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A Relativistic Relative of the Magnon S-Matrix: We construct a relativistic scattering theory based on a q deformation and
large string tension limit of the magnon S-matrix of the string world sheet
theory in AdS_5 x S^5. The S-matrix falls naturally into a previously studied
class associated to affine quantum groups, in this case for a twisted affine
loop superalgebra associated to an outer automorphism of sl(2|2). This infinite
algebra includes the celebrated triply extended psl(2|2) x R^3 algebra, but
only two of the centres, the lightcone components of the 2-momentum, are
non-vanishing. The algebra has the interpretation as an extended supersymmetry
algebra including a non-trivial R-symmetry. The representation theory of this
algebra has some complications in that tensor products are reducible but
indecomposable, however, we find that structure meshes perfectly with the
bootstrap, or fusion, equations of S-matrix theory. The bootstrap equations can
then be used inductively to generate the complete S-matrix. Unlike the magnon
theory, the relativistic theory only has a finite set of states and we find
that - at least when the deformation parameter q is a root of unity - the
spectrum matches precisely the soliton spectrum of the relativistic theory
underlying the Pohlmeyer reduction of the string world sheet theory known as
the semi-symmetric space sine-Gordon theory.
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Perturbed Conformal Field Theory on Fluctuating Sphere: General properties of perturbed conformal field theory interacting with
quantized Liouville gravity are considered in the simplest case of spherical
topology. We discuss both short distance and large distance asymptotic of the
partition function. The crossover region is studied numerically for a simple
example of the perturbed Yang-Lee model, complemented in general with arbitrary
conformal ``spectator'' matter. The latter is not perturbed and remains
conformal along the flow, thus giving a control over the Liouville central
charge. The partition function is evaluated numerically from combined analytic
and perturbative information. In this paper we use the perturbative information
up to third order. At special points the four-point integral can be evaluated
and compared with our data. At the solvable point of minimal Liouville gravity
we are in remarkably good agreement with the matrix model predictions.
Possibilities to compare the result with random lattice simulations is
discussed.
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Baxterization, dynamical systems, and the symmetries of integrability: We resolve the `baxterization' problem with the help of the automorphism
group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations.
This infinite group of symmetries is realized as a non-linear (birational)
Coxeter group acting on matrices, and exists as such, {\em beyond the narrow
context of strict integrability}. It yields among other things an unexpected
elliptic parametrization of the non-integrable sixteen-vertex model. It
provides us with a class of discrete dynamical systems, and we address some
related problems, such as characterizing the complexity of iterations.
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Multi--dimensional IWP Solutions for Heterotic String Theory: We present extremal stationary solutions that generalize the
Israel-Wilson-Perjes class for the d+3-dimensional low-energy limit of
heterotic string theory with n >= d+1 U(1) gauge fields compactified on a
d-torus. A rotating axisymmetric dyonic solution is obtained using the matrix
Ernst potential formulation and expressed in terms of a single d+1 X d+1-matrix
harmonic function. By studying the asymptotic behaviour of the field
configurations we define the physical charges of the field system. The
extremality condition makes the charges to saturate the
Bogomol'nyi-Prasad-Sommerfield (BPS) bound. The gyromagnetic ratios of the
corresponding field configurations appear to have arbitrary values. A subclass
of rotating dyonic black hole-type solutions arises when the NUT charges are
set to zero. In the particular case d=1, n=6, which correspond to N=4, D=4
supergravity, the found dyon reproduces the supersymmetric dyonic solution
constructed by Bergshoeff et al.
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Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop: By applying the known expressions for SYM and SUGRA tree amplitudes, we write
generating functions for the NNMHV box coefficients of SYM as well as the MHV,
NMHV, and NNMHV box coefficients for SUGRA. The all-multiplicity generating
functions utilize covariant, on-shell superspace whereby the contribution from
arbitrary external states in the supermultiplet can be extracted by Grassmann
operators. In support of the relation between dual Wilson loops and SYM
scattering amplitudes at weak coupling, the SYM amplitudes are presented in a
manifestly dual superconformal form. We introduce ordered box coefficients for
calculating SUGRA quadruple cuts and prove that ordered coefficients generate
physical cut amplitudes after summing over permutations of the external legs.
The ordered box coefficients are produced by sewing ordered subamplitudes,
previously used in applying on-shell recursion relations at tree level. We
describe our verification of the results against the literature, and a formula
for extracting the contributions from external gluons or gravitons to NNMHV
superamplitudes is presented.
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Elastic Kink-Meson Scattering: In classical field theory, radiation does not reflect off of reflectionless
kinks. In quantum field theory, radiation quanta, called mesons, can be
reflected. We provide a general analytical formula for the leading order
amplitude and probability for the elastic scattering of mesons off of
reflectionless quantum kinks. In the case of the Sine-Gordon model we verify
that, due to a cancellation of six contributing processes, our general formula
yields an amplitude of zero, as is required by integrability.
|
W_{\infty} Gauge Transformations and the Electromagnetic Interactions of
Electrons in the Lowest Landau Level: We construct a $W_{\infty}$ gauge field theory of electrons in the lowest
Landau level. For this purpose we introduce an external gauge potential $\cal A
$ such that its $W_{\infty}$ gauge transformations cancel against the gauge
transformation of the electron field. We then show that the electromagnetic
interactions of electrons in the lowest Landau level are obtained through a
non-linear realization of $\cal A$ in terms of the $U(1)$ gauge potential
$A^{\m}$. As applications we derive the effective Lagrangians for circular
droplets and for the $\n =1$ quantum Hall system.
|
Cosmological String Gas on Orbifolds: It has long been known that strings wound around incontractible cycles can
play a vital role in cosmology. In particular, in a spacetime with toroidal
spatial hypersurfaces, the dynamics of the winding modes may help yield three
large spatial dimensions. However, toroidal compactifications are
phenomenologically unrealistic. In this paper we therefore take a first step
toward extending these cosmological considerations to $D$-dimensional toroidal
orbifolds. We use numerical simulation to study the timescales over which
"pseudo-wound" strings unwind on these orbifolds with trivial fundamental
group. We show that pseudo-wound strings can persist for many ``Hubble times''
in some of these spaces, suggesting that they may affect the dynamics in the
same way as genuinely wound strings. We also outline some possible extensions
that include higher-dimensional wrapped branes.
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Does the radioactive decay obey the Poisson statistics?: It is shown that a nontrivial quantum structure of our space at macroscopic
scales, which may exist as a relic of quantum gravity processes in the early
universe, gives rise to a new phenomenon: spontaneous origin of an interference
picture in every physical process. This explains why statistical distributions
in radioactivity measurements may be different from the Poisson distribution.
|
Nahm Equations and Boundary Conditions: We derive certain boundary conditions in Nahm's equations by considering a
system of N parallel D1-branes perpendicular to a D3-brane in type IIB string
theory.
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Semiclassical black holes expose forbidden charges and censor divergent
densities: Classically, the black hole (BH) horizon is a rigid surface of infinite
redshift; whereas the uncertainty principle dictates that the semiclassical
(would-be) horizon cannot be fixed in space nor can it exhibit any divergences.
We propose that this distinction underlies the BH information-loss paradox, the
apparent absence of BH hair, the so-called trans-Planckian problem and the
recent "firewall" controversy. We argue that the correct prescription is to
first integrate out the fluctuations of the background geometry and only then
evaluate matter observables. The basic idea is illustrated using a system of
two strongly coupled harmonic oscillators, with the heavier oscillator
representing the background. We then apply our proposal to matter fields near a
BH horizon, initially treating the matter fields as classical and the
background as semiclassical. In this case, the average value of the associated
current does not vanish; so that it is possible, in principle, to measure the
global charge of the BH. Then the matter is, in addition to the background,
treated quantum mechanically. We show that the average energy density of matter
as seen by an asymptotic observer is finite and proportional to the BH entropy,
rather than divergent. We discuss the implications of our results for the
various controversial issues concerning BH physics.
|
On microscopic structure of the QCD vacuum: We propose a new class of regular stationary axially symmetric solutions in a
pure QCD which correspond to monopole-antimonopole pairs at macroscopic scale.
The solutions represent vacuum field configurations which are locally stable
against quantum gluon fluctuations in any small space-time vicinity. This
implies that the monopole-antimonopole pair can serve as a structural element
in microscopic description of QCD vacuum formation through the monopole pair
condensation.
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Quasilocal energy for three-dimensional massive gravity solutions with
chiral deformations of AdS boundary conditions: We consider critical gravity in three dimensions; that is, the New Massive
Gravity theory formulated about Anti-de Sitter (AdS) space with the specific
value of the graviton mass for which it results dual to a two-dimensional
conformal field theory with vanishing central charge. As it happens with Kerr
black holes in four-dimensional critical gravity, in three-dimensional critical
gravity the Banados-Teitelboim-Zanelli black holes have vanishing mass and
vanishing angular momentum. However, provided suitable asymptotic conditions
are chosen, the theory may also admit solutions carrying non-vanishing charges.
Here, we give simple examples of exact solutions that exhibit falling-off
conditions that are even weaker than those of the so-called Log-gravity. For
such solutions, we define the quasilocal stress-tensor and use it to compute
conserved charges. Despite the drastic deformation of AdS3 asymptotic, these
solutions have finite mass and angular momentum.
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A Model for High Energy Scattering in Quantum Gravity: We present a model for high energy two body scattering in a quantum theory of
gravity. The model is applicable for center of mass energies higher than the
relevant Planck scale. At impact parameters smaller than the Schwarzchild
radius appropriate to the center of mass energy and total charge of the initial
state, the cross section is dominated by an inelastic process in which a single
large black hole is formed. The black hole then decays by Hawking radiation.
The elastic cross section is highly suppressed at these impact parameters
because of the small phase space for thermal decay into a high energy two body
state. For very large impact parameter the amplitude is dominated by
eikonalized single graviton exchange. At intermediate impact parameters the
scattering is more complicated, but since the Schwarzchild radius grows with
energy, we speculate that a more sophisticated eikonal calculation which uses
the nonlinear classical solutions of the field equations may provide a good
approximation at all larger impact parameters. We discuss the extent to which
black hole production will be observable in theories with low scale quantum
gravity and large dimensions.
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Worldvolume origin of Higher M Theories: Exceptional Periodicity (EP) has taught us that there are families of M
Theory-like superalgebras in spacetime dimensions $11,19,27,\dots$ up to
infinity. In this paper, we make the conjecture that M Theory at each level of
EP can be realized as a brane worldvolume theory of an M Theory superalgebra at
some higher level of EP.
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Lorentz-covariant sampling theory for fields: Sampling theory is a discipline in communications engineering involved with
the exact reconstruction of continuous signals from discrete sets of sample
points. From a physics perspective, this is interesting in relation to the
question of whether spacetime is continuous or discrete at the Planck scale,
since in sampling theory we have functions which can be viewed as equivalently
residing on a continuous or discrete space. Further, it is possible to
formulate analogues of sampling which yield discreteness without disturbing
underlying spacetime symmetries. In particular, there is a proposal for how
this can be adapted for Minkowski spacetime. Here we will provide a detailed
examination of the extension of sampling theory to this context. We will also
discuss generally how spacetime symmetries manifest themselves in sampling
theory, which at the surface seems in conflict with the fact that the
discreteness of the sampling is not manifestly covariant. Specifically, we will
show how the symmetry of a function space with a sampling property is
equivalent to the existence of a family of possible sampling lattices related
by the symmetry transformations.
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Recent Attempts in the Analysis of Black Hole Radiation: In this thesis, we first present a brief review of black hole radiation which
is commonly called Hawking radiation. The existence of Hawking radiation by
itself is well established by now because the same result is derived by several
different methods. On the other hand, there remain several aspects of the
effect which have yet to be clarified. We clarify some arguments in previous
works on the subject and then attempt to present the more satisfactory
derivations of Hawking radiation. To be specific, we examine the analyses in
the two recent derivations of Hawking radiation which are based on anomalies
and tunneling; both of these derivations were initiated by Wilczek and his
collaborators. We then present a simple derivation based on anomalies by
emphasizing a systematic use of covariant currents and covariant anomalies
combined with boundary conditions which have clear physical meaning. We also
extend a variant of the tunneling method proposed by Banerjee and Majhi to a
Kerr-Newman black hole by using the technique of the dimensional reduction near
the horizon. We directly derive the black body spectrum for a Kerr-Newman black
hole on the basis of the tunneling mechanism.We directly derive the black body
spectrum for a Kerr-Newman black hole on the basis of the tunneling mechanism.
|
Counting Photons in Static Electric and Magnetic Fields: We describe the electromagnetic field by the massless limit of a massive
vector field in the presence of a Coulomb gauge fixing term. The gauge fixing
term ensures that, in the massless limit, the longitudinal mode is removed from
the spectrum and only the two transverse modes survive. The system, coupled to
a classical conserved current, is quantized in the canonical formalism. The
classical field configurations due to time-independent electric charges and
currents are represented by coherent states of longitudinal and transverse
photons, respectively. The occupation number in these states is finite. In
particular, the number of longitudinal photons bound by an electric charge q is
given by N=q^2/(16\pi\hbar).
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Static multi-soliton solutions in the affine su(N+1) Toda models: We study some static multi-soliton configurations in the su(N + 1) Toda
models. Such configurations exist for N > 1. We construct explicitly a
multi-soliton solution for any N and study conditions for having such
solutions. The number of static solitons is limited by the rank of the su(N +
1) Lie algebra. We give some examples of non-static multi-soliton solutions
with static components.
|
Fermionic Path Integrals and Two-Dimensional Ising Model with Quenched
Site Disorder: The notion of the integral over the anticommuting Grassmann variables is
applied to analyze the fermionic structure of the 2D Ising model with quenched
site dilution. In the $N$-replica scheme, the model is explicitly reformulated
as a theory of interacting fermions on a lattice. For weak dilution, the
continuum-limit approximation implies the log-log singularity in the specific
heat near $T_c$.
|
Non-perpetual Eternal Inflation and the Emergent de Sitter Swampland
Conjecture: We introduce a novel correlation, $n_s$ - $\Delta N$, connecting CMB
parameters to the required total e-folds for eternal inflation. This
correlation provides a robust tool for evaluating eternal (string) inflation
models using CMB data and explores the impact of quantum fluctuations on
non-attractor phases. By generalizing eternal inflation criteria, our
parameterization simplifies rigorous testing of predictions and reveals a link
between refined de Sitter conjecture parameters and the eternal nature of the
cosmic landscape. This points to a general tendency towards eternal behavior in
low-energy effective field theories within the landscape, opening the
possibility for our cosmic stage to potentially embrace a 'multiverse'
scenario.
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Ad$S_5$ with two boundaries and holography of $\cal{N}=$4 SYM theory: According to the AdS/CFT correspondence, the ${\cal N}=4$ supersymmetric
Yang-Mills (SYM) theory is studied through its gravity dual whose configuration
has two boundaries at the opposite sides of the fifth coordinate. At these
boundaries, in general, the four dimensional (4D) metrics are different, then
we expect different properties for the theory living in two boundaries. It is
studied how these two different properties of the theory are obtained from a
common 5D bulk manifold in terms of the holographic method. We could show in
our case that the two theories on the different boundaries are described by the
Ad$S_5$, which is separated into two regions by a domain wall. This domain wall
is given by a special point of the fifth coordinate. Some issues of the
entanglement entropy related to this bulk configuration are also discussed.
|
Twisted C-brackets: We consider the double field formulation of the closed bosonic string theory,
and calculate the Poisson bracket algebra of the symmetry generators governing
both general coordinate and local gauge transformations. Parameters of both of
these symmetries depend on a double coordinate, defined as a direct sum of the
initial and T-dual coordinate. When no antisymmetric field is present, the
$C$-bracket appears as the Lie bracket generalization in a double theory. With
the introduction of the Kalb-Ramond field, the $B$-twisted $C$-bracket appears,
while with the introduction of the non-commutativity parameter, the
$\theta$-twisted $C$-bracket appears. We present the derivation of these
brackets and comment on their relations to analogous twisted Courant brackets
and T-duality.
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Building the Full Fermion-Photon Vertex of QED by Imposing
Multiplicative Renormalizability of the Schwinger-Dyson Equations for the
Fermion and Photon Propagators: In principle, calculation of a full Green's function in any field theory
requires knowledge of the infinite set of multi-point Green's functions, unless
one can find some way of truncating the corresponding Schwinger-Dyson
equations. For the fermion and boson propagators in QED this requires an {\it
ansatz} for the full three point vertex. Here we illustrate how the properties
of gauge invariance, gauge covariance and multiplicative renormalizability
impose severe constraints on this fermion-boson interaction, allowing a
consistent truncation of the propagator equations. We demonstrate how these
conditions imply that the 3-point vertex {\bf in the propagator equations} is
largely determined by the behaviour of the fermion propagator itself and not by
knowledge of the many higher point functions. We give an explicit form for the
fermion-photon vertex, which in the fermion and photon propagator fulfills
these constraints to all orders in leading logarithms for massless QED, and
accords with the weak coupling limit in perturbation theory at ${\cal
O}(\alpha)$. This provides the first attempt to deduce non-perturbative Feynman
rules for strong physics calculations of propagators in massless QED that
ensures a more consistent truncation of the 2-point Schwinger-Dyson equations.
The generalisation to next-to-leading order and masses will be described in a
longer publication.
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Chiral anomaly as a composite operator in the gradient flow exact
renormalization group formalism: The gradient flow exact renormalization group (GFERG) is an idea that
incorporates gauge invariant gradient flows into the formalism of the exact
renormalization group (ERG). GFERG introduces a Wilson action with a cutoff
while keeping vector gauge invariance manifestly. The details of the formalism
are still to be worked out. In this paper, we apply GFERG to construct the
Wilson action of massless Dirac fermions under the background chiral gauge
fields. By formulating the chiral anomaly as a ``composite operator,'' we make
the scale invariance of the anomaly manifest. We argue that the same result
extends to QCD.
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Homogeneous M2 duals: Motivated by the search for new gravity duals to M2 branes with $N>4$
supersymmetry --- equivalently, M-theory backgrounds with Killing superalgebra
$\mathfrak{osp}(N|4)$ for $N>4$ --- we classify homogeneous M-theory
backgrounds with symmetry Lie algebra $\mathfrak{so}(n) \oplus
\mathfrak{so}(3,2)$ for $n=5,6,7$. We find that there are no new backgrounds
with $n=6,7$ but we do find a number of new (to us) backgrounds with $n=5$. All
backgrounds are metrically products of the form $\operatorname{AdS}_4 \times
P^7$, with $P$ riemannian and homogeneous under the action of
$\operatorname{SO}(5)$, or $S^4 \times Q^7$ with $Q$ lorentzian and homogeneous
under the action of $\operatorname{SO}(3,2)$. At least one of the new
backgrounds is supersymmetric (albeit with only $N=2$) and we show that it can
be constructed from a supersymmetric Freund--Rubin background via a Wick
rotation. Two of the new backgrounds have only been approximated numerically.
(The second version of this paper includes an appendix by Alexander~S.~Haupt,
closing a gap in our original analysis.)
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A Note on the Neutrino Theory of Light: In this small note we ask several questions which are relevant to the
construction of the self-consistent neutrino theory of light. The previous
confusions in such attempts are explained in the more detailed publication.
|
Differential Structure on kappa-Minkowski Spacetime Realized as Module
of Twisted Weyl Algebra: The differential structure on the kappa-Minkowski spacetime from Jordanian
twist of Weyl algebra is constructed, and it is shown to be closed in
4-dimensions in contrast to the conventional formulation. Based on this
differential structure, we have formulated a scalar field theory in this
kappa-Minkowski spacetime.
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PiTP Lectures on Complexity and Black Holes: This is the first of three PiTP lectures on complexity and its role in black
hole physics.
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Snyder space revisited: We examine basis functions on momentum space for the three dimensional
Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the
SO(3) group manifold, and that the basis functions span either one of two
Hilbert spaces. This implies the existence of two distinct lattice structures
of space, on which continuous rotations and translations are unitarily
implementable.
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SUSY Breaking in Local String/F-Theory Models: We investigate bulk moduli stabilisation and supersymmetry breaking in local
string/F-theory models where the Standard Model is supported on a del Pezzo
surface or singularity. Computing the gravity mediated soft terms on the
Standard Model brane induced by bulk supersymmetry breaking in the LARGE volume
scenario, we explicitly find suppressions by M_s/M_P ~ V^{-1/2} compared to
M_{3/2}. This gives rise to several phenomenological scenarios, depending on
the strength of perturbative corrections to the effective action and the source
of de Sitter lifting, in which the soft terms are suppressed by at least
M_P/V^{3/2} and may be as small as M_P/V^2. Since the gravitino mass is of
order M_{3/2} ~ M_P/V, for TeV soft terms all these scenarios give a very heavy
gravitino (M_{3/2} >= 10^8 GeV) and generically the lightest moduli field is
also heavy enough (m >= 10 TeV) to avoid the cosmological moduli problem. For
TeV soft terms, these scenarios predict a minimal value of the volume to be V ~
10^{6-7} in string units, which would give a unification scale of order M_{GUT}
~ M_s V^{1/6} ~ 10^{16} GeV. The strong suppression of gravity mediated soft
terms could also possibly allow a scenario of dominant gauge mediation in the
visible sector but with a very heavy gravitino M_{3/2} > 1 TeV.
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Classical Hair in String Theory I: General Formulation: We discuss why classical hair is desirable for the description of black
holes, and show that it arises generically in a wide class of field theories
involving extra dimensions. We develop the canonical formalism for theories
with the matter content that arises in string theory. General covariance and
duality are used to determine the form of surface terms. We derive an effective
theory (reduced Hamiltonian) for the hair in terms of horizon variables. %
accessible to an observer at infinity. Solution of the constraints expresses
these variables in terms of hair accessible to an observer at infinity. We
exhibit some general properties of the resulting theory, including a formal
identification of the temperature and entropy. The Cveti\v{c}-Youm dyon is
described in some detail, as an important example.
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A relation between massive and massless string tree amplitudes: We uncover a relation between the scattering amplitudes of massive strings
and the $\alpha'$ expansion of the massless string amplitude at tree level.
More precisely, the n-point tree amplitude of n-1 massless and one massive
state is written as a linear combination of n+1 massless string amplitudes at
the $\alpha'^2$ order.
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AdS-Taub-NUT spacetimes and exact black bounces with scalar hair: We present a new family of exact four-dimensional Taub-NUT spacetimes in
Einstein-$\Lambda$ theory supplemented with a conformally coupled scalar field
exhibiting a power-counting super-renormalizable potential. The construction
proceeds as follows: A solution of a conformally coupled theory with a
conformal potential, henceforth the seed $(g_{\mu\nu},\phi)$, is transformed by
the action of a specific change of frame in addition with a simultaneous shift
of the seed scalar. The new configuration, $(\bar{g}_{\mu\nu},\bar{\phi})$,
solves the field equations of a conformally coupled theory with the
aforementioned super-renormalizable potential. The solution spectrum of the
seed is notoriously enhanced. We highlight the existence of two types of exact
black bounces given by de Sitter and anti-de Sitter geometries that transit
across three different configurations each. The de Sitter geometries transit
from a regular black hole with event and cosmological horizons to a bouncing
cosmology connecting two de Sitter Universes with different values of the
asymptotic cosmological constant. An intermediate phase represented by a de
Sitter wormhole or by a bouncing cosmology that connects two de Sitter
Universes is shown, this under the presence of a cosmological horizon. On the
other hand, the anti-de Sitter geometries transit from a regular black hole
with inner and event horizons to a wormhole that connects two asymptotic
boundaries with different constant curvatures. The intermediate phase is given
by an anti-de Sitter regular black hole with a single event horizon that
appears in two different settings. As a regular anti-de Sitter black hole
inside of an anti-de Sitter wormhole or as an anti-de Sitter regular black hole
with an internal cosmological bounce. These geometries are smoothly connected
by the mass parameter only. Other black holes, bouncing cosmologies and
wormholes are also found.
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A Note on the Near Horizon Charges for the Five Dimensional Myers-Perry
Black Holes: Inspired by the recent work on the spacetime structure near generic black
hole horizons [1], the near horizon charges for an explicit example in higher
dimensions than four (d > 4), namely for the five dimensional Myers-Perry
metric with two equal rotation parameter are found in Hamiltonian formalism.
Finding the supertranslation and the one-form superrotation, it is proved that
the Myers-Perry black hole with two equal rotation parameter a = b does not
satisfy the gauge flatness condition due to the non-vanishing associated field
strength in five dimensional spacetime. It is shown that as the near horizon
limit of such a metric satisfies a specific set of boundary conditions, the
near horizon algebra can be represented as an infinitely many copies of
Heisenberg algebras as a generalisation to the Kerr case in four dimensions.
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Dielectric-branes in Non-supersymmetric SO(3)-invariant Perturbation of
Three-dimensional N=8 Yang-Mills Theory: We study non-supersymmetric SO(3)-invariant deformations of d=3, N=8 super
Yang-Mills theory and their type IIA string theory dual. By adding both gaugino
mass and scalar mass, dielectric D4-brane potential coincides with D5-brane
potential in type IIB theory. We find the region of parameter space where the
non-supersymmetric vacuum is described by stable dielectric NS5-branes. By
considering the generalized action for NS5-branes in the presence of D4-flux,
we also analyze the properties of dielectric NS5-branes.
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BPS D3-branes on smooth ALE manifolds: In this talk I review the recent construction of a new family of classical
BPS solutions of type IIB supergravity describing 3-branes transverse to a
6-dimensional space with topology $\mathbb{R}^{2}\times$ALE. They are
characterized by a non-trivial flux of the supergravity 2-forms through the
homology 2-cycles of a generic smooth ALE manifold. These solutions have two
Killing spinors and thus preserve $\mathcal{N}=2$ supersymmetry. They are
expressed in terms of a quasi harmonic function $H$ (the ``warp factor''),
whose properties was studied in detail in the case of the simplest ALE, namely
the Eguchi-Hanson manifold. The equation for $H$ was identified as an instance
of the confluent Heun equation.
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Where in the String Landscape is Quintessence: We argue that quintessence may reside in certain corners of the string
landscape. It arises as a linear combination of internal space components of
higher rank forms, which are axion-like at low energies, and may mix with
4-forms after compactification of the Chern-Simons terms to 4D due to internal
space fluxes. The mixing induces an effective mass term, with an action which
{\it preserves} the axion shift symmetry, breaking it spontaneously after the
background selection. With several axions, several 4-forms, and a low string
scale, as in one of the setups already invoked for dynamically explaining a
tiny residual vacuum energy in string theory, the 4D mass matrix generated by
random fluxes may have ultralight eigenmodes over the landscape, which are
quintessence. We illustrate how this works in simplest cases, and outline how
to get the lightest mass to be comparable to the Hubble scale now, $H_0 \sim
10^{-33} {\rm eV}$. The shift symmetry protects the smallest mass from
perturbative corrections in field theory. Further, if the ultralight eigenmode
does not couple directly to any sector strongly coupled at a high scale, the
non-perturbative field theory corrections to its potential will also be
suppressed. Finally, if the compactification length is larger than the string
length by more than an order of magnitude, the gravitational corrections may
remain small too, even when the field value approaches $M_{Pl}$.
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Reggeization of N=8 Supergravity and N=4 Yang--Mills Theory: We show that the gluon of N=4 Yang--Mills theory lies on a Regge trajectory,
which then implies that the graviton of N=8 supergravity also lies on a Regge
trajectory. This is consistent with the conjecture that N=8 supergravity is
ultraviolet finite in perturbation theory.
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Non-linear WKB Analysis of the String Equation: We apply non-linear WKB analysis to the study of the string equation. Even
though the solutions obtained with this method are not exact, they approximate
extremely well the true solutions, as we explicitly show using numerical
simulations. ``Physical'' solutions are seen to be separatrices corresponding
to degenerate Riemann surfaces. We obtain an analytic approximation in
excellent agreement with the numerical solution found by Parisi et al. for the
$k=3$ case.
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Little IIB Matrix Model: We study the zero-dimensional reduced model of D=6 pure super Yang-Mills
theory and argue that the large N limit describes the (2,0) Little String
Theory. The one-loop effective action shows that the force exerted between two
diagonal blocks of matrices behaves as 1/r^4, implying a six-dimensional
spacetime. We also observe that it is due to non-gravitational interactions. We
construct wave functions and vertex operators which realize the D=6, (2,0)
tensor representation. We also comment on other "little" analogues of the IIB
matrix model and Matrix Theory with less supercharges.
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Mass formulae and staticity condition for dark matter charged black
holes: The Arnowitt-Deser-Misner formalism is used to derive variations of mass,
angular momentum and canonical energy for Einstein-Maxwell {\it dark matter}
gravity in which the auxiliary gauge field coupled via kinetic mixing term to
the ordinary Maxwell one, which mimics properties of {\it hidden sector}.
Inspection of the initial data for the manifold with an interior boundary,
having topology of $S^2$, enables us to find the generalised first law of black
hole thermodynamics in the aforementioned theory. It has been revealed that the
stationary black hole solution being subject to the condition of encompassing a
bifurcate Killing horizon with a bifurcation sphere, which is non-rotating,
must be static and has vanishing {\it magnetic} Maxwell and {\it dark matter}
sector fields, on static slices of the spacetime under consideration.
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Fractons in curved space: We consistently couple simple continuum field theories with fracton
excitations to curved spacetime backgrounds. We consider homogeneous and
isotropic fracton field theories, with a conserved $U(1)$ charge and dipole
moment. Coupling to background fields allows us to consistently define a
stress-energy tensor for these theories and obtain the respective Ward
identities. Along the way, we find evidence for a mixed gauge-gravitational
anomaly in the symmetric tensor gauge theory which naturally couples to
conserved dipoles. Our results generalise to systems with arbitrarily higher
conserved moments, in particular, a conserved quadrupole moment.
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Further results on Functional Determinants of Laplacians in Simplicial
Complexes: We investigate the functional determinant of the laplacian on piece-wise flat
two-dimensional surfaces, with conical singularities in the interior and/or
corners on the boundary. Our results extend earlier investigations of the
determinants on smooth surfaces with smooth boundaries. The differences to the
smooth case are: a) different ``interaction energies'' between pairs of conical
singularities than one would expect from a naive extrapolation of the results
for a smooth surface; and b) ``self-energies'' of the singularities.
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Tropical Amplitudes For Colored Lagrangians: Recently a new formulation for scattering amplitudes in Tr($\Phi^3$) theory
has been given based on simple combinatorial ideas in the space of kinematic
data. This allows all-loop integrated amplitudes to be expressed as ''curve
integrals'' defined using tropical building blocks - the ''headlight
functions''. This paper shows how the formulation extends to the amplitudes of
more general Lagrangians. We will present a number of different ways of
introducing tropical ''numerator functions'' that allow us to describe general
Lagrangian interactions. The simplest family of these ''tropical numerators''
computes the amplitudes of interesting Lagrangians with infinitely many
interactions. We also describe methods for tropically formulating the
amplitudes for general Lagrangians. One uses a variant of ''Wick contraction''
to glue together numerator factors for general interaction vertices. Another
uses a natural characterization of polygons on surfaces to give a novel
combinatorial description of all possible diagrams associated with arbitrary
valence interactions.
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N=2 Moduli Spaces and N=1 Dualities for SO(n_c) and USp(2n_c) SuperQCD: We determine the exact global structure of the moduli space of $N{=}2$
supersymmetric $SO(n)$ and $\USp(2n)$ gauge theories with matter
hypermultiplets in the fundamental representations, using the
non-renormalization theorem for the Higgs branches and the exact solutions for
the Coulomb branches. By adding an $(N{=}2)$--breaking mass term for the
adjoint chiral field and varying the mass, the $N{=}2$ theories can be made to
flow to either an ``electric'' $N{=}1$ supersymmetric QCD or its $N{=}1$ dual
``magnetic'' version. We thus obtain a derivation of the $N{=}1$ dualities of
Seiberg.
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Spatially Modulated Vacua in a Lorentz-invariant Scalar Field Theory: Spatial modulation has been studied for a long time in condensed matter,
nuclear matter and quark matter, so far in non-relativistic field theories. In
this paper, spatially modulated vacua at zero temperature and zero density are
studied in relativistic field theories. We first propose an adaptation of the
Nambu-Goldstone theorem to higher derivative theories under the assumption of
the absence of ghosts: when a global symmetry is spontaneously broken due to
vacuum expectation values of space-time derivatives of fields, a
Nambu-Goldstone (NG) boson appears without a canonical kinetic (quadratic
derivative) term with a quartic derivative term in the modulated direction
while a Higgs boson appears with a canonical kinetic term. We demonstrate this
in a simple model allowing (meta)stable modulated vacuum of a phase modulation
(Fulde-Ferrell state), where an NG mode associated with spontaneously broken
translational and $U(1)$ symmetries appears.
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On Hawking Radiation of 3D Rotating Hairy Black Holes: We study the Hawking radiation of 3D rotating hairy black holes. More
concretely, we compute the transition probability of a bosonic and fermionic
particle in such backgrounds. Thew, we show that the transition probability is
independent of the nature of the particle. It is observed that the charge of
the scalar hair B and the rotation parameter a control such a probability.
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Non-Perturbative Mass Renormalization in Quenched QED from the Worldline
Variational Approach: Following Feynman's successful treatment of the polaron problem we apply the
same variational principle to quenched QED in the worldline formulation. New
features arise from the description of fermions by Grassmann trajectories, the
supersymmetry between bosonic and fermionic variables and the much more
singular structure of a renormalizable gauge theory like QED in 3+1 dimensions.
We take as trial action a general retarded quadratic action both for the
bosonic and fermionic degrees of freedom and derive the variational equations
for the corresponding retardation functions. We find a simple analytic,
non-perturbative, solution for the anomalous mass dimension gamma_m(alpha) in
the MS scheme. For small couplings we compare our result with recent four-loop
perturbative calculations while at large couplings we find that gamma_m(alpha)
becomes proportional to (alpha)^(1/2). The anomalous mass dimension shows no
obvious sign of the chiral symmetry breaking observed in calculations based on
the use of Dyson-Schwinger equations, however we find that a perturbative
expansion of gamma_m(alpha) diverges for alpha > 0.7934. Finally, we
investigate the behaviour of gamma_m(alpha) at large orders in perturbation
theory.
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On the Physical Propagators of QED: The true variables in QED are the transverse photon components and Dirac's
physical electron, constructed out of the fermionic field and the longitudinal
components of the photon. We calculate the propagators in terms of these
variables to one loop and demonstrate their gauge invariance. The physical
electron propagator is shown not to suffer from infrared divergences in any
gauge. In general, all physical Green's functions are gauge invariant and
infrared-finite.
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Gravitational waves from spectator Gauge-flation: We investigate the viability of inflation with a spectator sector comprised
of non-Abelian gauge fields coupled through a higher order operator. We dub
this model "spectator Gauge-flation". We study the predictions for the
amplitude and tensor tilt of chiral gravitational waves and conclude that a
slightly red-tilted tensor power spectrum is preferred $n_T=-{\cal O}(0.01)$.
As with related models, the enhancement of chiral gravitational waves with
respect to the single-field vacuum gravitational wave background is controlled
by the parameter $\gamma=g^2 Q^2/H^2$, where $g$ is the gauge coupling, $H$ is
the Hubble scale and $Q$ is the VEV of the $SU(2)$ sector. The requirement that
the $SU(2)$ is a spectator sector leads to a maximum allowed value for
$\gamma$, thereby constraining the possible amplification. In order to provide
concrete predictions, we use an $\alpha$-attractor T-model potential for the
inflaton sector. Potential observation of chiral gravitational waves with
significantly tilted tensor spectra would then indicate the presence of
additional couplings of the gauge fields to axions, like in the spectator
axion-SU(2) model, or additional gauge field operators.
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Spectral flow as a map between N=(2,0)-models: The space of $(2,0)$ models is of particular interest among all
heterotic-string models because it includes the models with the minimal
$SO(10)$ unification structure, which is well motivated by the Standard Model
of particle physics data. The fermionic $\mathbb{Z}_2\times \mathbb{Z}_2$
heterotic-string models revealed the existence of a new symmetry in the space
of string configurations under the exchange of spinors and vectors of the
$SO(10)$ GUT group, dubbed spinor-vector duality. Such symmetries are important
for the understanding of the landscape of string vacua and ultimately for the
possible operation of a dynamical vacuum selection mechanism in string theory.
In this paper we generalize this idea to arbitrary internal rational Conformal
Field Theories (RCFTs). We explain how the spectral flow operator normally
acting within a general $(2,2)$ theory can be used as a map between $(2,0)$
models. We describe the details, give an example and propose more simple
currents that can be used in a similar way.
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Kaluza-Klein from Colour-Kinematics Duality for Massive Fields: We consider a broad class of massive four dimensional effective theories
describing an infinite tower of charged massive spin 1 states, interacting with
massless spin 1 and spin 0. The spectrum is chosen to be the same as that
appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the
absence of any spurious poles in a possible double copy formulation. The
effective theories are characterized by multiple different couplings between
different fields which are unconstrained by symmetries and low energy criteria.
Remarkably, by demanding that the scattering amplitudes preserve
colour-kinematics duality for different scattering processes, required for the
existence of a massive double copy, we find that our 4d Lagrangian is fixed
uniquely to the Kaluza-Klein compactification of 5d Yang-Mills theory together
with its known double copy consistent higher derivative operators.
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Infra-red dynamics of D1-branes at the conifold: We study the infra-red dynamics of D1-branes at the conifold. We show using
methods developed to study the infra-red dynamics of (4,4) theories, the
infra-red degrees of freedom of the (2,2) theory of a single D1-brane at the
conifold is that of a linear dilaton with background charge of $\sqrt{2}$ and a
compact scalar. The gauge theory of $N$ D1-branes at the conifold is used to
formulate the matrix string in the conifold background.
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Gravity theory on Poisson manifold with $R$-flux: A novel gravity theory based on Poisson Generalized Geometry is investigated.
A gravity theory on a Poisson manifold equipped with a Riemannian metric is
constructed from a contravariant version of the Levi-Civita connection, which
is based on the Lie algebroid of a Poisson manifold. Then, we show that in
Poisson Generalized Geometry the $R$-fluxes are consistently coupled with such
a gravity. An $R$-flux appears as a torsion of the corresponding connection in
a similar way as an $H$-flux which appears as a torsion of the connection for-
mulated in the standard Generalized Geometry. We give an analogue of the
Einstein-Hilbert action coupled with an $R$-flux, and show that it is invariant
under both $\beta$-diffeomorphisms and $\beta$-gauge transformations.
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Renormalisation group and the Planck scale: I discuss the renormalisation group approach to gravity, its link to Steven
Weinberg's asymptotic safety scenario, and give an overview of results with
applications to particle physics and cosmology.
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The Superparticle on the Surface S_2: A superparticle action which is globally supersymmetric in the target space
is proposed. The supersymmetry is the supersymmetric extension of the rotation
group O(3).
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On Matrix Model Formulations of Noncommutative Yang-Mills Theories: We study stability of noncommutative spaces in matrix models and discuss the
continuum limit which leads to noncommutative Yang-Mills theories (NCYM). It
turns out that most of noncommutative spaces in bosonic models are unstable.
This indicates perturbative instability of fuzzy R^D pointed out by Van
Raamsdonk and Armoni et al. persists to nonperturbative level in these cases.
In this sense, these bosonic NCYM are not well-defined, or at least their
matrix model formulations studied in this paper do not work. We also show that
noncommutative backgrounds are stable in a supersymmetric matrix model deformed
by a cubic Myers term, though the deformation itself breaks supersymmetry.
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Källén-Lehmann representation of noncommutative quantum
electrodynamics: Noncommutative (NC) quantum field theory is the subject of many analyses on
formal and general aspects looking for deviations and, therefore, potential
noncommutative spacetime effects. Within of this large class, we may now pay
some attention to the quantization of NC field theory on lower dimensions and
look closely at the issue of dynamical mass generation to the gauge field. This
work encompasses the quantization of the two-dimensional massive quantum
electrodynamics and three-dimensional topologically massive quantum
electrodynamics. We begin by addressing the problem on a general dimensionality
making use of the perturbative Seiberg-Witten map to, thus, construct a general
action, to only then specify the problem to two and three dimensions. The
quantization takes place through the K\"all\'en-Lehmann spectral representation
and Yang-Feldman-K\"all\'en formulation, where we calculate the respective
spectral density function to the gauge field. Furthermore, regarding the photon
two-point function, we discuss how its infrared behavior is related to the term
generated by quantum corrections in two dimensions, and, moreover, in three
dimensions, we study the issue of nontrivial {\theta}-dependent corrections to
the dynamical mass generation.
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Flavor-Dependence and Higher Orders of Gauge-Independent Solutions in
Strong Coupling Gauge Theory: The fermion flavor $N_f$ dependence of non-perturbative solutions in the
strong coupling phase of the gauge theory is reexamined based on the
interrelation between the inversion method and the Schwinger-Dyson equation
approach. Especially we point out that the apparent discrepancy on the value of
the critical coupling in QED will be resolved by taking into account the higher
order corrections which inevitably lead to the flavor-dependence. In the
quenched QED, we conclude that the gauge-independent critical point
$\alpha_c=2\pi/3$ obtained by the inversion method to the lowest order will be
reduced to the result $\alpha_c=\pi/3$ of the Schwinger-Dyson equation in the
infinite order limit, but its convergence is quite slow. This is shown by
adding the chiral-invariant four-fermion interaction.
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Recursion Relations for One-Loop Gravity Amplitudes: We study the application of recursion relations to the calculation of finite
one-loop gravity amplitudes. It is shown explicitly that the known four, five,
and six graviton one-loop amplitudes for which the external legs have identical
outgoing helicities, and the four graviton amplitude with helicities (-,+,+,+)
can be derived from simple recursion relations. The latter amplitude is derived
by introducing a one-loop three-point vertex of gravitons of positive helicity,
which is the counterpart in gravity of the one-loop three-plus vertex in
Yang-Mills. We show that new issues arise for the five point amplitude with
helicities (-,+,+,+,+), where the application of known methods does not appear
to work, and we discuss possible resolutions.
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N=1, D=10 Tensionless Superbranes II: We consider a model for tensionless (null) p-branes with N=1 global
supersymmetry in 10-dimensional Minkowski space-time. We give an action for the
model and show that it is reparametrization and kappa-invariant. We also find
some solutions of the classical equations of motion. In the case of null
superstring (p=1), we obtain the general solution in arbitrary gauge.
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Fluctuations in finite density holographic quantum liquids: We study correlators of the global U(1) currents in holographic models which
involve N=4 SYM coupled to the finite density matter in the probe brane sector.
We find the spectral density associated with the longitudinal response to be
exhausted by the zero sound pole and argue that this could be consistent with
the behavior of Fermi liquid with vanishing Fermi velocity. However the
transversal response shows an unusual momentum independent behavior. Inclusion
of magnetic field leads to a gap in the dispersion relation for the zero sound
mode propagating in the plane of magnetic field. For small values of the
magnetic field B the gap in the spectrum scales linearly with B, which is
consistent with Kohn's theorem for nonrelativistic fermions with pairwise
interaction. We do not find signatures of multiple Landau levels expected in
Landau Fermi liquid theory. We also consider the influence of generic higher
derivative corrections on the form of the spectral function.
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Kahler spinning particles: We construct the U(N) spinning particle theories, which describe particles
moving on Kahler spaces. These particles have the same relation to the N=2
string as usual spinning particles have to the NSR string. We find the
restrictions on the target space of the theories coming from supersymmetry and
from global anomalies. Finally, we show that the partition functions of the
theories agree with what is expected from their spectra, unlike that of the N=2
string in which there is an anomalous dependence on the proper time.
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The Intermediate Coupling Regime in the AdS/CFT Correspondence: The correspondence between the 't Hooft limit of N=4 super Yang-Mills theory
and tree-level IIB superstring theory on AdS(5)xS(5) in a Ramond-Ramond
background at values of lambda=g^2 N ranging from infinity to zero is examined
in the context of unitarity. A squaring relation for the imaginary part of the
holographic scattering of identical string fields in the two-particle channels
is found, and a mismatch between weak and strong 't Hooft coupling is pointed
out within the correspondence. Several interpretations and implications are
proposed.
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The Topological G2 String: We construct new topological theories related to sigma models whose target
space is a seven dimensional manifold of G_2 holonomy. We define a new type of
topological twist and identify the BRST operator and the physical states.
Unlike the more familiar six dimensional case, our topological model is defined
in terms of conformal blocks and not in terms of local operators of the
original theory. We also present evidence that one can extend this definition
to all genera and construct a seven-dimensional topological string theory. We
compute genus zero correlation functions and relate these to Hitchin's
functional for three-forms in seven dimensions. Along the way we develop the
analogue of special geometry for G_2 manifolds. When the seven dimensional
topological twist is applied to the product of a Calabi-Yau manifold and a
circle, the result is an interesting combination of the six dimensional A- and
B-models.
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Monopole operators in N=4 Chern-Simons theories and wrapped M2-branes: Monopole operators in Abelian N=4 Chern-Simons theories described by circular
quiver diagrams are investigated. The magnetic charges of non-diagonal U(1)
gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of
untwisted and twisted hypermultiplets, respectively. For monopole operators
corresponding to the root vectors, we propose a correspondence between the
monopole operators and states of a wrapped M2-brane in the dual geometry.
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The representations of Temperley-Lieb-Jones algebras: Representations of braid group obtained from rational conformal field
theories can be used to obtain explicit representations of Temperley-Lieb-Jones
algebras. The method is described in detail for SU(2)$_k$ Wess - Zumino
conformal field theories and its generalization to an arbitrary rational
conformal field theory outlined. Explicit definition of an associated linear
trace operation in terms of a certain matrix element in the space of conformal
blocks of such a conformal theory is presented. Further for every primary field
of a rational conformal field theory, there is a subfactor of hyperfinite
II$_1$ factor with trivial relative commutant. The index of the subfactor is
given in terms of identity - identity element of certain duality matrix for
conformal blocks of four-point correlators. Jones formula for index ( $<$ 4 )
for subfactors corresponds to spin ${\frac{1}{2}}$ representation of SU(2)$_k$
Wess-Zumino conformal field theory. Definition of the trace operation also
provides a method of obtaining link invariants explicitly.
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Tetrahedral and Cubic Monopoles: Using a numerical implementation of the ADHMN construction, we compute the
fields and energy densities of a charge three monopole with tetrahedral
symmetry and a charge four monopole with octahedral symmetry. We then construct
a one parameter family of spectral curves and Nahm data which represent charge
four monopoles with tetrahedral symmetry, which includes the monopole with
octahedral symmetry as a special case. In the moduli space approximation, this
family describes a novel kind of four monopole scattering and we use our
numerical scheme to construct the energy density at various times during the
motion.
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Acausality in Nonlocal Gravity Theory: We investigate the nonlocal gravity theory by deriving nonlocal equations of
motion using the traditional variation principle in a homogeneous background.
We focus on a class of models with a linear nonlocal modification term in the
action. It is found that the resulting equations of motion contain the advanced
Green's function, implying that there is an acausality problem. As a
consequence, a divergence arises in the solutions due to contributions from the
future infinity unless the Universe will go back to the radiation dominated era
or become the Minkowski spacetime in the future. We also discuss the relation
between the original nonlocal equations and its biscalar-tensor representation
and identify the auxiliary fields with the corresponding original nonlocal
terms. Finally, we show that the acusality problem cannot be avoided by any
function of nonlocal terms in the action.
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Lectures on Mirror Symmetry and Topological String Theory: These are notes of a series of lectures on mirror symmetry and topological
string theory given at the Mathematical Sciences Center at Tsinghua University.
The N=2 superconformal algebra, its deformations and its chiral ring are
reviewed. A topological field theory can be constructed whose observables are
only the elements of the chiral ring. When coupled to gravity, this leads to
topological string theory. The identification of the topological string A- and
B-models by mirror symmetry leads to surprising connections in mathematics and
provides tools for exact computations as well as new insights in physics. A
recursive construction of the higher genus amplitudes of topological string
theory expressed as polynomials is reviewed.
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Superconformal invariants for scattering amplitudes in N=4 SYM theory: Recent studies of scattering amplitudes in planar N=4 SYM theory revealed the
existence of a hidden dual superconformal symmetry. Together with the
conventional superconformal symmetry it gives rise to powerful restrictions on
the planar scattering amplitudes to all loops. We study the general form of the
invariants of both symmetries. We first construct an integral representation
for the most general dual superconformal invariants and show that it allows a
considerable freedom in the choice of the integration measure. We then perform
a half-Fourier transform to twistor space, where conventional conformal
symmetry is realized locally, derive the resulting conformal Ward identity for
the integration measure and show that it admits a unique solution. Thus, the
combination of dual and conventional superconformal symmetries, together with
invariance under helicity rescalings, completely fixes the form of the
invariants. The expressions obtained generalize the known tree and one-loop
superconformal invariants and coincide with the recently proposed coefficients
of the leading singularities of the scattering amplitudes as contour integrals
over Grassmannians.
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Constructing the correlation function of four stress-tensor multiplets
and the four-particle amplitude in N=4 SYM: We present a construction of the integrand of the correlation function of
four stress-tensor multiplets in N=4 SYM at weak coupling. It does not rely on
Feynman diagrams and makes use of the recently discovered symmetry of the
integrand under permutations of external and integration points. This symmetry
holds for any gauge group, so it can be used to predict the integrand both in
the planar and non-planar sectors. We demonstrate the great efficiency of
graph-theoretical tools in the systematic study of the possible permutation
symmetric integrands. We formulate a general ansatz for the correlation
function as a linear combination of all relevant graph topologies, with
arbitrary coefficients. Powerful restrictions on the coefficients come from the
analysis of the logarithmic divergences of the correlation function in two
singular regimes: Euclidean short-distance and Minkowski light-cone limits. We
demonstrate that the planar integrand is completely fixed by the procedure up
to six loops and probably beyond. In the non-planar sector, we show the absence
of non-planar corrections at three loops and we reduce the freedom at four
loops to just four constants. Finally, the correlation function/amplitude
duality allows us to show the complete agreement of our results with the
four-particle planar amplitude in N=4 SYM.
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A Geometric Representation for the Proca Model: The Proca model is quantized in an open-path dependent representation that
generalizes the Loop Representation of gauge theories. The starting point is a
gauge invariant Lagrangian that reduces to the Proca Lagrangian when certain
gauge is selected.
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Recent results for Yang-Mills theory restricted to the Gribov region: We summarize recent results for the Gribov-Zwanziger Lagrangian which
includes the effect of restricting the path integral to the first Gribov
region. These include the two loop MSbar and one loop MOM gap equations for the
Gribov mass.
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Anomaly Inflow at Singularities: Many noncompact Type I orbifolds satisfy tadpole constraints yet are
anomalous. We present a generalization of the anomaly inflow mechanism for some
of these cases in six and four dimensions.
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Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type: Recently was shown that standard odd and even-dimensional General Relativity
can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant
under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld
Lagrangian invariant under a subalgebra $\cal{L}^{B_{2n+1}}$ respectively. Very
Recently, it was shown that the generalized In\"on\"u-Wigner contraction of the
generalized AdS-Maxwell algebras provides Maxwell algebras types $\cal{M}_{m}$
which correspond to the so called $B_{m}$ Lie algebras. In this article we
report on a simple model that suggests a mechanism by which standard
odd-dimensional General Relativity may emerge as a weak coupling constant limit
of a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the Maxwell
algebra type $\cal{M}_{2m+1}$, if and only if $m\geq p$. Similarly, we show
that standard even-dimensional General Relativity emerges as a weak coupling
constant limit of a $(2p)$-dimensional Born-Infeld type Lagrangian invariant
under a subalgebra $\cal{L}^{\cal{M}_{2m}}$ of the Maxwell algebra type, if and
only if $m\geq p$. It is shown that when $m<p$ this is not possible for a
$(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the
$\cal{M}_{2m+1}$ and for a $(2p)$-dimensional Born-Infeld type Lagrangian
invariant under $\cal{L}^{\cal{M}_{2m}}$ algebra.
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Hypersymmetry bounds and three-dimensional higher-spin black holes: We investigate the hypersymmetry bounds on the higher spin black hole
parameters that follow from the asymptotic symmetry superalgebra in higher-spin
anti-de Sitter gravity in three spacetime dimensions. We consider anti-de
Sitter hypergravity for which the analysis is most transparent. This is a
$osp(1\vert 4) \oplus osp(1\vert 4)$ Chern-Simons theory which contains,
besides a spin-$2$ field, a spin-$4$ field and a spin-$5/2$ field. The
asymptotic symmetry superalgebra is then the direct sum of two-copies of the
hypersymmetric extension $W_{(2,\frac52,4)}$ of $W_{(2,4)}$, which contains
fermionic generators of conformal weight $5/2$ and bosonic generators of
conformal weight $4$ in addition to the Virasoro generators. Following standard
methods, we derive bounds on the conserved charges from the anticommutator of
the hypersymmetry generators. The hypersymmetry bounds are nonlinear and are
saturated by the hypersymmetric black holes, which turn out to possess
$1/4$-hypersymmetry and to be "extreme", where extremality can be defined in
terms of the entropy: extreme black holes are those that fulfill the
extremality bounds beyond which the entropy ceases to be a real function of the
black hole parameters. We also extend the analysis to other $sp(4)$-solitonic
solutions which are maximally (hyper)symmetric.
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Choptuik Scaling and The Merger Transition: The critical solution in Choptuik scaling is shown to be closely related to
the critical solution in the black-string black-hole transition (the merger),
through double analytic continuation, and a change of a boundary condition. The
interest in studying various space-time dimensions D for both systems is
stressed. Gundlach-Hod-Piran off-critical oscillations, familiar in the
Choptuik set-up, are predicted for the merger system and are predicted to
disappear above a critical dimension D*=10. The scaling constants, Delta(D),
gamma(D), are shown to combine naturally to a single complex number.
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Scale-dependent Hausdorff dimensions in 2d gravity: By appropriate scaling of coupling constants a one-parameter family of
ensembles of two-dimensional geometries is obtained, which interpolates between
the ensembles of (generalized) causal dynamical triangulations and ordinary
dynamical triangulations. We study the fractal properties of the associated
continuum geometries and identify both global and local Hausdorff dimensions.
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Zeta function regularization, anomaly and complex mass term: If the zeta function regularization is used and a complex mass term
considered for fermions, the phase does not appear in the fermion determinant.
This is not a drawback of the regularization, which can recognize the phase
through source terms, as demonstrated by the anomaly equation which is
explicitly derived here for a complex mass term.
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Non-linear Holographic Entanglement Entropy Inequalities for Single
Boundary 2D CFT: Significant work has gone into determining the minimal set of entropy
inequalities that determine the holographic entropy cone. Holographic systems
with three or more parties have been shown to obey additional inequalities that
generic quantum systems do not. We consider a two dimensional conformal field
theory that is a single boundary of a holographic system and find four
additional non-linear inequalities which are derived from strong subadditivity
and the formula for the entanglement entropy of a region on the conformal field
theory. We also present an equality obtained by application of a hyperbolic
extension of Ptolemy's theorem to a two dimensional conformal field theory.
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Spontaneously Generated Tensor Field Gravity: An arbitrary local theory of a symmetric two-tensor field $H_{\mu \nu}$ in
Minkowski spacetime is considered, in which the equations of motion are
required to be compatible with a nonlinear length-fixing constraint $H_{\mu
\nu}^{2}=\pm M^{2}$ leading to spontaneous Lorentz invariance violation, SLIV
($M$ is the proposed scale for SLIV). Allowing the parameters in the Lagrangian
to be adjusted so as to be consistent with this constraint, the theory turns
out to correspond to linearized general relativity in the weak field
approximation, while some of the massless tensor Goldstone modes appearing
through SLIV are naturally collected in the physical graviton. In essence the
underlying diffeomophism invariance emerges as a necessary condition for the
tensor field $H_{\mu \nu}$ not to be superfluously restricted in degrees of
freedom, apart from the constraint due to which the true vacuum in the theory
is chosen by SLIV. The emergent theory appears essentially nonlinear, when
expressed in terms of the pure Goldstone tensor modes and contains a plethora
of new Lorentz and $CPT$ violating couplings. However, these couplings do not
lead to physical Lorentz violation once this tensor field gravity is properly
extended to conventional general relativity.
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AdS/CFT v.s. String Loops: The one string-loop correction to the energies of two impurity BMN states are
computed using IIB light-cone string field theory with an improved 3-string
vertex that has been proposed by Dobashi and Yoneya. As in previous published
computations, the string vertices are truncated to the 2-impurity channel. The
result is compared with the prediction from non-planar corrections in the BMN
limit of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It is found to agree
at leading order -- one-loop in Yang-Mills theory -- and is close but not quite
in agreement at order two Yang-Mills loops. Furthermore, in addition to the
leading 1/2 power in the t'Hooft coupling, which is generic in string field
theory, and which we have previously argued cancels, we find that the 3/2 and
5/2 powers are also miraculously absent.
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Form factor representation of the correlation function of the two
dimensional Ising model on a cylinder: The correlation function of the two dimensional Ising model with the nearest
neighbours interaction on the finite size lattice with the periodical boundary
conditions is derived. The expressions similar to the form factor expansion are
obtained both for the paramagnetic and ferromagnetic regions of coupling
parameter. The peculiarities caused by finite size are analyzed. The scaling
limit of the lattice form factor expansion is evaluated.
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Stringy scaling of n-point hard string scattering amplitudes: Motivated by the recent calculation of the SL(K+3,C) symmetry of n-point
Lauricella string scattering amplitudes (SSA) of open bosonic string theory, we
calculate ratios of the solvable infinite linear relations of arbitrary n-point
hard SSA (HSSA). We discover a general stringy scaling behavior for all n-point
HSSA to all string loop orders. For the special case of n=4, the stringy
scaling behavior reduces to the infinite linear relations and constant ratios
among HSSA conjectured by Gross [8] and later corrected and calculated by the
method of decoupling of zero-norm states [11].
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Extremal Charged Black Holes and Superradiantly Unstable Quasinormal
Modes: It was recently shown that the extremal charged black holes in STU
supergravity suffer from superradiant instability owing to the existence of the
unstable (low-frequency) quasibound states associated with a charged massive
scalar field. In this paper, we show numerically that for some charge
configurations, these black holes can also excite the (higher-frequency)
superradiantly unstable quasinormal modes. We find empirically that the
unstable modes are closely related to having a volcano-shaped effective
potential in the Schr\"odinger-like wave equation.
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Lorentzian Vacuum Transitions for Anisotropic Universes: The vacuum transition probabilities for anisotropic universes in the presence
of a scalar field potential in the Wentzel-Kramers-Brillouin approximation are
studied. We follow the work by Cespedes et al [Phys. Rev. D 104, 026013
(2021)], which discuss these transitions in the isotropic context using the
Wheeler-DeWitt equation, the Lorentzian Hamiltonian approach and the thin wall
limit. First, we propose a general procedure to adapt their formalism to
compute the decay rates for any superspace model. Then we apply it to compute
the transition probabilities of an Friedmann-Lemaitre-Robertson-Walker (FLRW)
metric with both positive and zero curvature, reproducing in this way one of
the results obtained at Cespedes et al. We then proceed to apply the formalism
to three anisotropic metrics, namely, Kantowski-Sachs, Bianchi III and biaxial
Bianchi IX to compute the rate decays for these three cases. In the process we
find that this method involves some conditions which relates the effective
number of independent degrees of freedom resulting on all probabilities being
described with only two independent variables. For the Bianchi III metric, we
find that a general effect of anisotropy is to decrease the transition
probability as the degree of anisotropy is increased, having as the isotropic
limit the flat FLRW result.
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All-loop cuts from the Amplituhedron: The definition of the amplituhedron in terms of sign flips involves both
one-loop constraints and the "mutual positivity" constraint. To gain an
understanding of the all-loop integrand of $\mathcal{N}=4$ sYM requires
understanding the crucial role played by mutual positivity. This paper is an
attempt towards developing a procedure to introduce the complexities of mutual
positivity in a systematic and controlled manner. As the first step in this
procedure, we trivialize these constraints and understand the geometry
underlying the remaining constraints to all loops and multiplicities. We
present a host of configurations which correspond to various faces of the
amplituhedron. The results we derive are valid at all multiplicities and loop
orders for the maximally helicity violating (MHV) configurations. These include
detailed derivations for the results in arXiv:1810.08208 [hep-th]. We conclude
by indicating how one might move beyond trivial mutual positivity by presenting
a series of configuration which re-introduce it bit by bit.
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Cross-Order Integral Relations from Maximal Cuts: We study the ABDK relation using maximal cuts of one- and two-loop integrals
with up to five external legs. We show how to find a special combination of
integrals that allows the relation to exist, and how to reconstruct the terms
with one-loop integrals squared. The reconstruction relies on the observation
that integrals across different loop orders can have support on the same
generalized unitarity cuts and can share global poles. We discuss the
appearance of nonhomologous integration contours in multivariate residues.
Their origin can be understood in simple terms, and their existence enables us
to distinguish contributions from different integrals. Our analysis suggests
that maximal and near-maximal cuts can be used to infer the existence of
integral identities more generally.
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BRST-anti-BRST covariant theory for the second class constrained
systems. A general method and examples: The BRST-anti-BRST covariant extension is suggested for the split involution
quantization scheme for the second class constrained theories. The constraint
algebra generating equations involve on equal footing a pair of BRST charges
for second class constraints and a pair of the respective anti-BRST charges.
Formalism displays explicit Sp(2) \times Sp(2) symmetry property. Surprisingly,
the the BRST-anti-BRST algebra must involve a central element, related to the
nonvanishing part of the constraint commutator and having no direct analogue in
a first class theory. The unitarizing Hamiltonian is fixed by the requirement
of the explicit BRST-anti-BRST symmetry with a much more restricted ambiguity
if compare to a first class theory or split involution second class case in the
nonsymmetric formulation. The general method construction is supplemented by
the explicit derivation of the extended BRST symmetry generators for several
examples of the second class theories, including self--dual nonabelian model
and massive Yang Mills theory.
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BCS instabilities of electron stars to holographic superconductors: We study fermion pairing and condensation towards an ordered state in
strongly coupled quantum critical systems with a holographic AdS/CFT dual. On
the gravity side this is modeled by a system of charged fermion interacting
through a BCS coupling. At finite density such a system has a BCS instability.
We combine the relativistic version of mean-field BCS with the semi-classical
fluid approximation for the many-body state of fermions. The resulting
groundstate is the AdS equivalent of a charged neutron star with a
superconducting core. The spectral function of the fermions confirms that the
ground state is ordered through the condensation of the pair operator. A
natural variant of the BCS star is shown to exist where the gap field couples
Stueckelberg-like to the AdS Maxwell field. This enhances the tendency of the
system to superconduct.
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Natural inflation with multiple sub-Planckian axions: We extend the Kim-Nilles-Peloso (KNP) alignment mechanism for natural
inflation to models with $N>2$ axions, which obtains a super-Planckian
effective axion decay constant $f_{\textrm{eff}}\gg M_{Pl}$ through an
alignment of the anomaly coefficients of multiple axions having sub-Planckian
fundamental decay constants $f_0\ll M_{Pl}$. The original version of the KNP
mechanism realized with two axions requires that some of the anomaly
coefficients should be of the order of $f_{\textrm{eff}}/f_0$, which would be
uncomfortably large if $f_{\rm eff}/f_0 \gtrsim {\cal O}(100)$ as suggested by
the recent BICEP2 results. We note that the KNP mechanism can be realized with
the anomaly coefficients of $\mathcal{O}(1)$ if the number of axions $N$ is
large as $N\ln N\gtrsim 2\ln (f_{\textrm{eff}}/f_0)$, in which case the
effective decay constant can be enhanced as $f_{\rm eff}/f_0 \sim \sqrt{N
!}\,n^{N-1}$ for $n$ denoting the typical size of the integer-valued anomaly
coefficients. Comparing to the other multiple axion scenario, the N-flation
scenario which requires $N \sim f_{\textrm{eff}}^2/f_0^2$, the KNP mechanism
has a virtue of not invoking to a too large number of axions, although it
requires a specific alignment of the anomaly coefficients, which can be
achieved with a probability of ${\cal O}(f_0/f_{\rm eff})$ under a random
choice of the anomaly coefficients. We also present a simple model realizing a
multiple axion monodromy along the inflaton direction.
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Alternative to Higgs and Unification: In this paper, we discuss the self-consistency condition for the spherical
symmetric Klein-Gordon equation, and then discuss a natural possibility that
gravity and weak coupling constants g_G and g_W may be defined after g_{EM}. In
this point of view, gravity and the weak force are subsidiary derived from
electricity. Particularly, SU(2)_L * U(1) unification is derived without
assuming a phase transition.
A possible origin of the Higgs mechanism is proposed. Each particle pair of
the standard model is associated with the corresponding asymptotic expansion of
an eigen function.
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A Simple Holographic Superconductor with Momentum Relaxation: We study a holographic superconductor model with momentum relaxation due to
massless scalar fields linear to spatial coordinates($\psi_I = \beta
\delta_{Ii} x^i$), where $\beta$ is the strength of momentum relaxation. In
addition to the original superconductor induced by the chemical
potential($\mu$) at $\beta=0$, there exists a new type of superconductor
induced by $\beta$ even at $\mu=0$. It may imply a new `pairing' mechanism of
particles and antiparticles interacting with $\beta$, which may be interpreted
as `impurity'. Two parameters $\mu$ and $\beta$ compete in forming a
superconducting phase. As a result, the critical temperature behaves
differently depending on $\beta/\mu$. It decreases when $\beta/\mu$ is small
and increases when $\beta/\mu$ is large, which is a novel feature compared to
other models. After analysing ground states and phase diagrams for various
$\beta/\mu$, we study optical electric($\sigma$), thermoelectric($\alpha$), and
thermal($\bar{\kappa}$) conductivities. When the system undergoes a phase
transition from a normal to a superconducting phase, $1/\omega$ pole appears in
the imaginary part of the electric conductivity, implying infinite DC
conductivity. If $\beta/\mu <1$, at small $\omega$, a two-fluid model with an
imaginary $1/\omega$ pole and the Drude peak works for $\sigma$, $\alpha$, and
$\bar{\kappa}$, but if $\beta/\mu >1$ a non-Drude peak replaces the Drude peak.
It is consistent with the coherent/incoherent metal transition in its metal
phase. The Ferrell-Glover-Tinkham (FGT) sum rule is satisfied for all cases
even when $\mu=0$.
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Unitary representations of N-conformal Galilei group: All unitary irreducible representations of centrally extended (N-odd)
N-conformal Galilei group are constructed. The "on-shell" action of the group
is derived and shown to coincide, in special but most important case, with that
obtained in: J. Gomis, K. Kamimura, Phys. Rev. {\bf D85} (2012), 045023.
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Symmetries and supersymmetries of the Dirac operators in curved
spacetimes: It is shown that the main geometrical objects involved in all the symmetries
or supersymmetries of the Dirac operators in curved manifolds of arbitrary
dimensions are the Killing vectors and the Killing-Yano tensors of any ranks.
The general theory of external symmetry transformations associated to the usual
isometries is presented, pointing out that these leave the standard Dirac
equation invariant providing the correct spin parts of the group generators.
Furthermore, one analyzes the new type of symmetries generated by the
covariantly constant Killing-Yano tensors that realize certain square roots of
the metric tensor. Such a Killing-Yano tensor produces simultaneously a
Dirac-type operator and the generator of a one-parameter Lie group connecting
this operator with the standard Dirac one. In this way the Dirac operators are
related among themselves through continuous transformations associated to
specific discrete ones. It is shown that the groups of this continuous symmetry
can be only U(1) or SU(2), as those of the (hyper-)Kahler spaces, but arising
even in cases when the requirements for these special geometries are not
fulfilled. To exemplify, the Euclidean Taub-NUT space with its Dirac-type
operators is presented in much details, pointing out that there is an
infinite-loop superalgebra playing the role of a closed dynamical algebraic
structure. As a final topic, we go to consider the properties of the Dirac-type
operators of the Minkowski spacetime.
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Vortex Lattices and Crystalline Geometries: We consider $AdS_2 \times R^2$ solutions supported by a magnetic field, such
as those which arise in the near-horizon limit of magnetically charged $AdS_4$
Reissner-Nordstrom black branes. In the presence of an electrically charged
scalar field, such magnetic solutions can be unstable to spontaneous formation
of a vortex lattice. We solve the coupled partial differential equations which
govern the charged scalar, gauge field, and metric degrees of freedom to lowest
non-trivial order in an expansion around the critical point, and discuss the
corrections to the free energy and thermodynamic functions arising from the
formation of the lattice. We describe how such solutions can also be
interpreted, via S-duality, as characterizing infrared crystalline phases of
conformal field theories doped by a chemical potential, but in zero magnetic
field; the doped conformal field theories are dual to geometries that exhibit
dynamical scaling and hyperscaling violation.
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Gravity and its Mysteries: Some Thoughts and Speculations: I gave a rambling talk about gravity and its many mysteries at Chen-Ning
Yang's 85th Birthday Celebration held in November 2007. I don't have any
answers.
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Spin Two Glueball Mass and Glueball Regge Trajectory from Supergravity: We calculate the mass of the lowest lying spin two glueball in N=1 super
Yang-Mills from the dual Klebanov-Strassler background. We show that the Regge
trajectory obtained is linear; the 0++, 1-- and 2++ states lie on a line of
slope 0.23 -measured in units of the conifold deformation. We also compare mass
ratios with lattice data and find agreement within one standard deviation.
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The Gravitino Swampland Conjecture: We extend the swampland from effective field theories (EFTs) inconsistent
with quantum gravity to EFTs inconsistent with quantum supergravity. This
enlarges the swampland to include EFTs that become inconsistent when the
gravitino is quantized. We propose the Gravitino Swampland Conjecture: the
gravitino sound speed must be non-vanishing in all EFTs that are low energy
limits of quantum supergravity. This seemingly simple statement has important
consequences for both theories and observations. The conjecture is consistent
with and supported by the KKLT and LVS scenarios for moduli stabilization in
string theory.
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A Classical and Spinorial Description of the Relativistic Spinning
Particle: In a previous work we showed that spin can be envisioned as living in a phase
space that is dual to the standard phase space of position and momentum. In
this work we demonstrate that the second class constraints inherent in this
"Dual Phase Space" picture can be solved by introducing a spinorial
parameterization of the spinning degrees of freedom. This allows for a purely
first class formulation that generalizes the usual relativistic description of
spinless particles and provides several insights into the nature of spin and
its relationship with spacetime and locality. In particular, we find that the
spin motion acts as a Lorentz contraction on the four-velocity and that, in
addition to proper time, spinning particles posses a second gauge invariant
observable which we call proper angle. Heuristically, this proper angle
represents the amount of Zitterbewegung necessary for a spin transition to
occur. Additionally, we show that the spin velocity satisfies a causality
constraint, and even more stringently, that it is constant along classical
trajectories. This leads to the notion of "half-quantum" states which violate
the classical equations of motion, and yet do not experience an exponential
suppression in the path integral. Finally we give a full analysis of the
Poisson bracket structure of this new parametrization.
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Confinement in the q-state Potts model: an RG-TCSA study: In the ferromagnetic phase of the q-state Potts model, switching on an
external magnetic field induces confinement of the domain wall excitations. For
the Ising model (q = 2) the spectrum consists of kink-antikink states which are
the analogues of mesonic states in QCD, while for q = 3, depending on the sign
of the field, the spectrum may also contain three-kink bound states which are
the analogues of the baryons. In recent years the resulting "hadron" spectrum
was described using several different approaches, such as quantum mechanics in
the confining linear potential, WKB methods and also the Bethe-Salpeter
equation. Here we compare the available predictions to numerical results from
renormalization group improved truncated conformal space approach (RG-TCSA).
While mesonic states in the Ising model have already been considered in a
different truncated Hamiltonian approach, this is the first time that a
precision numerical study is performed for the 3-state Potts model. We find
that the semiclassical approach provides a very accurate description for the
mesonic spectrum in all the parameter regime for weak magnetic field, while the
low-energy expansion from the Bethe-Salpeter equation is only valid for very
weak fields where it gives a slight improvement over the semiclassical results.
In addition, we confirm the validity of the recent predictions for the baryon
spectrum obtained from solving the quantum mechanical three-body problem.
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Lattice analogues of W-algebras and Classical Integrable Equations: We propose a regular way to construct lattice versions of $W$-algebras, both
for quantum and classical cases. In the classical case we write the algebra
explicitly and derive the lattice analogue of Boussinesq equation from the
Hamiltonian equations of motion. Connection between the lattice
Faddeev-Takhtadjan-Volkov algebra [1] and q-deformed Virasoro is also
discussed.
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String Field Theory of $c\leq 1$ Noncritical Strings: We construct a string field Hamiltonian for a noncritical string theory with
the continuum limit of the Ising model or its generalization as the matter
theory on the worldsheet. It consists of only three string vertices as in the
case for $c=0$. We also discuss a general consistency condition that should be
satisfied by this kind of string field Hamiltonian.
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Generalized geometric vacua with eight supercharges: We investigate compactifications of type II and M-theory down to $AdS_5$ with
generic fluxes that preserve eight supercharges, in the framework of
Exceptional Generalized Geometry. The geometric data and gauge fields on the
internal manifold are encoded in a pair of generalized structures corresponding
to the vector and hyper-multiplets of the reduced five-dimensional
supergravity. Supersymmetry translates into integrability conditions for these
structures, generalizing, in the case of type IIB, the Sasaki-Einstein
conditions. We show that the ten and eleven-dimensional type IIB and M-theory
Killing-spinor equations specialized to a warped $AdS_5$ background imply the
generalized integrability conditions.
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Construction of exact Riemannian instanton solutions: We give the exact construction of Riemannian (or stringy) instantons, which
are classical solutions of 2d Yang-Mills theories that interpolate between
initial and final string configurations. They satisfy the Hitchin equations
with special boundary conditions. For the case of U(2) gauge group those
equations can be written as the sinh-Gordon equation with a delta function
source. Using techniques of integrable theories based on the zero curvature
conditions, we show that the solution is a condensate of an infinite number of
one-solitons with the same topological charge and with all possible rapidities.
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On equivalence of Floer's and quantum cohomology: (In the revised version the relevant aspect of noncompactness of the moduli
of instantons is discussed. It is shown nonperturbatively that any BRST trivial
deformation of A-model which does not change the ranks of BRST cohomology does
not change the topological correlation functions either) We show that the Floer
cohomology and quantum cohomology rings of the almost Kahler manifold M, both
defined over the Novikov ring of the loop space LM of M, are isomorphic. We do
it using a BRST trivial deformation of the topological A-model. As an example
we compute the Floer = quantum cohomology of the 3-dimensional flag space Fl_3.
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Simple Construction of Elliptic Boundary K-Matrix: We give the infinite-dimensional representation for the elliptic $ K
$-operator satisfying the boundary Yang-Baxter equation. By restricting the
functional space to finite-dimensional space, we construct the elliptic $ K
$-matrix associated to Belavin's completely $ \mathbb{Z} $-symmetric $ R
$-matrix.
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Calabi-Yau Genus-One Fibrations and Twisted Dimensional Reductions of
F-theory: In this brief note we explore the space of genus one and elliptic fibrations
within CY manifolds, their organizing principles, and how they relate to the
set of all CY manifolds. We provide examples of genus one fibered manifolds
that exhibit different Hodge numbers -- and physically lead to different gauge
groups - than their Jacobian fibrations. We suggest a physical mechanism for
understanding this difference in twisted circle reductions of 6-dimensional
compactifications of F-theory.
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Quantum Mechanics of Integrable Spins on Coadjoint Orbits: We investigate classical integrable spins defined on the reduced phase spaces
of coadjoint orbits of $G= SU(N)$ and study quantum mechanics of them.
After discussions on a complete set of commuting functions on each orbit and
construction of integrable spin models on the flag manifolds, we quantize a
concrete example of integrable spins on SU(3) flag manifold in the coherent
state quantization scheme and solve explicitly the time-dependent Schr\"odinger
equation.
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Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations: We consider AdS_5 x S^5 string states with several large angular momenta
along AdS_5 and S^5 directions which are dual to single-trace Super-Yang-Mills
(SYM) operators built out of chiral combinations of scalars and covariant
derivatives. In particular, we focus on the SU(3) sector (with three spins in
S^5) and the SL(2) sector (with one spin in AdS_5 and one in S^5), generalizing
recent work hep-th/0311203 and hep-th/0403120 on the SU(2) sector with two
spins in S^5. We show that, in the large spin limit and at the leading order in
the effective coupling expansion, the string sigma model equations of motion
reduce to matrix Landau-Lifshitz equations. We then demonstrate that the
coherent-state expectation value of the one-loop SYM dilatation operator
restricted to the corresponding sector of single trace operators is also
effectively described by the same equations. This implies a universal leading
order equivalence between string energies and SYM anomalous dimensions, as well
as a matching of integrable structures. We also discuss the more general 5-spin
sector and comment on SO(6) states dual to non-chiral scalar operators.
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Null Geodesics in Brane World Universe: We study null bulk geodesic motion in the brane world cosmology in the RS2
scenario and in the static universe in the bulk of the charged topological AdS
black hole. We obtain equations describing the null bulk geodesic motion as
observed in one lower dimensions. We find that the null geodesic motion in the
bulk of the brane world cosmology in the RS2 scenario is observed to be under
the additional influence of extra non-gravitational force by the observer on
the three-brane, if the brane universe does not possess the Z_2 symmetry. As
for the null geodesic motion in the static universe in the bulk of the charged
AdS black hole, the extra force is realized even when the brane universe has
the Z_2 symmetry.
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Casimir piston for massless scalar fields in three dimensions: We study the Casimir piston for massless scalar fields obeying Dirichlet
boundary conditions in a three dimensional cavity with sides of arbitrary
lengths $a,b$ and $c$ where $a$ is the plate separation. We obtain an exact
expression for the Casimir force on the piston valid for any values of the
three lengths. As in the electromagnetic case with perfect conductor
conditions, we find that the Casimir force is negative (attractive) regardless
of the values of $a$, $b$ and $c$. Though cases exist where the interior
contributes a positive (repulsive) Casimir force, the total Casimir force on
the piston is negative when the exterior contribution is included. We also
obtain an alternative expression for the Casimir force that is useful
computationally when the plate separation $a$ is large.
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Thermodynamical Behaviour of Composite Stringy Black Holes: We study the thermodynamical and geometrical behaviour of the black holes
that arise as solutions of the heterotic string action. We discuss the
near-horizon scaling behaviour of the solutions that are described by
two-dimensional Anti-de Sitter Space AdS(2). We find that finite-energy
excitations of AdS(2) are suppressed only for scaling limits characterised by a
dilaton which is constant near the horizon, whereas this suppression does not
occur when the dilaton is non constant.
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Baxter operators for arbitrary spin II: This paper presents the second part of our study devoted to the construction
of Baxter operators for the homogeneous closed XXX spin chain with the quantum
space carrying infinite or finite-dimensional $s\ell_2$ representations. We
consider the Baxter operators used in \cite{BLZ,Shortcut}, formulate their
construction uniformly with the construction of our previous paper. The
building blocks of all global chain operators are derived from the general
Yang-Baxter operators and all operator relations are derived from general
Yang-Baxter relations. This leads naturally to the comparison of both
constructions and allows to connect closely the treatment of the cases of
infinite-dimensional representation of generic spin and finite-dimensional
representations of integer or half-integer spin. We proof not only the
relations between the operators but present also their explicit forms and
expressions for their action on polynomials representing the quantum states.
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Quantum tunneling from paths in complex time: We study quantum mechanical tunneling using complex solutions of the
classical field equations. Simple visualization techniques allow us to unify
and generalize previous treatments, and straightforwardly show the connection
to the standard approach using Euclidean instanton solutions. We demonstrate
that the negative modes of solutions along various contours in the complex time
plane reveal which paths give the leading contribution to tunneling and which
do not, and we provide a criterion for identifying the negative modes. Central
to our approach is the solution of the background and perturbation equations
not only along a single path, but over an extended region of the complex time
plane. Our approach allows for a fully continuous and coherent treatment of
classical evolution interspersed by quantum tunneling events, and is applicable
in situations where singularities are present and also where Euclidean
solutions might not exist.
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Retrofitting O'Raifeartaigh Models with Dynamical Scales: We provide a method for obtaining simple models of supersymmetry breaking,
with all small mass scales generated dynamically, and illustrate it with
explicit examples. We start from models of perturbative supersymmetry breaking,
such as O'Raifeartaigh and Fayet models, that would respect an $R$ symmetry if
their small input parameters transformed as the superpotential does. By
coupling the system to a pure supersymmetric Yang-Mills theory (or a more
general supersymmetric gauge theory with dynamically small vacuum expectation
values), these parameters are replaced by powers of its dynamical scale in a
way that is naturally enforced by the symmetry. We show that supersymmetry
breaking in these models may be straightforwardly mediated to the
supersymmetric Standard Model, obtain complete models of direct gauge
mediation, and comment on related model building strategies that arise in this
simple framework.
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Gravity from quantum mechanics of finite matrices: We revisit the Berenstein-Maldacena-Nastase (BMN) conjecture relating
M-theory on a PP-wave background and Matrix Quantum Mechanics (MQM) of $N\times
N$ matrices. In particular, we study the BMN MQM at strong coupling and finite
$N$ and derive an effective Hamiltonian that describes non-relativistic free
particles in a harmonic trap. The energy spectrum predicted by this Hamiltonian
matches the supergravity excitation spectrum around the PP-wave background, if
we further assume the existence of bound states. Our derivation is based on the
strong coupling expansion of the wavefunction and supersedes the naive path
integral approach that can lead to incorrect results, as we demonstrate in a
simple toy model. We conclude with open questions about various regimes of the
theory when we vary the size of the matrices, the coupling and the temperature.
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Weyl-Conformally-Invariant Lightlike p-Brane Theories: New Aspects in
Black Hole Physics and Kaluza-Klein Dynamics: We introduce and study in some detail the properties of a novel class of
Weyl-conformally invariant p-brane theories which describe intrinsically
lightlike branes for any odd world-volume dimension. Their dynamics
significantly differs from that of the ordinary (conformally non-invariant)
Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant
lightlike brane- (WILL-brane) equations of motion in various gravitational
models of physical relevance exhibiting various new phenomena. In D=4 the
WILL-membrane serves as a material and charged source for gravity and
electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it
automatically positions itself on (``straddles'') the common event horizon of
the corresponding matching black hole solutions, thus providing an explicit
dynamical realization of the membrane paradigm in black hole physics. In
product spaces of interest in Kaluza-Klein theories the WILL-brane wraps
non-trivially around the compact (internal)dimensions and still describes
massless mode dynamics in the non-compact (space-time) dimensions. Due to
nontrivial variable size of the internal compact dimensions we find new types
of physically interesting solutions describing massless brane modes trapped on
bounded planar circular orbits with non-trivial angular momentum, and with
linear dependence between energy and angular momentum.
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A Landau-type quantization from a Lorentz symmetry violation background
with crossed electric and magnetic fields: We investigate the arising of an analogue of the Landau quantization from a
background of the violation of the Lorentz symmetry established by a time-like
4-vector and a field configuration of crossed electric and magnetic field. We
also analyse the effects on this Landau-type system subject to a hard-wall
confining potential by showing a particular case where a discrete spectrum of
energy can be obtained. Further, we analyse the effects of a linear confining
potential on the Landau-type system. We show that a quantum effect
characterized by the dependence of the cyclotron frequency on the quantum
numbers of the system can arise in this analogue of the Landau system. As an
example, we calculate the cyclotron frequency associated with ground state of
the system.
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Romans type IIA theory and the heterotic strings: In this paper we study $T^2$ compactification of 6-dimensional massive type
IIA supergravity in presence of
Ramond-Ramond background fluxes. The resulting theory in four dimensions is
shown to possess $SL(2,R)\times SL(2,R)\times O(4,20)$ duality symmetry. It is
shown that specific elements of this symmetry relate massive type IIA
compactified on $K3\times T^2$ (with fluxes along $K3$) to the ordinary type
IIA compactified on $K3\times T^2$ (with fluxes along $T^2$). In turn, this
relationship is exploited to relate Romans theory to heterotic strings. The
D8-brane (domain-wall) wrapped on $K3\times T^2$ is related to {\it pure
gravity} heterotic solution which is a direct product of 6-dimensional flat
spacetime and a 4-dimensional Taub-NUT instanton.
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Boundary remnant of Yangian symmetry and the structure of rational
reflection matrices: For the classical principal chiral model with boundary, we give the subset of
the Yangian charges which remains conserved under certain integrable boundary
conditions, and extract them from the monodromy matrix. Quantized versions of
these charges are used to deduce the structure of rational solutions of the
reflection equation, analogous to the 'tensor product graph' for solutions of
the Yang-Baxter equation. We give a variety of such solutions, including some
for reflection from non-trivial boundary states, for the SU(N) case, and
confirm these by constructing them by fusion from the basic solutions.
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Nonperturbative effects and resurgence in JT gravity at finite cutoff: We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at
finite cutoff, as given by its proposed formulation in terms of a
$T\bar{T}$-deformed Schwarzian quantum mechanics. Our starting point is a
careful computation of the disk partition function to all orders in the
perturbative expansion in the cutoff parameter. We show that the perturbative
series is asymptotic and that it admits a precise completion exploiting the
analytical properties of its Borel transform, as prescribed by resurgence
theory. The final result is then naturally interpreted in terms of the
nonperturbative branch of the $T\bar{T}$-deformed spectrum. The finite-cutoff
trumpet partition function is computed by applying the same strategy. In the
second part of the paper, we propose an extension of this formalism to
arbitrary topologies, using the basic gluing rules of the undeformed case. The
Weil-Petersson integrations can be safely performed due to the nonperturbative
corrections and give results that are compatible with the flow equation
associated with the $T\bar{T}$ deformation. We derive exact expressions for
general topologies and show that these are captured by a suitable deformation
of the Eynard-Orantin topological recursion. Finally, we study the "slope" and
"ramp" regimes of the spectral form factor as functions of the cutoff
parameter.
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Surface States in Holographic Weyl Semimetals: We study the surface states of a strongly coupled Weyl semimetal within
holography. By explicit numerical computation of an inhomogeneous holographic
Weyl semimetal we observe the appearance of an electric current restricted to
the surface in presence of electric chemical potential. The total current is
universal in the sense that it only depends on the topology of the phases
showing that the bulk-boundary correspondence holds even at strong coupling.
The implications of this result are subtle and may shed some light on anomalous
transport at weak coupling.
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The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its
extension at $N=\infty$ by singular fixed points: We study the $O(N)$ model in dimension three (3$d$) at large and infinite $N$
and show that the line of fixed points found at $N=\infty$ --the
Bardeen-Moshe-Bander (BMB) line-- has an intriguing origin at finite $N$. The
large $N$ limit that allows us to find the BMB line must be taken on particular
trajectories in the $(d,N)$-plane: $d=3-\alpha/N$ and not at fixed dimension
$d=3$. Our study also reveals that the known BMB line is only half of the true
line of fixed points, the second half being made of singular fixed points. The
potentials of these singular fixed points show a cusp for a finite value of the
field and their finite $N$ counterparts a boundary layer.
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Projectivised representations of $U_q osp(2,2)$: We construct representations of the enveloping algebra $U_q osp(2,2)$ in
terms of finite difference operators and we discuss this result in the
framework of quasi-exactly-solvable equations.
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A non-standard matter distribution in the RS1 model and the coupling
constant of the radion: In the zero mode approximation we solve exactly the equations of motion for
linearized gravity in the Randall-Sundrum model with a non-standard
distribution of matter in the neighbourhood of the negative tension brane. It
is shown that the form of this distribution can strongly affect the coupling of
the radion to matter. We believe that such a situation can arise in models with
a realistic mechanisms of matter localization.
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F-term uplifting and the supersymmetric integration of heavy moduli: We study in detail the stability properties of the simplest F-term uplifting
mechanism consistent with the integration of heavy moduli. This way of
uplifting vacua guarantees that the interaction of the uplifting sector with
the moduli sector is consistent with integrating out the heavy fields in a
supersymmetric way. The interactions between light and heavy fields are
characterized in terms of the Kahler invariant function, G = K + log |W|^2,
which is required to be separable in the two sectors. We generalize earlier
results that when the heavy fields are stabilized at a minimum of the Kahler
function G before the uplifting (corresponding to stable AdS maxima of the
potential), they remain in a perturbatively stable configuration for
arbitrarily high values of the cosmological constant (or the Hubble parameter
during inflation). By contrast, supersymmetric minima and saddle points of the
scalar potential are always destabilized for sufficiently large amount of
uplifting. We prove that these results remain unchanged after including gauge
couplings in the model. We also show that in more general scenarios, where the
Kahler function is not separable in the light and heavy sectors, the minima of
the Kahler function still have better stability properties at large uplifting
than other types of critical points.
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Coupling between Galileon and massive gravity with composite metrics: We investigate the coupling between a Galileon scalar field and massive
gravity through composite metrics. We derive the full set of equations of
motion for a flat Friedmann-Robertson-Walker background, and study linear
perturbations around it. Generally, the nonminimal coupling with the composite
metric will excite all 6 degrees of freedom of the spatial metric
perturbations, one of which may correspond to the Boulware-Deser ghost.
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Black Hole Evaporation, Quantum Hair and Supertranslations: In a black hole, hair and quantum information retrieval are interrelated
phenomena. The existence of any new form of hair necessarily implies the
existence of features in the quantum-mechanically evaporated radiation.
Classical supertranslation hair can be only distinguished from global
diffeomorphisms if we have access to the interior of the black hole. Indirect
information on the interior can only be obtained from the features of the
quantum evaporation. Supertranslations $(T^-,T^+) \in BMS_{-}\otimes BMS_{+}$
can be used as bookkepers of the probability distributions of the emitted
quanta where the first element describes the classical injection of energy and
the second one is associated to quantum-mechanical emission. The connection
between $T^-$ and $T^+$ is determined by the interior quantum dynamics of the
black hole. We argue that restricting to the diagonal subgroup is only possible
for decoupled modes, which do not bring any non-trivial information about the
black hole interior and therefore do not constitute physical hair. We show that
this is also true for gravitational systems without horizon, for which both
injection and emission can be described classically. Moreover, we discuss and
clarify the role of infrared physics in purification.
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String vacuum backgrounds with covariantly constant null Killing vector
and 2d quantum gravity: We consider a $2d$ sigma model with a $2+N$ - dimensional Minkowski signature
target space metric having a covariantly constant null Killing vector. We study
solutions of the conformal invariance conditions in $2+N$ dimensions and find
that generic solutions can be represented in terms of the RG flow in $N$ -
dimensional ``transverse space'' theory. The resulting conformal invariant
sigma model is interpreted as a quantum action of the $2d$ scalar (``dilaton")
quantum gravity model coupled to a (non-conformal) `transverse' sigma model.
The conformal factor of the $2d$ metric is identified with a light cone
coordinate of the $2+N$ - dimensional sigma model. We also discuss the case
when the transverse theory is conformal (with or without the antisymmetric
tensor background) and reproduce in a systematic way the solutions with flat
transverse space known before.
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On the Hamiltonian Analysis of Spin-3 Chern-Simons-Like Theories of
Gravity: In this paper, we consider spin-3 Chern-Simons-like theories of gravity as
extended theories of spin-3 gravity in (2+1)- dimension. In order to determine
the number of local degrees of freedom we present the Hamiltonian formulation
of these theories. We extract the Hamiltonian density, then we find primary and
secondary constraints of these theories. Then we obtain the Poisson brackets of
the primary and the secondary constraints. After that we count the number of
local degrees of freedom of spin-3 Chern-Simons-like theories of gravity. We
apply this method on spin-3 Einstein-Cartan gravity and spin-3 topologically
massive gravity. According to the our results the spin-3 Einstein-Cartan
gravity and the spin-3 topologically massive gravity have respectively zero and
one bulk local degree of freedom.
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Summing Up Instantons in Three-Dimensional Yang-Mills Theories: We show that the four derivative terms in the effective action of
three-dimensional N=8 Yang-Mills theory are determined by supersymmetry. These
terms receive both perturbative and non-perturbative corrections. Using our
technique for constraining the effective action, we are able to determine the
exact form of the eight fermion terms in the supersymmetric completion of the
$F^4$ term, including all instanton corrections. As a consequence, we argue
that the integral of the Euler density over $k$ monopole moduli space in SU(2)
Yang-Mills is determined by our non-renormalization theorem for all values of
$k$.
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Twisted Bundle on Noncommutative Space and U(1) Instanton: We study the notion of twisted bundles on noncommutative space. Due to the
existence of projective operators in the algebra of functions on the
noncommutative space, there are twisted bundles with non-constant dimension.
The U(1) instanton solution of Nekrasov and Schwarz is such an example. As a
mathematical motivation for not excluding such bundles, we find gauge
transformations by which a bundle with constant dimension can be equivalent to
a bundle with non-constant dimension.
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Dynamical renormalization and universality in classical multifield
cosmological models: We study the scaling behavior of classical multifield cosmological models
with complete scalar manifold $({\cal M},{\cal G})$ and positive smooth scalar
potential $\Phi$, introducing a dynamical renormalization group action which
relates their UV and IR limits. We show that the RG flow of such models
interpolates between a modification of the geodesic flow of $({\cal M},{\cal
G})$ (obtained in the UV limit) and the gradient flow of $({\cal M},{\cal
G},V)$ (obtained in the IR limit), where the classical effective potential $V$
is proportional to $\sqrt{2\Phi}$. Using this fact, we show that two-field
models whose scalar manifold has constant Gaussian curvature equal to $-1$, $0$
or $1$ are infrared universal in the sense that they suffice to describe the
first order IR approximants of cosmological orbits for all two-field models
with positive smooth scalar potential.
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Thermodynamics, Euclidean Gravity and Kaluza-Klein Reduction: The aim of this paper is to find out a correspondence between one-loop
effective action $W_E$ defined by means of path integral in Euclidean gravity
and the free energy $F$ obtained by summation over the modes. The analysis is
given for quantum fields on stationary space-times of a general form. For such
problems a convenient procedure of a "Wick rotation" from Euclidean to
Lorentzian theory becomes quite non-trivial implying transition from one real
section of a complexified space-time manifold to another. We formulate
conditions under which $F$ and $W_E$ can be connected and establish an explicit
relation of these functionals. Our results are based on the Kaluza-Klein method
which enables one to reduce the problem on a stationary space-time to
equivalent problem on a static space-time in the presence of a gauge
connection. As a by-product, we discover relation between the asymptotic
heat-kernel coefficients of elliptic operators on a $D$ dimensional stationary
space-times and the heat-kernel coefficients of a $D-1$ dimensional elliptic
operators with an Abelian gauge connection.
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Collective-Field Excitations in the Calogero Model: We consider the large-N Calogero model in the \h\ collective-field approach
based on the $1/N$ expansion. The Bogomol'nyi limit appears and the
corresponding equation for the semiclassical configuration gives the correct
ground-state energy. Using the method of the orthogonal polynomial we find the
excitation spectrum of density fluctuations around the semiclassical solution
for any value of the statistical parametar $\l$. The wave functions of the
excited states are explicitly constructed as a product of Hermite polynomials
in terms of the collective modes.The two-point correlation function is
calculated as a series expansion in $1/\rho$ for any intermediate statistics.
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A potential for Generalized Kahler Geometry: We show that, locally, all geometric objects of Generalized Kahler Geometry
can be derived from a function K, the "generalized Kahler potential''. The
metric g and two-form B are determined as nonlinear functions of second
derivatives of K. These nonlinearities are shown to arise via a quotient
construction from an auxiliary local product (ALP) space.
|
On Equivalence of Topological and Quantum 2d Gravity: We demonstrate the equivalence of Virasoro constraints imposed on continuum
limit of partition function of Hermitean 1-matrix model and the Ward identities
of Kontsevich's model. Since the first model describes ordinary $d = 2$ quantum
gravity, while the second one is supposed to coincide with Witten's topological
gravity, the result provides a strong implication that the two models are
indeed the same.
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Confining Strings: We propose a hypothesis that all gauge theories are equivalent to a certain
non-standard string theory. Different gauge groups are accounted for by weights
ascribed to the world sheets of different topologies. The hypothesis is checked
in the case of the compact abelian theories, where we show how condensing
monopole -instanton fields are reproduced by the summation over surfaces. In
the non-abelian case we prove that the loop equations are satisfied modulo
contact terms. The structure of these terms unfortunately remains undetermined.
|
Towards inflation and dark energy cosmologies from modified Gauss-Bonnet
theory: We consider a physically viable cosmological model that has a field dependent
Gauss-Bonnet coupling in its effective action, in addition to a standard scalar
field potential. The presence of such terms in the four dimensional effective
action gives rise to several novel effects, such as a four dimensional flat
Friedmann-Robertson-Walker universe undergoing a cosmic inflation at early
epoch, as well as a cosmic acceleration at late times. The model predicts,
during inflation, spectra of both density perturbations and gravitational waves
that may fall well within the experimental bounds. Furthermore, this model
provides a mechanism for reheating of the early universe, which is similar to a
model with some friction terms added to the equation of motion of the scalar
field, which can imitate energy transfer from the scalar field to matter
|
On Shape Dependence and RG Flow of Entanglement Entropy: We use a mix of field theoretic and holographic techniques to elucidate
various properties of quantum entanglement entropy. In (3+1)-dimensional
conformal field theory we study the divergent terms in the entropy when the
entangling surface has a conical or a wedge singularity. In (2+1)-dimensional
field theory with a mass gap we calculate, for an arbitrary smooth entanglement
contour, the expansion of the entropy in inverse odd powers of the mass. We
show that the shape-dependent coefficients that arise are even powers of the
extrinsic curvature and its derivatives. A useful dual construction of a
(2+1)-dimensional theory, which allows us to exhibit these properties, is
provided by the CGLP background. This smooth warped throat solution of
11-dimensional supergravity describes renormalization group flow from a
conformal field theory in the UV to a gapped one in the IR. For this flow we
calculate the recently introduced renormalized entanglement entropy and confirm
that it is a monotonic function.
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Blushift of a tachyon in the charged 2D black hole: We study the propagation of string fields (metric $G_{\mu\nu}$, Mawxell gauge
potential $A_{\mu}$, dilaton $\Phi$, and tachyon $T$) in a two-dimensional (2D)
charged black hole. It is shown that the tachyon is a propagating field both
inside and outside the black hole. This becomes infinitely blueshifted at the
inner horizon. We confirm that the inner horizon is unstable, whereas the outer
horizon is stable.
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Baryonium in Confining Gauge Theories: We show a new class of embedding solutions of D5 brane, which wraps on $S^5$
in the AdS${}_5\times S^5$ space-time and contains fundamental strings as U(1)
flux to form a baryon vertex. The new solution given here is different from the
baryon vertex since it consists of two same side (north or south) poles of
$S^5$ as cusps, which are put on different points in our three dimensional
space. This implies that the same magnitude of electric displacement exists at
each cusp, but their orientations are opposite due to the flux number
conservation. This configuration is therefore regarded as a D5-$\bar{D5}$ bound
state, and we propose this as the vertex of a baryonium state, which is made of
a baryon and an anti-baryon. By attaching quarks and anti-quarks to the two
cusps of this vertex, it is possible to construct a realistic baryonium.
|
Note on asymptotic symmetries and soft gluon theorems: Recently, the leading soft gluon theorem with single soft emission was shown
to be the Ward identity of a two dimensional $\cal G$-Kac-Moody symmetry. In
this note, we show that the leading soft gluon theorem can be interpreted as
the Ward identity for the asymptotic symmetries of non-Abelian gauge theory. We
further argue that the sub-leading soft gluon theorem can follow from the same
symmetry.
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Quantum geometry and gravitational entropy: Most quantum states have wavefunctions that are widely spread over the
accessible Hilbert space and hence do not have a good description in terms of a
single classical geometry. In order to understand when geometric descriptions
are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of
asymptotically AdS_5 x S^5 universes. In this sector we devise a
"coarse-grained metric operator" whose eigenstates are well described by a
single spacetime topology and geometry. We show that such half-BPS universes
have a non-vanishing entropy if and only if the metric is singular, and that
the entropy arises from coarse-graining the geometry. Finally, we use our
entropy formula to find the most entropic spacetimes with fixed asymptotic
moments beyond the global charges.
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On The S-Matrix of Ising Field Theory in Two Dimensions: We explore the analytic structure of the non-perturbative S-matrix in
arguably the simplest family of massive non-integrable quantum field theories:
the Ising field theory (IFT) in two dimensions, which may be viewed as the
Ising CFT deformed by its two relevant operators, or equivalently, the scaling
limit of the Ising model in a magnetic field. Our strategy is that of collider
physics: we employ Hamiltonian truncation method (TFFSA) to extract the
scattering phase of the lightest particles in the elastic regime, and combine
it with S-matrix bootstrap methods based on unitarity and analyticity
assumptions to determine the analytic continuation of the 2 to 2 S-matrix
element to the complex s-plane. Focusing primarily on the "high temperature"
regime in which the IFT interpolates between that of a weakly coupled massive
fermion and the E8 affine Toda theory, we will numerically determine 3-particle
amplitudes, follow the evolution of poles and certain resonances of the
S-matrix, and exclude the possibility of unknown wide resonances up to
reasonably high energies.
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Renormalization Group Running of Newton's G: The Static Isotropic Case: Corrections are computed to the classical static isotropic solution of
general relativity, arising from non-perturbative quantum gravity effects. A
slow rise of the effective gravitational coupling with distance is shown to
involve a genuinely non-perturbative scale, closely connected with the
gravitational vacuum condensate, and thereby, it is argued, related to the
observed effective cosmological constant. Several analogies between the
proposed vacuum condensate picture of quantum gravitation, and non-perturbative
aspects of vacuum condensation in strongly coupled non-abelian gauge theories
are developed. In contrast to phenomenological approaches, the underlying
functional integral formulation of the theory severely constrains possible
scenarios for the renormalization group evolution of couplings. The expected
running of Newton's constant $G$ is compared to known vacuum polarization
induced effects in QED and QCD. The general analysis is then extended to a set
of covariant non-local effective field equations, intended to incorporate the
full scale dependence of $G$, and examined in the case of the static isotropic
metric. The existence of vacuum solutions to the effective field equations in
general severely restricts the possible values of the scaling exponent $\nu$.
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Five-dimensional N=4, SU(2) X U(1) Gauged Supergravity from Type IIB: We construct the complete and explicit non-linear Kaluza-Klein ansatz for
deriving the bosonic sector of N=4 SU(2)\times U(1) gauged five-dimensional
supergravity from the reduction of type IIB supergravity on S^5. This provides
the first complete example of such an S^5 reduction that includes non-abelian
gauge fields, and it allows any bosonic solution of the five-dimensional N=4
gauged theory to be embedded in D=10.
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The Epstein-Glaser approach to pQFT: graphs and Hopf algebras: The paper aims at investigating perturbative quantum field theory (pQFT) in
the approach of Epstein and Glaser (EG) and, in particular, its formulation in
the language of graphs and Hopf algebras (HAs). Various HAs are encountered,
each one associated with a special combination of physical concepts such as
normalization, localization, pseudo-unitarity, causality and an associated
regularization, and renormalization. The algebraic structures, representing the
perturbative expansion of the S-matrix, are imposed on the operator-valued
distributions which are equipped with appropriate graph indices. Translation
invariance ensures the algebras to be analytically well-defined and graded
total symmetry allows to formulate bialgebras. The algebraic results are given
embedded in the physical framework, which covers the two recent EG versions by
Fredenhagen and Scharf that differ with respect to the concrete recursive
implementation of causality. Besides, the ultraviolet divergences occuring in
Feynman's representation are mathematically reasoned. As a final result, the
change of the renormalization scheme in the EG framework is modeled via a HA
which can be seen as the EG-analog of Kreimer's HA.
|
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills
Theory: The classical Kepler problem, as well as its quantum mechanical version, the
Hydrogen atom, enjoy a well-known hidden symmetry, the conservation of the
Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there
a relativistic quantum field theory extension that preserves this symmetry? In
this Letter we show that the answer is positive: in the non-relativistic limit,
we identify the dual conformal symmetry of planar $\mathcal{N}=4$ super
Yang-Mills with the well-known symmetries of the Hydrogen atom. We point out
that the dual conformal symmetry offers a novel way to compute the spectrum of
bound states of massive $W$ bosons in the theory. We perform nontrivial tests
of this setup at weak and strong coupling, and comment on the possible
extension to arbitrary values of the coupling.
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Charged black lens in de Sitter space: We obtain a charged black lens solution in the five-dimensional
Einstein-Maxwell-Chern-Simons theory with a positive cosmological constant. It
is shown that the solution obtained here describes the formation of a black
hole with the spatial cross section of a sphere from that of the lens space of
L(n,1) in five-dimensional de Sitter space.
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Arithmetic and Attractors: We study relations between some topics in number theory and supersymmetric
black holes. These relations are based on the ``attractor mechanism'' of N=2
supergravity. In IIB string compactification this mechanism singles out certain
``attractor varieties.'' We show that these attractor varieties are constructed
from products of elliptic curves with complex multiplication for N=4 and N=8
compactifications. The heterotic dual theories are related to rational
conformal field theories. In the case of N=4 theories U-duality inequivalent
backgrounds with the same horizon area are counted by the class number of a
quadratic imaginary field. The attractor varieties are defined over fields
closely related to class fields of the quadratic imaginary field. We discuss
some extensions to more general Calabi-Yau compactifications and explore
further connections to arithmetic including connections to Kronecker's
Jugendtraum and the theory of modular heights. The paper also includes a short
review of the attractor mechanism. A much shorter version of the paper
summarizing the main points is the companion note entitled ``Attractors and
Arithmetic'' (hep-th/9807056).
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Noncommutative $R^d$ via closed star product: We consider linear star products on $R^d$ of Lie algebra type. First we
derive the closed formula for the polydifferential representation of the
corresponding Lie algebra generators. Using this representation we define the
Weyl star product on the dual of the Lie algebra. Then we construct a gauge
operator relating the Weyl star product with the one which is closed with
respect to some trace functional, $Tr( f\star g)= Tr( f\cdot g)$. We introduce
the derivative operator on the algebra of the closed star product and show that
the corresponding Leibnitz rule holds true up to a total derivative. As a
particular example we study the space $R^3_\theta$ with $\mathfrak{su}(2)$ type
noncommutativity and show that in this case the closed star product is the one
obtained from the Duflo quantization map. As a result a Laplacian can be
defined such that its commutative limit reproduces the ordinary commutative
one. The deformed Leibnitz rule is applied to scalar field theory to derive
conservation laws and the corresponding noncommutative currents.
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Non-linear theory for multiple M2 branes: We present a manifestly SO(8) invariant non-linear Lagrangian for describing
the non-abelian dynamics of the bosonic degrees of freedom of N coinciding M2
branes in flat spacetime. The theory exhibits a gauge symmetry structure of the
BF type (semidirect product of SU(N) and translations) and at low energies it
reduces exactly to the bosonic part of the Lorentzian Bagger-Lambert Lagrangian
for group SU(N). There are eight scalar fields satisfying a free-scalar
equation. When one of them takes a large expectation value, the non-linear
Lagrangian gets simplified and the theory can be connected to the non-abelian
Lagrangian describing the dynamics of N coinciding D2 branes. As an
application, we show that the BPS fuzzy funnel solution describing M2 branes
ending into a single M5 brane is an exact solution of the non-linear system.
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Out of Equilibrium Quantum Field Theory --- Perturbation Theory and
Generalized Boltzmann Equation: This paper describes perturbative framework, on the basis of the
closed-time-path formalism, in terms of quasiparticle picture for studying
quasiuniform relativistic quantum field systems near equilibrium and
nonequilibrium quasistationary systems. Two calculational schemes are
introduced, the one is formulated on the basis of the initial-particle
distribution function and the one is formulated on the basis of the
``physical''-particle distribution function. It is shown that both schemes are
equivalent and lead to a generalized kinetic or Boltzmann equation. Concrete
procedure of computing a generic amplitude is presented.
|
Stable bound orbits around a supersymmetric black lens: In higher-dimensional Schwarzschild black hole spacetimes, there are no
stable bound orbits of particles. In contrast to this, it is shown that there
are stable bound orbits in a five-dimensional black lens spacetime.
|
Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS$_5$
blackholes: Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardy-like
limit of the superconformal index of the 4d $\mathcal{N}=4$ theory with
complexified fugacities which encodes the entropy of the dual supersymmetric
AdS$_5$ blackholes. Here we study the Cardy-like asymptotics of the index
within the rigorous framework of elliptic hypergeometric integrals, thereby
filling a gap in their derivation of the blackhole entropy function, finding a
new blackhole saddle-point, and demonstrating novel bifurcation phenomena in
the asymptotics of the index as a function of fugacity phases. We also comment
on the relevance of the supersymmetric Casimir energy to the blackhole entropy
function in the present context.
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On lightcone string field theory from Super Yang-Mills and holography: We investigate the issues of holography and string interactions in the
duality between SYM and the pp wave background. We argue that the Penrose
diagram of the maximally supersymmetric pp-wave has a one dimensional boundary.
This fact suggests that the holographic dual of the pp-wave can be described by
a quantum mechanical system. We believe this quantum mechanical system should
be formulated as a matrix model. From the SYM point of view this matrix model
is built out of the lowest lying KK modes of the SYM theory on an $S^3$
compactification, and it relates to a wave which has been compactified along
one of the null directions. String interactions are defined by finite time
amplitudes on this matrix model. For closed strings they arise as in AdS-CFT,
by free SYM diagrams. For open strings, they arise from the diagonalization of
the hamiltonian to first order in perturbation theory. Estimates of the leading
behaviour of amplitudes in SYM and string theory agree, although they are
performed in very different regimes. Corrections are organized in powers of
$1/(\mu \alpha ' p^+)^2$ and $g^2(\mu \alpha ' p^+)^4$.
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Cotton Double Copy for Gravitational Waves: We construct a double copy relation between the Cotton spinor and the dual
field strength spinor of topologically massive theories, as the
three-dimensional analogue of the Weyl double copy. The relationship holds in
curved backgrounds for wave solutions. We give an explicit proof for Type N
spacetimes and show examples satisfying the Cotton double copy.
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Can an odd number of fermions be created due to chiral anomaly?: We describe a possibility of creation of an odd number of fractionally
charged fermions in 1+1 dimensional Abelian Higgs model. We point out that for
1+1 dimensions this process does not violate any symmetries of the theory, nor
makes it mathematically inconsistent. We construct the proper definition of the
fermionic determinant in this model and underline its non-trivial features that
are of importance for realistic 3+1 dimensional models with fermion number
violation.
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Hydrodynamic gradient expansion in gauge theory plasmas: We utilize the fluid-gravity duality to investigate the large order behavior
of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma
system. This corresponds to the inclusion of dissipative terms and transport
coefficients of very high order. Using the dual gravity description, we
calculate numerically the form of the stress tensor for a boost-invariant flow
in a hydrodynamic expansion up to terms with 240 derivatives. We observe a
factorial growth of gradient contributions at large orders, which indicates a
zero radius of convergence of the hydrodynamic series. Furthermore, we identify
the leading singularity in the Borel transform of the hydrodynamic energy
density with the lowest nonhydrodynamic excitation corresponding to a
`nonhydrodynamic' quasinormal mode on the gravity side.
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Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an
analytic approach: The Sachdev-Ye-Kitaev (SYK) model provides an uncommon example of a chaotic
theory that can be analysed analytically. In the deep infrared limit, the
original model has an emergent conformal (reparametrisation) symmetry that is
broken both spontaneously and explicitly. The explicit breaking of this
symmetry comes about due to pseudo-Nambu-Goldstone modes that are not exact
zero-modes of the model. In this paper, we study a version of the model which
preserves the reparametrisation symmetry at all length scales. We study the
heavy-light correlation functions of the operators in the conformal spectrum of
the theory. The three point functions of such operators allow us to demonstrate
that matrix elements of primaries ${\cal O}_n$ of the CFT$_1$ take the form
postulated by the Eigenstate Thermalisation Hypothesis. We also discuss the
implications of these results for the states in AdS$_2$ gravity dual.
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Integrable Symplectic Trilinear Interaction Terms for Matrix Membranes: Cubic interactions are considered in 3 and 7 space dimensions, respectively,
for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum
configurations are discussed. Their associated first order equations are
transformed to Nahm's equations, and are hence seen to be integrable, for the
3-dimensional case, by virtue of the explicit Lax pair provided. The
constructions introduced also apply to commutator or Moyal Bracket analogues.
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Wilson loop in a $T\bar{T}$ like deformed $\rm{CFT}_2$: In this paper we study string theory in the background $\mathcal{M}_3$ that
interpolates between $AdS_3$ in the IR and linear dilaton spacetime
$\mathbb{R}^{1,1}\times\mathbb{R}_\phi$ in the UV. Via holographic duality this
background corresponds to $\rm{CFT}_2$ deformed by a dimension $(2,2)$
operator. Here we discuss the holographic Wilson loop in such a model and shed
more light in support of the non-local structure of the theory (Little String
Theory (LST)) in the UV. We also discuss quantum and thermal phase transitions
of the boundary theory.
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Mean-field theory based on the \mathfrak{Jacobi~hsp} := semi-direct sum
\mathfrak{h}_N \rtimes \mathfrak{sp}(2N,\mathbb{R})_\mathbb{C} algebra of
boson operators: In this paper, we give an expression for canonical transformation group with
Grassmann variables, basing on the \mathfrak{Jacobi~hsp} \!:= semi-direct sum
\mathfrak{h}_{N} \rtimes \mathfrak{sp}(2N,\mathbb{R})_\mathbb{C} algebra of
boson operators. We assume a mean-field Hamiltonian (MFH) linear in the
\mathfrak{Jacobi} generators. We diagonalize the boson MFH. We show a new
aspect of eigenvalues of the MFH. An excitation energy arisen from additional
self-consistent field (SCF) parameters has never been seen in the traditional
boson MFT. We derive this excitation energy. We extend the Killing potential in
the \frac{Sp(2N,\mathbb{R})_\mathbb{C}}{U(N)} coset space to the one in the
\frac{Sp(2N+2,\mathbb{R})_\mathbb{C}}{U(N+1)} coset space and make clear the
geometrical structure of K\"{a}hler manifold, a non-compact symmetric space
\frac{Sp(2N+2,\mathbb{R})_\mathbb{C}}{U(N+1)}. The \mathfrak{Jacobi~hsp}
transformation group is embedded into an Sp(2N+2,\mathbb{R})_\mathbb{C} group
and an \frac{Sp(2N+2,\mathbb{R})_\mathbb{C}}{U(N+1)} coset variable is
introduced. Under such mathematical manipulations, extended bosonization of
Sp(2N+2,\mathbb{R})_\mathbb{C} Lie operators, vacuum function and differential
forms for extended boson are presented by using integral representation of
boson state on the \frac{Sp(2N+2,\mathbb{R})_\mathbb{C}}{U(N+1)} coset
variables.
|
Fractional Bosonic Strings: The aim of this paper is to present a simple generalization of bosonic string
theory in the framework of the theory of fractional variational problems.
Specifically, we present a fractional extension of the Polyakov action, for
which we compute the general form of the equations of motion and discuss the
connection between the new fractional action and a generalization the
Nambu-Goto action. Consequently, we analyse the symmetries of the modified
Polyakov action and try to fix the gauge, following the classical procedures.
Then we solve the equations of motion in a simplified setting. Finally, we
present an Hamiltonian description of the classical fractional bosonic string
and introduce the fractional light-cone gauge. It is important to remark that,
throughout the whole paper, we thoroughly discuss how to recover the known
results as an "integer" limit of the presented model.
|
Higgs Mechanism in Nonlocal Field Theories: We study spontaneous gauge symmetry breaking and the Higgs mechanism in
nonlocal field theories. Motivated by the level truncated action of string
field theory, we consider a class of nonlocal field theories with an
exponential factor of the d'Alembertian attached to the kinetic and mass terms.
Modifications of this kind are known to make mild the UV behavior of loop
diagrams and thus have been studied not only in the context of string theory
but also as an alternative approach to quantum gravity. In this paper we argue
that such a nonlocal theory potentially includes a ghost mode near the nonlocal
scale in the particle spectrum of the symmetry broken phase. This is in sharp
contrast to local field theories and would be an obstruction to making a simple
nonlocal model a UV complete theory. We then discuss a possible way out by
studying nonlocal theories with extra symmetries such as gauge symmetries in
higher spacetime dimensions.
|
Viscosities and shift in a chiral superfluid: a holographic study: We consider a holographic model of chiral superfluidity whose bulk is
Einstein Yang-Mills and compute viscosity and conductivity responses away from
the probe limit. We calculate Hall viscosity and analyze its relationship to
the superfluid density and the shift. We find that the relationship between
these quantities derived from effective field theory at zero temperature
persists for all temperatures: for $p\pm ip$ their ratio is equal to $\mp1/2$.
At low temperatures the system develops a Lifshitz throat, indicating an
anisotropic scaling symmetry in the infrared dynamics.
|
Conservation Laws and Geometry of Perturbed Coset Models: We present a Lagrangian description of the $SU(2)/U(1)$ coset model perturbed
by its first thermal operator. This is the simplest perturbation that changes
sign under Krammers--Wannier duality. The resulting theory, which is a
2--component generalization of the sine--Gordon model, is then taken in
Minkowski space. For negative values of the coupling constant $g$, it is
classically equivalent to the $O(4)$ non--linear $\s$--model reduced in a
certain frame. For $g > 0$, it describes the relativistic motion of vortices in
a constant external field. Viewing the classical equations of motion as a zero
curvature condition, we obtain recursive relations for the infinitely many
conservation laws by the abelianization method of gauge connections. The higher
spin currents are constructed entirely using an off--critical generalization of
the $W_{\infty}$ generators. We give a geometric interpretation to the
corresponding charges in terms of embeddings. Applications to the chirally
invariant $U(2)$ Gross--Neveu model are also discussed.
|
Effective hydrodynamics of black D3-branes: The long-wavelength effective field theory of world-volume fluctuations of
black D3-branes is shown to be a hydrodynamical system to leading order in a
gradient expansion. We study the system on a fiducial `cutoff' surface: the
fluctuating geometry imprints its dynamics on the surface via an induced stress
tensor whose conservation encapsulates the hydrodynamical description. For a
generic non-extremal D3-brane, as we move our cutoff surface from the
asymptotically flat near-boundary region to the near-horizon region, this
hydrodynamical system interpolates between a non-conformal relativistic fluid
and a non-relativistic incompressible fluid. We also consider the dependence on
the deviation from extremality of the D3-branes. In the near-extremal case we
recover the description in terms of a conformal relativistic fluid encountered
in the AdS/CFT context. We argue that this system allows us therefore to
explore the various connections that have hitherto been suggested relating the
dynamics of gravitational systems and fluid dynamics. In particular, we go on
to show that the blackfold effective field theory approach allows us to capture
this hydrodynamical behaviour and moreover subsumes the constructions
encountered in the fluid/gravity correspondence and the black hole membrane
paradigm, providing thereby a universal language to explore the effective
dynamics of black branes.
|
D-Branes, RR-Fields and Duality on Noncommutative Manifolds: We develop some of the ingredients needed for string theory on noncommutative
spacetimes, proposing an axiomatic formulation of T-duality as well as
establishing a very general formula for D-brane charges. This formula is
closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is
proved here. Our approach relies on a very general form of Poincare duality,
which is studied here in detail. Among the technical tools employed are
calculations with iterated products in bivariant K-theory and cyclic theory,
which are simplified using a novel diagram calculus reminiscent of Feynman
diagrams.
|
Infrared phases of 3d massless CS-QCD and large $N_f$: We compute anomalous dimensions of quartic operators which are singlets under
the $\mathrm{U}(N_f)$ global symmetry in Yang-Mills theories with Chern-Simons
level $k$ in three dimensions coupled to $N_f$ Dirac fermions. In order to have
analytic control, we consider the regime $N_f\gg N_c\gg 1$, where the problem
is reduced to the study of a flavor-adjoint and a flavor-singlet bilinears
whose square give the quartic operators of interest. We provide evidence that
these operators hit marginality, signaling instabilities which, for
$\frac{2k}{N_f}<1$ suggest the spontaneous breaking of the global symmetry, and
no symmetry breaking otherwise. For $k=N_f/2-1$ (the value corresponding to the
domain walls of 4d QCD at $\theta=\pi$), the critical value $N_f^*$ is
tantalizingly close to the lower end of the conformal window of QCD$_4$,
suggesting a connection between conformal and global symmetry breaking in the
4d theory and in its domain walls. We also study, at $k=0$, other quartic
operators containing a singlet when branched under
$\mathrm{U}\left(\frac{N_f}{2}\right)\times
\mathrm{U}\left(\frac{N_f}{2}\right)$, finding that they hit marginality
precisely at the same point as their flavor-neutral cousins. Using the same
technology we study bosonic CS-QCD$_3$, finding no hint of symmetry breaking
where our analysis is applicable.
|
The Inevitability of Sphalerons in Field Theory: The topological structure of field theory often makes inevitable the
existence of stable and unstable localised solutions of the field equations.
These are minima and saddle points of the energy. Saddle point solutions
occurring this way are known as sphalerons, and the most interesting one is in
the electroweak theory of coupled W, Z and Higgs bosons. The topological ideas
underpinning sphalerons are reviewed here.
|
Symmetric calorons of higher charges and their large period limits: Periodic instantons, also called calorons, are the BPS solutions to the pure
Yang-Mills theories on $\mathbb{R}^3\times S^1$. It is known that the calorons
interconnect with the instantons and the BPS monopoles as the ratio of their
size to the period of $S^1$ varies. We give, in this paper, the action density
configurations of the $SU(2)$ calorons of higher instanton charges with several
platonic symmetries through the numerical Nahm transform, after the
construction of the analytic Nahm data. The calorons considered are 5-caloron
with octahedral symmetry, 7-caloron with icosahedral symmetry, and 4-caloron
interconnecting tetrahedral and octahedral symmetries. We also consider the
large period, or the instanton, limits of the Nahm data, i.e., the ADHM limits,
and observe the similar spatial distributions of the action densities with the
calorons.
|
Non-relativistic twistor theory and Newton--Cartan geometry: We develop a non-relativistic twistor theory, in which Newton--Cartan
structures of Newtonian gravity correspond to complex three-manifolds with a
four-parameter family of rational curves with normal bundle ${\mathcal
O}\oplus{\mathcal O}(2)$. We show that the Newton--Cartan space-times are
unstable under the general Kodaira deformation of the twistor complex
structure. The Newton--Cartan connections can nevertheless be reconstructed
from Merkulov's generalisation of the Kodaira map augmented by a choice of a
holomorphic line bundle over the twistor space trivial on twistor lines. The
Coriolis force may be incorporated by holomorphic vector bundles, which in
general are non--trivial on twistor lines. The resulting geometries agree with
non--relativistic limits of anti-self-dual gravitational instantons.
|
Universality of DC Electrical Conductivity from Holography: We propose a universal formula of dc electrical conductivity in rotational-
and translational- symmetries breaking systems via the holographic duality.
This formula states that the ratio of the determinant of the dc electrical
conductivities along any spatial directions to the black hole area density in
zero-charge limit has a universal value. As explicit illustrations, we give
several examples elucidating the validation of this formula: We construct an
anisotropic black brane solution, which yields linear in temperature for the
in-plane resistivity and insulating behavior for the out-of-plane resistivity;
We also construct a spatially isotropic black brane solution that both the
linear-T and quadratic-T contributions to the resistivity can be realized.
|
Gauge theories on hyperbolic spaces and dual wormhole instabilities: We study supergravity duals of strongly coupled four dimensional gauge
theories formulated on compact quotients of hyperbolic spaces. The resulting
background geometries are represented by Euclidean wormholes, which complicates
establishing the precise gauge theory/string theory correspondence dictionary.
These backgrounds suffer from the non-perturbative instabilities arising from
the D3 - anti-D3 pair production in the background four-form potential. We
discuss conditions for suppressing this Schwinger-like instability. We find
that Euclidean wormholes arising in this construction develop a naked
singularity, before they can be stabilized.
|
Cosmological Backreaction for a Test Field Observer in a Chaotic
Inflationary Model: In an inhomogeneous universe, an observer associated with a particular matter
field does not necessarily measure the same cosmological evolution as an
observer in a homogeneous and isotropic universe. Here we consider, in the
context of a chaotic inflationary background model, a class of observers
associated with a "clock field" for which we use a light test field. We compute
the effective expansion rate and fluid equation of state in a gauge invariant
way, taking into account the quantum fluctuations of the long wavelength modes,
and working up to second order in perturbation theory and in the slow-roll
approximation. We find that the effective expansion rate is smaller than what
would be measured in the absence of fluctuations. Within the stochastic
approach we study the bounds for which the approximations we make are
consistent.
|
Path Integral for the Dirac Equation: A c-number path integral representation is constructed for the solution of
the Dirac equation. The integration is over the real trajectories in the
continuous three-space and other two canonical pairs of compact variables
controlling the spin and the chirality flips.
|
Fission, Fusion, and 6D RG Flows: We show that all known 6D SCFTs can be obtained iteratively from an
underlying set of UV progenitor theories through the processes of "fission" and
"fusion." Fission consists of a tensor branch deformation followed by a special
class of Higgs branch deformations characterized by discrete and continuous
homomorphisms into flavor symmetry algebras. Almost all 6D SCFTs can be
realized as fission products. The remainder can be constructed via one step of
fusion involving these fission products, whereby a single common flavor
symmetry of decoupled 6D SCFTs is gauged and paired with a new tensor multiplet
at the origin of moduli space, producing an RG flow "in reverse" to the UV.
This leads to a streamlined labeling scheme for all known 6D SCFTs in terms of
a few pieces of group theoretic data. The partial ordering of continuous
homomorphisms $\mathfrak{su}(2) \rightarrow \mathfrak{g}_{\text{flav}}$ for
$\mathfrak{g}_{\text{flav}}$ a flavor symmetry also points the way to a
classification of 6D RG flows.
|
Holographic RG flows with nematic IR phases: We construct zero-temperature geometries that interpolate between a Lifshitz
fixed point in the UV and an IR phase that breaks spatial rotations but
preserves translations. We work with a simple holographic model describing two
massive gauge fields coupled to gravity and a neutral scalar. Our construction
can be used to describe RG flows in non-relativistic, strongly coupled quantum
systems with nematic order in the IR. In particular, when the dynamical
critical exponent of the UV fixed point is z=2 and the IR scaling exponents are
chosen appropriately, our model realizes holographically the scaling properties
of the bosonic modes of the quadratic band crossing model.
|
From strings in 6d to strings in 5d: We show how recent progress in computing elliptic genera of strings in six
dimensions can be used to obtain expressions for elliptic genera of strings in
five-dimensional field theories which have a six-dimensional parent. We further
connect our results to recent mathematical results about sheaf counting on
ruled surfaces.
|
Topological Effects on Non-Relativistic Eigenvalue Solutions Under
AB-Flux Field with Pseudoharmonic- and Mie-type Potentials: In this paper, we investigate the quantum dynamics of a non-relativistic
particle confined by the Aharonov-Bohm quantum flux field with
pseudoharmonic-type potential in the background of topological defect produced
by a point-like global monopole. We solve the radial Schr\"{o}dinger equation
analytically and determine the exact eigenvalue solution of the quantum system.
Afterwards, we consider a Mie-type potential in the quantum system and solve
the radial equation analytically and obtain the eigenvalue solution. We analyze
the effects of the topological defect and the quantum flux with these
potentials on the energy eigenvalue and wave function of the non-relativistic
particles. In fact, it is shown that the energy levels and wave functions are
influenced by the topological defect shifted the result compared to the flat
space results. In addition, the quantum flux field also shifted the eigenvalue
solutions and an analogue of the Aharonov-Bohm effect for bound-states is
observed. Finally, we utilize these eigenvalue solutions to some known diatomic
molecular potential models and presented the energy eigenvalue and wave
function
|
Instability of D-dimensional extremally charged Reissner-Nordstrom(-de
Sitter) black holes: Extrapolation to arbitrary D: In our earlier work (PRL 103 (2009) 161101) it was shown that nonextremal
highly charged Reissner-Nordstrom-de Sitter black holes are gravitationally
unstable in D>6-dimensional space-times. Here, we find accurate threshold
values of the $\Lambda$-term at which the instability of the extremally charged
black holes starts. The larger $D$ is, the smaller is the threshold value of
$\Lambda$. We have shown that the ratio $\rho = r_{h}/r_{cos}$ (where $r_{cos}$
and $r_{h}$ are the cosmological and event horizons) is proportional to
$e^{-(D-4)/2}$ at the onset of instability for D=7,8,...11, implying that the
same law should fulfill for arbitrary D. This is numerical evidence that
extremally charged Reissner-Nordstrom-de Sitter black holes are gravitationally
unstable for D>6, while asymptotically flat extremally charged
Reissner-Nordstrom black holes are stable for all D. The instability is not
connected to the horizon instability discussed recently in the literature, and,
unlike the later one, develops also outside the event horizon, that is, it can
be seen by an external observer. In addition, for the nonextremal case through
fitting of the numerical data we obtained an approximate analytical formula
which relates values of charge and the $\Lambda$-term at the onset of
instability.
|
Non-local Symmetries of Nonlinear Field Equations: an Algebraic Approach: An algebraic method is devised to look for non-local symmetries of the
pseudopotential type of nonlinear field equations. The method is based on the
use of an infinite-dimensional subalgebra of the prolongation algebra $L$
associated with the equations under consideration. Our approach, which is
applied by way of example to the Dym and the Korteweg-de Vries equations,
allows us to obtain a general formula for the infinitesimal operator of the
non-local symmetries expressed in terms of elements of $L$. The method could be
exploited to investigate the symmetry properties of other nonlinear field
equations possessing nontrivial prolongations.
|
Matrix model criticality and resonant tunneling: We suggest that the Hermitian matrix models with resonant tunneling may
exhibit novel criticality. Some features of the proposed criticality are
explored. In particular, we argue that the new critical point is connected with
the first-order transition.
|
On the dyon partition function in N=2 theories: We study the entropy function of two N =2 string compactifications obtained
as freely acting orbifolds of N=4 theories : the STU model and the FHSV model.
The Gauss-Bonnet term for these compactifications is known precisely. We apply
the entropy function formalism including the contribution of this four
derivative term and evaluate the entropy of dyons to the first subleading order
in charges for these models. We then propose a partition function involving the
product of three Siegel modular forms of weight zero which reproduces the
degeneracy of dyonic black holes in the STU model to the first subleading order
in charges. The proposal is invariant under all the duality symmetries of the
STU model. For the FHSV model we write down an approximate partition function
involving a Siegel modular form of weight four which captures the entropy of
dyons in the FHSV model in the limit when electric charges are much larger than
magnetic charges.
|
Properties of noncommutative axionic electrodynamics: Using the gauge-invariant but path-dependent variables formalism, we compute
the static quantum potential for noncommutative axionic electrodynamics, and
find a radically different result than the corresponding commutative case. We
explicitly show that the static potential profile is analogous to that
encountered in both non-Abelian axionic electrodynamics and in Yang-Mills
theory with spontaneous symmetry breaking of scale symmetry.
|
SYM N=4 in light-cone gauge and the "bridge" identities: The light-cone gauge allows to single out a set of ``transverse'' fields
(TF), whose Green functions are free from UV divergences in SYM N=4. Green
functions with external lines involving the remaining fields do instead exhibit
divergences: indeed those fields can be expressed, by solving their equations
of motion, as composite operators in terms of ``transverse'' fields. A set of
exact identities (bridge identities) automatically realize their insertions in
a path-integral formulation.
|
Holographic Quantum Gravity and Horizon Instability: In this Essay, we will look at the relation between the No Transmission
principle and the Strong cosmic censorship (SCC), which we will highlight in
the background of quantum gravity. We show that taking quantum gravity into
account, one can provide a complete picture of the instability of the inner
horizon and the principle that two independent CFTs, under the gauge-gravity
duality, imply that the dual bulks must also be independent in that there must
not exist a way to transmit a signal between the two spacetimes. We show that
this can simply be interpreted as SCC, and that the inner horizon must be
unstable (at either linear or nonlinear orders) to be in accordance with
holographic quantum gravity.
|
Towards matrix model representation of HOMFLY polynomials: We investigate possibilities of generalizing the TBEM eigenvalue matrix
model, which represents the non-normalized colored HOMFLY polynomials for torus
knots as averages of the corresponding characters. We look for a model of the
same type, which is a usual Chern-Simons mixture of the Gaussian potential,
typical for Hermitean models, and the sine Vandermonde factors, typical for the
unitary ones. We mostly concentrate on the family of twist knots, which
contains a single torus knot, the trefoil. It turns out that for the trefoil
the TBEM measure is provided by an action of Laplace exponential on the Jones
polynomial. This procedure can be applied to arbitrary knots and provides a
TBEM-like integral representation for the N=2 case. However, beyond the torus
family, both the measure and its lifting to larger N contain non-trivial
corrections in \hbar=\log q. A possibility could be to absorb these corrections
into a deformation of the Laplace evolution by higher Casimir and/or
cut-and-join operators, in the spirit of Hurwitz tau-function approach to knot
theory, but this remains a subject for future investigation.
|
On fixed points of quantum gravity: We study the short distance behaviour of euclidean quantum gravity in the
light of Weinberg's asymptotic safety scenario. Implications of a non-trivial
ultraviolet fixed point are reviewed. Based on an optimised renormalisation
group, we provide analytical flow equations in the Einstein-Hilbert truncation.
A non-trivial ultraviolet fixed point is found for arbitrary dimension. We
discuss a bifurcation pattern in the spectrum of eigenvalues at criticality,
and the large dimensional limit of quantum gravity. Implications for quantum
gravity in higher dimensions are indicated.
|
Invariants of the heat equation for non-minimal operators: A special class of non-minimal operators which are relevant for quantum field
theory is introduced. The general form of the heat kernel coefficients of these
operators on manifolds without boundary is described. New results are presented
for the traces of the first two heat kernel coefficients for vector, Yang-Mills
and perturbative gravity. It is argued that non-minimal operators can be used
to define gauge-fixing independent actions and solve the conformal mode problem
in quantum gravity.
|
Orbifolds as Melvin Geometry: In this paper we explicitly show that the various noncompact abelian
orbifolds are realized as special limits of parameters in type II (NSNS) Melvin
background and its higher dimensional generalizations. As a result the
supersymmetric ALE spaces (A-type C^2/Z_N) and nonsupersymmetric orbifolds in
type II and type 0 theory are all connected with each other by the exactly
marginal deformation. Our results provide new examples of the duality between
type II and type 0 string theory. We also discuss the decay of unstable
backgrounds in this model which include closed string tachyons.
|
4th order similarity renormalization of a model hamiltonian: We study the similarity renormalization scheme for hamiltonians to the fourth
order in perturbation theory using a model hamiltonian for fermions coupled to
bosons. We demonstrate that the free finite parts of counterterms can be chosen
in such a way that the T-matrix is covariant up to the fourth order and the
eigenvalue equation for the physical fermion reduces to the Dirac equation.
Through this choice, the systematic renormalization scheme reproduces the model
solution originally proposed by G{\l}azek and Perry.
|
Bubbling the Newly Grown Black Ring Hair: New families of BPS black ring solutions with four electric and four dipole
magnetic charges have recently been explicitly constructed and uplifted to
M-theory. These solutions were found to belong to a CFT with central charge
different compared to the one of the STU model. Because of their importance to
AdS/CFT, here we give the microstate description of these geometries in terms
of topological bubbles and supertubes. The fourth charge results in an
additional flux through the topological cycles that resolve the brane
singularities. The analog of these solutions in the IIB frame yield a
generalized regular supertube with three electric charges and one dipole
charge. Direct comparison is also made with the previously-known bubbled
geometries.
|
Future of the universe in modified gravitational theories: Approaching
to the finite-time future singularity: We investigate the future evolution of the dark energy universe in modified
gravities including $F(R)$ gravity, string-inspired scalar-Gauss-Bonnet and
modified Gauss-Bonnet ones, and ideal fluid with the inhomogeneous equation of
state (EoS). Modified Friedmann-Robertson-Walker (FRW) dynamics for all these
theories may be presented in universal form by using the effective ideal fluid
with an inhomogeneous EoS without specifying its explicit form. We construct
several examples of the modified gravity which produces accelerating
cosmologies ending at the finite-time future singularity of all four known
types by applying the reconstruction program. Some scenarios to resolve the
finite-time future singularity are presented. Among these scenarios, the most
natural one is related with additional modification of the gravitational action
in the early universe. In addition, late-time cosmology in the non-minimal
Maxwell-Einstein theory is considered. We investigate the forms of the
non-minimal gravitational coupling which generates the finite-time future
singularities and the general conditions for this coupling in order that the
finite-time future singularities cannot emerge. Furthermore, it is shown that
the non-minimal gravitational coupling can remove the finite-time future
singularities or make the singularity stronger (or weaker) in modified gravity.
|
Kinks in two-dimensional Anti-de Sitter Space: Soliton solutions in scalar field theory defined on a two-dimensional Anti-de
Sitter background space-time are investigated. It is shown that the lowest
soliton excitation generically has frequency equal to the inverse radius of the
space-time. Analytic and numerical soliton solutions are determined in "phi to
the fourth" scalar field theory with a negative mass-squared. The classical
soliton mass is calculated as a function of the ratio of the square of the mass
scale of the field theory over the curvature of the space-time. For the case
that this ratio equals unity, the soliton excitation spectrum is determined
algebraically and the one-loop radiative correction to the soliton mass is
computed in the semi-classical approximation.
|
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