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High Energy String Collisions in a Compact Space: When high energy strings scatter at fixed angle, their amplitudes
characteristically fall off exponentially with energy, ${\cal A} \sim \exp(-s
\times const.)$. We show that in a compact space this suppression disappears
for certain kinematic configurations. Amplitudes are power-law behaved and
therefore greatly enhanced. In spacetime this corresponds to fixed-angle
scattering, with fixed transfer in the compact dimensions. On the worldsheet
this process is described by a stationary configuration of effective charges
and vortices with vanishing total energy. It is worldsheet duality---and not
spacetime duality---that plays a role. | Super Yang-Mills, Matrix Models and Geometric Transitions: I explain two applications of the relationship between four dimensional N=1
supersymmetric gauge theories, zero dimensional gauged matrix models, and
geometric transitions in string theory. The first is related to the spectrum of
BPS domain walls or BPS branes. It is shown that one can smoothly interpolate
between a D-brane state, whose weak coupling tension scales as Nc or 1/gs, and
a closed string solitonic state, whose weak coupling tension scales as Nc^2 or
1/gs^2. This is part of a larger theory of N=1 quantum parameter spaces. The
second is a new purely geometric approach to sum exactly over planar diagrams
in zero dimension. It is an example of open/closed string duality. |
Quiver Mutations, Seiberg Duality and Machine Learning: We initiate the study of applications of machine learning to Seiberg duality,
focusing on the case of quiver gauge theories, a problem also of interest in
mathematics in the context of cluster algebras. Within the general theme of
Seiberg duality, we define and explore a variety of interesting questions,
broadly divided into the binary determination of whether a pair of theories
picked from a series of duality classes are dual to each other, as well as the
multi-class determination of the duality class to which a given theory belongs.
We study how the performance of machine learning depends on several variables,
including number of classes and mutation type (finite or infinite). In
addition, we evaluate the relative advantages of Naive Bayes classifiers versus
Convolutional Neural Networks. Finally, we also investigate how the results are
affected by the inclusion of additional data, such as ranks of gauge/flavor
groups and certain variables motivated by the existence of underlying
Diophantine equations. In all questions considered, high accuracy and
confidence can be achieved. | On the semiclassical treatment of Hawking radiation: In the context of the semiclassical treatment of Hawking radiation we prove
the universality of the reduced canonical momentum for the system of a massive
shell self gravitating in a spherical gravitational field within the Painlev\'e
family of gauges. We show that one can construct modes which are regular on the
horizon both by considering as hamiltonian the exterior boundary term and by
using as hamiltonian the interior boundary term. The late time expansion is
given in both approaches and their time Fourier expansion computed to reproduce
the self reaction correction to the Hawking spectrum. |
Note About Canonical Formalism for Normalized Gravity And Vacuum Energy
Sequestering Model: This short note is devoted to the Hamiltonian analysis of the normalized
general relativity and recently proposed model of vacuum energy sequestering.
The common property of these models is the presence of the global variables. We
discuss the meaning of these global variables in the context of the canonical
formalism and argue that their presence lead to the non-local form of the
Hamiltonian constraint. | Black holes and information: A new take on an old paradox: Interest in the black hole information paradox has recently been catalyzed by
the newer "firewall" argument. The crux of the updated argument is that
previous solutions which relied on observer complementarity are in violation of
the quantum condition of monogamy of entanglement; with the prescribed remedy
being to discard the equivalence principle in favor of an energy barrier (or
firewall) at the black hole horizon. Differing points of view have been put
forward, including the "ER=EPR" counterargument and the final-state solution,
both of which can be viewed as potential resolutions to the apparent conflict
between quantum monogamy and Einstein equivalence. After reviewing these recent
developments, this paper argues that the ER=EPR and final-state solutions can
-- thanks to observer complementarity -- be seen as the same resolution of the
paradox but from two different perspectives: inside and outside the black hole. |
Labeling Schemes for Tetrahedron Equations and Dualities between Them: Zamolodchikov's tetrahedron equations, which were derived by considering the
scattering of straight strings, can be written in three different labeling
schemes: one can use as labels the states of the vacua between the strings, the
states of the string segments, or the states of the particles at the
intersections of the strings. We give a detailed derivation of the three
corresponding tetrahedron equations and show also how the Frenkel-Moore
equations fits in as a {\em nonlocal} string labeling. We discuss then how an
analog of the Wu-Kadanoff duality can be defined between each pair of the above
three labeling schemes. It turns out that there are two cases, for which one
can simultaneously construct a duality between {\em all} three pairs of
labelings. | $L_\infty$-algebra of braided electrodynamics: Using the recently developed formalism of braided noncommutative field
theory, we construct an explicit example of braided electrodynamics, that is, a
noncommutative $U(1)$ gauge theory coupled to a Dirac fermion. We construct the
braided $L_\infty$-algebra of this field theory and apply the formalism to
obtain the braided equations of motion, action functional and conserved matter
current. The braided deformation leads to a modification of the charge
conservation. Finally, the Feynman integral appearing in the one-loop
contribution to the vacuum polarization diagram is calculated. There are no
non-planar diagrams, but the UV/IR mixing appears nevertheless. We comment on
this unexpected result. |
Twisted Gauge Theories: Gauge theories on a space-time that is deformed by the Moyal-Weyl product are
constructed by twisting the coproduct for gauge transformations. This way a
deformed Leibniz rule is obtained, which is used to construct gauge invariant
quantities. The connection will be enveloping algebra valued in a particular
representation of the Lie algebra. This gives rise to additional fields, which
couple only weakly via the deformation parameter and reduce in the commutative
limit to free fields. Consistent field equations that lead to conservation laws
are derived and some properties of such theories are discussed. | Landau gauge Jacobian and BRST symmetry: We propose a generalisation of the Faddeev-Popov trick for Yang-Mills fields
in the Landau gauge. The gauge-fixing is achieved as a genuine change of
variables. In particular the Jacobian that appears is the modulus of the
standard Faddeev-Popov determinant. We give a path integral representation of
this in terms of auxiliary bosonic and Grassman fields extended beyond the
usual set for standard Landau gauge BRST. The gauge-fixing Lagrangian density
appearing in this context is local and enjoys a new extended BRST and anti-BRST
symmetry though the gauge-fixing Lagrangian density in this case is not BRST
exact. |
Conformal blocks in Virasoro and W theories: duality and the
Calogero-Sutherland model: We study the properties of the conformal blocks of the conformal field
theories with Virasoro or W-extended symmetry. When the conformal blocks
contain only second-order degenerate fields, the conformal blocks obey second
order differential equations and they can be interpreted as ground-state wave
functions of a trigonometric Calogero-Sutherland Hamiltonian with non-trivial
braiding properties. A generalized duality property relates the two types of
second order degenerate fields. By studying this duality we found that the
excited states of the Calogero-Sutherland Hamiltonian are characterized by two
partitions, or in the case of WA_{k-1} theories by k partitions. By extending
the conformal field theories under consideration by a u(1) field, we find that
we can put in correspondence the states in the Hilbert state of the extended
CFT with the excited non-polynomial eigenstates of the Calogero-Sutherland
Hamiltonian. When the action of the Calogero-Sutherland integrals of motion is
translated on the Hilbert space, they become identical to the integrals of
motion recently discovered by Alba, Fateev, Litvinov and Tarnopolsky in
Liouville theory in the context of the AGT conjecture. Upon bosonisation, these
integrals of motion can be expressed as a sum of two, or in general k, bosonic
Calogero-Sutherland Hamiltonian coupled by an interaction term with a
triangular structure. For special values of the coupling constant, the
conformal blocks can be expressed in terms of Jack polynomials with pairing
properties, and they give electron wave functions for special Fractional
Quantum Hall states | Stringy and Membranic Theory of Swimming of Micro-organisms: When the swimming of micro-organisms is viewed from the string and membrane
theories coupled to the velocity field of the fluid, a number of interesting
results are derived; 1) importance of the area (or volume) preserving algebra,
2) usefulness of the $N$-point Reggeon (membranic) amplitudes, and of the gas
to liquid transition in case of the red tide issues, 3) close relation between
the red tide issue and the generation of Einstein gravity, and 4) possible
understanding of the three different swimming ways of micro-organisms from the
singularity structure of the shape space. |
An Effective Description of the Landscape - II: We continue our analysis of establishing the reliability of "simple"
effective theories where massive fields are "frozen" rather than integrated
out, in a wide class of four dimensional theories with global or local N=1
supersymmetry. We extend our previous work by adding gauge fields and O(1)
Yukawa-like terms for the charged fields in the superpotential. For generic
Kaehler potentials, a meaningful freezing is allowed for chiral multiplets
only, whereas in general heavy vector fields have to properly be integrated
out. Heavy chiral fields can be frozen if they approximately sit to
supersymmetric solutions along their directions and, in supergravity, if the
superpotential at the minimum is small, so that a mass hierarchy between heavy
and light fields is ensured. When the above conditions are met, we show that
the simple effective theory is generally a reliable truncation of the full one. | Exact Half-BPS Flux Solutions in M-theory II: Global solutions
asymptotic to AdS_7 x S^4: General local half-BPS solutions in M-theory, which have $SO(2,2)\times
SO(4)\times SO(4)$ symmetry and are asymptotic to $AdS_{7}\times S^{4}$, were
constructed in exact form by the authors in [arXiv:0806.0605]. In the present
paper, suitable regularity conditions are imposed on these local solutions, and
corresponding globally well-defined solutions are explicitly constructed. The
physical properties of these solutions are analyzed, and interpreted in terms
of the gravity duals to extended 1+1-dimensional half-BPS defects in the
6-dimensional CFT with maximal supersymmetry. |
The signals from the brane-world black Hole: We have studied the wave dynamics and the Hawking radiation for the scalar
field as well as the brane-localized gravitational field in the background of
the braneworld black hole with tidal charge containing information of the extra
dimension. Comparing with the four-dimensional black holes, we have observed
the signature of the tidal charge which presents the signals of the extra
dimension both in the wave dynamics and the Hawking radiation. | Singular Liouville fields and spiky strings in $\rr^{1,2}$ and
$SL(2,\rr)$: The closed string dynamics in $\rr^{1,2}$ and $SL(2,\rr)$ is studied within
the scheme of Pohlmeyer reduction. In both spaces two different classes of
string surfaces are specified by the structure of the fundamental quadratic
forms. The first class in $\rr^{1,2}$ is associated with the standard lightcone
gauge strings and the second class describes spiky strings and their conformal
deformations on the Virasoro coadjoint orbits. These orbits correspond to
singular Liouville fields with the monodromy matrixes $\pm I$. The first class
in $SL(2,\rr)$ is parameterized by the Liouville fields with vanishing chiral
energy functional. Similarly to $\rr^{1,2}$, the second class in $SL(2,\rr)$
describes spiky strings, related to the vacuum configurations of the
$SL(2,\rr)/U(1)$ coset model. |
Subtracted Geometry From Harrison Transformations: We consider the rotating non-extremal black hole of N=2 D=4 STU supergravity
carrying three magnetic charges and one electric charge. We show that its
subtracted geometry is obtained by applying a specific SO(4,4) Harrison
transformation on the black hole. As previously noted, the resulting subtracted
geometry is a solution of the N=2 S=T=U supergravity. | Large-Order Perturbation Theory in Infrared-Unstable Superrenormalizable
Field Theories: We study the factorial divergences of Euclidean $\phi^3_5$, a problem with
connections both to high-energy multiparticle scattering in d=4 and to d=3 (or
high-temperature) gauge theory, which like $\phi^3_5$ is infrared-unstable and
superrenormalizable. At large external momentum p (or small mass M) and large
order N one might expect perturbative bare skeleton graphs to behave roughly
like $N!(ag^2/p)^N$ with a>0, so that no matter how large p is there is an
$N\sim g^2/p$ giving rise to strong perturbative amplitudes. The semi-
classical Lipatov technique (which works only in the presence of a mass) is
blind to this momentum dependence, so we proceed by direct summation of bare
skeleton graphs. We find that the various limits of large N, large p, and small
M do not commute, and that when $N\gg p^2/M^2$ there is a Borel singularity
associated with $g^2/M$, not $g^2/p$. This is described by the zero-momentum
Lipatov technique, and we find the necessary soliton for $\phi^3_5$; the
corresponding sphaleron-like solution for unbroken Yang-Mills theory has long
been known. We also show that the massless theories have no classical solitons.
We discuss non-perturbative effects based partly on known physical arguments
concerning the cancellation by solitons of imaginary parts due to the pert-
urbative Borel singularity, and partly on the dressing of bare skeleton graphs
by dressed propagators showing non-perturbative mass generation, as happens in
d=3 gauge theory. |
The boundary supersymmetric sine-Gordon model revisited: We argue that, contrary to previous claims, the supersymmetric sine-Gordon
model with boundary has a two-parameter family of boundary interactions which
preserves both integrability and supersymmetry. We also propose the
corresponding boundary S matrix for the first supermultiplet of breathers. | Universal black hole stability in four dimensions: We show that four-dimensional black holes become stable below certain mass
when the Einstein-Hilbert action is supplemented with higher-curvature terms.
We prove this to be the case for an infinite family of ghost-free theories
involving terms of arbitrarily high order in curvature. The new black holes,
which are non-hairy generalizations of Schwarzschild's solution, present a
universal thermodynamic behavior for general values of the higher-order
couplings. In particular, small black holes have infinite lifetimes. When the
evaporation process makes the semiclassical approximation break down (something
that occurs after a time which is usually infinite for all practical purposes),
the resulting object retains a huge entropy, in stark contrast with
Schwarzschild's case. |
General Kaluza-Klein black holes with all six independent charges in
five-dimensional minimal supergravity: Using the SL(2,R)-duality in a dimensionally reduced spacetime in (the
bosonic sector of) five-dimensional minimal supergravity, we construct general
Kaluza-Klein black hole solutions which carry six independent charges, its
mass, angular momentum along four dimensions, electric and magnetic charges of
the Maxwell fields in addition to Kaluza-Klein electric and magnetic monopole
charges. | Gauge Defect Networks in Two-Dimensional CFT: An interpretation of the gauge anomaly of the two-dimensional multi-phase
sigma model is presented in terms of an obstruction to the existence of a
topological defect network implementing a local trivialisation of the gauged
sigma model. |
Classification of Solvable Feynman Path Integrals: A systematic classification of Feynman path integrals in quantum mechanics is
presented and a table of solvable path integrals is given which reflects the
progress made during the last ten years or so, including, of course, the main
contributions since the invention of the path integral by Feynman in 1942. An
outline of the general theory is given. Explicit formul\ae\ for the so-called
basic path integrals are presented on which our general scheme to classify and
calculate path integrals in quantum mechanics is based. | Quantum Gravity in 30 Questions: Quantum gravity is the missing piece in our understanding of the fundamental
interactions today. Given recent observational breakthroughs in gravity,
providing a quantum theory for what lies beyond general relativity is more
urgent than ever. However, the complex history of quantum gravity and the
multitude of available approaches can make it difficult to get a grasp of the
topic and its main challenges and opportunities. We provide a guided tour of
quantum gravity in the form of 30 questions, aimed at a mixed audience of
learners and practitioners. The issues covered range from basic motivational
and background material to a critical assessment of the status quo and future
of the subject. The emphasis is on structural issues and our current
understanding of quantum gravity as a quantum field theory of dynamical
geometry beyond perturbation theory. We highlight the identification of quantum
observables and the development of effective numerical tools as critical to
future progress. |
Exact spectrum of the XXZ open spin chain from the q-Onsager algebra
representation theory: The transfer matrix of the XXZ open spin-1/2 chain with general integrable
boundary conditions and generic anisotropy parameter (q is not a root of unity
and |q|=1) is diagonalized using the representation theory of the q-Onsager
algebra. Similarly to the Ising and superintegrable chiral Potts models, the
complete spectrum is expressed in terms of the roots of a characteristic
polynomial of degree d=2^N. The complete family of eigenstates are derived in
terms of rational functions defined on a discrete support which satisfy a
system of coupled recurrence relations. In the special case of linear relations
between left and right boundary parameters for which Bethe-type solutions are
known to exist, our analysis provides an alternative derivation of the results
by Nepomechie et al. and Cao et al.. In the latter case the complete family of
eigenvalues and eigenstates splits in two sets, each associated with a
characteristic polynomial of degree $d< 2^N$. Numerical checks performed for
small values of $N$ support the analysis. | (0,2) Elephants: We enumerate massless E6 singlets for (0,2)-compactifications of the
heterotic string on a Calabi-Yau threefold with the "standard embedding" in
three distinct ways. In the large radius limit of the threefold, these singlets
count deformations of the Calabi-Yau together with its tangent bundle. In the
"small-radius" limit we apply Landau-Ginzburg methods. In the orbifold limit we
use a combination of geometry and free field methods. In general these counts
differ. We show how to identify states between these phases and how certain
states vanish from the massless spectrum as one deforms the complex structure
or Kaehler form away from the Gepner point. The appearance of extra singlets
for particular values of complex structure is explored in all three pictures,
and our results suggest that this does not depend on the Kaehler moduli. |
Deconstructing (2,0) Proposals: We examine the relationships between three proposals for the six-dimensional
(2,0) theory: the DLCQ of hep-th/9707079, hep-th/9712117, the deconstruction
prescription of hep-th/0110146, and the five-dimensional maximally
supersymmetric Yang-Mills proposal of 1012.2880, 1012.2882. We show that
hep-th/0110146 gives a deconstruction of five-dimensional maximally
supersymmetric Yang-Mills. The proposal of hep-th/9707079, hep-th/9712117 uses
a subset of the degrees of freedom of five-dimensional Yang-Mills and we show
that compactification of it on a circle of finite radius agrees with the DLCQ
arising from the proposal of 1012.2880, 1012.2882 or from the deconstruction
proposal of hep-th/0110146. | Loop Equations as a Generalized Virasoro Constraints: The loop equations in the $U(N)$ lattice gauge theory are represented in the
form of constraints imposed on a generating functional for the Wilson loop
correlators. These constraints form a closed algebra with respect to
commutation. This algebra generalizes the Virasoro one, which is known to
appear in one-matrix models in the same way. The realization of this algebra in
terms of the infinitesimal changes of generators of the loop space is given.
The representations on the tensor fields on the loop space, generalizing the
integer spin conformal fields, are constructed. The structure constants of the
algebra under consideration being independent of the coupling constants, almost
all the results are valid in the continuum. |
Effective action for higher spin fields on (A)dS backgrounds: We study the one loop effective action for a class of higher spin fields by
using a first-quantized description. The latter is obtained by considering
spinning particles, characterized by an extended local supersymmetry on the
worldline, that can propagate consistently on conformally flat spaces. The
gauge fixing procedure for calculating the worldline path integral on a loop is
delicate, as the gauge algebra contains nontrivial structure functions.
Restricting the analysis on (A)dS backgrounds simplifies the gauge fixing
procedure, and allows us to produce a useful representation of the one loop
effective action. In particular, we extract the first few heat kernel
coefficients for arbitrary even spacetime dimension D and for spin S identified
by a curvature tensor with the symmetries of a rectangular Young tableau of D/2
rows and [S] columns. | Determinant and Character of W-infinity algebra: We diagonalize the Hilbert space of some subclass of the quasifinite module
of the \Winf algebra. States are classified according to their eigenvalues for
infinitely many commuting charges and the Young diagrams. The parameter
dependence of their norms is explicitly derived. The full character formulae of
the degenerate representations are given as summation of the bilinear
combinations of the Schur polynomials. |
Eternal Inflation with alpha'-Corrections: Higher-order alpha'-corrections are a generic feature of type IIB string
compactifications. In KKLT-like models of moduli stabilization they provide a
mechanism of breaking the no-scale structure of the volume modulus. We present
a model of inflation driven by the volume modulus of flux compactifications of
the type IIB superstring. Using the effects of gaugino condensation on
D7-branes and perturbative alpha'-corrections the volume modulus can be
stabilized in a scalar potential which simultaneously contains saddle points
providing slow-roll inflation with about 130 e-foldings. We can accommodate the
3-year WMAP data with a spectral index of density fluctuations n_s=0.93. Our
model allows for eternal inflation providing the initial conditions of
slow-roll inflation. | Rotating strings and energy loss in non-conformal holography: We study the energy lost by an accelerating quark probe in the quark-gluon
plasma produced in the heavy ion collisions in an approximate setting where the
acceleration of the probe is due to uniform circular motion. The energy loss
rate of the rotating probe is calculated at strong coupling in the confining
SU(N) gauge theory based on N D4 branes on a circle, using the rotating string
solutions in the dual gravitational background. The system is known to exhibit
a confinement-deconfinement transition at a finite temperature T_c. We
investigate energy loss both in the low and the high T phases. The high T phase
is similar to the previously studied case of the conformal plasma, yet we find
qualitative differences due to non-conformality of the underlying theory. The
low T phase, on the other hand exhibits novel interesting behavior: We find a
dual gravitational mechanism that yields a lower bound on the emitted energy of
the rotating quark, proportional to the mass gap in the glueball spectrum. The
low T energy loss is argued to be completely due to glueball brehmstrahlung,
hence the energy loss rate calculated here determines the Lienard potential for
syncrotron radiation in this confining gauge theory at strong coupling. |
Cosmological Time Crystal: Cyclic Universe with a small $Λ$ in a
toy model approach: A new form Time Crystal has been proposed and some of its consequences have
been studied. The model is a generalization of the Friedmann-Robertson-Walker
(FRW) cosmology endowed with noncommutative geometry corrections. In the
mini-superspace approach the scale factor undergoes the time periodic behavior,
or Sisyphus dynamics, which allows us to interpret this Cosmological Time
Crystal as a physically motivated toy model to simulate cyclic universe.
Analyzing our model purely from Time Crystal perspective reveals many novelties
such as a complex singularity structure (more complicated than the previously
encountered swallowtail catastrophe) and a richer form of Sisyphus dynamics. In
the context of cosmology, the system can serve as a toy model in which, apart
from inducing a form of cyclic universe feature, it is possible to generate an
arbitrarily small positive effective Cosmological Constant. We stress that the
model is purely geometrical without introduction of matter degrees of freedom. | Scanning of the Supersymmetry Breaking Scale and the Gravitino Mass in
Supergravity: We consider the minimal three-form ${\cal N}=1$ supergravity coupled to
nilpotent three-form chiral superfields. The supersymmetry breaking is sourced
by the three-forms of the chiral multiplets, while the value of the gravitino
mass is controlled by the three-form of the supergravity multiplet. The
three-forms can nucleate membranes which scan both the supersymmetry breaking
scale and the gravitino mass. The peculiar supergravity feature that the
cosmological constant is the sum of a positive contribution from the
supersymmetry breaking scale and a negative contribution from the gravitino
mass makes the cosmological constant jump. This can lead to a
phenomenologically allowed small value of the cosmological constant even though
the supersymmetry breaking scale and the gravitino mass are dynamically large. |
Off-shell (4,4) supersymmetric sigma models with torsion in harmonic
superspace: We present a manifestly supersymmetric off-shell formulation of a wide class
of $(4,4)$ $2D$ sigma models with torsion and both commuting and non-commuting
left and right complex structures in the harmonic superspace with a double set
of $SU(2)$ harmonic variables. The distinguishing features of the relevant
superfield action are: (i) in general nonabelian and nonlinear gauge invariance
ensuring a correct number of physical degrees of freedom; (ii) an infinite
tower of auxiliary fields. This action is derived from the most general one by
imposing the integrability condition which follows from the commutativity of
the left and right analyticity-preserving harmonic derivatives. For a
particular class of such models we explicitly demonstrate the non-commutativity
of complex structures on the bosonic target. | Stability of self-accelerating Universe in modified gravity with
dynamical torsion: the case of small background torsion: We consider the model of modified gravity with dynamical torsion. This model
was found to have promising stability properties about various backgrounds. The
model admits a self-accelerating solution. We have shown previously that if the
parameters are adjusted in such a way that the torsion is much greater than the
effective cosmological constant, the self-accelerating solution is unstable:
there are exponentially growing modes. Here we study the scalar perturbations
in the case when the torsion is of the order of the effective cosmological
constant. We find that there are no exponential instabilities. |
Electromagnetic radiation in even-dimensional spacetimes: The basic concepts and mathematical constructions of the Maxwell--Lorentz
electrodynamics in flat spacetime of an arbitrary even dimension $d=2n$ are
briefly reviewed. We show that the retarded field strength ${\cal
F}^{(2n)}_{\mu\nu}$ due to a point charge living in a $2n$-dimensional world
can be algebraically expressed in terms of the retarded vector potentials
${\cal A}^{(2m)}_{\mu}$ generated by this charge as if it were accommodated in
$2m$-dimensional worlds nearby, $2\le m\le n+1$. With this finding, the rate of
radiated energy-momentum of the electromagnetic field takes a compact form. | Massive Gravity Theories and limits of Ghost-free Bigravity models: We construct a class of theories which extend New Massive Gravity to higher
orders in curvature in any dimension. The lagrangians arise as limits of a new
class of bimetric theories of Lovelock gravity, which are unitary theories free
from the Boulware-Deser ghost. These Lovelock bigravity models represent the
most general non-chiral ghost-free theories of an interacting massless and
massive spin-two field in any dimension. The scaling limit is taken in such a
way that unitarity is explicitly broken, but the Boulware-Deser ghost remains
absent. This automatically implies the existence of a holographic $c$-theorem
for these theories. We also show that the Born-Infeld extension of New Massive
Gravity falls into our class of models demonstrating that this theory is also
free of the Boulware-Deser ghost. These results extend existing connections
between New Massive Gravity, bigravity theories, Galileon theories and
holographic $c$-theorems. |
Ginsparg-Wilson Relation and Admissibility Condition in Noncommutative
Geometry: Ginsparg-Wilson relation and admissibility condition have the key role to
construct lattice chiral gauge theories. They are also useful to define the
chiral structure in finite noncommutative geometries or matrix models. We
discuss their usefulness briefly. | Solution of the Three--Anyon Problem: We solve, by separation of variables, the problem of three anyons with a
harmonic oscillator potential. The anyonic symmetry conditions from cyclic
permutations are separable in our coordinates. The conditions from two-particle
transpositions are not separable, but can be expressed as reflection symmetry
conditions on the wave function and its normal derivative on the boundary of a
circle. Thus the problem becomes one-dimensional. We solve this problem
numerically by discretization. $N$-point discretization with very small $N$ is
often a good first approximation, on the other hand convergence as $N\to\infty$
is sometimes very slow. |
On quantum group symmetries of conformal field theories: The appearance of quantum groups in conformal field theories is traced back
to the Poisson-Lie symmetries of the classical chiral theory. A geometric
quantization of the classical theory deforms the Poisson-Lie symmetries to the
quantum group ones. This elucidates the fundamental role of chiral symmetries
that quantum groups play in conformal models. As a byproduct, one obtains a
more geometric approach to the representation theory of quantum groups. | Wilsonian renormalisation of CFT correlation functions: Field theory: We examine the precise connection between the exact renormalisation group
with local couplings and the renormalisation of correlation functions of
composite operators in scale-invariant theories. A geometric description of
theory space allows us to select convenient non-linear parametrisations that
serve different purposes. First, we identify normal parameters in which the
renormalisation group flows take their simplest form; normal correlators are
defined by functional differentiation with respect to these parameters. The
renormalised correlation functions are given by the continuum limit of
correlators associated to a cutoff-dependent parametrisation, which can be
related to the renormalisation group flows. The necessary linear and non-linear
counterterms in any arbitrary parametrisation arise in a natural way from a
change of coordinates. We show that, in a class of minimal subtraction schemes,
the renormalised correlators are exactly equal to normal correlators evaluated
at a finite cutoff. To illustrate the formalism and the main results, we
compare standard diagrammatic calculations in a scalar free-field theory with
the structure of the perturbative solutions to the Polchinski equation close to
the Gaussian fixed point. |
Noncommutative Sp(2,R) Gauge Theories - A Field Theory Approach to
Two-Time Physics: Phase-space and its relativistic extension is a natural space for realizing
Sp(2,R) symmetry through canonical transformations. On a Dx2 dimensional
covariant phase-space, we formulate noncommutative field theories, where
Sp(2,R) plays a role as either a global or a gauge symmetry group. In both
cases these field theories have potential applications, including certain
aspects of string theories, M-theory, as well as quantum field theories. If
interpreted as living in lower dimensions, these theories realize Poincare'
symmetry linearly in a way consistent with causality and unitarity. In case
Sp(2,R) is a gauge symmetry, we show that the spacetime signature is determined
dynamically as (D-2,2). The resulting noncommutative Sp(2,R) gauge theory is
proposed as a field theoretical formulation of two-time physics: classical
field dynamics contains all known results of `two-time physics', including the
reduction of physical spacetime from D to (D-2) dimensions, with the associated
`holography' and `duality' properties. In particular, we show that the solution
space of classical noncommutative field equations put all massless scalar,
gauge, gravitational, and higher-spin fields in (D-2) dimensions on
equal-footing, reminiscent of string excitations at zero and infinite tension
limits. | On Theta Dependence of Glueballs from AdS/CFT: We study the theta dependence of the glueball spectrum in a strongly coupled
cousin of large N gluodynamics defined via the AdS/CFT correspondence. By
explicitly diagonalizing the 10d gravity equations in the presence of the RR
3-form and 1-form fluxes we found a mixing pattern for the lowest-spin lightest
glueballs. The mixing between the scalar and pseudoscalar states is not
suppressed, suggesting that the CP-odd effects persist in the large N theory.
As a consequence, the lightest mass eigenstate ceases to be a parity
eigenstate. We found the former as a linear combination of a scalar and
pseudoscalar glueballs. On the other hand, the mass eigenvalues in a theory
with and without the theta term remain equal in the large N limit. |
Non-Connected Gauge Groups and the Plethystic Program: We present in the context of supersymmetric gauge theories an extension of
the Weyl integration formula, first discovered by Robert Wendt, which applies
to a class of non-connected Lie groups. This allows to count in a systematic
way gauge-invariant chiral operators for these non-connected gauge groups.
Applying this technique to $\mathrm{O}(n)$, we obtain, via the ADHM
construction, the Hilbert series for certain instanton moduli spaces. We
validate our general method and check our results via a Coulomb branch
computation, using three-dimensional mirror symmetry. | String creation and cosmology: I argue that string creation may have played a role in reheating the universe
after inflation. For strings in four dimensions that arise from branes wrapping
cycles in the extra dimensions, estimates from effective field theory show that
the string tension need only fall a couple of orders of magnitude below the
Planck scale in order for string creation to extract a significant fraction of
the energy in coherent motion of the inflaton field. I also comment on a
special four-dimensional background which involves only Neveu-Schwarz fields
and offers the possibility of studying closed string creation on the
worldsheet. |
Momentum spectra of particles produced in a single pulse of an electric
field: We study particle creation in a single pulse of an electric field in scalar
quantum electrodynamics. We first identify parameter regions of the theory
where the dynamical pair creation and Schwinger mechanism respectively dominate
each other. Then, analytical expressions for the total characteristics of
particle creation are determined for the case where the Schwinger mechanism
dominates. We also compare our results with those produced in a constant
electric field with a finite-time interval. These results coincide at a strong
field regime, however they differ in general field strength. We identify the
reason of this difference with a nonperturbative effect of high-frequency
photons in external electric fields. | Propagation of a scalar field with non-minimal coupling in three
dimensions: Hawking radiation and Quasinormal modes: In this paper we investigate an exact spectrum of quasi normal modes (QNMs)
for perturbations of a scalar field coupled non-minimally with the Einstein
tensor of an uncharged, non-rotating Banados, Teitelboim, and Zanelli (BTZ)
black hole in three-dimensional spacetime. Due to the geometry around the black
hole, the scalar field encounters an effective potential barrier. We study this
potential numerically and derive exact numerical results for the greybody
factors (GFs) and discuss their profiles in terms of the coupling constant and
black hole parameters. We then proceed to derive the Hawking radiation spectrum
for BTZ black hole. |
Intense radiation from a relativistic electron rotating about a
dielectric ball: The radiation from a relativistic electron uniformly rotating along an orbit
in the equatorial plane of a dielectric ball was calculated taking into account
the dielectric losses of energy and dispersion of electromagnetic oscillations
inside the substance of ball. It was shown that due to the presence of ball the
radiation from the particle at some harmonics may be several dozens of times
more intense than that from the particle rotating in an infinite homogeneous
(and transparent) dielectric. The generation of such a high power radiation is
possible only at some particular values of the ratio of ball radius to that of
electron orbit and when the Cherenkov condition for the ball material and the
velocity of particle "image" on the ball surface is met. | Lorentz Gauge Theory and Spinor Interaction: A gauge theory of the Lorentz group, based on the different behavior of
spinors and vectors under local transformations, is formulated in a flat
space-time and the role of the torsion field within the generalization to
curved space-time is briefly discussed. The spinor interaction with the new
gauge field is then analyzed assuming the time gauge and stationary solutions,
in the non-relativistic limit, are treated to generalize the Pauli equation. |
T-branes, Anomalies and Moduli Spaces in 6D SCFTs: The worldvolume theory of M5-branes on an ADE singularity
$\mathbb{R}^5/\Gamma_G$ can be Higgsed in various ways, corresponding to the
possible nilpotent orbits of $G$. In the F-theory dual picture, this
corresponds to activating T-brane data along two stacks of 7-branes and yields
a tensor branch realization for a large class of 6D SCFTs. In this paper, we
show that the moduli spaces and anomalies of these T-brane theories are related
in a simple, universal way to data of the nilpotent orbits. This often works in
surprising ways and gives a nontrivial confirmation of the conjectured
properties of T-branes in F-theory. We use this result to formally engineer a
class of theories where the IIA picture na\"ively breaks down. We also give a
proof of the $a$-theorem for all RG flows within this class of T-brane
theories. | Exact Microscopic Entropy of Non-Supersymmetric Extremal Black Rings: In this brief note we show that the horizon entropy of the largest known
class of non-supersymmetric extremal black rings, with up to six parameters, is
exactly reproduced for all values of the ring radius using the same conformal
field theory of the four-charge four-dimensional black hole. A particularly
simple case is a dipole black ring without any conserved charges. The mass gets
renormalized, but the first corrections it receives can be easily understood as
an interaction potential energy. Finally, we stress that even if the entropy is
correctly reproduced, this only implies that one sector of chiral excitations
has been identified, but an understanding of excitations in the other sector is
still required in order to capture the black ring dynamics. |
On classical and semiclassical properties of the Liouville theory with
defects: The Lagrangian of the Liouville theory with topological defects is analyzed
in detail and general solution of the corresponding defect equations of motion
is found. We study the heavy and light semiclassical limits of the defect
two-point function found before via the bootstrap program. We show that the
heavy asymptotic limit is given by the exponential of the Liouville action with
defects, evaluated on the solutions with two singular points. We demonstrate
that the light asymptotic limit is given by the finite dimensional path
integral over solutions of the defect equations of motion with a vanishing
energy-momentum tensor. | Non-Abelian Duality in the String Effective Action: We study the symmetry of the one-loop effective action of bosonic string
theory under non-Abelian T-duality transformations. It is shown that the
original Lagrangian and its dual are proportional. This result implies that the
corresponding reduced low energy effective actions are equivalent and leads to
a functional relation between the Weyl anomaly coefficients of the original and
dual two-dimensional non-linear sigma models. {}Finally, we apply this
formalism to some simple examples. |
More on Massive 3D Supergravity: Completing earlier work on three dimensional (3D) N=1 supergravity with
curvature-squared terms, we construct the general supergravity extension of
cosmological massive gravity theories. We expand about supersymmetric anti-de
Sitter vacua, finding the conditions for bulk unitarity and the critical points
in parameter space at which the spectrum changes. We discuss implications for
the dual conformal field theory. | Bulk-boundary thermodynamic equivalence: a topology viewpoint: Setting the cosmological constant to be dynamical, we study the bulk and
boundary thermodynamics of charged Anti-de Sitter black holes. We develop
mass/energy formulas in terms of thermodynamic state functions for the extended
thermodynamics, mixed thermodynamics, and boundary conformal field theory
thermodynamics. We employ the residue method to study the topological
properties of the phase transitions. Our analysis reveals that the bulk and
boundary thermodynamics are topologically equivalent for both criticalities and
first-order phase transitions in the canonical ensembles, as well as for the
Hawking-Page(-like) phase transitions in the grand canonical ensembles.
Additionally, those three kinds of phase transitions are shown to be
distinguished by their unique topological charges. Our results exemplify the
gravity-gauge duality in terms of topology. |
Topological twisted sigma model with H-flux revisited: In this paper we revisit the topological twisted sigma model with H-flux. We
explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian
geometry. we show that the resulting action consists of a BRST exact term and
pullback terms, which only depend on one of the two generalized complex
structures and the B-field. We then discuss the topological feature of the
model. | Superspin chains and supersymmetric gauge theories: We discuss the possible extensions of Bethe/gauge correspondence to quantum
integrable systems based on the super-Lie algebras of A type. Along the way we
propose the analogues of Nakajima quiver varieties whose cohomology and
K-theory should carry the representations of the corresponding Yangian and the
quantum affine algebras, respectively. We end up with comments on the N=4
planar super-Yang-Mills theory in four dimensions. |
Nonlinear Supersymmetry Without the GSO Projection and Unstable D9-Brane: Orientable open string theories containing both bosons and fermions without
the GSO projection are expected to have the 10 dimensional N=2(A) space-time
supersymmetry in a spontaneously broken phase. We study the low-energy theorem
for the nonlinearly realized N=2 supersymmetry using the effective action for
an unstable D9-brane. It is explicitly confirmed that the 4-fermion open string
amplitudes without the GSO projection obey the low-energy theorem derived from
the nonlinear N=2 supersymmetry. An intimate connection between the existence
of the hidden supersymmetry and the open-open string (s-t) duality is pointed
out. | Thermodynamics of Gauss-Bonnet-Dilaton Lifshitz Black Branes: We explore an effective supergravity action in the presence of a massless
gauge field which contains the Gauss-Bonnet term as well as a dilaton field. We
construct a new class of black brane solutions of this theory with the Lifshitz
asymptotic by fixing the parameters of the model such that the asymptotic
Lifshitz behavior can be supported. Then we construct the well-defined finite
action through the use of the counterterm method. We also obtain two
independent constants along the radial coordinate by combining the equations of
motion. Calculations of these two constants at infinity through the use of the
large-$r$ behavior of the metric functions show that our solution respects the
no-hair theorem. Furthermore, we combine these two constants in order to get a
constant $C$ which is proportional to the energy of the black brane. We
calculate this constant at the horizon in terms of the temperature and entropy,
and at large-$r$ in terms of the geometrical mass. By calculating the value of
the energy density through the use of the counterterm method, we obtain the
relation between the energy density, the temperature, and the entropy. This
relation is the generalization of the well-known Smarr formula for AdS black
holes. Finally, we study the thermal stability of our black brane solution and
show that it is stable under thermal perturbations. |
Naturalness via scale invariance and non-trivial UV fixed points in a 4d
O(N) scalar field model in the large-N limit: We try to use scale-invariance and the 1/N expansion to construct a
non-trivial 4d O(N) scalar field model with controlled UV behavior and
naturally light scalar excitations. The principle is to fix interactions at
each order in 1/N by requiring the effective action for arbitrary background
fields to be scale-invariant. We find a line of non-trivial UV fixed-points in
the large-N limit, parameterized by a dimensionless coupling. Nether action nor
measure is scale invariant, but the effective action is. Scale invariance makes
it natural to set a mass deformation to zero. The model has phases where O(N)
invariance is unbroken or spontaneously broken. Masses of the lightest
excitations above the unbroken vacuum are found. Slowly varying quantum
fluctuations are incorporated at order 1/N. We find the 1/N correction to the
potential, beta function of mass and anomalous dimensions of fields that
preserve a line of fixed points for constant backgrounds. | Genuine Dyons in Born-Infeld Electrodynamics: Study of magnetic monopoles in the original version of Born-Infeld (BI)
electrodynamics is performed. It then is realized that interesting new physics
emerge and they include exotic behavior of radial electric monopole field such
as its regularity as $r\to 0$ and its changing behavior with the absence or
presence of the radial magnetic monopole field. This last point has been
interpreted as the manifestation of the existence of point-like dyons in
abelian BI theory. Two pieces of clear evidences in favor of this dyon
interpretation are provided. It is also demonstrated that despite these unique
features having no analogues in standard Maxwell theory, the cherished Dirac
quantisation condition remains unchanged. Lastly, comments are given concerning
that dyons found here in the original version of BI electrodynamics should be
distinguished from the ones with the same name or BIons being studied in the
recent literature on D-brane physics. |
The Infinite Symmetry and Interplay Between Integer and Fractional
Quantum Hall Effect: It is shown, that a spectrum generating algebras and wave functions for the
integral and fractional quantum Hall effect are related by the non-unitary
similarity transformation. This transformation corresponds to the introduction
of the complex Chern-Simons gauge fields, in terms of which the second
quantized form of FQHE can be developed | Boundary renormalisation group flows of unitary superconformal minimal
models: In this paper we investigate renormalisation group flows of supersymmetric
minimal models generated by the boundary perturbing field (\hat
G_{-1/2}\phi_{1,3}). Performing the Truncated Conformal Space Approach analysis
the emerging pattern of the flow structure is consistent with the theoretical
expectations. According to the results, this pattern can be naturally extended
to those cases for which the existing predictions are uncertain. |
Type II strings are Exceptional: We construct the exceptional sigma model: a two-dimensional sigma model
coupled to a supergravity background in a manifestly (formally)
$E_{D(D)}$-covariant manner. This formulation of the background is provided by
Exceptional Field Theory (EFT), which unites the metric and form fields of
supergravity in $E_{D(D)}$ multiplets before compactification. The realisation
of the local symmetries of EFT on the worldsheet uniquely fixes the
Weyl-invariant Lagrangian and allows us to relate our action to the usual type
IIA fundamental string action and a form of the type IIB $(m,n)$ action. This
uniqueness "predicts" the correct form of the couplings to gauge fields in both
Neveu-Schwarz and Ramond sectors, without invoking supersymmetry. | A Superspace formulation of Yang-Mills theory on sphere: A superspace approach to the Becchi-Rouet-Stora-Tyutin (BRST) formalism for
the Yang-Mills theory on an n-dimensional unit sphere, S_1^{n}, is developed in
a manifestly covariant manner based on the rotational supersymmetry
characterized by the supergroup OSp(n+1|2). This is done by employing an
(n+2)-dimensional unit supersphere, S_1^{n|2}, parametrized by n commutative
and 2 anticommutative coordinate variables so that it includes S_1^{n} as a
subspace and realizes the OSp(n+1|2) supersymmetry. In this superspace
formulation, referred to as the supersphere formulation, the so-called
horizontality condition is concisely expressed in terms of the rank-3 field
strength tensor of a Yang-Mills superfield on S_1^{n|2}. The supersphere
formulation completely covers the BRST gauge-fixing procedure for the
Yang-Mills theory on S_1^{n} provided by us [R. Banerjee and S. Deguchi, Phys.
Lett. B 632 (2006) 579, arXiv:hep-th/0509161]. Furthermore, this formulation
admits the (massive) Curci-Ferrari model defined on S_1^{n}, describing the
gauge-fixing and mass terms on S_1^{n} together as a mass term on S_1^{n|2}. |
Heating up the Baryonic Branch with U-duality: a unified picture of
conifold black holes: We study different aspects of a U-duality recently presented by Maldacena and
Martelli and apply it to non-extremal backgrounds. In particular, starting from
new non-extremal wrapped D5 branes we generate new non-extremal generalizations
of the Baryonic Branch of the Klebanov-Strassler solution. We also elaborate on
different conceptual aspects of these U-dualities, like its action on (extremal
and non-extremal) Dp branes, dual models for Yang-Mills-like theories, generic
asymptotics and decoupling limit of the generated solutions. | Chiral vortices in relativistic hydrodynamics: Towards modelling the charge asymmetry observed in heavy ion collisions, we
present here analytic solutions of relativistic hydrodynamics containing parity
violating and anomalous terms at the first order in the hydrodynamic
approximation. These terms can induce chiral magnetic and chiral vortical
effect leading to the generation of the charge asymmetry. We also consider
sphaleron solutions with non trivial winding number to model the phenomenon. We
calculate the net chiral charge difference produced in our solutions. We
anticipate their relevance also in the context of baryogenesis in early
universe, neutron star and some condensed matter situations. |
On Ricci flat Supermanifolds: We study the Ricci flatness condition on generic supermanifolds. It has been
found recently that when the fermionic complex dimension of the supermanifold
is one the vanishing of the super-Ricci curvature implies the bosonic
submanifold has vanishing scalar curvature. We prove that this phenomena is
only restricted to fermionic complex dimension one. Further we conjecture that
for complex fermionic dimension larger than one the Calabi-Yau theorem holds
for supermanifolds. | On the viability of bigravity cosmology: We revisit the question of viability of bigravity cosmology as a candidate
for dark energy. In the context of the low energy limit model, where matter
couples to a single metric, we study linear perturbations around homogeneous
and isotropic backgrounds to derive the Poisson's equation for the Newtonian
potential. Extending to second order perturbations, we identify the Vainshtein
radius below which non-linear scalar self interactions conspire to reproduce GR
on local scales. We combine all of these results to determine the parameter
space that allows a late time de-Sitter attractor compatible with observations
and a successful Vainsthein mechanism. We find that the requirement on having a
successful Vainsthein mechanism is not compatible with the existence of
cosmological solutions at early times. |
Dark energy and dark matter from nonlocal ghost-free gravity theory: We suggest a class of generally covariant ghost-free nonlocal gravity models
generating de Sitter or Anti-de Sitter background with an arbitrary value of
the effective cosmological constant and featuring a mechanism of dark matter
simulation. These models interpolate between the general relativistic phase on
a flat spacetime background and their strongly coupled infrared (Anti)-de
Sitter phase with two propagating massless graviton modes. | On closed-string twist-field correlators and their open-string
descendants: In a recent paper we have proposed the possibility that the lightest massive
string states could be identified with open strings living at intersections of
D-branes forming small angles. In this note, we reconsider the relevant
twist-field correlation functions and perform the analysis of the sub-dominant
physical poles in the various channels. Our derivation is new in that it is
based on the algebraic procedure for the construction of open string models
starting from their closed-string `parents' rather than on the stress-tensor
method. We also indicate possible generalizations and diverse applications of
our approach. |
Memoirs of an Early String Theorist: I worked on String Theory over a period of five years during the First String
Era, the most intellectually satisfying years of my scientific life. One of the
early prospectors in the String Theory Mine, I was fortunate enough to
contribute to the birth of this subject, which retains after these many years,
its magical hold on our imaginations and expectations. | The Spacetime Superalgebras from M-branes in M-brane Backgrounds: We derive the spacetime superalgebras explicitly from ``test'' M-brane
actions in M-brane backgrounds to the lowest order in $\theta$ via canonical
formalism, and discuss various BPS saturated configurations on the basis of
their central charges which depend on the harmonic functions determined by the
backgrounds. All the 1/4 supersymmetric intersections of two M-branes obtained
previously are deduced from the requirement of the test branes to be so ``gauge
fixed'' in the brane backgrounds as to preserve 1/4 supersymmetry. Furthermore,
some of 1/2-supersymmetric bound states of two M-branes are deduced from the
behavior of the harmonic functions in the limits of vanishing distances of the
two branes. The possibilities of some triple intersections preserving 1/4
supersymmetry are also discussed. |
Hořava gravity is asymptotically free (in 2+1 dimensions): We compute the $\beta$-functions of marginal couplings in projectable
Ho\v{r}ava gravity in $2+1$ spacetime dimensions. We show that the
renormalization group flow has an asymptotically-free fixed point in the
ultraviolet (UV), establishing the theory as a UV-complete model with dynamical
gravitational degrees of freedom. Therefore, this theory may serve as a
toy-model to study fundamental aspects of quantum gravity. Our results
represent a step forward towards understanding the UV properties of realistic
versions of Ho\v{r}ava gravity. | A method for obtaining quantum doubles from the Yang-Baxter R-matrices: We develop the approach of Faddeev, Reshetikhin, Takhtajan [1] and of Majid
[2] that enables one to associate a quasitriangular Hopf algebra to every
regular invertible constant solution of the quantum Yang-Baxter equations. We
show that such a Hopf algebra is actually a quantum double. |
$\mathcal{N}=2$ Supersymmetry with Central Charge: A Twofold
Implementation: In this work, we analyze an extended $\mathcal{N}=2$ supersymmetry with
central charge and develop its superspace formulation under two distinct
viewpoints. Initially, in the context of classical mechanics, we discuss the
introduction of deformed supersymmetric derivatives and their consequence on
the deformation of one-dimensional non-linear sigma model. After that,
considering a field-theoretical framework, we present an implementation of this
superalgebra in two dimensions, such that one of the coordinates is related to
the central charge. As an application, in this two-dimensional scenario, we
consider topological (bosonic) configurations of a special self-coupled matter
model and present a non-trivial fermionic solution. | Entanglement Tsunami in (1+1)-Dimensions: We study the time dependence of the entanglement entropy of disjoint
intervals following a global quantum quench in (1+1)-dimensional CFTs at
large-$c$ with a sparse spectrum. The result agrees with a holographic
calculation but differs from the free field theory answer. In particular, a
simple model of free quasiparticle propagation is not adequate for CFTs with a
holographic dual. We elaborate on the entanglement tsunami proposal of Liu and
Suh and show how it can be used to reproduce the holographic answer. |
Fermionic formulas for (1,p) logarithmic model characters in Φ_{2,1}
quasiparticle realisation: We give expressions for the characters of $(1,p)$ logarithmic conformal field
models in the Gordon-type form. The formulas are obtained in terms of
``quasiparticles'' that are Virasoro $\Phi_{2,1}$ primary fields and generalize
the symplectic fermions. | A truly marginal deformation of SL(2,R) in a null direction: We perform a marginal deformation of the SL(2,R) WZW model in a null
direction. If we send the deformation parameter to infinity we obtain a linear
dilaton background plus two free bosons. We show in addition that such a
background can be obtained by a duality transformation of the undeformed WZW
model. In the end we indicate how to generalize the given procedure. |
Biorthogonal Polynomials for Potentials of two Variables and External
Sources at the Denominator: We construct biorthogonal polynomials for a measure over the complex plane
which consists in the exponential of a potential V(z,z*) and in a set of
external sources at the numerator and at the denominator. We use the pseudonorm
of these polynomials to calculate the resolvent integral for correlation
functions of traces of powers of complex matrices (under certain conditions). | Complex geometry of conifolds and 5-brane wrapped on 2-sphere: We investigate solutions of type II supergravity which have the product R^4 x
M^6 structure with non-compact M^6 factor and which preserve at least four
supersymmetries. In particular, we consider various conifolds and the N=1
supersymmetric NS5-brane wrapped on 2-sphere solution recently discussed in
hep-th/0008001. In all of these cases, we explicitly construct the complex
structures, and the Kaehler and parallel (3,0) forms of the corresponding M^6.
In addition, we verify that the above solutions preserve, respectively, eight
and four supersymmetries of type II theory. We also demonstrate that the
ordinary and fractional D3-brane solutions on singular, resolved and deformed
conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as
special cases from a universal ansatz for the supergravity fields and a single
1-d action governing their radial evolution. We show that like the 3-branes on
conifolds, the NS5-brane on 2-sphere background can be found as a solution of
first order system following from a superpotential. |
Noncommutative gauge theories and Lorentz symmetry: We explicitly derive, following a Noether-like approach, the criteria for
preserving Poincare invariance in noncommutative gauge theories. Using these
criteria we discuss the various spacetime symmetries in such theories. It is
shown that, interpreted appropriately, Poincare invariance holds. The analysis
is performed in both the commutative as well as noncommutative descriptions and
a compatibility between the two is also established. | Formation of Spherical D2-brane from Multiple D0-branes: We study D-branes in SU(2) WZW model by means of the boundary state
techniques. We realize the ``fuzzy sphere'' configuration of multiple D0-branes
as the boundary state with the insertion of suitable Wilson line. By making use
of the path-integral representation we show that this boundary state preserves
the appropriate boundary conditions and leads to the Cardy state describing a
spherical D2-brane under the semi-classical approximation. This result directly
implies that the spherical D2-brane in SU(2) WZW model can be well described as
the bound state of D0-branes.
After presenting the supersymmetric extension, we also investigate the BPS
and the non-BPS configurations of D-branes in the NS5 background. We
demonstrate that the non-BPS configurations are actually unstable, since they
always possess the open string tachyons. We further notice that the stable BPS
bound state constructed by the tachyon condensation is naturally interpreted as
the brane configuration of fuzzy sphere. |
Boundary and Interface CFTs from the Conformal Bootstrap: We explore some consequences of the crossing symmetry for defect conformal
field theories, focusing on codimension one defects like flat boundaries or
interfaces. We study surface transitions of the 3d Ising and other O(N) models
through numerical solutions to the crossing equations with the method of
determinants. In the extraordinary transition, where the low-lying spectrum of
the surface operators is known, we use the bootstrap equations to obtain
information on the bulk spectrum of the theory. In the ordinary transition the
knowledge of the low-lying bulk spectrum allows to calculate the scale
dimension of the relevant surface operator, which compares well with known
results of two-loop calculations in 3d. Estimates of various OPE coefficients
are also obtained. We also analyze in 4-epsilon dimensions the renormalization
group interface between the O(N) model and the free theory and check
numerically the results in 3d. | Gauge Theory Wilson Loops and Conformal Toda Field Theory: The partition function of a family of four dimensional N=2 gauge theories has
been recently related to correlation functions of two dimensional conformal
Toda field theories. For SU(2) gauge theories, the associated two dimensional
theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case
the relation has been extended showing that the expectation value of gauge
theory loop operators can be reproduced in Liouville theory inserting in the
correlators the monodromy of chiral degenerate fields. In this paper we study
Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental
representation of the gauge group and show that they are associated to
monodromies of a certain chiral degenerate operator of A_{N-1} Toda field
theory. The orientation of the curve along which the monodromy is evaluated
selects between fundamental and anti-fundamental representation. The analysis
is performed using properties of the monodromy group of the generalized
hypergeometric equation, the differential equation satisfied by a class of four
point functions relevant for our computation. |
Dispersion relations and exact bounds on CFT correlators: We derive new crossing-symmetric dispersion formulae for CFT correlators
restricted to the line. The formulae are equivalent to the sum rules implied by
what we call master functionals, which are analytic extremal functionals which
act on the crossing equation. The dispersion relations provide an equivalent
formulation of the constraints of the Polyakov bootstrap and hence of crossing
symmetry on the line. The built in positivity properties imply simple and exact
lower and upper bounds on the values of general CFT correlators on the
Euclidean section, which are saturated by generalized free fields. Besides
bounds on correlators, we apply this technology to determine new universal
constraints on the Regge limit of arbitrary CFTs and obtain very simple and
accurate representations of the 3d Ising spin correlator. | Brane Tilings as On-shell Diagrams: A new way of computing scattering amplitudes in a certain very important QFT
(N=4 SYM) has recently been developed, in which an algebraic structure called
the positive Grassmannian plays a very important role. The mathematics of the
positive Grassmannian involve, among other things, bipartite graphs, which also
appear in the formulation of a certain class of conformal field theories that
are currently being generalized into Bipartite Field Theories (BFT). The fact
that the same structures appear in two such different realms of physics
suggests a deeper connection between the two that is yet to be fully unveiled.
Here we explore that potential connection by looking at the graphs of a certain
class of BFTs, the brane tilings, in terms of the new mathematics developed for
the computation of the amplitudes. This way we produce a set of data that will
hopefully be useful in the development of that connection. |
String MSSM through flipped SU(5) from Z_{12} orbifold: In a $Z_{12-I}$ orbifold compactification through an intermediate flipped
SU(5), the string MSSM (${\cal S}$MSSM) spectra (three families, one pair of
Higgs doublets, and neutral singlets) are obtained with the Yukawa coupling
structure. The GUT $\sin^2\theta_W^0=\frac38$, even with exotics in the twisted
sector, can be run to the observed electroweak scale value by mass parameters
of vectorlike exotics near the GUT scale. We also obtain R-parity and
doublet-triplet splitting. | Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for
Wormholes: We consider the question of entanglement conservation in the context of the
ER=EPR correspondence equating quantum entanglement with wormholes. In quantum
mechanics, the entanglement between a system and its complement is conserved
under unitary operations that act independently on each; ER=EPR suggests that
an analogous statement should hold for wormholes. We accordingly prove a new
area theorem in general relativity: for a collection of dynamical wormholes and
black holes in a spacetime satisfying the null curvature condition, the maximin
area for a subset of the horizons (giving the largest area attained by the
minimal cross section of the multi-wormhole throat separating the subset from
its complement) is invariant under classical time evolution along the outermost
apparent horizons. The evolution can be completely general, including horizon
mergers and the addition of classical matter satisfying the null energy
condition. This theorem is the gravitational dual of entanglement conservation
and thus constitutes an explicit characterization of the ER=EPR duality in the
classical limit. |
Twenty-five years of two-dimensional rational conformal field theory: In this article we try to give a condensed panoramic view of the development
of two-dimensional rational conformal field theory in the last twenty-five
years. | Quaternionic Root Systems and Subgroups of the $Aut(F_{4})$: Cayley-Dickson doubling procedure is used to construct the root systems of
some celebrated Lie algebras in terms of the integer elements of the division
algebras of real numbers, complex numbers, quaternions and octonions. Starting
with the roots and weights of SU(2) expressed as the real numbers one can
construct the root systems of the Lie algebras of SO(4),SP(2)=
SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the
division algebras. The roots themselves display the group structures besides
the octonionic roots of E_{8} which form a closed octonion algebra. The
automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the
largest crystallographic group in 4-dimensional Euclidean space, is realized as
the direct product of two binary octahedral group of quaternions preserving the
quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such
as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed
as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic
subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192
with different conjugacy classes occur as maximal subgroups in the finite
subgroups of the Lie group $G_{2}$ of orders 12096 and 1344 and proves to be
useful in their constructions. The triality of SO(8) manifesting itself as the
cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used
to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and
F_{4} respectively. |
A note on the three dimensional sine--Gordon equation: Using a simple ansatz for the solutions of the three dimensional
generalization of the sine--Gordon and Toda model introduced by Konopelchenko
and Rogers, a class of solutions is found by elementary methods. It is also
shown that these equations are not evolution equations in the sense that
solution to the initial value problem is not unique. | Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length
Scenario: In this work we calculate the correction to the ground state energy of the
hydrogen atom due to contributions arising from the presence of a minimal
length. The minimal length scenario is introduced by means of modifying the
Dirac equation through a deformed Heisenberg algebra (kempf algebra). With the
introduction of the Coulomb potential in the new Dirac energy operator, we
calculate the energy shift of the ground state of the hydrogen atom in first
order of the parameter related to the minimal length via perturbation theory. |
Consistent truncations with massive modes and holography: We review the basic features of some recently found consistent Kaluza-Klein
truncations including massive modes. We emphasize the general ideas underlying
the reduction procedure, then we focus on type IIB supergravity on
5-dimensional manifolds admitting a Sasaki-Einstein structure, which leads to
half-maximal gauged supergravity in five dimensions. Finally, we comment on the
holographic picture of consistency. | Integrable Structure of $5d$ $\mathcal{N}=1$ Supersymmetric Yang-Mills
and Melting Crystal: We study loop operators of $5d$ $\mathcal{N}=1$ SYM in $\Omega$ background.
For the case of U(1) theory, the generating function of correlation functions
of the loop operators reproduces the partition function of melting crystal
model with external potential. We argue the common integrable structure of $5d$
$\mathcal{N}=1$ SYM and melting crystal model. |
N=2 Born-Infeld Attractors: We derive new types of $U(1)^n$ Born-Infeld actions based on N=2 special
geometry in four dimensions. As in the single vector multiplet (n=1) case, the
non--linear actions originate, in a particular limit, from quadratic
expressions in the Maxwell fields. The dynamics is encoded in a set of
coefficients $d_{ABC}$ related to the third derivative of the holomorphic
prepotential and in an SU(2) triplet of N=2 Fayet-Iliopoulos charges, which
must be suitably chosen to preserve a residual N=1 supersymmetry. | BRST properties of spin fields: For the closed superstring, spin fields and bi-spinor states are defined
directly in four spacetime dimensions. Explicit operator product expansions are
given, including those for the internal superconformal field theory, which are
consistent with locality and BRST invariance for the string vertices. The most
general BRST picture changing for these fields is computed. A covariant
notation for the spin decomposition of these states is developed in which
non-vanishing polarizations are selected automatically. The kinematics of the
three-gluon dual model amplitude in both the Neveu-Schwarz and Ramond sectors
in the Lorentz gauges is calculated and contrasted. Modular invariance and
enhanced gauge symmetry of four-dimensional models incorporating these states
is described. |
Metric-Independent Measures for Supersymmetric Extended Object Theories
on Curved Backgrounds: For Green-Schwarz superstring sigma-model on curved backgrounds, we introduce
a non-metric measure $\Phi \equiv \epsilon^{i j} \epsilon^{I J} (\partial_i
\varphi^I) (\partial_j \varphi^J)$ with two scalars $\varphi^I (I = 1, 2)$ used
in Two Measure Theory (TMT). As in the flat-background case, the string tension
$T= (2 \pi \alpha ' )^{-1}$ emerges as an integration constant for the
A_i-field equation. This mechanism is further generalized to supermembrane
theory, and to super p-brane theory, both on general curved backgrounds. This
shows the universal applications of dynamical measure of TMT to general
supersymmetric extended objects on general curved backgrounds. | A Liouville String Approach to Microscopic Time and Cosmology: In the non-critical string framework that we have proposed recently, the time
$t$ is identified with a dynamical local renormalization group scale, the
Liouville mode, and behaves as a statistical evolution parameter, flowing
irreversibly from an infrared fixed point - which we conjecture to be a
topological string phase - to an ultraviolet one - which corresponds to a
static critical string vacuum. When applied to a toy two-dimensional model of
space-time singularities, this formalism yields an apparent renormalization of
the velocity of light, and a $t$-dependent form of the uncertainty relation for
position and momentum of a test string. We speculate within this framework on a
stringy alternative to conventional field-theoretical inflation, and the decay
towards zero of the cosmological constant in a maximally-symmetric space. |
Fermions in AdS and Gross-Neveu BCFT: We study the boundary critical behavior of conformal field theories of
interacting fermions in the Gross-Neveu universality class. By a Weyl
transformation, the problem can be studied by placing the CFT in an anti de
Sitter space background. After reviewing some aspects of free fermion theories
in AdS, we use both large $N$ methods and the epsilon expansion near 2 and 4
dimensions to study the conformal boundary conditions in the Gross-Neveu CFT.
At large $N$ and general dimension $d$, we find three distinct boundary
conformal phases. Near four dimensions, where the CFT is described by the
Wilson-Fisher fixed point of the Gross-Neveu-Yukawa model, two of these phases
correspond respectively to the choice of Neumann or Dirichlet boundary
condition on the scalar field, while the third one corresponds to the case
where the bulk scalar field acquires a classical expectation value. One may
flow between these boundary critical points by suitable relevant boundary
deformations. We compute the AdS free energy on each of them, and verify that
its value is consistent with the boundary version of the F-theorem. We also
compute some of the BCFT observables in these theories, including bulk
two-point functions of scalar and fermions, and four-point functions of
boundary fermions. | Orbifoldization, covering surfaces and uniformization theory: The connection between the theory of permutation orbifolds, covering surfaces
and uniformization is investigated, and the higher genus partition functions of
an arbitrary permutation orbifold are expressed in terms of those of the
original theory. |
Exceptional geometry and Borcherds superalgebras: We study generalized diffeomorphisms in exceptional geometry with U-duality
group E_{n(n)} from an algebraic point of view. By extending the Lie algebra
e_n to an infinite-dimensional Borcherds superalgebra, involving also the
extension to e_{n+1}, the generalized Lie derivatives can be expressed in a
simple way, and the expressions take the same form for any n less than 8. The
closure of the transformations then follows from the Jacobi identity and the
grading of e_{n+1} with respect to e_n. | Reconstructing the Universe: We provide detailed evidence for the claim that nonperturbative quantum
gravity, defined through state sums of causal triangulated geometries,
possesses a large-scale limit in which the dimension of spacetime is four and
the dynamics of the volume of the universe behaves semiclassically. This is a
first step in reconstructing the universe from a dynamical principle at the
Planck scale, and at the same time provides a nontrivial consistency check of
the method of causal dynamical triangulations. A closer look at the quantum
geometry reveals a number of highly nonclassical aspects, including a dynamical
reduction of spacetime to two dimensions on short scales and a fractal
structure of slices of constant time. |
Scheme invariants in phi^4 theory in four dimensions: We provide an analysis of the structure of renormalisation scheme invariants
for the case of $\phi^4$ theory, relevant in four dimensions. We give a
complete discussion of the invariants up to four loops and include some partial
results at five loops, showing that there are considerably more invariants than
one might naively have expected. We also show that one-vertex reducible
contributions may consistently be omitted in a well-defined class of schemes
which of course includes MSbar. | Colliding Branes in Heterotic M-theory: We study the collision of two flat, parallel end-of-the-world branes in
heterotic M-theory. By insisting that there is no divergence in the Riemann
curvature as the collision approaches, we are able to single out a unique
solution possessing the local geometry of (2d compactified Milne)/Z_2 x R_3,
times a finite-volume Calabi-Yau manifold in the vicinity of the collision. At
a finite time before and after the collision, a second type of singularity
appears momentarily on the negative-tension brane, representing its bouncing
off a zero of the bulk warp factor. We find this singularity to be remarkably
mild and easily regularised. The various different cosmological solutions to
heterotic M-theory previously found by other authors are shown to merely
represent different portions of a unique flat cosmological solution to
heterotic M-theory. |
Non-perturbative evolution equations for the tricritical theory: The N component scalar tricritical theory is considered in a non-perturbative
setting. We derive non-perturbative beta functions for the relevant couplings
in $d\leq 3$. The beta functions are obtained through the use of an exact
evolution equation for the so called effective average action. In d=3 it is
established the existence of an ultraviolet stable fixed point for N>4. This
confirms earlier results obtained using the 1/N expansion where such a fixed
point is believed to exist at least for $N\gtrsim 1000$. | Higher dimensional higher derivative $φ^4$ theory: We construct several towers of scalar quantum field theories with an $O(N)$
symmetry which have higher derivative kinetic terms. The Lagrangians in each
tower are connected by lying in the same universality class at the
$d$-dimensional Wilson-Fisher fixed point. Moreover the universal theory is
studied using the large $N$ expansion and we determine $d$-dimensional critical
exponents to $O(1/N^2)$. We show that these new universality classes emerge
naturally as solutions to the linear relation of the dimensions of the fields
deduced from the underlying force-matter interaction of the universal critical
theory. To substantiate the equivalence of the Lagrangians in each tower we
renormalize each to several loop orders and show that the renormalization group
functions are consistent with the large $N$ critical exponents. While we focus
on the first two new towers of theories and renormalize the respective
Lagrangians to $16$ and $18$ dimensions there are an infinite number of such
towers. We also briefly discuss the conformal windows and the extension of the
ideas to theories with spin-$\frac{1}{2}$ and spin-$1$ fields as well as the
idea of lower dimension completeness. |
Quantum Mechanics on Moduli Spaces: It has been assumed that it is possible to approximate the interactions of
quantized BPS solitons by quantising a dynamical system induced on a moduli
space of soliton parameters. General properties of the reduction of quantum
systems by a Born-Oppenheimer approximation are described here and applied to
sigma models and their moduli spaces in order to learn more about this
approximation. New terms arise from the reduction proceedure, some of them
geometrical and some of them dynamical in nature. The results are generalised
to supersymmetric sigma models, where most of the extra terms vanish. | Universal Deformations: QFTs with local topological operators feature unusual sectors called
"universes," which are separated by infinite-tension domain walls. We show that
such systems have relevant deformations with exactly-calculable effects. These
deformations allow one to dial the vacuum energy densities of the universes. We
describe applications of these deformations to confinement in 2d gauge
theories, as well as a curious violation of the effective field theory
naturalness principle. |
Holographic energy loss in non-relativistic backgrounds: In this paper, we study some aspects of energy loss in non-relativistic
theories from holography. We analyze the energy lost by a rotating heavy point
particle along a circle of radius $l$ with angular velocity $\omega$ in
theories with general dynamical exponent $z$ and hyperscaling violation
exponent $\theta$. It is shown that this problem provides a novel perspective
on the energy loss in such theories. A general computation at zero and finite
temperature is done and it is shown that how the total energy loss rate depends
non-trivially on two characteristic exponents $(z,\theta)$. We find that at
zero temperature there is a special radius $l_c$ where the energy loss is
independent of different values of $(\theta,z)$. Also at zero temperature,
there is a crossover between a regime in which the energy loss is dominated by
the linear drag force and by the radiation because of the acceleration of the
rotating particle. We find that the energy loss of the particle decreases by
increasing $\theta$ and $z$. We note that, unlike in the zero temperature,
there is no special radius $l_c$ at finite temperature case. | On "dynamical mass" generation in Euclidean de Sitter space: We consider the perturbative treatment of the minimally coupled, massless,
self-interacting scalar field in Euclidean de Sitter space. Generalizing work
of Rajaraman, we obtain the dynamical mass m^2 \propto sqrt{lambda} H^2 of the
scalar for non-vanishing Lagrangian masses and the first perturbative quantum
correction in the massless case. We develop the rules of a systematic
perturbative expansion, which treats the zero-mode non-perturbatively, and goes
in powers of sqrt{lambda}. The infrared divergences are self-regulated by the
zero-mode dynamics. Thus, in Euclidean de Sitter space the interacting,
massless scalar field is just as well-defined as the massive field. We then
show that the dynamical mass can be recovered from the diagrammatic expansion
of the self-energy and a consistent solution of the Schwinger-Dyson equation,
but requires the summation of a divergent series of loop diagrams of
arbitrarily high order. Finally, we note that the value of the long-wavelength
mode two-point function in Euclidean de Sitter space agrees at leading order
with the stochastic treatment in Lorentzian de Sitter space, in any number of
dimensions. |
Quantum hoop conjecture: Black hole formation by particle collisions: We address the issue of (quantum) black hole formation by particle collision
in quantum physics. We start by constructing the horizon wave-function for
quantum mechanical states representing two highly boosted non-interacting
particles that collide in flat one-dimensional space. From this wave-function,
we then derive a probability that the system becomes a black hole as a function
of the initial momenta and spatial separation between the particles. This
probability allows us to extend the hoop conjecture to quantum mechanics and
estimate corrections to its classical counterpart. | Massive T-duality in six dimensions: A massive version of T-duality in six dimensions is given, that maps the K3
compactification of Romans' theory onto the K3 compactification of Type IIB
theory. This is done by performing a (standard) Kaluza-Klein reduction on
six-dimensional massive Type IIA and a Scherk-Schwarz reduction on Type IIB,
mapping both theories onto the same five-dimensional theory. We also comment
shortly on the difficulties arising if one intends to construct a massive
generalisation of the six-dimensional string-string duality. |
Asymptotic completeness, global existence and the infrared problem for
the Maxwell-Dirac equations: In this monograph we prove that the nonlinear Lie algebra representation
given by the manifestly covariant Maxwell-Dirac (M-D) equations is integrable
to a global nonlinear representation $U$ of the Poincar\'e group ${\cal P}_0$
on a differentiable manifold ${\cal U}_\infty$ of small initial conditions for
the M-D equations. This solves, in particular, the Cauchy problem for the M-D
equations, namely existence of global solutions for initial data in ${\cal
U}_\infty$ at $t=0$. The existence of modified wave operators $\Omega_+$ and
$\Omega_-$ and asymptotic completeness is proved. The asymptotic
representations $U^{(\epsilon)}_g = \Omega^{-1}_\epsilon \circ U_g \circ
\Omega_\epsilon$, $\epsilon = \pm$, $g \in {\cal P}_0$, turn out to be
nonlinear. A cohomological interpretation of the results in the spirit of
nonlinear representation theory and its connection to the infrared tail of the
electron is given. | A Note on Interactions of (Non-Commutative) Instantons Via AdS/CFT: We consider the interaction between instantons and anti-instantons in
four-dimensional N=4 super-Yang-Mills theory at large N and large 't Hooft
coupling as described by D-instantons via AdS/CFT duality. We give an estimate
of the strength of the interaction in various regimes. We discuss also the case
of Non-Commutative super Yang-Mills theory where the interaction between
instantons and anti-instantons can be used as a way to probe the locality
properties of the theory in the supergravity picture, without explicit
reference to the definition of local operators. |
The Kaluza-Klein Melvin Solution in M-theory: We study some aspects of the Kaluza-Klein Melvin solution in M-theory. The
associated magnetic field has a maximal critical value $B=\pm 1/R$ where $R$ is
the radius of the compactification circle. It is argued that the Melvin
background of type IIA with magnetic field $B$ and of type 0A with magnetic
field $B'=B-1/R$ are equivalent. Evidence for this conjecture is provided using
a further circle compactification and a `9-11' flip. We show that partition
functions of nine-dimensional type IIA strings and of a $(-1)^F\sigma_{1/2}$
type IIA orbifold both with NS-NS Melvin fluxtubes are related by such shift of
the magnetic field. Then the instabilities of both IIA and 0A Melvin solutions
are analyzed. For each theory there is an instanton associated to the decay of
spacetime. In the IIA case the decay mode is associated to the nucleation of
$D6/D\bar{6}$-brane pairs, while in the 0A case spacetime decays through
Witten's bubble production. | Generalizing the $\mathfrak{bms}_{3}$ and 2D-conformal algebras by
expanding the Virasoro algebra: By means of the Lie algebra expansion method, the centrally extended
conformal algebra in two dimensions and the $\mathfrak{bms}_{3}$ algebra are
obtained from the Virasoro algebra. We extend this result to construct new
families of expanded Virasoro algebras that turn out to be infinite dimensional
lifts of the so-called $\mathfrak{B}_{k}$, $\mathfrak{C}_{k}$ and
$\mathfrak{D}_{k}$ algebras recently introduced in the literature in the
context of (super)gravity. We also show how some of these new
infinite-dimensional symmetries can be obtained from expanded Ka\v{c}-Moody
algebras using modified Sugawara constructions. Applications in the context of
three-dimensional gravity are briefly discussed. |
Black Holes and Instabilities of Negative Tension Branes: We consider the collision in 2+1 dimensions of a black hole and a negative
tension brane on an orbifold. Because there is no gravitational radiation in
2+1 dimensions, the horizon area shrinks when part of the brane falls through.
This provides a potential violation of the generalized second law of
thermodynamics. However, tracing the details of the dynamical evolution one
finds that it does not proceed from equilibrium configuration to equilibrium
configuration. Instead, a catastrophic space-time singularity develops similar
to the `big crunch' of $\Omega >1$ FRW space-times. In the context of classical
general relativity, our result demonstrates a new instability of constructions
with negative tension branes. | The Ground Ring of N=2 Minimal String Theory: We study the $\NN=2$ string theory or the $\NN=4$ topological string on the
deformed CHS background. That is, we consider the $\NN=2$ minimal model coupled
to the $\NN=2$ Liouville theory. This model describes holographically the
topological sector of Little String Theory. We use degenerate vectors of the
respective $\NN=2$ Verma modules to find the set of BRST cohomologies at ghost
number zero--the ground ring, and exhibit its structure. Physical operators at
ghost number one constitute a module of the ground ring, so the latter can be
used to constrain the S-matrix of the theory. We also comment on the
inequivalence of BRST cohomologies of the $\NN=2$ string theory in different
pictures. |
On Action Functionals for Interacting Brane Systems: We present an action functional and derive equations of motion for a coupled
system of a bosonic Dp--brane and an open string ending on the Dp-brane. With
this example we address the key issues of the recently proposed method
(hep-th/9905144, hep-th/9906041) for the construction of manifestly
supersymmetric action functionals for interacting superbrane systems. We
clarify, in particular, how the arbitrariness in sources localized on the
intersection is related to the standard description of the flat D-branes as
rigid planes where the string for endpoints 'live'. | Partition functions of non-Lagrangian theories from the holomorphic
anomaly: The computation of the partition function in certain quantum field theories,
such as those of the Argyres-Douglas or Minahan-Nemeschansky type, is
problematic due to the lack of a Lagrangian description. In this paper, we use
the holomorphic anomaly equation to derive the gravitational corrections to the
prepotential of such theories at rank one by deforming them from the conformal
point. In the conformal limit, we find a general formula for the partition
function as a sum of hypergeometric functions. We show explicit results for the
round sphere and the Nekrasov-Shatashvili phases of the $\Omega$ background.
The first case is relevant for the derivation of extremal correlators in flat
space, whereas the second one has interesting applications for the study of
anharmonic oscillators. |
Charge and mass effects on the evaporation of higher-dimensional
rotating black holes: To study the dynamics of discharge of a brane black hole in TeV gravity
scenarios, we obtain the approximate electromagnetic field due to the charged
black hole, by solving Maxwell's equations perturbatively on the brane. In
addition, arguments are given for brane metric corrections due to backreaction.
We couple brane scalar and brane fermion fields with non-zero mass and charge
to the background, and study the Hawking radiation process using well known low
energy approximations as well as a WKB approximation in the high energy limit.
We argue that contrary to common claims, the initial evaporation is not
dominated by fast Schwinger discharge. | Universal renormalization procedure for higher curvature gravities in
D$\leq$5: We implement a universal method for renormalizing AdS gravity actions
applicable to arbitrary higher curvature theories in up to five dimensions. The
renormalization procedure considers the extrinsic counterterm for Einstein-AdS
gravity given by the Kounterterms scheme, but with a theory-dependent coupling
constant that is fixed by the requirement of renormalization for the vacuum
solution. This method is shown to work for a generic higher curvature gravity
with arbitrary couplings except for a zero measure subset, which includes
well-known examples where the asymptotic behavior is modified and the AdS vacua
are degenerate, such as Chern-Simons gravity in 5D, Conformal Gravity in 4D and
New Massive Gravity in 3D. In order to show the universality of the scheme, we
perform a decomposition of the equations of motion into their normal and
tangential components with respect to the Poincare coordinate and study the
Fefferman-Graham expansion of the metric. We verify the cancellation of
divergences of the on-shell action and the well-posedness of the variational
principle. |
Monstrous M-theory: In $26+1$ space-time dimensions, we introduce a gravity theory whose massless
spectrum can be acted upon by the Monster group when reduced to $25+1$
dimensions. This theory generalizes M-theory in many respects and we name it
Monstrous M-theory, or M$^{2}$-theory. Upon Kaluza-Klein reduction to $25+1$
dimensions, the M$^{2}$-theory spectrum irreducibly splits as
$\mathbf{1}\oplus\mathbf{196,883}$, where $\mathbf{1}$ is identified with the
dilaton, and $\mathbf{196,883}$ is the dimension of the smallest non-trivial
representation of the Monster. This provides a field theory explanation of the
lowest instance of the Monstrous Moonshine, and it clarifies the definition of
the Monster as the automorphism group of the Griess algebra, by showing that
such an algebra is not merely a sum of unrelated spaces, but descends from
massless states for M$^{2}$-theory, which includes Horowitz and Susskind's
bosonic M-theory as a subsector. Further evidence is provided by the
decomposition of the coefficients of the partition function of Witten's
extremal Monster SCFT in terms of representations of $SO_{24}$, the massless
little group in $25+1$; the purely bosonic nature of the involved
$SO_{24}$-representations may be traced back to the unique feature of $24$
dimensions, which allow for a non-trivial generalization of the triality
holding in $8$ dimensions. Last but not least, a certain subsector of
M$^{2}$-theory, when coupled to a Rarita-Schwinger massless field in $26+1$,
exhibits the same number of bosonic and fermionic degrees of freedom; we cannot
help but conjecture the existence of a would-be $\mathcal{N}=1$ supergravity
theory in $26+1$ space-time dimensions. | Heat kernel approach to relations between covariant and consistent
currents in chiral gauge theories: We apply the heat kernel method to relations between covariant and consistent
currents in anomalous chiral gauge theories. Banerjee et al. have shown that
the relation between these currents is expressed by a "functional curl" of the
covariant current. Using the heat kernel method, we evaluate the functional
curl explicitly in arbitrary even dimensions. We also apply the heat kernel
method to evaluate Osabe and Suzuki's results of the difference between
covariant and consistent currents in two and four dimensions. Applying the
arguments of Banerjee et al. to gravitational anomalies, we investigate the
relationship between the covariant and consistent energy-momentum tensors. The
relation is found to be expressed by a functional curl of the covariant
energy-momentum tensor. |
Infrared Behaviour of Softly Broken SQCD and Its Dual: Applying the recently obtained results on the renormalization of soft
supersymmetry-breaking parameters, we investigate the infrared behaviour of the
softly broken supersymmetric QCD as well as its dual theory in the conformal
window. Under general assumptions on $\beta$-functions, it is shown that the
soft supersymmetry-breaking parameters asymptotically vanish in the infrared
limit so that superconformal symmetry in softly broken supersymmetric QCD and
in its dual theory revives at the infrared fixed point, provided the soft
scalar masses satisfy certain renormalization group invariant relations. If
these relations are not satisfied, there exist marginal operators in both
theories that lead to the breaking of supersymmetry and also colour symmetry. | Field theory model giving rise to "quintessential inflation" without the
cosmological constant and other fine tuning problems: A field theory is developed based on the idea that the effective action of
yet unknown fundamental theory, at energy scale below M_{p} has the form of
expansion in two measures: S=\intd^{4}x[\Phi L_{1}+\sqrt{-g}L_{2}] where the
new measure \Phi is defined using the third-rank antisymmetric tensor. In the
new variables (Einstein frame) all equations of motion take canonical GR form
and therefore models are free of the well-known "defects" that distinguish the
Brans-Dicke type theories from GR. All novelty is revealed only in an unusual
structure of the effective potential U(\phi) and interactions which turns over
intuitive ideas based on our experience in field theory. E.g. the greater
\Lambda we admit in L_{2}, the smaller U(\phi) will be in the Einstein picture.
Field theory models are suggested with explicitly broken global continuos
symmetry which in the Einstein frame has the form \phi\to\phi+const. The
symmetry restoration occurs as \phi\to\infty. A few models are presented where
U is produced with the following shape: for \phi<-M_{p}, U has the form typical
for inflation model, e. g. U=\lambda\phi^4 with \lambda\sim 10^{-14};
for\phi>-M_{p}, U has mainly exponential form U\sim e^{-a\phi/M_{p}} with
variable a: a=14 for -M_{p}<\phi<M_{p} that admits nucleosynthesis; a=2 for
\phi>M_{p} that implies quintessence era. There is no need in any fine tuning
to prevent appearance of the CC term or any other terms that could violate
flatness of U at \phi\ggM_{p}. \lambda\sim 10^{-14} is obtained without fine
tuning as well. Quantized matter fields models, including gauge theories with
SSB can be incorporated without altering mentioned above results. Direct
fermion-inflaton coupling resembles Wetterich's model but it does not lead to
any observable effect at present. SSB does not raise any problem with CC. |
Holography of Little Inflation: For several crucial microseconds of its early history, the Universe consisted
of a Quark-Gluon Plasma. As it cooled during this era, it traced out a
trajectory in the quark matter phase diagram. The form taken by this trajectory
is not known with certainty, but is of great importance: it determines, for
example, whether the cosmic plasma passed through a first-order phase change
during the transition to the hadron era, as has recently been suggested by
advocates of the "Little Inflation" model. Just before this transition, the
plasma was strongly coupled and therefore can be studied by holographic
techniques. We show that holography imposes a strong constraint (taking the
form of a bound on the baryonic chemical potential relative to the temperature)
on the domain through which the cosmic plasma could pass as it cooled, with
important consequences for Little Inflation. In fact, we find that holography
applied to Little Inflation implies that the cosmic plasma must have passed
quite close to the quark matter critical point, and might therefore have been
affected by the associated fluctuation phenomena. | Tachyon Condensates and String Theoretic Inflation: Cosmological solutions of the beta function equations for the background
fields of the closed bosonic string are investigated at the one-loop level.
Following recent work of Kostelecky and Perry, it is assumed that the spatial
sections of the space-time are conformally flat. Working in the sigma-model
frame, the non-trivial tachyon potential is utilized to determine solutions
with sufficient inflation to solve the smoothness and flatness problems. The
graceful exit and density perturbation constraints can also be successfully
implemented. |
On the gravitational energy of the Kaluza Klein monopole: We use local counterterm prescriptions for asymptotically flat space to
compute the action and conserved quantities in five-dimensional Kaluza-Klein
theories. As an application of these prescriptions we compute the mass of the
Kaluza-Klein magnetic monopole. We find consistent results with previous
approaches that employ a background subtraction. | Discrete Gauge Symmetries and the Weak Gravity Conjecture: In theories with discrete Abelian gauge groups, requiring that black holes be
able to lose their charge as they evaporate leads to an upper bound on the
product of a charged particle's mass and the cutoff scale above which the
effective description of the theory breaks down. This suggests that a
non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to
gauge symmetries that are discrete, despite there being no associated massless
field, therefore pushing the conjecture beyond the slogan that `gravity is the
weakest force'. Here, we take a step towards making this expectation more
precise by studying $\mathbb{Z}_N$ and $\mathbb{Z}_2^N$ gauge symmetries
realised via theories of spontaneous symmetry breaking. We show that applying
the WGC to a dual description of an Abelian Higgs model leads to constraints
that allow us to saturate but not violate existing bounds on discrete
symmetries based on black hole arguments. In this setting, considering the
effect of discrete hair on black holes naturally identifies the cutoff of the
effective theory with the scale of spontaneous symmetry breaking, and provides
a mechanism through which discrete hair can be lost without modifying the
gravitational sector. We explore the possible implications of these arguments
for understanding the smallness of the weak scale compared to $M_{Pl}$. |
A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs
from S-fold SCFTs: We introduce a novel class of two-dimensional non-unitary rational conformal
field theories (RCFTs) whose modular data are identical to the generalized
Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are
related to the three-dimensional non-unitary Haagerup topological field
theories, recently constructed by a topological twisting of three-dimensional
${\cal N}=4$ rank-zero superconformal field theories (SCFTs), called S-fold
SCFTs. We propose that, up to the overall factors, the half-indices of the
rank-zero SCFTs give the explicit Nahm representation of four conformal
characters of the RCFTs including the vacuum character. Using the theory of
Bantay-Gannon, we can successfully complete them into the full admissible
conformal characters of the RCFTs. | Graded Majorana spinors: In many mathematical and physical contexts spinors are treated as Grassmann
odd valued fields. We show that it is possible to extend the classification of
reality conditions on such spinors by a new type of Majorana condition. In
order to define this graded Majorana condition we make use of
pseudo-conjugation, a rather unfamiliar extension of complex conjugation to
supernumbers. Like the symplectic Majorana condition, the graded Majorana
condition may be imposed, for example, in spacetimes in which the standard
Majorana condition is inconsistent. However, in contrast to the symplectic
condition, which requires duplicating the number of spinor fields, the graded
condition can be imposed on a single Dirac spinor. We illustrate how graded
Majorana spinors can be applied to supersymmetry by constructing a globally
supersymmetric field theory in three-dimensional Euclidean space, an example of
a spacetime where standard Majorana spinors do not exist. |
The Gross-Neveu-Yukawa Archipelago: We perform a bootstrap analysis of a mixed system of four-point functions of
bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global
symmetry. Our results provide rigorous bounds on the scaling dimensions of the
O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these
theories to live in isolated islands in the space of CFT data. We focus on the
cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed
matter systems, and compare our bounds to previous analytical and numerical
results. | The simplest description of charge propagation in a strong background: Exploiting the gauge freedom associated with the Volkov description of a
charge propagating in a plane wave background, we identify a new type of gauge
choice which significantly simplifies the theory. This allows us to develop a
compact description of the propagator for both scalar and fermionic matter, in
a circularly polarised background. It is shown that many of the usually
observed structures are gauge artefacts. We then analyse the full ultraviolet
behaviour of the one-loop corrections for such charges. This enables us to
identify and contrast the different renormalisation prescriptions needed for
both types of matter. |
Type IIB Orientifolds, F-theory, Type I Strings on Orbifolds and Type I
- Heterotic Duality: We consider six and four dimensional ${\cal N}=1$ supersymmetric orientifolds
of Type IIB compactified on orbifolds. We give the conditions under which the
perturbative world-sheet orientifold approach is adequate, and list the four
dimensional ${\cal N}=1$ orientifolds (which are rather constrained) that
satisfy these conditions. We argue that in most cases orientifolds contain
non-perturbative sectors that are missing in the world-sheet approach. These
non-perturbative sectors can be thought of as arising from D-branes wrapping
various collapsed 2-cycles in the orbifold. Using these observations, we
explain certain ``puzzles'' in the literature on four dimensional orientifolds.
In particular, in some four dimensional orientifolds the ``naive'' tadpole
cancellation conditions have no solution. However, these tadpole cancellation
conditions are derived using the world-sheet approach which we argue to be
inadequate in these cases due to appearance of additional non-perturbative
sectors. The main tools in our analyses are the map between F-theory and
orientifold vacua and Type I-heterotic duality. Utilizing the consistency
conditions we have found in this paper, we discuss consistent four dimensional
chiral ${\cal N}=1$ Type I vacua which are non-perturbative from the heterotic
viewpoint. | Wilson's numerical renormalization group and AdS_3 geometry: We discuss the relation between the Wilson's numerical renormalization
group(NRG) for the Kondo impurity problem and a field theory in the background
AdS_3 space time, where the radial coordinate plays a role of the controlling
parameter of the effective mass scale. We find that the Wilson NRG can be
described by the boundary Rindler field and then the cutoff parameter \lambda
of the Wilson NRG is related to the AdS radius L through \lambda = 2k_F/\omega
L, where k_F is the effective Fermi wave number. It is also found that the
Rindler space is discretized with the lattice space of a=\pi/k_F. |
The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches: We compute the spectrum of scaling dimensions of Coulomb branch operators in
4d rank-2 $\mathcal{N}{=}2$ superconformal field theories. Only a finite
rational set of scaling dimensions is allowed. It is determined by using
information about the global topology of the locus of metric singularities on
the Coulomb branch, the special K\"ahler geometry near those singularities, and
electric-magnetic duality monodromies along orbits of the $\rm\, U(1)_R$
symmetry. A set of novel topological and geometric results are developed which
promise to be useful for the study and classification of Coulomb branch
geometries at all ranks. | Addendum to Computational Complexity and Black Hole Horizons: In this addendum to [arXiv:1402.5674] two points are discussed. In the first
additional evidence is provided for a dual connection between the geometric
length of an Einstein-Rosen bridge and the computational complexity of the
quantum state of the dual CFT's. The relation between growth of complexity and
Page's ``Extreme Cosmic Censorship" principle is also remarked on.
The second point involves a gedanken experiment in which Alice measures a
complete set of commuting observables at her end of an Einstein-Rosen bridge is
discussed. An apparent paradox is resolved by appealing to the properties of
GHZ tripartite entanglement. |
Extending the Geometry of Heterotic Spectral Cover Constructions: In this work we extend the well-known spectral cover construction first
developed by Friedman, Morgan, and Witten to describe more general vector
bundles on elliptically fibered Calabi-Yau geometries. In particular, we
consider the case in which the Calabi-Yau fibration is not in Weierstrass form,
but can rather contain fibral divisors or multiple sections (i.e. a higher rank
Mordell-Weil group). In these cases, general vector bundles defined over such
Calabi-Yau manifolds cannot be described by ordinary spectral data. To
accomplish this we employ well established tools from the mathematics
literature of Fourier-Mukai functors. We also generalize existing tools for
explicitly computing Fourier-Mukai transforms of stable bundles on elliptic
Calabi-Yau manifolds. As an example of these new tools we produce novel
examples of chirality changing small instanton transitions. The goal of this
work is to provide a geometric formalism that can substantially increase the
understood regimes of heterotic/F-theory duality. | Chaotic scattering of highly excited strings: Motivated by the desire to understand chaos in the $S$-matrix of string
theory, we study tree level scattering amplitudes involving highly excited
strings. While the amplitudes for scattering of light strings have been a
hallmark of string theory since its early days, scattering of excited strings
has been far less studied. Recent results on black hole chaos, combined with
the correspondence principle between black holes and strings, suggest that the
amplitudes have a rich structure. We review the procedure by which an excited
string is formed by repeatedly scattering photons off of an initial tachyon
(the DDF formalism). We compute the scattering amplitude of one arbitrary
excited string and any number of tachyons in bosonic string theory. At high
energies and high mass excited state these amplitudes are determined by a
saddle-point in the integration over the positions of the string vertex
operators on the sphere (or the upper half plane), thus yielding a
generalization of the "scattering equations". We find a compact expression for
the amplitude of an excited string decaying into two tachyons, and study its
properties for a generic excited string. We find the amplitude is highly
erratic as a function of both the precise excited string state and of the
tachyon scattering angle relative to its polarization, a sign of chaos. |
Quantum Effects in Black Holes from the Schwarzschild Black String?: The holographic conjecture for black holes localized on a 3-brane in
Randall-Sundrum braneworld models RS2 predicts the existence of a classical 5D
time dependent solution dual to a 4D evaporating black hole. After briefly
reviewing recent criticism and presenting some difficulties in the holographic
interpretation of the Gregory-Laflamme instability, we simulate some basic
features of such a solution by studying null geodesics of the Schwarzschild
black string, in particular those propagating nontrivially in the bulk, and
using holographic arguments. | Gravitational Couplings of D-branes and O-planes: An explicit calculation is performed to check all the tangent bundle
gravitational couplings of Dirichlet branes and Orientifold planes by
scattering $q$ gravitons with a $p+1$ form Ramond-Ramond potential in the
world-volume of a $D(p+2q)$-brane. The structure of the D-brane Wess-Zumino
term in the world-volume action is confirmed, while a different O-plane
Wess-Zumino action is obtained. |
Dielectric function of the QCD vacuum: It is shown that the inverse of the ghost form factor in the Hamilton
approach to Yang-Mills theory in Coulomb gauge can be interpreted as the color
dielectric function of the QCD vacuum. Furthermore the horizon condition to the
ghost form factor implies that in the infrared the QCD vacuum is a perfect
color diaelectric medium and therefore a dual superconductor. The dielectric
function is explicitly calculated within a previously developed variational
approach, using a specific ansatz for the vacuum wave functional. | On Elliptic Algebras and Large-n Supersymmetric Gauge Theories: In this note we further develop the duality between supersymmetric gauge
theories in various dimensions and elliptic integrable systems such as
Ruijsenaars-Schneider model and periodic intermediate long wave hydrodynamics.
These models arise in instanton counting problems and are described by certain
elliptic algebras. We discuss the correspondence between the two types of
models by employing the large-n limit of the dual gauge theory. In particular
we provide non-Abelian generalization of our previous result on the
intermediate long wave model. |
Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory: We introduce a non-perturbative framework for computing structure constants
of single-trace operators in the N=4 SYM theory at large N. Our approach
features new vertices, with hexagonal shape, that can be patched together into
three- and possibly higher-point correlators. These newborn hexagons are more
elementary and easier to deal with than the three-point functions. Moreover,
they can be entirely constructed using integrability, by means of a suitable
bootstrap program. In this letter, we present our main results and conjectures
for these vertices, and match their predictions for the three-point functions
with both weak and strong coupling data available in the literature. | Geometric counter-vertex for open string scattering on D-branes: In arXiv:0801.0218 [hep-th] it was conjectured that quantum effects of open
strings moving on D-branes generate the D-brane geometry through a
counter-vertex operator. The conjecture has been checked at one-loop in
arXiv:0806.3330 [hep-th]. Here we discuss the two-loop extension. |
Direct Integration for Mirror Curves of Genus Two and an Almost
Meromorphic Siegel Modular Form: This work considers aspects of almost holomorphic and meromorphic Siegel
modular forms from the perspective of physics and mathematics. The first part
is concerned with (refined) topological string theory and the direct
integration of the holomorphic anomaly equations. Here, a central object to
compute higher genus amplitudes, which serve as the generating functions of
various enumerative invariants, is provided by the so-called propagator. We
derive a universal expression for the propagator for geometries that have
mirror curves of genus two which is given by the derivative of the logarithm of
Igusa's cusp form of weight 10. In addition, we illustrate our findings by
solving the refined topological string on the resolutions of the three toric
orbifolds of order three, five and six.
In the second part, we give explicit expressions for lowering and raising
operators on Siegel modular forms, and define almost holomorphic Siegel modular
forms based on them. Extending the theory of Fourier-Jacobi expansions to
almost holomorphic Siegel modular forms and building up on recent work by
Pitale, Saha, and Schmidt, we can show that there is no analogue of the almost
holomorphic elliptic second Eisenstein series. In the case of genus 2, we
provide an almost meromorphic substitute for it. This, in particular, leads us
to a generalization of Ramanujan's differential equation for the second
Eisenstein series.
The two parts are intertwined by the observation that the meromorphic
analogue of the almost holomorphic second Eisenstein series coincides with the
physical propagator. In addition, the generalized Ramanujan identities match
precisely the physical consistency conditions that need to be imposed on the
propagator. | G+++ Invariant Formulation of Gravity and M-Theories: Exact Intersecting
Brane Solutions: The set of exact solutions of the non-linear realisations of the G+++
Kac-Moody algebras is further analysed. Intersection rules for extremal branes
translate into orthogonality conditions on the positive real roots
characterising each brane. It is proven that all the intersecting extremal
brane solutions of the maximally oxidised theories have their algebraic
counterparts as exact solutions in the G+++ invariant theories. The proof is
extended to include the intersecting extremal brane solutions of the exotic
phases of the maximally oxidised theories. |
Order parameter fluctuations in the holographic superconductor: We investigate the effect of order parameter fluctuations in the holographic
superconductor. In particular, using a fully backreacted bulk geometry, the
intrinsic spectral functions of the order parameter in both the normal and the
superconducting phase are computed. We also present a vector-like large-$N$
version of the Ginzburg-Landau model that accurately describes our
long-wavelength results in both phases. The large-$N$ limit of the latter model
explains why the Higgs mode and the second-sound mode are not present in the
spectral functions. Our results indicate that the holographic superconductor
describes a relativistic multi-component superfluid in the universal regime of
the BEC-BCS crossover. | Higher-Order Gravitational Couplings and Modular Forms in $N=2,D=4$
Heterotic String Compactifications: The restrictions of target--space duality are imposed at the perturbative
level on the holomorphic Wilsonian couplings that encode certain higher-order
gravitational interactions in $N=2, D=4$ heterotic string compactifications. A
crucial role is played by non-holomorphic corrections. The requirement of
symplectic covariance and an associated symplectic anomaly equation play an
important role in determining their form. For models which also admit a type-II
description, this equation coincides with the holomorphic anomaly equation for
type-II compactifications in the limit that a specific K\"ahler-class modulus
grows large. We explicitly evaluate some of the higher-order couplings for a
toroidal compactification with two moduli $T$ and $U$, and we express them in
terms of modular forms. |
Critical distance and Crofton form in confining geometries: For two symmetric strips with equal and finite size and in the background of
several confining geometries, we numerically calculate the critical distance
between these two mixed systems where the mutual information between them drops
to zero and show that this quantity could be a useful correlation measure in
probing the phase structures of holographic QCD models. The models that we
consider here are Sakai-Sugimoto and deformed Sakai-Sugimoto, Klebanov-Tseytlin
and Maldacena Nunez. For evaluating the structures of these holographic
supergravity geometries from the perspective of the bulk reconstruction, we
also calculate their Crofton forms and show that there is a universal behavior
in the confining backgrounds where a "well functionality" is present around the
IR cutoff point, and far from the IR wall the scalar part of the Crofton form
would become constant, demonstrating the effects of the wall of the confining
models on the phase structures. This work is the shorter version of our
previous work arXiv:2110.12970 with few more results about the connections
between phases. | Local Fractional Supersymmetry for Alternative Statistics: A group theory justification of one dimensional fractional supersymmetry is
proposed using an analogue of a coset space, just like the one introduced in
$1D$ supersymmetry. This theory is then gauged to obtain a local fractional
supersymmetry {\it i.e.} a fractional supergravity which is then quantized {\it
\`a la Dirac} to obtain an equation of motion for a particle which is in a
representation of the braid group and should describe alternative statistics. A
formulation invariant under general reparametrization is given, by means of a
curved fractional superline. |
Euclidean path integral, entanglement entropy, and quantum boundary
conditions: To understand the information loss paradox in a consistent way, we provide a
brief big picture that describes both outside and inside a black hole. We
summary several ideas including the Euclidean path integral, the entanglement
entropy, and the quantum gravitational treatment for the singularity. This
integrated discussion can provide an alternative point of view toward the
ultimate resolution of the information loss paradox. | Casimir-Polder repulsion near edges: wedge apex and a screen with an
aperture: Although repulsive effects have been predicted for quantum vacuum forces
between bodies with nontrivial electromagnetic properties, such as between a
perfect electric conductor and a perfect magnetic conductor, realistic
repulsion seems difficult to achieve. Repulsion is possible if the medium
between the bodies has a permittivity in value intermediate to those of the two
bodies, but this may not be a useful configuration. Here, inspired by recent
numerical work, we initiate analytic calculations of the Casimir-Polder
interaction between an atom with anisotropic polarizability and a plate with an
aperture. In particular, for a semi-infinite plate, and, more generally, for a
wedge, the problem is exactly solvable, and for sufficiently large anisotropy,
Casimir-Polder repulsion is indeed possible, in agreement with the previous
numerical studies. In order to achieve repulsion, what is needed is a
sufficiently sharp edge (not so very sharp, in fact) so that the directions of
polarizability of the conductor and the atom are roughly normal to each other.
The machinery for carrying out the calculation with a finite aperture is
presented. As a motivation for the quantum calculation, we carry out the
corresponding classical analysis for the force between a dipole and a metallic
sheet with a circular aperture, when the dipole is on the symmetry axis and
oriented in the same direction. |
Massless and Massive Three Dimensional Super Yang-Mills Theory and
Mini-Twistor String Theory: We propose various ways of adding mass terms to three-dimensional twistor
string theory. We begin with a review of mini-twistor space--the reduction of
D=4 twistor space to D=3. We adapt the two proposals for twistor string theory,
Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model,
we identify the enhanced R-symmetry. We then construct B-model topological
string theories that, we propose, correspond to D=3 Yang-Mills theory with
massive spinors and massive and massless scalars in the adjoint representation
of the gauge group. We also analyze the counterparts of these constructions in
Berkovits's model. Some of our constructions can be lifted to D=4, where
infinitesimal mass terms correspond to VEVs of certain superconformal gravity
fields. | Radiation reaction and renormalization in classical electrodynamics of
point particle in any dimension: The effective equations of motion for a point charged particle taking account
of radiation reaction are considered in various space-time dimensions. The
divergencies steaming from the pointness of the particle are studied and the
effective renormalization procedure is proposed encompassing uniformly the
cases of all even dimensions. It is shown that in any dimension the classical
electrodynamics is a renormalizable theory if not multiplicatively beyond d=4.
For the cases of three and six dimensions the covariant analogs of the
Lorentz-Dirac equation are explicitly derived. |
Coupling Brane Fields to Bulk Supergravity: In this note we present a simple, general prescription for coupling brane
localized fields to bulk supergravity. We illustrate the procedure by
considering 6D N=2 bulk supergravity on a 2D orbifold, with brane fields
localized at the fixed points. The resulting action enjoys the full 6D N=2
symmetries in the bulk, and those of 4D N=1 supergravity at the brane
positions. | Quintessence and the Swampland: The numerically controlled regime of
moduli space: We provide a detailed discussion of the main theoretical and phenomenological
challenges of quintessence model building in any numerically controlled regime
of the moduli space of string theory. We argue that a working quintessence
model requires a leading order non-supersymmetric (near) Minkowski vacuum with
an axionic flat direction. This axion, when lifted by subdominant
non-perturbative effects, could drive hilltop quintessence only for highly
tuned initial conditions and a very low inflationary scale. Our analysis has
two important implications. Firstly, scenarios which are in agreement with the
swampland conjectures, such as those that include runaways, or supersymmetric
AdS and Minkowski vacua, cannot give rise to phenomenologically viable
quintessence with full computational control. This raises doubts on the
validity of the swampland dS conjecture since it would imply a strong tension
between quantum gravity and observations. Secondly, if data should prefer
dynamical dark energy, axion models based on alignment mechanisms look more
promising than highly contrived hilltop scenarios. |
Beauty is Attractive: Moduli Trapping at Enhanced Symmetry Points: We study quantum effects on moduli dynamics arising from the production of
particles which are light at special points in moduli space. The resulting
forces trap the moduli at these points, which often exhibit enhanced symmetry.
Moduli trapping occurs in time-dependent quantum field theory, as well as in
systems of moving D-branes, where it leads the branes to combine into stacks.
Trapping also occurs in an expanding universe, though the range over which the
moduli can roll is limited by Hubble friction. We observe that a scalar field
trapped on a steep potential can induce a stage of acceleration of the
universe, which we call trapped inflation. Moduli trapping ameliorates the
cosmological moduli problem and may affect vacuum selection. In particular,
rolling moduli are most powerfully attracted to the points with the largest
number of light particles, which are often the points of greatest symmetry.
Given suitable assumptions about the dynamics of the very early universe, this
effect might help to explain why among the plethora of possible vacuum states
of string theory, we appear to live in one with a large number of light
particles and (spontaneously broken) symmetries. In other words, some of the
surprising properties of our world might arise not through pure chance or
miraculous cancellations, but through a natural selection mechanism during
dynamical evolution. | Incarnations of Instantons: Yang-Mills instantons in a pure Yang-Mills theory in four Euclidean space can
be promoted to particle-like topological solitons in d=4+1 dimensional
space-time. When coupled to Higgs fields, they transform themselves in the
Higgs phase into Skyrmions, lumps and sine-Gordon kinks, with trapped inside a
non-Abelian domain wall, non-Abelian vortex and monopole string, respectively.
Here, we point out that a closed monopole string, non-Abelian vortex sheet and
non-Abelian domain wall in $S^1$, $S^2$ and $S^3$ shapes, respectively, are all
Yang-Mills instantons if their $S^1$, $S^2$ and $S^3$ moduli, respectively, are
twisted along their world-volumes. |
Non-Invertible Symmetries from Holography and Branes: We propose a systematic approach to deriving symmetry generators of Quantum
Field Theories in holography. Central to this are the Gauss law constraints in
the Hamiltonian quantization of Symmetry Topological Field Theories (SymTFTs),
which are obtained from supergravity. In turn we realize the symmetry
generators from world-volume theories of D-branes in holography. Our main focus
is on non-invertible symmetries, which have emerged in the past year as a new
type of symmetry in $d\geq 4$ QFTs. We exemplify our proposal in the
holographic confinement setup, dual to 4d $\mathcal{N}=1$ Super-Yang Mills. In
the brane-picture, the fusion of non-invertible symmetries naturally arises
from the Myers effect on D-branes. In turn, their action on line defects is
modeled by the Hanany-Witten effect. | Entropy and String Black Hole Correspondence: We make some observations regarding string/black hole correspondence with a
view to understanding the nature of the quantum degrees of freedom of a black
hole in string theory. In particular, we compare entropy change in analogous
string and black hole processes in order to support the interpretation of the
area law entropy as arising from stringy constituents. |
Tachyon Solution in Cubic Neveu-Schwarz String Field Theory: A class of exact analytic solutions in the modified cubic fermionic string
field theory with the GSO(-) sector is presented. This class contains the
GSO(-) tachyon field and reproduces the correct value for the nonBPS D-brane
tension. | Anyonic Bogomol'nyi Solitons in a Gauged O(3) Sigma Model: We introduce the self-dual abelian gauged $O(3)$ sigma models where the
Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge
field. These models have quite rich structures and various limits. Our models
are found to exhibit both symmetric and broken phases of the gauge group. We
discuss the pure Chern-Simons limit in some detail and study rotationally
symmetric solitons. |
Supercritical N = 2 string theory: The N=2 string is examined in dimensions above the critical dimension (D=4)
in a linear dilaton background. We demonstrate that string states in this
background propagate in a single physical time dimension, as opposed to two
such dimensions present when the dilaton gradient vanishes in D=4. We also find
exact solutions describing dynamical dimensional reduction and transitions from
N=2 string theory to bosonic string theory via closed-string tachyon
condensation. | An introduction to quantum gravity: Quantum gravity was born as that branch of modern theoretical physics that
tries to unify its guiding principles, i.e., quantum mechanics and general
relativity. Nowadays it is providing new insight into the unification of all
fundamental interactions, while giving rise to new developments in mathematics.
The various competing theories, e.g. string theory and loop quantum gravity,
have still to be checked against observations. We review the classical and
quantum foundations necessary to study field-theory approaches to quantum
gravity, the passage from old to new unification in quantum field theory,
canonical quantum gravity, the use of functional integrals, the properties of
gravitational instantons, the use of spectral zeta-functions in the quantum
theory of the universe, Hawking radiation, some theoretical achievements and
some key experimental issues. |
A supersymmetric model for graphene: In this work, we focus on the fermionic structure of the low-energy
excitations of graphene (a monolayer of carbon atoms) to propose a new
supersymmetric field-theoretic model for this physical system. In the current
literature, other proposals for describing graphene physics have been
contemplated at the level of supersymmetric quantum mechanics. Also, by
observing the inhomogeneities between neighbor carbon atoms, Jackiw {\it et
al.} have set up an interesting chiral Abelian gauge theory. We show in this
paper that our formulation encompasses models discussed previously as sectors
of an actually richer (supersymmetric) planar gauge model. Possible
interpretations for the fields involved in the present graphene model are
proposed and the question of supersymmetry breaking is discussed. | Quantum dilaton supergravity in 2D with non-minimally coupled matter: General N=(1,1) dilaton supergravity in two dimensions allows a background
independent exact quantization of the geometric part, if these theories are
formulated as specific graded Poisson-sigma models. In this work the extension
of earlier results to models with non-minimally coupled matter is presented. In
particular, the modifications of the constraint algebra due to non-minimal
couplings are calculated and it is shown that quartic ghost-terms do not arise.
Consequently the path-integral quantization as known from bosonic theories and
supergravity with minimally coupled matter can be taken over. |
A perturbative CFT dual for pure NS-NS AdS$_3$ strings: We construct a CFT dual to string theory on AdS$_3$ with pure NS-NS flux. It
is given by a symmetric orbifold of a linear dilaton theory deformed by a
marginal operator from the twist-2 sector. We compute two- and three-point
functions on the CFT side to 4th order in conformal perturbation theory at
large $N$. They agree with the string computation at genus 0, thus providing
ample evidence for a duality. We also show that the full spectra of both short
and long strings on the CFT and the string side match. The duality should be
understood as perturbative in $N^{-1}$. | The renormalisation bialgebra and operads: In a recent preprint, Brouder and Schmitt give a careful construction of a
`renormalisation' Hopf algebra out of an arbitrary bialgebra. In this note, we
point out that this is a special case of the construction of the cooperad of a
bialgebra (Berger-Moerdijk) combined with the construction of a bialgebra from
a cooperad (Frabetti-Van der Laan). |
How tropical are seven- and eight-particle amplitudes?: We study tropical Grassmanians Tr$(k,n)$ in relation to cluster algebras, and
assess their applicability to $n$-particle amplitudes for $n=7,8$. In
$\mathcal{N}=4$ super Yang-Mills theory, we first show that while the totally
positive part of Tr$(4,7)$ may encompass the iterated discontinuity structure
of the seven-point Maximally Helicity Violating (MHV) amplitude, it is too
small for the Next-to-MHV helicity configuration. Then, using Tr$(4,8)$ we
propose a finite set of 356 cluster $\mathcal{A}$-coordinates expected to
contain the rational symbol letters of the eight-particle MHV amplitude, and
discuss how the remaining square-root letters may be obtained from limits of
infinite mutation sequences. Finally, we use a triangulation of the totally
positive part of Tr$(3,8)$ to obtain the associated generalised biadjoint
scalar amplitude in a form containing a near-minimal amount of spurious poles. | Mass and Angular momentum of Black Holes in New Massive Gravity: We obtain mass and angular momentum of black holes as conserved charges in
three dimensional new massive gravity, after presenting the explicit expression
for the potential of the conserved charges. This confirms the expression of
those charges obtained in several ways, in particular through AdS/CFT
correspondence, and shows us that the first law of black hole thermodynamics is
valid in these black holes. We also comment about conserved charges in new type
black holes with the emphasis on the AdS/CFT correspondence as guiding
principle. |
Mesons From String Theory: A brief historical synopsis of the connection between gauge theories and
string theory is given. Meson configurations known as k-strings are examined
from string theory via the gauge/gravity correspondence. Backgrounds dual to
k-strings in both 2+1 and 3+1 are discussed. The energy of k-strings to lowest
order consists of a tension term, proportional to the length, L, of the
k-string, i.e., the size of the mesons in the configuration. The first quantum
correction is a Coulombic 1/L correction, known as a Luscher term, plus a
constant. Acquiring tensions and Luscher terms via the gauge/gravity
correspondence is discussed. | Renormalization of the Inverse Square Potential: The quantum-mechanical D-dimensional inverse square potential is analyzed
using field-theoretic renormalization techniques. A solution is presented for
both the bound-state and scattering sectors of the theory using cutoff and
dimensional regularization. In the renormalized version of the theory, there is
a strong-coupling regime where quantum-mechanical breaking of scale symmetry
takes place through dimensional transmutation, with the creation of a single
bound state and of an energy-dependent s-wave scattering matrix element. |
Semiclassical approximation in Batalin-Vilkovisky formalism: The geometry of supermanifolds provided with $Q$-structure (i.e. with odd
vector field $Q$ satisfying $\{ Q,Q\} =0$), $P$-structure (odd symplectic
structure ) and $S$-structure (volume element) or with various combinations of
these structures is studied. The results are applied to the analysis of
Batalin-Vilkovisky approach to the quantization of gauge theories. In
particular the semiclassical approximation in this approach is expressed in
terms of Reidemeister torsion. | Fluxbranes: Moduli Stabilisation and Inflation: Fluxbrane inflation is a stringy version of D-term inflation in which two
fluxed D7-branes move towards each other until their (relative) gauge flux
annihilates. Compared to brane-antibrane inflation, the leading-order
inflationary potential of this scenario is much flatter. In the present paper
we first discuss a new explicit moduli stabilisation procedure combining the F-
and D-term scalar potentials: It is based on fluxed D7-branes in a geometry
with three large four-cycles of hierarchically different volumes. Subsequently,
we combine this moduli stabilisation with the fluxbrane inflation idea,
demonstrating in particular that CMB data (including cosmic string constraints)
can be explained within our setup of hierarchical large volume CY
compactifications. We also indicate how the eta-problem is expected to
re-emerge through higher-order corrections and how it might be overcome by
further refinements of our model. Finally, we explain why recently raised
concerns about constant FI terms do not affect the consistent, string-derived
variant of D-term inflation discussed in this paper. |
Monopole, gluino and charge condensates in gauge theories with broken
N=2 supersymmetry: We consider chiral condensates in SU(2) gauge theory with broken N=2
supersymmetry and one fundamental flavor in the matter sector. Matter and
gaugino condensates are determined by integrating out the adjoint field. The
only nonperturbative input is the Affleck-Dine-Seiberg one-instanton
superpotential. The results are consistent with those obtained by the
`integrating in' procedure. We then calculate monopole, dyon, and charge
condensates using the Seiberg-Witten approach. The key observation is that the
monopole and charge condensates vanish at the Argyres-Douglas point where the
monopole and charge vacua collide. We interpret this phenomenon as a
deconfinement of electric and magnetic charges at the Argyres-Douglas point. | On external backgrounds and linear potential in three dimensions: For a three-dimensional theory with a coupling $\phi \epsilon ^{\mu \nu
\lambda} v_\mu F_{\nu \lambda}$, where $v_\mu$ is an external constant
background, we compute the interaction potential within the structure of the
gauge-invariant but path-dependent variables formalism. While in the case of a
purely timelike vector the static potential remains Coulombic, in the case of a
purely spacelike vector the potential energy is the sum of a Bessel and a
linear potentials, leading to the confinement of static charges. This result
may be considered as another realization of the known Polyakov's result. |
BPS-Saturated Bound States of Tilted P-Branes in Type II String Theory: We found BPS-saturated solutions of M-theory and Type II string theory which
correspond to (non-marginally) bound states of p-branes intersecting at angles
different from pi/2. These solutions are obtained by starting with a BPS
marginally bound (orthogonally) intersecting configurations of two p-branes
(e.g, two four-branes of Type II string theory), performing a boost
transformation at an angle with respect to the world-volume of the
configuration, performing T-duality transformation along the boost-direction,
S-duality transformation, and T- transformations along the direction
perpendicular to the boost transformation. The resulting configuration is
non-marginally bound BPS-saturated solution whose static metric possesses the
off-diagonal term which cannot be removed by a coordinate transformation, and
thus signifies an angle (different from pi/2) between the resulting
intersecting p-branes. Additional new p-branes are bound to this configuration,
in order to ensure the stability of such a static, tilted configuration. | Holographic entanglement entropy and complexity of microstate geometries: We study holographic entanglement entropy and holographic complexity in a
two-charge, $\frac{1}{4}$-BPS family of solutions of type IIB supergravity,
controlled by one dimensionless parameter. All the geometries in this family
are asymptotically AdS$_3 \times \mathbb{S}^3 \times \mathbb{T}^4$ and, varying
the parameter that controls them, they interpolates between the global AdS$_3
\times \mathbb{S}^3 \times \mathbb{T}^4$ and the massless BTZ$_3 \times
\mathbb{S}^3 \times \mathbb{T}^4$ geometry. Due to AdS/CFT duality, these
geometries are dual to pure CFT heavy states.
We find that there is no emergence of entanglement shadow for all the values
of the parameter and we discuss the relation with the massless BTZ result,
underlying the relevance of the nature of the dual states.
We also compute the holographic complexity of formation of these geometries,
finding a nice monotonic function that interpolates between the pure AdS$_3$
result and the massless BTZ one. |
BPS submodels of the Skyrme model: We show that the standard Skyrme model without pion mass term can be
expressed as a sum of two BPS submodels, i.e., of two models whose static field
equations, independently, can be reduced to first order equations. Further,
these first order (BPS) equations have nontrivial solutions, at least locally.
These two submodels, however, cannot have common solutions. Our findings also
shed some light on the rational map approximation. Finally, we consider certain
generalisations of the BPS submodels. | De-singularizing the extremal GMGHS black hole via higher derivatives
corrections: The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is an
influential solution of the low energy heterotic string theory. As it is well
known, it presents a singular extremal limit. We construct a regular extension
of the GMGHS extremal black hole in a model with $\mathcal{O}(\alpha')$
corrections in the action, by solving the fully non-linear equations of motion.
The de-singularization is supported by the $\mathcal{O}(\alpha')$-terms. The
regularised extremal GMGHS BHs are asymptotically flat, possess a regular
(non-zero size) horizon of spherical topology, with an $AdS_2\times S^2$ near
horizon geometry, and their entropy is proportional to the electric charge. The
near horizon solution is obtained analytically and some illustrative bulk
solutions are constructed numerically. |
Exact solutions, energy and charge of stable Q-balls: In this work we deal with nontopological solutions of the Q-ball type in two
spacetime dimensions. We study models of current interest, described by a
Higgs-like and other, similar potentials which unveil the presence of exact
solutions. We use the analytic results to investigate how to control the energy
and charge to make the Q-balls stable. | Nonlinear electrodynamics in Bianchi spacetimes: We study the effects produced by nonlinear electrodynamics in spacetimes
conformal to Bianchi metrics. In the presence of Born-Infeld type fields these
models accelerate, expand and isotropize. This effect is compared with the
corresponding to a linear electromagnetic field; it turns out that for the same
geometry, Maxwell fields does not favour inflation as much as Born-Infeld
field. The behavior of the nonlinear radiation is analyzed in terms of the
equation of state. The energy conditions are analyzed as well, showing that the
Born-Infeld field violates the strong energy condition. |
The alpha'-Expansion of Calabi-Yau Compactifications: We consider alpha'-corrections to Calabi-Yau compactifications of type II
string theory. These were discussed from the string worldsheet approach many
years ago in terms of supersymmetric non-linear sigma-models by Nemeschansky
and Sen as well as Gross and Witten. There it was shown that once
alpha'-corrections are included, the internal manifold solving the string
equations of motion is still Calabi-Yau though not Ricci flat. In this brief
note we review these results and compare with a space-time effective field
theory approach, in which we show that SU(3)-holonomy manifolds become
SU(3)-structure manifolds once such corrections are included. | On spectrally flowed local vertex operators in AdS$_3$: We provide a novel local definition for spectrally flowed vertex operators in
the SL(2,$\mathbb{R}$)-WZW model, generalising the proposal of Maldacena and
Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all $\omega >
1$. This allows us to establish the precise connection between the computation
of correlators using the so-called spectral flow operator, and the methods
introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local
Ward identities. We show that the auxiliary variable $y$ used in the latter
paper arises naturally from a point-splitting procedure in the space-time
coordinate. The recursion relations satisfied by spectrally flowed correlators,
which take the form of partial differential equations in $y$-space, then
correspond to null-state conditions for generalised spectral flowed operators.
We highlight the role of the SL(2,$\mathbb{R}$) series identifications in this
context, and prove the validity of the conjecture put forward in
[arXiv:2105.12130] for $y$-space structure constants of three-point functions
with arbitrary spectral flow charges. |
Simplifying the Type $A$ Argyres-Douglas Landscape: A well-established organisational principle for Argyres--Douglas-type
$\mathcal{N}=2$ superconformal field theories in four dimensions is to
characterise such theories by the data defining a(n irregular) Hitchin system
on $\mathbb{CP}^1$. The dictionary between Hitchin system data and various
features of the corresponding SCFT has been studied extensively, but the
overall structure of the resulting space of SCFTs still appears quite
complicated. In this work, we systematically delineate a variety of
simplifications that arise within this class of constructions due to several
large classes of isomorphisms between SCFTs associated with inequivalent
Hitchin system data (and their exactly marginal gaugings). We restrict to the
most studied class of theories, namely the type $A$ theories without outer
automorphism twists. | Vacuum instability in slowly varying electric fields: Nonperturbative methods have been well-developed for QED with the so-called
t-electric potential steps. In this case a calculation technique is based on
the existence of specific exact solutions (in and out solutions) of the Dirac
equation. However, there are only few cases when such solutions are known.
Here, we demonstrate that for t-electric potential steps slowly varying with
time there exist physically reasonable approximations that maintain the
nonperturbative character of QED calculations even in the absence of the exact
solutions. Defining the slowly varying regime in general terms, we can observe
a universal character of vacuum effects caused by a strong electric field. In
the present article, we find universal approximate representations for the
total density of created pairs and vacuum mean values of the current density
and energy-momentum tensor that hold true for arbitrary t-electric potential
steps slowly varying with time. These representations do not require knowledge
of the corresponding solutions of the Dirac equation, they have a form of
simple functionals of a given slowly varying electric field. We establish
relations of these representations with leading terms of the derivative
expansion approximation. These results allow one to formulate some
semiclassical approximations that are not restricted by the smallness of
differential mean numbers of created pairs. |
Non-Perturbative Formulation of Time-Dependent String Solutions: We formulate here a new world-sheet renormalization-group technique for the
bosonic string, which is non-perturbative in the Regge slope alpha' and based
on a functional method for controlling the quantum fluctuations, whose
magnitudes are scaled by the value of alpha'. Using this technique we exhibit,
in addition to the well-known linear-dilaton cosmology, a new, non-perturbative
time-dependent background solution. Using the reparametrization invariance of
the string S-matrix, we demonstrate that this solution is conformally invariant
to alpha', and we give a heuristic inductive argument that conformal invariance
can be maintained to all orders in alpha'. This new time-dependent string
solution may be applicable to primordial cosmology or to the exit from
linear-dilaton cosmology at large times. | Gluon-Meson Duality: The QCD-vacuum is characterized by the Higgs phenomenon for colored scalar
fields. In this dual picture the gluons appear as the octet of vector mesons.
Also quarks and baryons are identified. Gluon-meson and quark-baryon duality
can account in a simple way for realistic masses of all low-mass hadrons and
for their interactions. |
Planck 2013 and Superconformal Symmetry: We explain why the concept of a spontaneously broken superconformal symmetry
is useful to describe inflationary models favored by the Planck. Non-minimal
coupling of complex scalars to curvature, N(X, X*) R, is compulsory for
superconformal symmetry. Here N is the Kahler potential of the embedding moduli
space, including the inflaton and the conformon. It appears that such a
non-minimal coupling allows generic chaotic models of inflation to reach an
agreement with the observable (n_{s},r) values. We describe here the
superconformal versions of the cosmological attractors whose bosonic part was
presented in lectures of A. Linde in this volume. A distinguishing feature of
this class of models is that they tend to lead to very similar predictions
which are not very sensitive with respect to strong modifications of the
theory. The (super)conformal symmetry underlying (super)gravity allows a
universal description of a large class of models which agree with observations
and predict the tensor to scalar ratio 10^{-3} < r < 10^{-1}. | Extra Dimensions and Fuzzy Branes in String-inspired Nonlocal Field
Theory: Particle physics models with extra dimensions of space (EDS's) and branes
shed new light on electroweak and flavor hierarchies with a rich TeV scale
phenomenology. This article highlights new model building issues with EDS's and
branes, arising in the framework of weakly nonlocal field theories. It is shown
that a brane-localized field is still delocalized in the bulk on a small
distance from the brane position: fields localized on such distant fuzzy branes
are thus allowed to interact directly with suppressed couplings. Directions for
model building are also given: (i) with fuzzy branes, a new realization of
split fermions in an EDS is presented, naturally generating flavor hierarchies;
(ii) with a warped EDS, the usual warp transmutation of a brane-localized mass
term is revisited, where it is shown that the nonlocal scale is also redshifted
and provides a smooth UV cutoff for the Higgs boson mass. This framework is
expected to have natural UV completions in string theory, but the possibility
to embed it in recent UV complete weakly nonlocal quantum field theories is
commented. |
General covariant Horava-Lifshitz gravity without projectability
condition and its applications to cosmology: We consider an extended theory of Horava-Lifshitz gravity with the detailed
balance condition softly breaking, but without the projectability condition.
With the former, the number of independent coupling constants is significantly
reduced. With the latter and by extending the original foliation-preserving
diffeomorphism symmetry $ {{Diff}}(M, {\cal{F}})$ to include a local U(1)
symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related
to them disappear, including the instability, strong coupling, and different
speeds in the gravitational sector. When the theory couples to a scalar field,
we find that the scalar field is not only stable in both the ultraviolet (UV)
and infrared (IR), but also free of the strong coupling problem, because of the
presence of high-order spatial derivative terms of the scalar field.
Furthermore, applying the theory to cosmology, we find that due to the
additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is
necessarily flat. We also investigate the scalar, vector, and tensor
perturbations of the flat FRW universe, and derive the general linearized field
equations for each kind of the perturbations. | Thermal nature of de Sitter spacetime and spontaneous excitation of
atoms: We consider, in de Sitter spacetime, both freely falling and static two-level
atoms in interaction with a conformally coupled massless scalar field in the de
Sitter-invariant vacuum, and separately calculate the contributions of vacuum
fluctuations and radiation reaction to the atom's spontaneous excitation rate.
We find that spontaneous excitations occur even for the freely falling atom as
if there is a thermal bath of radiation at the Gibbons-Hawking temperature and
we thus recover, in a different physical context, the results of Gibbons and
Hawking that reveals the thermal nature of de Sitter spacetime. Similarly, for
the case of the static atom, our results show that the atom also perceives a
thermal bath which now arises as a result of the intrinsic thermal nature of de
Sitter spacetime and the Unruh effect associated with the inherent acceleration
of the atom. |
Spectrum of a duality-twisted Ising quantum chain: The Ising quantum chain with a peculiar twisted boundary condition is
considered. This boundary condition, first introduced in the framework of the
spin-1/2 XXZ Heisenberg quantum chain, is related to the duality
transformation, which becomes a symmetry of the model at the critical point.
Thus, at the critical point, the Ising quantum chain with the duality-twisted
boundary is translationally invariant, similar as in the case of the usual
periodic or antiperiodic boundary conditions. The complete energy spectrum of
the Ising quantum chain is calculated analytically for finite systems, and the
conformal properties of the scaling limit are investigated. This provides an
explicit example of a conformal twisted boundary condition and a corresponding
generalised twisted partition function. | The coset construction for non-equilibrium systems: We propose a systematic coset construction of non-equilibrium effective field
theories (EFTs) governing the long-distance and late-time dynamics of
relativistic, finite-temperature condensed matter systems. Our non-equilibrium
coset construction makes significant advances beyond more standard coset
constructions in that it takes advantage of recently-developed techniques,
which allow the formulation of non-equilibrium effective actions that account
for quantum and thermal fluctuations as well as dissipation. Because these
systems exist at finite temperature, the EFTs live on the closed-time-path of
the Schwinger-Keldysh contour. Since the coset construction and the
non-equilibrium effective actions may be unfamiliar to many readers, we include
brief introductions to these topics in an effort to make this paper
self-contained. To demonstrate the legitimacy of this coset construction, we
successfully reproduce the known EFTs for fluids and superfluids at finite
temperature. Then, to demonstrate its utility, we construct novel EFTs for
solids, supersolids, and four phases of liquid crystals, all at finite
temperature. We thereby combine the non-equilibrium effective action and the
coset construction to create a powerful tool that can be used to study
many-body systems out of thermal equilibrium. |
The Complete Black Brane Solutions in D-dimensional Coupled Gravity
System: In this paper, we use only the equation of motion for an interacting system
of gravity, dilaton and antisymmetric tensor to study the black brane
solutions. By making use of the property of Schwarzian derivative, we obtain
the complete solution of this system of equations. For some special values we
obtain the well-known BPS brane and black brane solutions. | Holography Beyond the Penrose Limit: The flat pp-wave background geometry has been realized as a particular
Penrose limit of AdS_5 x S^5. It describes a string that has been infinitely
boosted along an equatorial null geodesic in the S^5 subspace. The string
worldsheet Hamiltonian in this background is free. Finite boosts lead to
curvature corrections that induce interacting perturbations of the string
worldsheet Hamiltonian. We develop a systematic light-cone gauge quantization
of the interacting worldsheet string theory and use it to obtain the
interacting spectrum of the so-called `two-impurity' states of the string. The
quantization is technically rather intricate and we provide a detailed account
of the methods we use to extract explicit results. We give a systematic
treatment of the fermionic states and are able to show that the spectrum
possesses the proper extended supermultiplet structure (a non-trivial fact
since half the supersymmetry is nonlinearly realized). We test holography by
comparing the string energy spectrum with the scaling dimensions of
corresponding gauge theory operators. We confirm earlier results that agreement
obtains in low orders of perturbation theory, but breaks down at third order.
The methods presented here can be used to explore these issues in a wider
context than is specifically dealt with in this paper. |
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