical horizon. A recently derived
inequality showed that this belief is incorrect: one must have order unity
corrections to low energy evolution at the horizon (i.e. fuzzballs) to remove
entanglement between radiation and the hole. In this paper we take several
models of `small corrections' and compute the entanglement entropy numerically;
in each case this entanglement is seen to monotonically grow, in agreement with
the general inequality. We also construct a model of `burning paper', where the
entanglement is found to rise and then return to zero, in agreement with the
general arguments of Page. We then note that the fuzzball structure of string
microstates offers a version of `complementarity'. Low energy evolution is
modified by order unity, resolving the information problem, while for high
energy infalling modes ($E>> kT$) we may be able to replace correlators by
their ensemble averaged values. Israel (and others) have suggested that this
ensemble sum can be represented in the thermo-field-dynamics language as an
entangled sum over two copies of the system, giving the two sides of the
extended black hole diagram. Thus high energy correlators in a microstate may
be approximated by correlators in a spacetime with horizons, with the ensemble
sum over microstates acting like the `sewing' prescription of conformal field
theory. |
Almost-zero-energy Eigenvalues of Some Broken Supersymmetric Systems: For a quantum mechanical system with broken supersymmetry, we present a
simple method of determining the ground state when the corresponding energy
eigenvalue is sufficiently small. A concise formula is derived for the
approximate ground state energy in an associated, well-separated, asymmetric
double-well-type potential. Our discussion is also relevant for the analysis of
the fermion bound state in the kink-antikink scalar background. | Physical Account of Weyl Anomaly from Dirac Sea: We derive the Weyl anomaly in two dimensional space-time by considering the
Dirac sea regularized some negatively counted formally bosonic extra species.In
fact we calculate the trace of the energy-momentum tensor of the Dirac sea in a
background gravitational field. It has to be regularized, since otherwise the
Dirac sea is bottomless and thus causes divergence. The new regularization
method consists in adding various massive species some of which are to be
counted negative in the Dirac sea.The mass term in the Lagrangian of the
regularization fields have a dependence on the background gravitational field. |
Elementary modes of coupled oscillators with balanced loss and gain: We obtain the elementary modes of a system of parity-time reversal ( PT ) -
symmetric coupled oscillators with balanced loss and gain . These modes are
used to give a physical picture of the phase transition recently reported in
experiments with whispering - gallery microresonators. | Saturating the unitarity bound in AdS/CFT_(AdS): We investigate the holographic description of CFTs defined on the cylinder
and on AdS, which include an operator saturating the unitarity bound. The
standard Klein-Gordon field with the corresponding mass and boundary conditions
on global AdS_(d+1) and on an AdS_(d+1) geometry with AdS_d conformal boundary
contains ghosts. We identify a limit in which the singleton field theory is
obtained from the bulk theory with standard renormalized inner product, showing
that a unitary bulk theory corresponding to an operator which saturates the
unitarity bound can be formulated and that this yields a free field on the
boundary. The normalizability issues found for the standard Klein-Gordon field
on the geometry with AdS_d conformal boundary are avoided for the singleton
theory, which offers interesting prospects for multi-layered AdS/CFT. |
Torsional Constitutive Relations at Finite Temperature: The general form of the linear torsional constitutive relations at finite
temperature of the chiral current, energy-momentum tensor, and spin energy
potential are computed for a chiral fermion fluid minimally coupled to
geometric torsion and with nonzero chiral chemical potential. The corresponding
transport coefficients are explicitly calculated in terms of the energy and
number densities evaluated at vanishing torsion. A microscopic calculation of
these constitutive relations in some particular backgrounds is also presented,
confirming the general structure found. | The Logarithmic Conformal Field Theories: We study the correlation functions of logarithmic conformal field theories.
First, assuming conformal invariance, we explicitly calculate two-- and three--
point functions. This calculation is done for the general case of more than one
logarithmic field in a block, and more than one set of logarithmic fields. Then
we show that one can regard the logarithmic field as a formal derivative of the
ordinary field with respect to its conformal weight. This enables one to
calculate any $n$-- point function containing the logarithmic field in terms of
ordinary $n$--point functions. At last, we calculate the operator product
expansion (OPE) coefficients of a logarithmic conformal field theory, and show
that these can be obtained from the corresponding coefficients of ordinary
conformal theory by a simple derivation. |
Particle dynamics on AdS_2 x S^2 background with two-form flux: Different aspects of particle dynamics on AdS_2 x S^2 background with
two-form flux are discussed. These include solution of equations of motion, a
canonical transformation to conformal mechanics and an N=4 supersymmetric
extension. | The Spindle Index from Localization: We present a new supersymmetric index for three-dimensional ${\cal N}=2$
gauge theories defined on $\Sigma \times S^1$, where $\Sigma$ is a spindle,
with twist or anti-twist for the $R$-symmetry background gauge field. We start
examining general supersymmetric backgrounds of Euclidean new minimal
supergravity admitting two Killing spinors of opposite $R$-charges. We then
focus on $\Sigma \times S^1$ and demostrate how to realise twist and
anti-twist. We compute the supersymmetric partition functions on such
backgrounds via localization and show that these are captured by a general
formula, depending on the type of twist, which unifies and generalises the
superconformal and topologically twisted indices. |
Stable non-singular cosmologies in beyond Horndeski theory and disformal
transformations: In this note we collect, systemise and generalise the existing results for
relations between general Horndeski theories and beyond Horndeski theories via
disformal transformations of metric. We derive additional disformal
transformation rules relating Lagrangian functions of beyond Horndeski theory
and corresponding Horndeski theory and demonstrate that some of them become
singular at some moments(s) once one constructs a non-singular cosmological
solution in beyond Horndeski theory that is free from ghost, gradient
instabilities and strong gravity regime during the entire evolution of the
system. The key issue here is that such solutions are banned in Horndeski
theory due to existing no-go theorem. The proof of singular behaviour of
disformal relations in this case resolves the apparent contradiction between
the fact that Horndeski and beyond Horndeski theories appear related by field
redefinition but describe different physics in the context of non-singular
cosmologies. | Supersymmetric Yang-Mills Theory From Lorentzian Three-Algebras: We show that by adding a supersymmetric Faddeev-Popov ghost sector to the
recently constructed Bagger-Lambert theory based on a Lorentzian three algebra,
we obtain an action with a BRST symmetry that can be used to demonstrate the
absence of negative norm states in the physical Hilbert space. We show that the
combined theory, expanded about its trivial vacuum, is BRST equivalent to a
trivial theory, while the theory with a vev for one of the scalars associated
with a null direction in the three-algebra is equivalent to a reformulation of
maximally supersymmetric 2+1 dimensional Yang-Mills theory in which there a
formal SO(8) superconformal invariance. |
Confinement, asymptotic freedom and renormalons in type 0 string duals: Type 0B string theory has been proposed as the dual description of
non-supersymmetric SU(N) Yang-Mills theory coupled to six scalars, in four
dimensions. We study numerically and analytically the equations of motion of
type 0B gravity and we find RG trajectories of the dual theory that flow from
an asymptotically free UV regime to a confining IR regime. In the UV we find a
one-parameter family of solutions that approach asymptotically $AdS_5\times
S^5$ with a logarithmic flow of the coupling plus non-perturbative terms that
correctly reproduce all UV and IR renormalon singularities. The first UV
renormalon gives a contribution $\sim F_1(E)/E^2$ and we are able to predict
also the form of the function $F_1(E)$, which, from the YM side, corresponds to
summing all multiple-chain bubble graphs. The fact that the positions of the
renormalon singularities in the Borel plane come out correctly is a non-trivial
test of the conjectured duality. | Thermodynamics of Einstein-Proca AdS Black Holes: We study static spherically-symmetric solutions of the Einstein-Proca
equations in the presence of a negative cosmological constant. We show that the
theory admits solutions describing both black holes and also solitons in an
asymptotically AdS background. Interesting subtleties can arise in the
computation of the mass of the solutions and also in the derivation of the
first law of thermodynamics. We make use of holographic renormalisation in
order to calculate the mass, even in cases where the solutions have a rather
slow approach to the asymptotic AdS geometry. By using the procedure developed
by Wald, we derive the first law of thermodynamics for the black hole and
soliton solutions. This includes a non-trivial contribution associated with the
Proca "charge." The solutions cannot be found analytically, and so we make use
of numerical integration techniques to demonstrate their existence. |
Quasinormal Modes of Self-Dual Warped AdS$_3$ Black Hole in Topological
Massive Gravity: We consider the various perturbations of self-dual warped AdS$_3$ black hole
and obtain the exact expressions of quasinormal modes by imposing the vanishing
Dirichlet boundary condition at asymptotic infinity. It is expected that the
quasinormal modes agree with the poles of retarded Green's functions of the
dual CFT. Our results provide a quantitative test of the warped AdS/CFT
correspondence. | Casimir's energy of a conducting sphere and of a dilute dielectric ball: In this paper we sum over the spherical modes appearing in the expression for
the Casimir energy of a conducting sphere and of a dielectric ball (assuming
the same speed of light inside and outside), before doing the frequency
integration. We derive closed integral expressions that allow the calculations
to be done to all orders, without the use of regularization procedures. The
technique of mode summation using a contour integral is critically examined. |
Classical Liouville Action and Uniformization of Orbifold Riemann
Surfaces: We study the classical Liouville field theory on Riemann surfaces of genus
$g>1$ in the presence of vertex operators associated with branch points of
orders $m_i>1$. In order to do so, we consider the generalized Schottky space
$\mathfrak{S}_{g,n}(\boldsymbol{m})$ obtained as a holomorphic fibration over
the Schottky space $\mathfrak{S}_g$ of the (compactified) underlying Riemann
surface. Those fibers correspond to configuration spaces of $n$ orbifold points
of orders $\boldsymbol{m}=(m_1,\dots,m_n)$. Drawing on the previous work of
Park, Teo, and Takhtajan \cite{park2015potentials} as well as Takhtajan and
Zograf \cite{ZT_2018}, we define Hermitian metrics $\mathsf{h}_i$ for
tautological line bundles $\mathscr{L}_i$ over
$\mathfrak{S}_{g,n}(\boldsymbol{m})$. These metrics are expressed in terms of
the first coefficient of the expansion of covering map $J$ of the Schottky
domain. Additionally, we define the regularized classical Liouville action
$S_{\boldsymbol{m}}$ using Schottky global coordinates on Riemann orbisurfaces
with genus $g>1$. We demonstrate that $\exp{S_{\boldsymbol{m}}/\pi}$ serves as
a Hermitian metric on the $\mathbb{Q}$-line bundle
$\mathscr{L}=\bigotimes_{i=1}^{n}\mathscr{L}_i^{\otimes (1-1/m_i^2)}$ over
$\mathfrak{S}_{g,n}(\boldsymbol{m})$. Furthermore, we explicitly compute the
first and second variations of the smooth real-valued function
$\mathscr{S}_{\boldsymbol{m}}=S_{\boldsymbol{m}}-\pi\sum_{i=1}^n(m_i-\tfrac{1}{m_i})\log\mathsf{h}_{i}$
on the Schottky deformation space $\mathfrak{S}_{g,n}(\boldsymbol{m})$. We
establish two key results: (i) $\mathscr{S}_{\boldsymbol{m}}$ generates a
combination of accessory and auxiliary parameters, and (ii)
$-\mathscr{S}_{\boldsymbol{m}}$ acts as a K\"{a}hler potential for a specific
combination of Weil-Petersson and Takhtajan-Zograf metrics that appear in the
local index theorem for orbifold Riemann surfaces \cite{ZT_2018}. | Generalised Hydrodynamics of Particle Creation and Decay: Unstable particles rarely feature in conjunction with integrability in 1+1D
quantum field theory. However, the family of homogenous sine-Gordon models
provides a rare example where both stable and unstable bound states are present
in the spectrum whilst the scattering matrix is diagonal and solves the usual
bootstrap equations. In the standard scattering picture, unstable particles
result from complex poles of the $S$-matrix located in the unphysical sheet of
rapidity space. Since they are not part of the asymptotic spectrum, their
presence is only felt through the effect they have on physical quantities
associated either to the theory as a whole (i.e.~scaling functions, correlation
functions) or to the stable particles themselves (i.e.~energy/particle
density). In two recent publications, the effect of unstable particles in
different out-of-equilibrium settings has been studied. It has been shown that
their presence is associated with specific signatures in many quantities of
physical interest. A good way to select those quantities is to adopt the
generalised hydrodynamic approach and to consider the effective velocities and
particle densities of the stable particles in the theory. For an initial state
given by a spacial gaussian profile of temperatures peaked at the origin, time
evolution gives rise to particle and spectral particle densities that exhibit
hallmarks of the creation and decay of unstable particles. While these
signatures have been observed numerically elsewhere, this paper explores their
quantitative and qualitative dependence on the parameters of the problem. We
also consider other initial states characterised by "inverted gaussian" and
"double gaussian" temperature profiles. |
Partition Functions, the Bekenstein Bound and Temperature Inversion in
Anti-de Sitter Space and its Conformal Boundary: We reformulate the Bekenstein bound as the requirement of positivity of the
Helmholtz free energy at the minimum value of the function L=E- S/(2\pi R),
where R is some measure of the size of the system. The minimum of L occurs at
the temperature T=1/(2\pi R). In the case of n-dimensional anti-de Sitter
spacetime, the rather poorly defined size R acquires a precise definition in
terms of the AdS radius l, with R=l/(n-2). We previously found that the
Bekenstein bound holds for all known black holes in AdS. However, in this paper
we show that the Bekenstein bound is not generally valid for free quantum
fields in AdS, even if one includes the Casimir energy. Some other aspects of
thermodynamics in anti-de Sitter spacetime are briefly touched upon. | Position-space cuts for Wilson line correlators: We further develop the formalism for taking position-space cuts of eikonal
diagrams introduced in [Phys.Rev.Lett. 114 (2015), no. 18 181602,
arXiv:1410.5681]. These cuts are applied directly to the position-space
representation of any such diagram and compute its discontinuity to the leading
order in the dimensional regulator. We provide algorithms for computing the
position-space cuts and apply them to several two- and three-loop eikonal
diagrams, finding agreement with results previously obtained in the literature.
We discuss a non-trivial interplay between the cutting prescription and
non-Abelian exponentiation. We furthermore discuss the relation of the
imaginary part of the cusp anomalous dimension to the static interquark
potential. |
Large N Renormalization Group Approach to Matrix Models: We summarize our recent results on the large N renormalization group (RG)
approach to matrix models for discretized two-dimensional quantum gravity. We
derive exact RG equations by solving the reparametrization identities, which
reduce infinitely many induced interactions to a finite number of them. We find
a nonlinear RG equation and an algorithm to obtain the fixed points and the
scaling exponents. They reproduce the spectrum of relevant operators in the
exact solution. The RG flow is visualized by the linear approximation. | Geometry of Spin(10) Symmetry Breaking: We provide a new characterisation of the Standard Model gauge group GSM as a
subgroup of Spin(10). The new description of GSM relies on the geometry of pure
spinors. We show that GSM is the subgroup that stabilises a pure spinor Psi_1
and projectively stabilises another pure spinor Psi_2, with Psi_1, Psi_2
orthogonal and such that their arbitrary linear combination is still a pure
spinor. Our characterisation of GSM relies on the facts that projective pure
spinors describe complex structures on R^{10}, and the product of two commuting
complex structures is a what is known as a product structure. For the pure
spinors Psi_1, Psi_2 satisfying the stated conditions the complex structures
determined by Psi_1, Psi_2 commute and the arising product structure is R^{10}
= R^6 + R^4, giving rise to a copy of Pati-Salam gauge group inside Spin(10).
Our main statement then follows from the fact that GSM is the intersection of
the Georgi-Glashow SU(5) that stabilises Psi_1, and the Pati-Salam Spin(6) x
Spin(4) arising from the product structure determined by Psi_1, Psi_2. We have
tried to make the paper self-contained and provided a detailed description of
the creation/annihilation operator construction of the Clifford algebras Cl(2n)
and the geometry of pure spinors in dimensions up to and including ten. |
Temperature Correlations of Quantum Spins: Isotropic XY is considered. It describes interaction of quantum spins on
1-dimesional lattice. Alternatevly one can call the model XXO Hiesenberg
antiferromagnet. We solved long standing problem of evaluation of temperature
corelations. We proved that correlation function of the model is $\tau $
function of Ablowitz-Ladik PDE. We explicitly evaluated asymptotics. | Stable interactions in higher derivative field theories of derived type: We consider the general higher derivative field theories of derived type. At
free level, the wave operator of derived-type theory is a polynomial of the
order $n\geq 2$ of another operator $W$ which is of the lower order. Every
symmetry of $W$ gives rise to the series of independent higher order symmetries
of the field equations of derived system. In its turn, these symmetries give
rise to the series of independent conserved quantities. In particular, the
translation invariance of operator $W$ results in the series of conserved
tensors of the derived theory. The series involves $n$ independent conserved
tensors including canonical energy-momentum. Even if the canonical energy is
unbounded, the other conserved tensors in the series can be bounded, that will
make the dynamics stable. The general procedure is worked out to switch on the
interactions such that the stability persists beyond the free level. The stable
interaction vertices are inevitably non-Lagrangian. The stable theory, however,
can admit consistent quantization. The general construction is exemplified by
the order $N$ extension of Chern-Simons coupled to the Pais-Uhlenbeck-type
higher derivative complex scalar field. |
D1/D5 systems in ${\cal N}=4$ string theories: We propose CFT descriptions of the D1/D5 system in a class of freely acting
Z_2 orbifolds/orientifolds of type IIB theory, with sixteen unbroken
supercharges. The CFTs describing D1/D5 systems involve N=(4,4) or N=(4,0)
sigma models on $(R^3\times S^1\times T^4\times (T^4)^N/S_N)/Z_2$, where the
action of Z_2 is diagonal and its precise nature depends on the model. We also
discuss D1(D5)-brane states carrying non-trivial Kaluza-Klein charges. The
resulting multiplicities for two-charge bound states are shown to agree with
the predictions of U-duality. We raise a puzzle concerning the multiplicities
of three-charge systems, which is generically present in all vacuum
configurations with sixteen unbroken supercharges studied so far, including the
more familiar type IIB on K3 case: the constraints put on BPS counting formulae
by U-duality are apparently in contradiction with any CFT interpretation. We
argue that the presence of RR backgrounds appearing in the symmetric product
CFT may provide a resolution of this puzzle. | A discrete leading symbol and spectral asymptotics for natural
differential operators: We initiate a systematic study of natural differential operators in
Riemannian geometry whose leading symbols are not of Laplace type. In
particular, we define a discrete leading symbol for such operators which may be
computed pointwise, or from spectral asymptotics. We indicate how this can be
applied to the computation of another kind of spectral asymptotics, namely
asymptotic expansions of fundamental solutions, and to the computation of
conformally covariant operators. |
On the Dirac Oscillator: In the present work we obtain a new representation for the Dirac oscillator
based on the Clifford algebra $C\ell_7.$ The symmetry breaking and the energy
eigenvalues for our model of the Dirac oscillator are studied in the
non-relativistic limit. | One-Loop Effective Action for Euclidean Maxwell Theory on Manifolds with
Boundary: This paper studies the one-loop effective action for Euclidean Maxwell theory
about flat four-space bounded by one three-sphere, or two concentric
three-spheres. The analysis relies on Faddeev-Popov formalism and
$\zeta$-function regularization, and the Lorentz gauge-averaging term is used
with magnetic boundary conditions. The contributions of transverse,
longitudinal and normal modes of the electromagnetic potential, jointly with
ghost modes, are derived in detail. The most difficult part of the analysis
consists in the eigenvalue condition given by the determinant of a $2 \times 2$
or $4 \times 4$ matrix for longitudinal and normal modes. It is shown that the
former splits into a sum of Dirichlet and Robin contributions, plus a simpler
term. This is the quantum cosmological case. In the latter case, however, when
magnetic boundary conditions are imposed on two bounding three-spheres, the
determinant is more involved. Nevertheless, it is evaluated explicitly as well.
The whole analysis provides the building block for studying the one-loop
effective action in covariant gauges, on manifolds with boundary. The final
result differs from the value obtained when only transverse modes are
quantized, or when noncovariant gauges are used. |
Virasoro Entanglement Berry Phases: We study the parallel transport of modular Hamiltonians encoding entanglement
properties of a state. In the case of 2d CFT, we consider a change of state
through action with a suitable diffeomorphism on the circle: one that
diagonalizes the adjoint action of the modular Hamiltonian. These vector fields
exhibit kinks at the interval boundary, thus together with their central
extension they differ from usual elements of the Virasoro algebra. The Berry
curvature associated to state-changing parallel transport is the
Kirillov-Kostant symplectic form on an associated coadjoint orbit, one which
differs appreciably from known Virasoro orbits. We find that the boundary
parallel transport process computes a bulk symplectic form for a Euclidean
geometry obtained from the backreaction of a cosmic brane, with Dirichlet
boundary conditions at the location of the brane. We propose that this gives a
reasonable definition for the symplectic form on an entanglement wedge. | BRST-Fixed Points and Topological Conformal Symmetry: We study the twisted version of the supersymmetric
$G/T=SU(n)/U(1)^{\otimes(n-1)} gauged Wess-Zumino-Witten model. By studying its
fixed points under BRST transformation this model is shown to be reduced to a
simple topological field theory, that is, the topological matter system in the
K.Li's theory of 2 dimensional gravity for the case of $n=2$, and its
generalization for $n \geq 3$. |
Minimal gauge invariant and gauge fixed actions for massive higher-spin
fields: Inspired by the rich structure of covariant string field theory, we propose a
minimal gauge invariant action for general massive integer spin n field. The
action consists of four totally symmetric tensor fields of order respectively
n, n-1, n-2 and n-3, and is invariant under the gauge transformation
represented by two also totally symmetric fields of order n-1 and n-2. This
action exactly has the same gauge structure as for the string field theory and
we discuss general covariant gauge fixing procedure using the knowledge of
string field theory. We explicitly construct the corresponding gauge fixed
action for each of general covariant gauge fixing conditions. | Interaction of symmetric higher-spin gauge fields: We show that the recently proposed equations for holomorphic sector of
higher-spin theory in $d=4$, also known as chiral, can be naturally extended to
describe interacting symmetric higher-spin gauge fields in any dimension. This
is achieved with the aid of Vasiliev's off shell higher-spin algebra. The
latter contains ideal associated to traces that has to be factored out in order
to set the equations on shell. To identify the ideal in interactions we observe
the global $sp(2)$ that underlies it to all orders. The $sp(2)$ field dependent
generators are found in closed form and appear to be remarkably simple. The
traceful higher-spin vertices are analyzed against locality and shown to be
all-order space-time spin-local in the gauge sector, as well as spin-local in
the Weyl sector. The vertices are found manifestly in the form of curious
integrals over hypersimplices. We also extend to any $d$ the earlier observed
in $d=4$ higher-spin shift symmetry known to be tightly related to
spin-locality. |
Quantum Liouville theory with heavy charges: We develop a general technique for solving the Riemann-Hilbert problem in
presence of a number of heavy charges and a small one thus providing the exact
Green functions of Liouville theory for various non trivial backgrounds. The
non invariant regularization suggested by Zamolodchikov and Zamolodchikov gives
the correct quantum dimensions; this is shown to one loop in the sphere
topology and for boundary Liouville theory and to all loop on the pseudosphere.
The method is also applied to give perturbative checks of the one point
functions derived in the bootstrap approach by Fateev Zamolodchikov and
Zamolodchikov in boundary Liouville theory and by Zamolodchikov and
Zamolodchikov on the pseudosphere, obtaining complete agreement. | BPS Z(N) String Tensions, Sine Law and Casimir Scaling and Integrable
Field Theories: We consider a Yang-Mills-Higgs theory with spontaneous symmetry breaking of
the gauge group G -> U(1)^r -> C(G), with C(G) being the center of G. We study
two vacua solutions of the theory which produce this symmetry breaking. We show
that for one of these vacua, the theory in the Coulomb phase has the mass
spectrum of particles and monopoles which is exactly the same as the mass
spectrum of particles and solitons of two dimensional affine Toda field theory.
That result holds also for N=4 Super Yang-Mills theories. On the other hand, in
the Higgs phase, we show that for each of the two vacua the ratio of the
tensions of the BPS Z(N) strings satisfy either the Casimir scaling or the sine
law scaling for G=SU(N). These results are extended to other gauge groups: for
the Casimir scaling, the ratios of the tensions are equal to the ratios of the
quadratic Casimir constant of specific representations; for the sine law
scaling, the tensions are proportional to the components of the left
Perron-Frobenius eigenvector of Cartan matrix and the ratios of tensions are
equal to the ratios of the soliton masses of affine Toda field theories. |
BTZ black hole with KdV-type boundary conditions: Thermodynamics
revisited: The thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black
hole endowed with Korteweg-de Vries (KdV)-type boundary conditions are
considered. This familiy of boundary conditions for General Relativity on
AdS$_{3}$ is labeled by a non-negative integer $n$, and gives rise to a dual
theory which possesses anisotropic Lifshitz scaling invariance with dynamical
exponent $z=2n+1$. We show that from the scale invariance of the action for
stationary and circularly symmetric spacetimes, an anisotropic version of the
Smarr relation arises, and we prove that it is totally consistent with the
previously reported anisotropic Cardy formula. The set of KdV-type boundary
conditions defines an unconventional thermodynamic ensemble, which leads to a
generalized description of the thermal stability of the system. Finally, we
show that at the self-dual temperature $T_{s}=
\frac{1}{2\pi}(\frac{1}{z})^{\frac{z}{z+1}}$, there is a Hawking-Page phase
transition between the BTZ black hole and thermal AdS$_{3}$ spacetime. | Inclusion of radiation in the CCM approach of the $φ^4$ model: We present an effective Lagrangian for the $\phi^4$ model that includes
radiation modes as collective coordinates. The coupling between these modes to
the discrete part of the spectrum, i.e., the zero mode and the shape mode,
gives rise to different phenomena which can be understood in a simple way in
our approach. In particular, the energy transfer between radiation, translation
and shape modes is carefully investigated in the single-kink sector. Finally,
we also discuss the inclusion of radiation modes in the study of oscillons.
This leads to relevant phenomena such as the oscillon decay and the
kink-antikink creation. |
Universality of Nonperturbative Effect in Type 0 String Theory: We derive the nonperturbative effect in type 0B string theory, which is
defined by taking the double scaling limit of a one-matrix model with a two-cut
eigenvalue distribution. However, the string equation thus derived cannot
determine the nonperturbative effect completely, at least without specifying
unknown boundary conditions. The nonperturbative contribution to the free
energy comes from instantons in such models. We determine by direct computation
in the matrix model an overall factor of the instanton contribution, which
cannot be determined by the string equation itself. We prove that it is
universal in the sense that it is independent of the detailed structure of
potentials in the matrix model. It turns out to be a purely imaginary number
and therefore can be interpreted as a quantity related to instability of the
D-brane in type 0 string theory. We also comment on a relation between our
result and boundary conditions for the string equation. | Inhomogeneous String Cosmologies: We present exact inhomogeneous and anisotropic cosmological solutions of
low-energy string theory containing dilaton and axion fields. The spacetime
metric possesses cylindrical symmetry. The solutions describe ever-expanding
universes with an initial curvature singularity and contain known homogeneous
solutions as subcases. The asymptotic form of the solution near the initial
singularity has a spatially-varying Kasner-like form. The inhomogeneous axion
and dilaton fields are found to evolve quasi-homogeneously on scales larger
than the particle horizon. When the inhomogeneities enter the horizon they
oscillate as non-linear waves and the inhomogeneities attentuate. When the
inhomogeneities are small they behave like small perturbations of homogeneous
universes. The manifestation of duality and the asymptotic behaviour of the
solutions are investigated. |
Higher-dimensional Rotating Charged Black Holes: Using the blackfold approach, we study new classes of higher-dimensional
rotating black holes with electric charges and string dipoles, in theories of
gravity coupled to a 2-form or 3-form field strength and to a dilaton with
arbitrary coupling. The method allows to describe not only black holes with
large angular momenta, but also other regimes that include charged black holes
near extremality with slow rotation. We construct explicit examples of electric
rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory,
with horizons of spherical and non-spherical topology. We also find new
families of solutions with string dipoles, including a new class of prolate
black rings. Whenever there are exact solutions that we can compare to, their
properties in the appropriate regime are reproduced precisely by our solutions.
The analysis of blackfolds with string charges requires the formulation of the
dynamics of anisotropic fluids with conserved string-number currents, which is
new, and is carried out in detail for perfect fluids. Finally, our results
indicate new instabilities of near-extremal, slowly rotating charged black
holes, and motivate conjectures about topological constraints on dipole hair. | Nonperturbative universal Chern-Simons theory: Closed simple integral representation through Vogel's universal parameters is
found both for perturbative and nonperturbative (which is inverse invariant
group volume) parts of free energy of Chern-Simons theory on $S^3$. This proves
the universality of that partition function. For classical groups it manifestly
satisfy N \rightarrow -N duality, in apparent contradiction with previously
used ones. For SU(N) we show that asymptotic of nonperturbative part of our
partition function coincides with that of Barnes G-function, recover
Chern-Simons/topological string duality in genus expansion and resolve
abovementioned contradiction. We discuss few possible directions of development
of these results: derivation of representation of free energy through
Gopakumar-Vafa invariants, possible appearance of non-perturbative additional
terms, 1/N expansion for exceptional groups, duality between string coupling
constant and K\"ahler parameters, etc. |
Matrix Model and beta-deformed N=4 SYM: This work is the result of the ideas developed by Ken Yoshida about the
possibility of extending the range of applications of the matrix model approach
to the computation of the holomorphic superpotential of the beta-deformed N=4
super Yang-Mills theory both in the presence of a mass term and in the massless
limit. Our formulae, while agreeing with all the existing results we can
compare with, are valid also in the case of spontaneously broken gauge
symmetry.
We dedicate this paper to the memory of Ken, an unforgettable friend for all
of us and a great scientist. | Quantum integrability and functional equations: In this thesis a general procedure to represent the integral Bethe Ansatz
equations in the form of the Reimann-Hilbert problem is given. This allows us
to study in simple way integrable spin chains in the thermodynamic limit. Based
on the functional equations we give the procedure that allows finding the
subleading orders in the solution of various integral equations solved to the
leading order by the Wiener-Hopf technics. The integral equations are studied
in the context of the AdS/CFT correspondence, where their solution allows
verification of the integrability conjecture up to two loops of the strong
coupling expansion. In the context of the two-dimensional sigma models we
analyze the large-order behavior of the asymptotic perturbative expansion.
Obtained experience with the functional representation of the integral
equations allowed us also to solve explicitly the crossing equations that
appear in the AdS/CFT spectral problem. |
Approximate BPS states: We consider dimensionally reduced three-dimensional supersymmetric
Yang-Mills-Chern-Simons theory. Although the N=1 supersymmetry of this theory
does not allow true massive Bogomol'nyi-Prasad-Sommerfield (BPS) states, we
find approximate BPS states which have non-zero masses that are almost
independent of the Yang-Mills coupling constant and which are a reflection of
the massless BPS states of the underlying N=1 super Yang-Mills theory. The
masses of these states at large Yang-Mills coupling are exactly at the
n-particle continuum thresholds. This leads to a relation between their masses
at zero and large Yang-Mills coupling. | Scalar Fields in BTZ Black Hole Spacetime and Entanglement Entropy: We study the quantum scalar fields in background of BTZ black hole spacetime.
We calculate the entanglement entropy using the discretized model, which
resembles a system of coupled harmonic oscillators. The leading term of the
entropy formula is standard Bakenstein-Hawking entropy and sub-leading
corresponds to quantum corrections to black hole entropy. We calculate the
co-efficent of sub-leading logarithmic corrections numerically. |
How to Build the Thermofield Double State: Given two copies of any quantum mechanical system, one may want to prepare
them in the thermofield double state for the purpose of studying thermal
physics or black holes. However, the thermofield double is a unique entangled
pure state and may be difficult to prepare. We propose a local interacting
Hamiltonian for the combined system whose ground state is approximately the
thermofield double. The energy gap for this Hamiltonian is of order the
temperature. Our construction works for any quantum system satisfying the
Eigenvalue Thermalization Hypothesis. | Weyl fermions in a non-abelian gauge background and trace anomalies: We study the trace and chiral anomalies of Weyl fermions in a non-abelian
gauge background in four dimensions. Using a Pauli-Villars regularization we
identify the trace anomaly, proving that it can be cast in a gauge invariant
form, even in the presence of the non-abelian chiral anomaly, that we rederive
to check the consistency of our methods. In particular, we find that the trace
anomaly does not contain any parity-odd topological contribution, whose
presence has been debated in the recent literature. |
Solitons in (1,1)-supersymmetric massive sigma model: We find the solitons of massive (1,1)-supersymmetric sigma models with target
space the groups $SO(2)$ and $SU(2)$ for a class of scalar potentials and
compute their charge, mass and moduli space metric. We also investigate the
massive sigma models with target space any semisimple Lie group and show that
some of their solitons can be obtained from embedding the $SO(2)$ and $SU(2)$
solitons. | The supersymmetric spinning polynomial: In this paper, we construct the supersymmetric spinning polynomials. These
are orthogonal polynomials that serve as an expansion basis for the residue or
discontinuity of four-point scattering amplitudes, respecting four-dimensional
super Poincare invariance. The polynomials are constructed by gluing on-shell
supersymmetric three-point amplitudes of one massive two massless multiplets,
and are identified with algebraic Jacobi-polynomials. Equipped with these we
construct the supersymmetric EFThedron, which geometrically defines the allowed
region of Wilson coefficients respecting UV unitarity and super Poincare
invariance. |
Identities in Nonlinear Realizations of Supersymmetry: In this paper, we emphasize that a UV SUSY-breaking theory can be realized
either linearly or nonlinearly. Both realizations form the dual descriptions of
the UV SUSY-breaking theory. Guided by this observation, we find subtle
identities involving the Goldstino field and matter fields in the standard
nonlinear realization from trivial ones in the linear realization. Rather
complicated integrands in the standard nonlinear realization are identified as
total-divergences. Especially, identities only involving the Goldstino field
reveal the self-consistency of the Grassmann algebra. As an application of
these identities, we prove that the nonlinear Kahler potential without or with
gauge interactions is unique, if the corresponding linear one is fixed. Our
identities pick out the total-divergence terms and guarantee this uniqueness. | Classification and stability of vacua in maximal gauged supergravity: This article presents a systematic study of critical points for the SL(8,
R)-type gauging in four dimensional maximal gauged supergravity. We determine
all the possible vacua for which the origin of the moduli space becomes a
critical point. We formulate a new tool which enables us to find analytically
the mass spectrum of the corresponding vacua in terms of eigenvalues of the
embedding tensor. When the cosmological constant is nonvanishing, it turns out
that many vacua obtained by the dyonic embedding admit a single deformation
parameter of the theory, in agreement with the results of the recent paper by
Dall'Agata, Inverso and Trigiante [arXiv:1209.0760]. Nevertheless, it is shown
that the resulting mass spectrum is independent of the deformation parameter
and can be classified according to the unbroken gauge symmetry at the vacua,
rather than the underlying gauging. We also show that the generic Minkowski
vacua exhibit instability. |
Four-point conformal blocks with three heavy background operators: We study CFT$_2$ Virasoro conformal blocks of the 4-point correlation
function $\langle \mathcal{O}_L \mathcal{O}_H \mathcal{O}_H \mathcal{O}_H
\rangle $ with three background operators $\mathcal{O}_H$ and one perturbative
operator $\mathcal{O}_L$ of dimensions $\Delta_L/\Delta_H \ll1$. The conformal
block function is calculated in the large central charge limit using the
monodromy method. From the holographic perspective, the background operators
create $AdS_3$ space with three conical singularities parameterized by
dimensions $\Delta_H$, while the perturbative operator corresponds to the
geodesic line stretched from the boundary to the bulk. The geodesic length
calculates the perturbative conformal block. We propose how to address the
block/length correspondence problem in the general case of higher-point
correlation functions $\langle \mathcal{O}_L \cdots \mathcal{O}_L \mathcal{O}_H
\cdots \mathcal{O}_H \rangle $ with arbitrary numbers of background and
perturbative operators. | Lifting of D1-D5-P states: We consider states of the D1-D5 CFT where only the left-moving sector is
excited. As we deform away from the orbifold point, some of these states will
remain BPS while others can `lift'. We compute this lifting for a particular
family of D1-D5-P states, at second order in the deformation off the orbifold
point. We note that the maximally twisted sector of the CFT is special: the
covering surface appearing in the correlator can only be genus one while for
other sectors there is always a genus zero contribution. We use the results to
argue that fuzzball configurations should be studied for the full class
including both extremal and near-extremal states; many extremal configurations
may be best seen as special limits of near extremal configurations. |
Nonequilibrium quantum fields from first principles: Calculations of nonequilibrium processes become increasingly feasable in
quantum field theory from first principles. There has been important progress
in our analytical understanding based on 2PI generating functionals. In
addition, for the first time direct lattice simulations based on stochastic
quantization techniques have been achieved. The quantitative descriptions of
characteristic far-from-equilibrium time scales and thermal equilibration in
quantum field theory point out new phenomena such as prethermalization. They
determine the range of validity of standard transport or semi-classical
approaches, on which most of our ideas about nonequilibrium dynamics were based
so far. These are crucial ingredients to understand important topical phenomena
in high-energy physics related to collision experiments of heavy nuclei, early
universe cosmology and complex many-body systems. | M-theory Compactifications on Manifolds with G2 Structure: In this paper we study M-theory compactifications on manifolds of G2
structure. By computing the gravitino mass term in four dimensions we derive
the general form for the superpotential which appears in such compactifications
and show that beside the normal flux term there is a term which appears only
for non-minimal G2 structure. We further apply these results to
compactifications on manifolds with weak G2 holonomy and make a couple of
statements regarding the deformation space of such manifolds. Finally we show
that the superpotential derived from fermionic terms leads to the potential
that can be derived from the explicit compactification, thus strengthening the
conjectures we make about the space of deformations of manifolds with weak G2
holonomy. |
Non-Commutative Geometry from Strings: To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G.
Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern
developments of noncommutative geometry in string theory. | BMN operators and string field theory: We extract from gauge theoretical calculations the matrix elements of the SYM
dilatation operator. By the BMN correspondence this should coincide with the
3-string vertex of light cone string field theory in the pp-wave background. We
find a mild but important discrepancy with the SFT results. If the modified
$O(g_2)$ matrix elements are used, the $O(g_2^2)$ anomalous dimensions are
exactly reproduced without the need for a contact interaction in the single
string sector. |
Dilogarithm ladders from Wilson loops: We consider a light-like Wilson loop in N=4 SYM evaluated on a regular
n-polygon contour. Sending the number of edges to infinity the polygon
approximates a circle and the expectation value of the light-like WL is
expected to tend to the localization result for the circular one. We show this
explicitly at one loop, providing a prescription to deal with the divergences
of the light-like WL and the large n limit. Taking this limit entails
evaluating certain sums of dilogarithms which, for a regular polygon, evaluate
to the same constant independently of n. We show that this occurs thanks to
underpinning dilogarithm identities, related to the so-called polylogarithm
ladders, which appear in rather different contexts of physics and mathematics
and enable us to perform the large n limit analytically. | Counting Vacua in Random Landscapes: It is speculated that the correct theory of fundamental physics includes a
large landscape of states, which can be described as a potential which is a
function of N scalar fields and some number of discrete variables. The
properties of such a landscape are crucial in determining key cosmological
parameters including the dark energy density, the stability of the vacuum, the
naturalness of inflation and the properties of the resulting perturbations, and
the likelihood of bubble nucleation events. We codify an approach to landscape
cosmology based on specifications of the overall form of the landscape
potential and illustrate this approach with a detailed analysis of the
properties of N-dimensional Gaussian random landscapes. We clarify the
correlations between the different matrix elements of the Hessian at the
stationary points of the potential. We show that these potentials generically
contain a large number of minima. More generally, these results elucidate how
random function theory is of central importance to this approach to landscape
cosmology, yielding results that differ substantially from those obtained by
treating the matrix elements of the Hessian as independent random variables. |
Colliding Hadrons as Cosmic Membranes and Possible Signatures of Lost
Momentum: We argue that in the TeV-gravity scenario high energy hadrons colliding on
the 3-brane embedded in D=4+n-dimensional spacetime, with n dimensions smaller
than the hadron size, can be considered as cosmic membranes. In the
5-dimensional case these cosmic membranes produce effects similar to cosmic
strings in the 4-dimensional world. We calculate the corrections to the eikonal
approximation for the gravitational scattering of partons due to the presence
of effective hadron cosmic membranes. Cosmic membranes dominate the momentum
lost in the longitudinal direction for colliding particles that opens new
channels for particle decays. | Gauge invariant approach to low-spin anomalous conformal currents and
shadow fields: Conformal low-spin anomalous currents and shadow fields in flat space-time of
dimension greater than or equal to four are studied. Gauge invariant
formulation for such currents and shadow fields is developed. Gauge symmetries
are realized by involving Stueckelberg and auxiliary fields. Gauge invariant
differential constraints for anomalous currents and shadow fields and
realization of global conformal symmetries are obtained. Gauge invariant
two-point vertices for anomalous shadow fields are also obtained. In
Stueckelberg gauge frame, these gauge invariant vertices become the standard
two-point vertices of CFT. Light-cone gauge two-point vertices of the anomalous
shadow fields are derived. AdS/CFT correspondence for anomalous currents and
shadow fields and the respective normalizable and non-normalizable solutions of
massive low-spin AdS fields is studied. The bulk fields are considered in
modified de Donder gauge that leads to decoupled equations of motion. We
demonstrate that leftover on-shell gauge symmetries of bulk massive fields
correspond to gauge symmetries of boundary anomalous currents and shadow
fields, while the modified (Lorentz) de Donder gauge conditions for bulk
massive fields correspond to differential constraints for boundary anomalous
currents and shadow fields. |
Static solutions with nontrivial boundaries for the
Einstein-Gauss-Bonnet theory in vacuum: The classification of certain class of static solutions for the
Einstein-Gauss-Bonnet theory in vacuum is performed in $d\geq5$ dimensions. The
class of metrics under consideration is such that the spacelike section is a
warped product of the real line and an arbitrary base manifold. It is shown
that for a generic value of the Gauss-Bonnet coupling, the base manifold must
be necessarily Einstein, with an additional restriction on its Weyl tensor for
$d>5$. The boundary admits a wider class of geometries only in the special case
when the Gauss-Bonnet coupling is such that the theory admits a unique
maximally symmetric solution. The additional freedom in the boundary metric
enlarges the class of allowed geometries in the bulk, which are classified
within three main branches, containing new black holes and wormholes in vacuum. | Voisin-Borcea Manifolds and Heterotic Orbifold Models: We study the relation between a heterotic T^6/Z6 orbifold model and a
compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with
non-trivial line bundles. This orbifold can be seen as a Z2 quotient of T^4/Z3
x T^2. We consider a two-step resolution, whose intermediate step is (K3 x
T^2)/Z2. This allows us to identify the massless twisted states which
correspond to the geometric Kaehler and complex structure moduli. We work out
the match of the two models when non-zero expectation values are given to all
twisted geometric moduli. We find that even though the orbifold gauge group
contains an SO(10) factor, a possible GUT group, the subgroup after higgsing
does not even include the standard model gauge group. Moreover, after higgsing,
the massless spectrum is non-chiral under the surviving gauge group. |
Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models: We compute the elliptic genus of abelian 2d (0,2) gauge theories
corresponding to brane brick models. These theories are worldvolume theories on
a single D1-brane probing a toric Calabi-Yau 4-fold singularity. We identify a
match with the elliptic genus of the non-linear sigma model on the same
Calabi-Yau background, which is computed using a new localization formula. The
matching implies that the quantum effects do not drastically alter the
correspondence between the geometry and the 2d (0,2) gauge theory. In theories
whose matter sector suffers from abelian gauge anomaly, we propose an ansatz
for an anomaly cancelling term in the integral formula for the elliptic genus.
We provide an example in which two brane brick models related to each other by
Gadde-Gukov-Putrov triality give the same elliptic genus. | Loop Fayet-Iliopoulos terms in $T^2/Z_2$ models: instability and moduli
stabilization: We study Fayet-Iliopoulos (FI) terms of six-dimensional supersymmetric
Abelian gauge theory compactified on a $T^2/Z_2$ orbifold. Such orbifold
compactifications can lead to localized FI-terms and instability of bulk zero
modes. We study 1-loop correction to FI-terms in more general geometry than the
previous works. We find induced FI-terms depend on the complex structure of the
compact space. We also find the complex structure of the torus can be
stabilized at a specific value corresponding to a self-consistent
supersymmetric minimum of the potential by such 1-loop corrections, which is
applicable to the modulus stabilization. |
Black hole excited states from broken translations in Euclidean time: We prepare an excited finite temperature state in ${\cal N}=4$ SYM by means
of a Euclidean path integral with a relevant deformation. The deformation
explicitly breaks imaginary-time translations along the thermal circle whilst
preserving its periodicity. We then study how the state relaxes to thermal
equilibrium in real time. Computations are performed using real-time AdS/CFT,
by constructing novel mixed-signature black holes in numerical relativity
corresponding to Schwinger-Keldysh boundary conditions. These correspond to
deformed cigar geometries in the Euclidean, glued to a pair of dynamical
spacetimes in the Lorentzian.
The maximal extension of the Lorentzian black hole exhibits a `causal
shadow', a bulk region which is spacelike separated from both boundaries. We
show that causal shadows are generic in path-integral prepared states where
imaginary-time translations along the thermal circle are broken. | $\mathcal N=2$ conformal gauge theories at large R-charge: the $SU(N)$
case: Conformal theories with a global symmetry may be studied in the double
scaling regime where the interaction strength is reduced while the global
charge increases. Here, we study generic 4d $\mathcal N=2$ $SU(N)$ gauge
theories with conformal matter content at large R-charge $Q_{\rm R}\to \infty$
with fixed 't Hooft-like coupling $\kappa = Q_{\rm R}\,g_{\rm YM}^{2}$. Our
analysis concerns two distinct classes of natural scaling functions. The first
is built in terms of chiral/anti-chiral two-point functions. The second
involves one-point functions of chiral operators in presence of
$\frac{1}{2}$-BPS Wilson-Maldacena loops. In the rank-1 $SU(2)$ case, the
two-point sector has been recently shown to be captured by an auxiliary chiral
random matrix model. We extend the analysis to $SU(N)$ theories and provide an
algorithm that computes arbitrarily long perturbative expansions for all
considered models, parametric in the rank. The leading and next-to-leading
contributions are cross-checked by a three-loops computation in $\mathcal N=1$
superspace. This perturbative analysis identifies maximally non-planar Feynman
diagrams as the relevant ones in the double scaling limit. In the
Wilson-Maldacena sector, we obtain closed expressions for the scaling
functions, valid for any rank and $\kappa$. As an application, we analyze
quantitatively the large 't Hooft coupling limit $\kappa\gg 1$ where we
identify all perturbative and non-perturbative contributions. The latter are
associated with heavy electric BPS states and the precise correspondence with
their mass spectrum is clarified. |
A new perspective in the dark energy puzzle from particle mixing
phenomenon: We report on recent results on particle mixing and oscillations in quantum
field theory. We discuss the role played in cosmology by the vacuum condensate
induced by the neutrino mixing phenomenon. We show that it can contribute to
the dark energy of the universe. | Does gravitational wave propagate in the five dimensional space-time
with Kaluza-Klein monopole?: The behavior of small perturbations around the Kaluza-Klein monopole in the
five dimensional space-time is investigated. The fact that the odd parity
gravitational wave does not propagate in the five dimensional space-time with
Kaluza-Klein monopole is found provided that the gravitational wave is constant
in the fifth direction. |
Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory: Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling
behavior in the limit when their Lorentz spin grows exponentially with the
twist. To describe the corresponding scaling function in planar N=4 SYM theory,
we analyze an integral equation recently proposed by Freyhult, Rej and
Staudacher and argue that at strong coupling it can be casted into a form
identical to the thermodynamical Bethe Ansatz equations for the nonlinear O(6)
sigma model. This result is in a perfect agreement with the proposal put
forward by Alday and Maldacena within the dual string description, that the
scaling function should coincide with the energy density of the nonlinear O(6)
sigma model embedded into AdS_5xS^5. | Holographic Cosmology and its Relevant Degrees of Freedom: We reconsider the options for cosmological holography. We suggest that a
global and time--symmetric version of the Fischler-Susskind bound is the most
natural generalization of the holographic bound encountered in AdS and De
Sitter space. A consistent discussion of cosmological holography seems to imply
an understanding of the notion of ``number of degrees of freedom'' that
deviates from its simple definition as the entropy of the current state. The
introduction of a more adequate notion of degree of freedom makes the suggested
variation of the Fischler-Susskind bound look like a stringent and viable bound
in all 4--dimensional cosmologies without a cosmological constant. |
Solvable Models in Two-Dimensional N=2 Theories: N=2 supersymmetric field theories in two dimensions have been extensively
studied in the last few years. Many of their properties can be determined along
the whole renormalization group flow, like their coupling dependence and
soliton spectra. We discuss here several models which can be solved completely,
when the number of superfields is taken to be large, by studying their
topological-antitopological fusion equations. These models are the CPN model,
sigma models on Grassmannian manifolds, and certain perturbed $N=2$ Minimal
model. | New Strings for Old Veneziano Amplitudes I.Analytical Treatment: The bosonic string theory evolved as an attempt to find physical/quantum
mechanical model capable of reproducing Euler's beta function (Veneziano
amplitude) and its multidimensional analogue. The multidimensional analogue of
beta function was studied mathematically for some time from different angles by
mathematicians such as Selberg, Weil and Deligne among many others. The results
of their studies apparently were not taken into account in physics literature
on string theory. In recent publication hep-th/0212189 [IJMPA 19 (2004) 1655]
an attempt was made to restore the missing links. The results of this
publication are incomplete, however, since no attempts were made at reproducing
known spectra of both open and closed bosonic string or at restoration of the
underlying model(s) reproducing such spectra. Nevertheless, discussed in this
publication the existing mathematical interpretation of the multidimensional
analogue of Euler's beta function as one of the periods associated with the
corresponding differential form "living" on the Fermat-type (hyper)surfaces,
happens to be crucial for restoration of the quantum/statistical mechanical
model reproducing such generalized beta function. Unlike the traditional
formulations, this new model is supersymmetric. Although details leading to the
restoration of this model are already presented in hep-th/0312294, the present
work is aimed at more focused exposition of some of earlier presented results
and is restricted mainly to the description of analytical properties of the
Veneziano and Veneziano-like amplitudes. As such, it constututes Part I of our
four parts work. Parts 2-4 will be devoted respectively to the group-theoretic,
symplectic and combinatorial treatments of this new string-like supersymmetric
model |
Universal aspects of the phase diagram of QCD with heavy quarks: The flavor dependence of the QCD phase diagram presents universal properties
in the heavy quark limit. For the wide class of models where the quarks are
treated at the one-loop level, we show, for arbitrary chemical potential, that
the flavor dependence of the critical quark masses-for which the
confinement-deconfinement transition is second order-is insensitive to the
details of the (confining) gluon dynamics and that the critical temperature is
constant along the corresponding critical line. We illustrate this with
explicit results in various such one-loop models studied in the literature:
effective matrix models for the Polyakov loop, the Curci-Ferrari model, and a
recently proposed Gribov-Zwanziger-type model. We further observe that the
predictions which follow from this one-loop universality property are well
satisfied by different calculations beyond one-loop order, including lattice
simulations. For degenerate quarks, we propose a simple universal law for the
flavor dependence of the critical mass, satisfied by all approaches. | Quantum Larmor radiation from a moving charge in an electromagnetic
plane wave background: We extend our previous work [Phys. Rev. D83 045030 (2011)], which
investigated the first-order quantum effect in the Larmor radiation from a
moving charge in a spatially homogeneous time-dependent electric field.
Specifically, we investigate the quantum Larmor radiation from a moving charge
in a monochromatic electromagnetic plane wave background based on the scalar
quantum electrodynamics at the lowest order of the perturbation theory. Using
the in-in formalism, we derive the theoretical formula of the total radiation
energy from a charged particle in the initial states being at rest and being in
a relativistic motion. Expanding the theoretical formula in terms of the Planck
constant \hbar, we obtain the first-order quantum effect on the Larmor
radiation. The quantum effect generally suppresses the total radiation energy
compared with the prediction of the classical Larmor formula, which is a
contrast to the previous work. The reason is explained by the fact that the
radiation from a moving charge in a monochromatic electromagnetic plane wave is
expressed in terms of the inelastic collisions between an electron and photons
of the background electromagnetic waves. |
Correlation functions in super Liouville theory: We calculate three- and four-point functions in super Liouville theory
coupled to super Coulomb gas on world sheets with spherical topology. We first
integrate over the zero mode and assume that a parameter takes an integer
value. After calculating the amplitudes, we formally continue the parameter to
an arbitrary real number. Remarkably the result is completely parallel to the
bosonic case, the amplitudes being of the same form as those of the bosonic
case. | Towards a Semiclassical Seismology of Black Holes: Black hole spacetimes are semiclassically not static. For black holes whose
lifetime is larger than the age of the universe we compute, in leading order,
the power spectrum of deviations of the electromagnetic charge from it's
average value, zero. Semiclassically the metric itself has a statistical
interpretation and we compute a lowerbound on its variance. (1 figure, at end
in encapsulated postscript - to locate use 'find figs') |
Consistent deformations of dual formulations of linearized gravity: A
no-go result: The consistent, local, smooth deformations of the dual formulation of
linearized gravity involving a tensor field in the exotic representation of the
Lorentz group with Young symmetry type (D-3,1) (one column of length D-3 and
one column of length 1) are systematically investigated. The rigidity of the
Abelian gauge algebra is first established. We next prove a no-go theorem for
interactions involving at most two derivatives of the fields. | Exotica and discreteness in the classification of string spectra: I discuss the existence of discrete properties in the landscape of free
fermionic heterotic-string vacua that were discovered via their classification
by SO(10) GUT models and its subgroups such as the Pati-Salam, Flipped SU(5)
and SU(4) x SU(2) x U(1) models. The classification is carried out by fixing a
set of basis vectors and varying the GGSO projection coefficients entering the
one-loop partition function. The analysis of the models is facilitated by
deriving algebraic expressions for the GSO projections that enable a
computerised analysis of the entire string spectrum and the scanning of large
spaces of vacua. The analysis reveals discrete symmetries like the
spinor-vector duality observed at the SO(10) level and the existence of
exophobic Pati-Salam vacua. Contrary to the Pati-Salam case the classification
shows that there are no exophobic Flipped SU(5) vacua with an odd number of
generations. It is observed that the SU(4) x SU(2) x U(1) models are
substantially more constrained. |
Scaling Limit of the Ising Model in a Field: The dilute A_3 model is a solvable IRF (interaction round a face) model with
three local states and adjacency conditions encoded by the Dynkin diagram of
the Lie algebra A_3. It can be regarded as a solvable version of an Ising model
at the critical temperature in a magnetic field. One therefore expects the
scaling limit to be governed by Zamolodchikov's integrable perturbation of the
c=1/2 conformal field theory. Indeed, a recent thermodynamic Bethe Ansatz
approach succeeded to unveil the corresponding E_8 structure under certain
assumptions on the nature of the Bethe Ansatz solutions. In order to check
these conjectures, we perform a detailed numerical investigation of the
solutions of the Bethe Ansatz equations for the critical and off-critical
model. Scaling functions for the ground-state corrections and for the lowest
spectral gaps are obtained, which give very precise numerical results for the
lowest mass ratios in the massive scaling limit. While these agree perfectly
with the E_8 mass ratios, we observe one state which seems to violate the
assumptions underlying the thermodynamic Bethe Ansatz calculation. We also
analyze the critical spectrum of the dilute A_3 model, which exhibits massive
excitations on top of the massless states of the Ising conformal field theory. | $EL_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies: We define a generalized form of $L_\infty$-algebras called
$EL_\infty$-algebras. As we show, these provide the natural algebraic framework
for generalized geometry and the symmetries of double field theory as well as
the gauge algebras arising in the tensor hierarchies of gauged supergravity.
Our perspective shows that the kinematical data of the tensor hierarchy is an
adjusted higher gauge theory, which is important for developing finite gauge
transformations as well as non-local descriptions. Mathematically,
$EL_\infty$-algebras provide small resolutions of the operad $\mathcal{L}ie$,
and they shed some light on Loday's problem of integrating Leibniz algebras. |
Perturbative Anti-Brane Potentials in Heterotic M-theory: We derive the perturbative four-dimensional effective theory describing
heterotic M-theory with branes and anti-branes in the bulk space. The
back-reaction of both the branes and anti-branes is explicitly included. To
first order in the heterotic strong-coupling expansion, we find that the forces
on branes and anti-branes vanish and that the KKLT procedure of simply adding
to the supersymmetric theory the probe approximation to the energy density of
the anti-brane reproduces the correct potential. However, there are additional
non-supersymmetric corrections to the gauge-kinetic functions and matter terms.
The new correction to the gauge kinetic functions is important in a discussion
of moduli stabilization. At second order in the strong-coupling expansion, we
find that the forces on the branes and anti-branes become non-vanishing. These
forces are not precisely in the naive form that one may have anticipated and,
being second order in the small parameter of the strong-coupling expansion,
they are relatively weak. This suggests that moduli stabilization in heterotic
models with anti-branes is achievable. | Norm of Bethe-wave functions in the continuum limit: The 6-vertex model with appropriately chosen alternating inhomogeneities
gives the so-called light-cone lattice regularization of the sine-Gordon
(Massive-Thirring) model. In this integrable lattice model we consider pure
hole states above the antiferromagnetic vacuum and express the norm of
Bethe-wave functions in terms of the hole's positions and the counting-function
of the state under consideration. In the light-cone regularized picture pure
hole states correspond to pure soliton (fermion) states of the sine-Gordon
(massive Thirring) model. Hence, we analyze the continuum limit of our new
formula for the norm of the Bethe-wave functions. We show, that the physically
most relevant determinant part of our formula can be expanded in the large
volume limit and turns out to be proportional to the Gaudin-determinant of pure
soliton states in the sine-Gordon model defined in finite volume. |
Weyl Degree of Freedom in The Nambu-Goto String Through Field
Transformation: We show how Weyl degrees of freedom, can be introduced in the Nambu-Goto
string in the path integral formulation using reparametrization invariant
measure. We first identify Weyl degrees in conformal gauge using BFV
formulation. Further we change Nambu-Goto string action to Polyakov action. The
generating functional in light-cone gauge is then obtained from the generating
func- tional corresponding to Polyakov action in conformal gauge by using
suitably constructed finite field dependent BRST transformation. | Quantized cosmological constant in 1+1 dimensional quantum gravity with
coupled scalar matter: A two dimensional matter coupled model of quantum gravity is studied in the
Dirac approach to constrained dynamics in the presence of a cosmological
constant. It is shown that after partial fixing to the conformal gauge the
requirement of a quantum realization of the conformal algebra for physical
quantum states of the fields naturally constrains the cosmological constant to
take values in a well determined and mostly discrete spectrum. Furthermore the
contribution of the quantum fluctuations of the single dynamical degree of
freedom in the gravitational sector, namely the conformal mode, to the
cosmological constant is negative, in contrast to the positive contributions of
the quantum fluctuations of the matter fields, possibly opening an avenue
towards addressing the cosmological constant problem in a more general context. |
New States of Gauge Theories on a Circle: We study a one-dimensional large-N U(N) gauge theory on a circle as a toy
model of higher dimensional Yang-Mills theories at finite temperature. To
investigate the profile of the thermodynamical potential in this model, we
evaluate a stochastic time evolution of several states, and find that an
unstable confinement phase at high temperature does not decay to a stable
deconfinement phase directly. Before it reaches the deconfinement phase, it
develops to several intermediate states. These states are characterised by the
expectation values of the Polyakov loop operators, which wind the temporal
circle different times. We reveal that these intermediate states are the saddle
point solutions of the theory, and similar solutions exist in a wide class of
SU(N) and U(N) gauge theories on S^1 including QCD and pure Yang-Mills theories
in various dimensions. We also consider a Kaluza-Klein gravity, which is the
gravity dual of the one-dimensional gauge theory on a spatial S^1, and show
that these solutions may be related to multi black holes localised on the S^1.
Then we present a connection between the stochastic time evolution of the gauge
theory and the dynamical decay process of a black string though the
Gregory-Laflamme instability. | Spontaneous N=2 --> N=1 local supersymmetry breaking with surviving
local gauge group: Generic partial supersymmetry breaking of $N=2$ supergravity with zero vacuum
energy and with surviving unbroken arbitrary gauge groups is exhibited.
Specific examples are given. |
Double-Well Potential : The WKB Approximation with Phase Loss and
Anharmonicity Effect: We derive a general WKB energy splitting formula in a double-well potential
by incorporating both phase loss and anharmonicity effect in the usual WKB
approximation. A bare application of the phase loss approach to the usual WKB
method gives better results only for large separation between two potential
minima. In the range of substantial tunneling, however, the phase loss approach
with anharmonicity effect considered leads to a great improvement on the
accuracy of the WKB approximation. | How fundamental are fundamental constants?: I argue that the laws of physics should be independent of one's choice of
units or measuring apparatus. This is the case if they are framed in terms of
dimensionless numbers such as the fine structure constant, alpha. For example,
the Standard Model of particle physics has 19 such dimensionless parameters
whose values all observers can agree on, irrespective of what clock, rulers,
scales... they use to measure them. Dimensional constants, on the other hand,
such as h, c, G, e, k..., are merely human constructs whose number and values
differ from one choice of units to the next. In this sense only dimensionless
constants are "fundamental". Similarly, the possible time variation of
dimensionless fundamental "constants" of nature is operationally well-defined
and a legitimate subject of physical enquiry. By contrast, the time variation
of dimensional constants such as c or G on which a good many (in my opinion,
confusing) papers have been written, is a unit-dependent phenomenon on which
different observers might disagree depending on their apparatus. All these
confusions disappear if one asks only unit-independent questions.
We provide a selection of opposing opinions in the literature and respond
accordingly. |
Unitarity in Maxwell-Carroll-Field-Jackiw electrodynamics: In this work we focus on the Carroll-Field-Jackiw (CFJ) modified
electrodynamics in combination with a CPT-even Lorentz-violating contribution.
We add a photon mass term to the Lagrange density and study the question
whether this contribution can render the theory unitary. The analysis is based
on the pole structure of the modified photon propagator as well as the validity
of the optical theorem. We find, indeed, that the massive CFJ-type modification
is unitary at tree-level. This result provides a further example for how a
photon mass can mitigate malign behaviors. | Current-driven tricritical point in large-$N_{c}$ gauge theory: We discover a new tricritical point realized only in non-equilibrium steady
states, using the AdS/CFT correspondence. Our system is a (3+1)-dimensional
strongly-coupled large-$N_{c}$ gauge theory. The tricritical point is
associated with a chiral symmetry breaking under the presence of an electric
current and a magnetic field. The critical exponents agree with those of the
Landau theory of equilibrium phase transitions. This suggests that the presence
of a Landau-like phenomenological theory behind our non-equilibrium phase
transitions. |
A spacetime derivation of the Lorentzian OPE inversion formula: Caron-Huot has recently given an interesting formula that determines OPE data
in a conformal field theory in terms of a weighted integral of the four-point
function over a Lorentzian region of cross-ratio space. We give a new
derivation of this formula based on Wick rotation in spacetime rather than
cross-ratio space. The derivation is simple in two dimensions but more involved
in higher dimensions. We also derive a Lorentzian inversion formula in one
dimension that sheds light on previous observations about the chaos regime in
the SYK model. | Flag manifold sigma models: spin chains and integrable theories: This review is dedicated to two-dimensional sigma models with flag manifold
target spaces, which are generalizations of the familiar $CP^{n-1}$ and
Grassmannian models. They naturally arise in the description of continuum
limits of spin chains, and their phase structure is sensitive to the values of
the topological angles, which are determined by the representations of spins in
the chain. Gapless phases can in certain cases be explained by the presence of
discrete 't Hooft anomalies in the continuum theory. We also discuss integrable
flag manifold sigma models, which provide a generalization of the theory of
integrable models with symmetric target spaces. These models, as well as their
deformations, have an alternative equivalent formulation as bosonic Gross-Neveu
models, which proves useful for demonstrating that the deformed geometries are
solutions of the renormalization group (Ricci flow) equations, as well as for
the analysis of anomalies and for describing potential couplings to fermions. |
N=2 Massive superparticle: the Minimality Principle and the k-symmetry: The electromagnetic interaction of massive superparticles with N=2 extended
Maxwell supermultiplet is studied. It is proved that the minimal coupling
breaks the k-symmetry. A non-minimal k-symmetric action is built and it is
established that the k-symmetry uniquely fixes the value of the superparticle's
anomalous magnetic moment | Fivebrane Lagrangian with Loop Corrections in Field-Theory Limit: Equations of motion and the lagrangian are derived explicitely for Dual D=10,
N=1 Supergravity considered as a field theory limit of a Fivebrane. It is used
the mass-shell solution of Heterotic String Bianchi Identites obtained in the
2-dimensional $\sigma$-model two-loop approximation and in the tree-level
Heterotic String approximation. As a result the Dual Supergravity lagrangian is
derived in the one-loop Five-Brane approximation and in the lowest
6-dimensional $\sigma$-model approximaton. |
Towards Timelike Singularity via AdS Dual: It is well known that Kasner geometry with space-like singularity can be
extended to bulk AdS-like geometry, furthermore one can study field theory on
this Kasner space via its gravity dual. In this paper, we show that there
exists a Kasner-like geometry with timelike singularity for which one can
construct a dual gravity description. We then study various extremal surfaces
including space-like geodesics in the dual gravity description. Finally, we
compute correlators of highly massive operators in the boundary field theory
with a geodesic approximation. | Compressible Matter at a Holographic Interface: We study the interface between a fractional topological insulator and an
ordinary insulator, both described using holography. By turning on a chemical
potential we induce a finite density of matter localized at the interface.
These are gapless surface excitations which are expected to have a fermionic
character. We study the thermodynamics of the system, finding a symmetry
preserving compressible state at low temperatures, whose excitations exhibit
hyperscaling violation. These results are consistent with the expectation of
gapless fermionic excitations forming a Fermi surface at finite density. |
Dual Non-Abelian Duality and the Drinfeld Double: The standard notion of the non-Abelian duality in string theory is
generalized to the class of $\si$-models admitting `non-commutative conserved
charges'. Such $\si$-models can be associated with every Lie bialgebra $(\cg
,\cgt)$ and they possess an isometry group iff the commutant
$[\cgt,\cgt]$ is not equal to $\cgt$. Within the enlarged class of the
backgrounds the non-Abelian duality {\it is} a duality transformation in the
proper sense of the word. It exchanges the roles of $\cg$ and $\cgt$ and it can
be interpreted as a symplectomorphism of the phase spaces of the mutually dual
theories. We give explicit formulas for the non-Abelian duality transformation
for any $(\cg,\cgt)$. The non-Abelian analogue of the Abelian modular space
$O(d,d;{\bf Z})$ consists of all maximally isotropic decompositions of the
corresponding Drinfeld double. | A note on the torque anomaly: I reproduce, in the case of a conical geometry, the torque anomaly recently
noted by Fulling, Mera and Trendafilova for the wedge. The expected
conservation equation is obtained by a variational method and a mathematical
cancellation of the anomaly is exhibited, motivated by the process of
truncating the cone at some inner radius. |
Finite Temperature Tunneling and Phase Transitions in SU(2)-Gauge Theory: A pure Yang-Mills theory extended by addition of a quartic term is considered
in order to study the transition from the quantum tunneling regime to that of
classical, i.e. thermal, behaviour. The periodic field configurations are
found, which interpolate between the vacuum and sphaleron field configurations.
It is shown by explicit calculation that only smooth second order transitions
occur for all permissible values of the parameter $\L$ introduced with the
quartic term. The theory is one of the rare cases which can be handled
analytically. | Gravitational corrections to the Euler-Heisenberg Lagrangian: We use the worldline formalism for calculating the one-loop effective action
for the Einstein-Maxwell background induced by charged scalars or spinors, in
the limit of low energy and weak gravitational field but treating the
electromagnetic field nonperturbatively. The effective action is obtained in a
form which generalizes the standard proper-time representation of the
Euler-Heisenberg Lagrangian. We compare with previous work and discuss possible
applications. |
Generalized action-angle coordinates in toric contact spaces: In this paper we are concerned with completely integrable Hamiltonian systems
in the setting of contact geometry. Unlike the symplectic case, contact
structures are automatically Hamiltonian. Using the Jacobi brackets defined on
contact manifolds, we discuss the commutativity of the first integrals for
contact Hamiltonian systems and introduce the generalized contact action-angle
variables. We exemplify the general scheme in the case of the five-dimensional
toric Sasaki-Einstein spaces $T^{1,1}$ and $Y^{p,q}$. | Spin $ 2 $ spectrum for marginal deformations of 4d $ \mathcal{N}=2 $
SCFTs: We compute spin $ 2 $ spectrum associated with massive graviton fluctuations
in $\gamma$-deformed Gaiotto-Maldacena background those are holographically
dual to marginal deformations of $\mathcal{N}=2$ SCFTs in four dimensions.
Under the special circumstances, we analytically estimate the spectra both for
the $ \gamma $- deformed Abelian T dual (ATD) as well as the non-Abelian T dual
(NATD) cases where we retain ourselves upto leading order in the deformation
parameter. Our analysis reveals a continuous spectra which is associated with
the breaking of the $ U(1) $ isometry (along the directions of the internal
manifold) in the presence of the $ \gamma $- deformation. We also comment on
the effects of adding flavour branes into the picture and the nature of the
associated spin $ 2 $ operators in the dual $ \mathcal{N}=1 $ SCFTs. |
Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons
Theory: Scattering amplitudes in three-dimensional N=6 Chern-Simons theory are shown
to be non-invariant with respect to the free representation of the osp(6|4)
symmetry generators. At tree and one-loop level these "anomalous" terms occur
only for non-generic, singular configurations of the external momenta and can
be used to determine the form of the amplitudes. In particular we show that the
symmetries predict that the one-loop six-point amplitude is non-vanishing and
confirm this by means of an explicit calculation using generalized unitarity
methods. We comment on the implications of this finding for any putative Wilson
loop/amplitude duality in N=6 Chern-Simons theory. | Duality and Topological Quantum Field Theory: We present a summary of the applications of duality to Donaldson-Witten
theory and its generalizations. Special emphasis is made on the computation of
Donaldson invariants in terms of Seiberg-Witten invariants using recent results
in N=2 supersymmetric gauge theory. A brief account on the invariants obtained
in the theory of non-abelian monopoles is also presented. |
Dimensional reduction, magnetic flux strings, and domain walls: We study some consequences of dimensionally reducing systems with massless
fermions and Abelian gauge fields from 3+1 to 2+1 dimensions. We first consider
fermions in the presence of an external Abelian gauge field. In the reduced
theory, obtained by compactifying one of the coordinates `a la Kaluza-Klein,
magnetic flux strings are mapped into domain wall defects. Fermionic zero
modes, localized around the flux strings of the 3+1 dimensional theory, become
also zero modes in the reduced theory, via the Callan and Harvey mechanism, and
are concentrated around the domain wall defects. We also study a dynamical
model: massless $QED_4$, with fermions confined to a plane, deriving the
effective action that describes the `planar' system. | Exact $\mathcal{N}=2^{*}$ Schur line defect correlators: We study the Schur line defect correlation functions in $\mathcal{N}=4$ and
$\mathcal{N}=2^*$ $U(N)$ super Yang-Mills (SYM) theory. We find exact
closed-form formulae of the correlation functions of the Wilson line operators
in the fundamental, antisymmetric and symmetric representations via the
Fermi-gas method in the canonical and grand canonical ensembles. All the Schur
line defect correlators are shown to be expressible in terms of multiple series
that generalizes the Kronecker theta function. From the large $N$ correlators
we obtain generating functions for the spectra of the D5-brane giant and the
D3-brane dual giant and find a correspondence between the fluctuation modes and
the plane partition diamonds. |
Affine Lie Algebras and S-Duality of N=4 Super Yang-Mills Theory for ADE
Gauge Groups on K3: We attempt to determine the partition function of ${\cal N}=4$ super
Yang-Mills theory for $ADE$ gauge groups on $K3$ and investigate the relation
with affine Lie algebras. In particular we describe eta functions, which
compose SU(N) partition function, by level $N$ $A_{N-1}$ theta functions.
Moreover we find $D,E$ theta functions, which satisfy the Montonen-Olive
duality for $D,E$ partition functions. | Bosonic Matrix Theory and Matrix Dbranes: We develop new tools for an in-depth study of our recent proposal for Matrix
Theory. We construct the anomaly-free and finite planar continuum limit of the
ground state with SO(2^{13}) symmetry matching with the tadpole and tachyon
free IR stable high temperature ground state of the open and closed bosonic
string. The correspondence between large N limits and spacetime effective
actions is demonstrated more generally for an arbitrary D25brane ground state
which might include brane-antibrane pairs or NS-branes and which need not have
an action formulation. Closure of the finite N matrix Lorentz algebra
nevertheless requires that such a ground state is simultaneously charged under
all even rank antisymmetric matrix potentials. Additional invariance under the
gauge symmetry mediated by the one-form matrix potential requires a ground
state charged under the full spectrum of antisymmetric (p+1)-form matrix
potentials with p taking any integer value less than 26. Matrix Dbrane
democracy has a beautiful large N remnant in the form of mixed Chern-Simons
couplings in the effective Lagrangian whenever the one-form gauge symmetry is
nonabelian. |
Monodromy, Duality and Integrability of Two Dimensional String Effective
Action: In this talk, we show how the monodromy matrix, ${\hat{\cal M}}$, can be
constructed for the two dimensional tree level string effective action. The
pole structure of ${\hat{\cal M}}$ is derived using its factorizability
property. It is shown that the monodromy matrix transforms non-trivially under
the non-compact T-duality group, which leaves the effective action invariant
and this can be used to construct the monodromy matrix for more complicated
backgrounds starting from simpler ones. We construct, explicitly, ${\hat{\cal
M}}$ for the exactly solvable Nappi-Witten model, both when B=0 and $B\neq 0$,
where these ideas can be directly checked. | Local charges in involution and hierarchies in integrable sigma-models: Integrable $\sigma$-models, such as the principal chiral model,
${\mathbb{Z}}_T$-coset models for $T \in {\mathbb{Z}}_{\geq 2}$ and their
various integrable deformations, are examples of non-ultralocal integrable
field theories described by (cyclotomic) $r/s$-systems with twist function. In
this general setting, and when the Lie algebra ${\mathfrak{g}}$ underlying the
$r/s$-system is of classical type, we construct an infinite algebra of local
conserved charges in involution, extending the approach of Evans, Hassan,
MacKay and Mountain developed for the principal chiral model and symmetric
space $\sigma$-model. In the present context, the local charges are attached to
certain `regular' zeros of the twist function and have increasing degrees
related to the exponents of the untwisted affine Kac-Moody algebra
$\widehat{{\mathfrak{g}}}$ associated with ${\mathfrak{g}}$. The Hamiltonian
flows of these charges are shown to generate an infinite hierarchy of
compatible integrable equations. |
AdS$_6$/CFT$_5$ with O7-planes: Type IIB AdS$_6$ solutions with orientifold 7-planes are constructed. The
geometry is a warped product of AdS$_6$ and S$^2$ over a Riemann surface
$\Sigma$ and the O7-planes correspond to a particular type of puncture on
$\Sigma$. The solutions are identified as near-horizon limits of $(p,q)$
5-brane webs with O7-planes. The dual 5d SCFTs have relevant deformations to
linear quiver gauge theories which have $SO(\cdot)$ or $USp(\cdot)$ nodes or
$SU(\cdot)$ nodes with hypermultiplets in symmetric or antisymmetric
representations, in addition to $SU(\cdot)$ nodes with fundamental
hypermultiplets. The S$^5$ free energies are obtained holographically and
matched to field theory computations using supersymmetric localization to
support the proposed dualities. | Dual D-Brane Actions: Dual super Dp-brane actions are constructed by carrying out a duality
transformation of the world-volume U(1) gauge field. The resulting world-volume
actions, which contain a (p - 2)-form gauge field, are shown to have the
expected properties. Specifically, the D1-brane and D3-brane transform in ways
that can be understood on the basis of the SL(2, Z) duality of type IIB
superstring theory. Also, the D2-brane and the D4-brane transform in ways that
are expected on the basis of the relationship between type IIA superstring
theory and 11d M theory. For example, the dual D4-brane action is shown to
coincide with the double-dimensional reduction of the recently constructed
M5-brane action. The implications for gauge-fixed D-brane actions are discussed
briefly. |
The Spectral Problem for the q-Knizhnik-Zamolodchikov Equation and
Continuous q-Jacobi Polynomials: The spectral problem for the q-Knizhnik-Zamolodchikov equations for
$U_{q}(\widehat{sl_2}) (0<q<1)$ at arbitrary level $k$ is considered. The case
of two-point functions in the fundamental representation is studied in
detail.The scattering states are given explicitly in terms of continuous
q-Jacobi polynomials, and the $S$-matrix is derived from their asymptotic
behavior. The level zero $S$-matrix is shown to coincide, up to a trivial
factor, with the kink-antikink $S$-matrix for the spin-$\frac{1}{2}$ XXZ
antiferromagnet. In the limit of infinite level we observe connections with
harmonic analysis on $p$-adic groups with the prime $p$ given by $p=q^{-2}$. | Extending the Thermodynamic Form Factor Bootstrap Program: Multiple
particle-hole excitations, crossing symmetry, and reparameterization
invariance: In this study, we further the thermodynamic bootstrap program which involves
a set of recently developed ideas used to determine thermodynamic form factors
of local operators in integrable quantum field theories. These form factors are
essential building blocks for dynamic correlation functions at finite
temperatures or non-equilibrium stationary states. In this work we extend this
program in three ways. Firstly, we demonstrate that the conjectured
annihilation pole axiom is valid in the low energy particle-hole excitations.
Secondly, we introduce a crossing relation, which establishes a connection
between form factors with different excitation content. Typically, the crossing
relation is a consequence of Lorentz invariance, but due to the finite energy
density of the considered states, Lorentz invariance is broken. Nonetheless a
crossing relation involving excitations with both particles and holes can
established using the finite volume representation of the thermodynamic form
factors. Finally, we demonstrate that the thermodynamic form factors satisfy a
reparameterization invariance, an invariance which encompasses crossing.
Reparameterization invariance exploits the fact that the details of the
representation of the thermodynamic state are unimportant. In the course of
developing these results, we demonstrate the internal consistency of the
thermodynamic form factor bootstrap program in a number of ways. Finally, we
provide explicit computations of form factors of conserved charges and
densities with crossed excitations and show our results can be used to infer
information about thermodynamic form factors in the Lieb-Liniger model. |
The fate of stringy AdS vacua and the WGC: The authors of arXiv:1610.01533 have recently proposed a stronger version of
the weak gravity conjecture (WGC), based on which they concluded that all those
non-supersymmetric AdS vacua that can be embedded within a constistent theory
of quantum gravity necessarily develop instabilities. In this paper we further
elaborate on this proposal by arguing that the aforementioned instabilities
have a perturbative nature and arise from the crucial interplay between the
closed and the open string sectors of the theory. | Localizing fields on brane in magnetized backgound: To localize the scalar, fermion, and abelian gauge fields on our 3-brane, a
simple mechanism with a hypothetical "magnetic field" in the bulk is proposed.
This mechanism is to treat all fields in the equal footing without ad hoc
consideration. In addition, the machanism can be easily realized in a flat
dimension six Minkowski space and it works even in the weak coupling limit. |
Geometrodynamical description of two-dimensional electrodynamics: Two-dimensional pure electrodynamics is mapped into two-dimensional gravity
in the first order formalism at classical and quantum levels. Due to the fact
that the degrees of freedom of these two theories do not match, we are enforced
to introduce extra fields from the beginning. These fields are introduced
through a BRST exact boundary term, so they are harmless to the physical
content of the theory. The map between electromagnetism and gravity fields
generate a non-trivial Jacobian, which brings extra features (but also harmless
to the physical content of the gravity theory) at quantum level. | Geometric Representation of Interacting Non-Relativistic Open Strings
using Extended Objects: Non-relativistic charged open strings coupled with Abelian gauge fields are
quantized in a geometric representation that generalizes the Loop
Representation. The model consists of open-strings interacting through a
Kalb-Ramond field in four dimensions. The geometric representation proposed
uses lines and surfaces that can be interpreted as an extension of the picture
of Faraday's lines of classical electromagnetism. This representation results
to be consistent, provided the coupling constant (the "charge" of the string)
is quantized. The Schr\"odinger equation in this representation is also
presented. |
The Prepotential of N=2 SU(2) x SU(2) Supersymmetric Yang-Mills Theory
with Bifundamental Matter: We study the non-perturbative, instanton-corrected effective action of the
N=2 SU(2) x SU(2) supersymmetric Yang-Mills theory with a massless
hypermultiplet in the bifundamental representation. Starting from the
appropriate hyperelliptic curve, we determine the periods and the exact
holomorphic prepotential in a certain weak coupling expansion. We discuss the
dependence of the solution on the parameter q=L2^2/L1^2 and several other
interesting properties. | Towards state locality in quantum field theory: free fermions: Hilbert spaces of states can be constructed in standard quantum field theory
only for infinitely extended spacelike hypersurfaces, precluding a more local
notion of state. In fact, the Reeh-Schlieder Theorem prohibits the localization
of states on pieces of hypersurfaces in the standard formalism. From the point
of view of geometric quantization the problem lies in the non-locality of the
complex structures associated to hypersurfaces in standard quantization. We
show that using a weakened version of the positive formalism puts this problem
into a new perspective. This is a local TQFT type formalism based on
super-operators and mixed state spaces rather than on amplitudes and pure state
spaces as the one of Atiyah-Segal. In particular, we show that in the case of
purely fermionic degrees of freedom the complex structure can be dispensed with
when the notion of state is suitably generalized. These generalized states do
localize on compact hypersurfaces with boundaries. For the simplest case of
free fermionic fields we embed this in a rigorous and functorial quantization
scheme yielding a local description of the quantum theory. Crucially, no
classical data is needed beyond the structures evident from a Lagrangian
setting. When the classical data is augmented with complex structures on
hypersurfaces, the quantum data correspondingly augment to the full positive
formalism. This scheme is applicable to field theory in curved spacetime, but
also to field theories without metric background. |
Emergent Supersymmetry in Local Equilibrium Systems: Many physical processes we observe in nature involve variations of
macroscopic quantities over spatial and temporal scales much larger than
microscopic molecular collision scales and can be considered as in local
thermal equilibrium. In this paper we show that any classical statistical
system in local thermal equilibrium has an emergent supersymmetry at low
energies. We use the framework of non-equilibrium effective field theory for
quantum many-body systems defined on a closed time path contour and consider
its classical limit. Unitarity of time evolution requires introducing
anti-commuting degrees of freedom and BRST symmetry which survive in the
classical limit. The local equilibrium is realized through a $Z_2$ dynamical
KMS symmetry. We show that supersymmetry is equivalent to the combination of
BRST and a specific consequence of the dynamical KMS symmetry, to which we
refer as the special dynamical KMS condition. In particular, we prove a theorem
stating that a system satisfying the special dynamical KMS condition is always
supersymmetrizable. We discuss a number of examples explicitly, including model
A for dynamical critical phenomena, a hydrodynamic theory of nonlinear
diffusion, and fluctuating hydrodynamics for relativistic charged fluids. | Novel Symmetry of Non-Einsteinian Gravity in Two Dimensions: The integrability of $R^2$-gravity with torsion in two dimensions is traced
to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian
phase space. It may be interpreted as a quadratically deformed
$iso(2,1)$-algebra with the deformation consisting of the Casimir operators of
the undeformed algebra. The locally conserved quantity encountered in the
explicit solution is identified as an element of the centre of this algebra.
Specific contractions of the algebra are related to specific limits of the
explicit solutions of this model. |
Large U(1) charges from flux breaking in 4D F-theory models: We study the massless charged spectrum of U(1) gauge fields in F-theory that
arise from flux breaking of a nonabelian group. The U(1) charges that arise in
this way can be very large. In particular, using vertical flux breaking, we
construct an explicit 4D F-theory model with a U(1) decoupled from other gauge
sectors, in which the massless/light fields have charges as large as 657. This
result greatly exceeds prior results in the literature. We argue heuristically
that this result may provide an upper bound on charges for light fields under
decoupled U(1) factors in the F-theory landscape. We also show that the charges
can be even larger when the U(1) is coupled to other gauge groups. | DBI Global Strings: In this note we present global string solutions which are a generalization of
the usual field theory global vortices when the kinetic term is DBI. Such
vortices can result from the spontaneous symmetry breaking in the potential
felt by a D3-brane. In a previous paper (0706.0485), the DBI instanton solution
was constructed which develops a "wrinkle" for stringy heights of the
potential. A similar effect is also seen for the DBI vortex solution. The
wrinkle develops for stringy heights of the potential. One recovers the usual
field theory global string for substringy potentials. As an example of the
symmetry breaking, we consider a mobile D3-brane on the warped deformed
conifold. Symmetry breaking can occur if the structure of the vacuum manifold
of the potential for the D3-brane changes as it moves through the throat
region. |
The $n$-component KP hierarchy and representation theory: Starting from free charged fermions we give equivalent definitions of the
$n\/$-component KP hierarchy, in terms of $\tau\/$-functions $\tau_\alpha\/$
(where $\alpha \in M =\/$ root lattice of $sl_n\/$), in terms of $n \times n\/$
matrix valued wave functions $W_\alpha(\alpha\in M)\/$, and in terms of
pseudodifferential wave operators $P_\alpha(\alpha\in M)\/$. These imply the
deformation and the zero curvature equations. We show that the 2-component KP
hierarchy contains the Davey-Stewartson system and the $n\geq3\/$ component KP
hierarchy continues the $n\/$-wave interaction equations. This allows us to
construct theis solutions. | Note on a Positronium Model from Flow Equations in Front Form Dynamics: In this note we address the problem of solving for the positronium mass
spectrum. We use front-form dynamics together with the method of flow
equations. For a special choice of the similarity function, the calculations
can be simplified by analytically integrating over the azimuthal angle. One
obtains an effective Hamiltonian and we solve numerically for its spectrum.
Comparing our results with different approaches we find encouraging properties
concerning the cutoff dependence of the results. |
Free Abelian 2-Form Gauge Theory: BRST Approach: We discuss various symmetry properties of the Lagrangian density of a four (3
+ 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge
theory is endowed with a Curci-Ferrari type condition which happens to be a key
signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the
above condition that the nilpotent BRST and anti-BRST symmetries of the theory
are found to be absolutely anticommuting in nature. For our present 2-form
gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry
properties of the Lagrangian densities and derive the corresponding conserved
charges. The algebraic structure, obeyed by the above conserved charges, is
deduced and the constraint analysis is performed with the help of the
physicality criteria where the conserved and nilpotent (anti-)BRST charges play
completely independent roles. These physicality conditions lead to the
derivation of the above Curci-Ferrari type restriction, within the framework of
BRST formalism, from the constraint analysis. | On Curvature Expansion of Higher Spin Gauge Theory: We examine the curvature expansion of a the field equations of a
four-dimensional higher spin gauge theory extension of anti-de Sitter gravity.
The theory contains massless particles of spin 0,2,4,... that arise in the
symmetric product of two spin 0 singletons. We cast the curvature expansion
into manifestly covariant form and elucidate the structure of the equations and
observe a significant simplification. |
SIP-potentials and self-similar potentials of Shabat and Spiridonov:
space asymmetric deformation: An appropriateness of a space asymmetry of shape invariant potentials with
scaling of parameters and potentials of Shabat and Spiridonov in calculation of
their forms, wave functions and discrete energy spectra has proved and has
demonstrated on a simple example. Parameters, defined space asymmetry, have
found. A new type of a hyerarchy, in which superpotentials with neighbouring
numbers are connected by space rotation relatively a point of origin of space
coordinates, has proposed. | The Classical Double Copy of a Point Charge: The classical double copy relates solutions to the equations of motion in
gauge theory and in gravity. In this paper, we present two double-copy
formalisms for relating the Coulomb solution in gauge theory to the
two-parameter Janis-Newman-Winicour solution in gravity. The latter is a
static, spherically symmetric, asymptotically flat solution that generically
includes a dilaton field, but also admits the Schwarzschild solution as a
special case. We first present the classical double copy as a perturbative
construction, similar to its formulation for scattering amplitudes, and then
present it as an exact map, with a novel generalisation of the Kerr-Schild
double copy motivated by double field theory. The latter formalism exhibits the
relation between the Kerr-Schild classical double copy and the string theory
origin of the double copy for scattering amplitudes. |
Inflation, moduli (de)stabilization and supersymmetry breaking: We study the cosmological inflation from the viewpoint of the moduli
stabilization. We study the scenario that the superpotential has a large value
during the inflation era enough to stabilize moduli, but it is small in the
true vacuum. This scenario is discussed by using a simple model, one type of
hybrid models. | Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3: We use the reduction of the string dynamics on AdS_4 x CP^3 to the
Neumann-Rosochatius integrable system. All constraints can be expressed simply
in terms of a few parameters. We analyze the giant magnon and single spike
solutions on R_t x CP^3 with two angular momenta in detail and find the
energy-charge relations. The finite-size effects of the giant magnon and single
spike solutions are analyzed. |
Integrable structures in matrix models and physics of 2d-gravity: A review of the appearence of integrable structures in the matrix model
description of $2d$-gravity is presented. Most of ideas are demonstrated at the
technically simple but ideologically important examples. Matrix models are
considered as a sort of "effective" description of continuum $2d$ field theory
formulation. The main physical role in such description is played by the
Virasoro-$W$ constraints which can be interpreted as a certain unitarity or
factorization constraints. Bith discrete and continuum (Generalized Kontsevich)
models are formulated as the solutions to those discrete (continuous)
Virasoro-$W$ constraints. Their integrability properties are proven using
mostly the determinant technique highly related to the representation in terms
of free fields. The paper also contains some new observations connected to
formulation of more general than GKM solutions and deeper understanding of
their relation to $2d$ gravity. | JT gravity, KdV equations and macroscopic loop operators: We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in
asymptotically Euclidean $AdS_2$ background using the matrix model description
recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that
the partition function of JT gravity is written as the expectation value of a
macroscopic loop operator in the old matrix model of 2d gravity in the
background where infinitely many couplings are turned on in a specific way.
Based on this expression we develop a very efficient method of computing the
partition function in the genus expansion as well as in the low temperature
expansion by making use of the Korteweg-de Vries constraints obeyed by the
partition function. We have computed both these expansions up to very high
orders using this method. It turns out that we can take a low temperature limit
with the ratio of the temperature and the genus counting parameter held fixed.
We find the first few orders of the expansion of the free energy in a closed
form in this scaling limit. We also study numerically the behavior of the
eigenvalue density and the Baker-Akhiezer function using the results in the
scaling limit. |
On the Poincare polynomials for Landau-Ginzburg Orbifolds: We construct the Poincare polynomials for Landau-Ginzburg orbifolds with
projection operators.Using them we show that special types of dualities
including Poincare duality are realized under certain conditions. When
Calabi-Yau interpretation exists, two simple formulae for Hodge numbers
$h^{2,1}$ and $h^{1,1}$ are obtained. | Flux tube solutions in noncommutative gauge theories: We derive nonperturbative classical solutions of noncommutative U(1) gauge
theory, with or without a Higgs field, representing static magnetic flux tubes
with arbitrary cross-section. The fields are nonperturbatively different from
the vacuum in at least some region of space. The flux of these tubes is
quantized in natural units. We also point out that magnetic monopole charge can
be fractionized by embedding the monopoles in a constant magnetic field. |
Finite Groups and Quantum Yang-Baxter Equation: We construct integrable modifications of 2d lattice gauge theories with
finite gauge groups. | "Stringy" Coherent States Inspired By Generalized Uncertainty Principle: In this Letter we have explicitly constructed Generalized Coherent States for
the Non-Commutative Harmonic Oscillator that directly satisfy the Generalized
Uncertainty Principle (GUP). Our results have a smooth commutative limit. The
states show fractional revival which provides an independent bound on the GUP
parameter. Using this and similar bounds we derive the largest possible value
of the (GUP induced) minimum length scale. Mandel parameter analysis shows that
the statistics is Sub-Poissionian. |
Vacuum Force and Confinement: We show that confinement of quarks and gluons can be explained by their
interaction with the vacuum Abelian gauge field $A_{\sf{vac}}$, which is
implicitly introduced by the canonical commutation relations and generates the
vacuum force. The background gauge field $A_{\sf{vac}}$, linear in coordinates
of $\mathbb{R}^3$, is inherently present in quantum mechanics: it is introduced
during the canonical quantization of phase space $(T^*\mathbb{R}^3, \omega )$
of a nonrelativistic particle, when a potential $\theta$ of the symplectic
2-form $\omega =\mathrm{d}\theta$ on $T^*\mathbb{R}^3$ is mapped into a
connection $A_{\sf{vac}}=-\mathrm{i}\theta$ on a complex line bundle
$L_{\sf{v}}$ over $T^*\mathbb{R}^3$ with gauge group U(1)$_{\sf{v}}$ and
curvature $F_{\sf{vac}}=\mathrm{d} A_{\sf{vac}}=-\mathrm{i}\omega$.
Generalizing this correspondence to the relativistic phase space
$T^*\mathbb{R}^{3,1}$, we extend the Dirac equation from $\mathbb{R}^{3,1}$ to
$T^*\mathbb{R}^{3,1}$ while maintaining the condition that fermions depend only
on $x\in\mathbb{R}^{3,1}$. The generalized Dirac equation contains the
interaction of fermions with $A_{\sf{vac}}$ and has particle-like solutions
localized in space. Thus, the wave-particle duality can be explained by turning
on or off the interaction with the vacuum field $A_{\sf{vac}}$. Accordingly,
confinement of quarks and gluons can be explained by the fact that their
interaction with $A_{\sf{vac}}$ is always on and therefore they can only exist
in bound states in the form of hadrons. | Link Homology from Homological Mirror Symmetry: We explain how to calculate link homology for a Lie algebra $\mathfrak{g}$
using the Fukaya category associated to a 2d A-model. Links are represented as
configurations of particular A-branes and link homology is given by Homs
between these A-branes. In the case of $\mathfrak{g}=\mathfrak{su}_2$, we
explain how to explicitly construct projective resolutions of the relevant
A-branes in terms of thimbles, whose algebra is known. This gives an explicit
algorithm for computing Khovanov homology. This algorithm can be extended to
all Lie algebras. |
Localization of supersymmetric field theories on non-compact hyperbolic
three-manifolds: We study supersymmetric gauge theories with an R-symmetry, defined on
non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a
supersymmetry-preserving quotient of Euclidean AdS$_3$. We compute the exact
partition function in these theories, using the method of localization, thus
reducing the problem to the computation of one-loop determinants around a
supersymmetric locus. We evaluate the one-loop determinants employing three
different techniques: an index theorem, the method of pairing of eigenvalues,
and the heat kernel method. Along the way, we discuss aspects of supersymmetry
in manifolds with a conformal boundary, including supersymmetric actions and
boundary conditions. | A novel non-perturbative approach to String Cosmology: We develop an exact functional method applied to the bosonic string on a
shperical world sheet, in graviton and dilaton backgrounds, consistent with
conformal invariance. In this method, quantum fluctuations are controled by the
amplitude of the kinetic term of the corresponding stringy sigma-model, and we
exhibit a novel non-perturbative non-critical string configuration which
appears as a fixed point of our evolution equation. We argue that this string
configuration is an exact solution, valid to all orders in alpha', which is
consistent with string scattering amplitudes. The dilaton configuration is
logarithmic in terms of the string coordinate X^0, and the amplitude of the
corresponding quantum fluctuations is independent of the target space dimension
D; for D=4, the corresponding Universe, in the Einstein frame, is static and
flat. A linearization around this fixed point leads to a slowly expanding,
decelerating Universe, reaching asymptotically (in Einstein time) the Minkowski
Universe. Moreover, the well-known linear (in terms of X^0) dilaton background,
which is a trivial fixed point of our evolution equation, is recovered by our
non trivial fixed point for early times. This feature explains the time
evolution from a linearly expanding Universe to a Minkowski Universe. |
Rotations and e, $ν$ Propagators, Part III: In Parts I and II we showed that e, $\nu$ propagators can be derived from
rotation invariant projection operators, thereby providing examples of how
quantities with spacetime symmetry can be obtained by constraining rotationally
symmetric objects. One constraint is the restriction of the basis; only two
kinds of bases were considered, one for the electron and one for the neutrino.
In this part, we find that, of a wide range of bases each consistent with the
constraint process, only the two kinds of bases considered in Parts I and II
give spacetime symmetric propagators. We interpret the result geometrically.
The spinor representation is unfaithful in four dimensional Euclidean space
which explains why spin 1/2 wave functions have four, not two, components. Then
we show how a basis relates to two planes in four dimensional Euclidean space.
A pair of planes spanning two or three dimensions does not allow spacetime
symmetry. Spacetime symmetry requires two planes that span four dimensions.
PACS: 11.30.-j, 11.30.Cp, and 03.65.Fd | Vacua of M-theory and N=2 strings: String and membrane dynamics may be unified into a theory of 2+2 dimensional
self-dual world-volumes living in a 10+2 dimensional target space. Some of the
vacua of this M-theory are described by the N=(2,1) heterotic string, whose
target space theory describes the world-volume dynamics of 2+2 dimensional
`M-branes'. All classes of string and membrane theories are realized as
particular vacua of the N=(2,1) string: Type IIA/B strings and supermembranes
arise in the standard moduli space of toroidal compactifications, while type
${\rm I}'$ and heterotic strings arise from a $\bf Z_2$ orbifold of the N=2
algebra. Yet another vacuum describes M-theory on a ${\bf T}^5/{\bf Z}_2$
orientifold, the type I string on $ {\bf T}^4$, and the six-dimensional
self-dual string. We find that open membranes carry `Chan-Paton fields' on
their boundaries, providing a common origin for gauge symmetries in M-theory.
The world-volume interactions of M-brane fluctuations agree with those of
Born-Infeld effective dynamics of the Dirichlet two-brane in the presence of a
non-vanishing electromagnetic field on the brane. |
Two Dimensional Quantum (4,4) Null Superstring in de Sitter Space: The (4,4) null superstring equations of motions and constraints on de Sitter
space are given by using the harmonic superspace. These are solved explicitly
by performing a perturbative expansion of the (4,4) superstring coordinates in
powers of c2, the world-sheet speed of light. The analytic expressions of the
zeroth and first order solutions are determined. On the other hand, we study
the quantization of the (4,4)null superstring in de Sitter space and we
describe its superalgebra. | Duality Induced Reflections and CPT: The linear particle-antiparticle conjugation $\ty C$ and position space
reflection $\ty P$ as well as the antilinear time reflection $\ty T$ are shown
to be inducable by the selfduality of representations for the operation groups
$\SU(2)$, $\SL(\C^2)$ and $\R$ for spin, Lorentz transformations and time
translations resp. The definition of a colour compatible linear
$\ty{CP}$-reflection for quarks as selfduality induced is impossible since
triplet and antitriplet $\SU(3)$-representations are not linearly equivalent. |
Contravariant Gravity on Poisson Manifolds and Einstein Gravity: A relation between gravity on Poisson manifolds proposed in arXiv:1508.05706
and Einstein gravity is investigated. The compatibility of the Poisson and
Riemann structures defines a unique connection, the contravariant Levi-Civita
connection, and leads to the idea of the contravariant gravity. The
Einstein-Hilbert-type action yields an equation of motion which is written in
terms of the analog of the Einstein tensor, and it includes couplings between
the metric and the Poisson tensor. The study of the Weyl transformation reveals
properties of those interactions. It is argued that this theory can have an
equivalent description as a system of Einstein gravity coupled to matter. As an
example, it is shown that the contravariant gravity on a two-dimensional
Poisson manifold can be described by a real scalar field coupled to the metric
in a specific manner. | Phase transitions in thick branes endorsed by entropic information: The so-called configurational entropy (CE) framework has proved to be an
efficient instrument to study nonlinear scalar field models featuring solutions
with spatially-localized energy, since its proposal by Gleiser and Stamapoulos.
Therefore, in this work, we apply this new physical quantity in order to
investigate the properties of degenerate Bloch branes. We show that it is
possible to construct a configurational entropy measure in functional space
from the field configurations, where a complete set of exact solutions for the
model studied displays both double and single-kink configurations. Our study
shows a rich internal structure of the configurations, where we observe that
the field configurations undergo a quick phase transition, which is endorsed by
information entropy. Furthermore, the Bloch configurational entropy is employed
to demonstrate a high organisational degree in the structure of the
configurations of the system, stating that there is a best ordering for the
solutions. |
A Microscopical Description of Giant Gravitons: We construct a non-Abelian world volume effective action for a system of
multiple M-theory gravitons. This action contains multipole moment couplings to
the eleven-dimensional background potentials. We use these couplings to study,
from the microscopical point of view, giant graviton configurations where the
gravitons expand into an M2-brane, with the topology of a fuzzy 2-sphere, that
lives in the spherical part of the AdS_7 x S^4 background or in the AdS part of
AdS_4 x S^7. When the number of gravitons is large we find perfect agreement
with the Abelian, macroscopical description of giant gravitons given in the
literature. | Three-loop renormalization of the quantum action for a four-dimensional
scalar model with quartic interaction with the usage of the background field
method and a cutoff regularization: The paper studies the quantum action for the four-dimensional real
$\phi^4$-theory in the case of a general formulation using the background field
method. The three-loop renormalization is performed with the usage of a cutoff
regularization in the coordinate representation. The absence of non-local
singular contributions and the correctness of the renormalization
$\mathcal{R}$-operation on the example of separate three-loop diagrams are also
discussed. The explicit form of the first three coefficients for the
renormalization constants and for the $\beta$-function is presented.
Consistency with previously known results is shown. |
Gauging of Lorentz Group WZW Model by its Null Subgroup: We consider the standard vector gauging of Lorentz group $ SO(3,1) $ WZW
model by its non-semisimple null Euclidean subgroup in two dimensions $ E(2) $.
The resultant effective action of the theory is seen to describe a one
dimensional bosonic field in the presence of external charge that we interpret
it as a Liouville field. Gauging a boosted $ SO(3) $ subgroup, we find that in
the limit of the large boost, the theory can be interpreted as an interacting
Toda theory. We also take the generalized non-standard bilinear form for
$SO(3,1) $ and gauge both $ SO(3) $ and $E(2)$ subgroups and discuss the
resultant theories. | Baryonic sphere: a spherical domain wall carrying baryon number: We construct a spherical domain wall which has baryon charge distributed on a
sphere of finite radius in a Skyrme model with a sixth order derivative term
and a modified mass term. Its distribution of energy density likewise takes the
form of a sphere. In order to localize the domain wall at a finite radius we
need a negative coefficient in front of the Skyrme term and a positive
coefficient of the sixth order derivative term to stabilize the soliton.
Increasing the pion mass pronounces the shell-like structure of the
configuration. |
Solution of the dispersionless Hirota equations: The dispersionless differential Fay identity is shown to be equivalent to a
kernel expansion providing a universal algebraic characterization and solution
of the dispersionless Hirota equations. Some calculations based on D-bar data
of the action are also indicated. | Universality of anomalous conductivities in theories with
higher-derivative holographic duals: Anomalous chiral conductivities in theories with global anomalies are
independent of whether they are computed in a weakly coupled quantum (or
thermal) field theory, hydrodynamics, or at infinite coupling from holography.
While the presence of dynamical gauge fields and mixed, gauge-global anomalies
can destroy this universality, in their absence, the non-renormalisation of
anomalous Ward identities is expected to be obeyed at all intermediate coupling
strengths. In holography, bulk theories with higher-derivative corrections
incorporate coupling constant corrections to the boundary theory observables in
an expansion around infinite coupling. In this work, we investigate the
coupling constant dependence and universality of anomalous conductivities (and
thus of the anomalous Ward identities) in general, four-dimensional systems
that possess asymptotically anti-de Sitter holographic duals with a
non-extremal black brane in five dimensions, and anomalous transport introduced
into the boundary theory via the bulk Chern-Simons action. We show that in bulk
theories with arbitrary gauge- and diffeomorphism-invariant higher-derivative
actions, anomalous conductivities, which can incorporate an infinite series of
(inverse) coupling constant corrections, remain universal. Owing to the
existence of the membrane paradigm, the proof reduces to a construction of bulk
effective theories at the horizon and the boundary. It only requires us to
impose the condition of horizon regularity and correct boundary conditions on
the fields. We also discuss ways to violate the universality by violating
conditions for the validity of the membrane paradigm, in particular, by adding
mass to the vector fields (a case with a mixed, gauge-global anomaly) and in
bulk geometries with a naked singularity. |
Birth of de Sitter Universe from time crystal: We show that a simple sub-class of Horndeski theory can describe a time
crystal Universe. The time crystal Universe can be regarded as a baby Universe
nucleated from a flat space, which is mediated by an extension of
Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory.
Remarkably, when a cosmological constant is included, de Sitter Universe can be
created by tunneling from the time crystal Universe. It gives rise to a past
completion of an inflationary Universe. | Abrikosov String in N=2 Supersymmetric QED: We study the Abrikosov-Nielsen-Olesen string in N=2 supersymmetric QED with
N=2-preserving superpotential, in which case the Abrikosov string is found to
be 1/2-BPS saturated. Adding a quadratic small perturbation in the
superpotential breaks N=2 supersymmetry to N=1 supersymmetry. Then the
Abrikosov string is no longer BPS saturated. The difference between the string
tensions for the non-BPS and BPS saturated situation is found to be negative to
the first order of the perturbation parameter. |
Gromov-Witten Invariants via Algebraic Geometry: Calculations of the number of curves on a Calabi-Yau manifold via an
instanton expansion do not always agree with what one would expect naively. It
is explained how to account for continuous families of instantons via
deformation theory and excess intersection theory. The essential role played by
degenerate instantons is also explained. This paper is a slightly expanded
version of the author's talk at the June 1995 Trieste Conference on S-Duality
and Mirror Symmetry. | Glueball Spectra from a Matrix Model of Pure Yang-Mills Theory: We present variational estimates for the low-lying energies of a simple
matrix model that approximates $SU(3)$ Yang-Mills theory on a three-sphere of
radius $R$. By fixing the ground state energy, we obtain the (integrated)
renormalization group (RG) equation for the Yang-Mills coupling $g$ as a
function of $R$. This RG equation allows to estimate the masses of other
glueball states, which we find to be in excellent agreement with lattice
simulations. |
A Toy Model for Topology Change Transitions: Role of Curvature
Corrections: We consider properties of near-critical solutions describing a test static
axisymmetric D-dimensional brane interacting with a bulk N-dimensional black
hole (N>D). We focus our attention on the effects connected with curvature
corrections to the brane action. Namely, we demonstrate that the second order
phase transition in such a system is modified and becomes first order. We
discuss possible consequences of these results for merger transitions between
caged black holes and black strings. | Chern-Simons States at Genus One: We present a rigorous analysis of the Schr\"{o}dinger picture quantization
for the $SU(2)$ Chern-Simons theory on 3-manifold torus$\times$line, with
insertions of Wilson lines. The quantum states, defined as gauge covariant
holomorphic functionals of smooth $su(2)$-connections on the torus, are
expressed by degree $2k$ theta-functions satisfying additional conditions. The
conditions are obtained by splitting the space of semistable
$su(2)$-connections into nine submanifolds and by analyzing the behavior of
states at four codimension $1$ strata. We construct the
Knizhnik-Zamolodchikov-Bernard connection allowing to compare the states for
different complex structures of the torus and different positions of the Wilson
lines. By letting two Wilson lines come together, we prove a recursion relation
for the dimensions of the spaces of states which, together with the (unproven)
absence of states for spins$\s>{_1\over^2}$level implies the Verlinde dimension
formula. |
Notes on the bulk viscosity of holographic gauge theory plasmas: A novel technique is used to compute the bulk viscosity of high temperature
holographic gauge theory plasmas with softly broken conformal symmetry. Working
in a black hole background which corresponds to a non-trivial solution to the
Navier-Stokes equation, and using a Ward identity for the trace of the
stress-energy tensor, it is possible to obtain an analytic expression for the
bulk viscosity. This can be used to verify the high temperature limit of a
conjectured bound on the bulk viscosity for these theories. The bound is
saturated when the conformal symmetry-breaking operator becomes marginal. | BRST symmetry for Regge-Teitelboim based minisuperspace models: The Einstein-Hilbert action in the context of Higher derivative theories is
considered for finding out their BRST symmetries. Being a constraint system,
the model is transformed in the minisuperspace language with the FRLW
background and the gauge symmetries are explored. Exploiting the first order
formalism developed by Banerjee et. al. the diffeomorphism symmetry is
extracted. From the general form of the gauge transformations of the field, the
analogous BRST transformations are calculated. The effective Lagrangian is
constructed by considering two gauge fixing conditions. Further, the BRST
(conserved) charge is computed which plays an important role in defining the
physical states from the total Hilbert space of states. The finite field
dependent BRST (FFBRST) formulation is also studied in this context where the
Jacobian for functional measure is illustrated specifically. |
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