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An Alternative Perturbative Expansion in Quantum Mechanics. Scaling and
cut-off Resummation: An alternative perturbative expansion in quantum mechanics which allows a
full expression of the scaling arbitrariness is introduced. This expansion is
examined in the case of the anharmonic oscillator and is conveniently resummed
using a method which consists in introducing an energy cut-off that is
carefully removed as the order of the expansion is increased. We illustrate
this technique numerically by computing the asymptotic behavior of the ground
state energy of the anharmonic oscillator for large couplings, and show how the
exploitation of the scaling arbitrariness substantially improves the
convergence of this perturbative expansion. | hep-th |
Particle scattering and vacuum instability by exponential steps: Particle scattering and vacuum instability in a constant inhomogeneous
electric field of particular peak configuration that consists of two
(exponentially increasing and exponentially decreasing) independent parts are
studied. It presents a new kind of external field where exact solutions of the
Dirac and Klein-Gordon equations can be found. We obtain and analyze in- and
out-solutions of the Dirac and Klein-Gordon equations in this configuration. By
their help we calculate probabilities of particle scattering and
characteristics of the vacuum instability. In particular, we consider in
details three configurations: a smooth peak, a sharp peak, and a strongly
asymmetric peak configuration. We find asymptotic expressions for total mean
numbers of created particles and for vacuum-to-vacuum transition probability.
We discuss a new regularization of the Klein step by the sharp peak and compare
this regularization with another one given by the Sauter potential. | hep-th |
On holography for (pseudo-)conformal cosmology: We propose a holographic dual for (pseudo-)conformal cosmological scenario,
with a scalar field that forms a moving domain wall in adS_5. The domain wall
separates two vacua with unequal energy densities. Unlike in the existing
construction, the 5d solution is regular in the relevant space-time domain. | hep-th |
Multipolar Expansions for the Relativistic N-Body Problem in the
Rest-Frame Instant Form: Dixon's multipoles for a system of N relativistic positive-energy scalar
particles are evaluated in the rest-frame instant form of dynamics. The Wigner
hyperplanes (intrinsic rest frame of the isolated system) turn out to be the
natural framework for describing multipole kinematics. In particular, concepts
like the {\it barycentric tensor of inertia} can be defined in special
relativity only by means of the quadrupole moments of the isolated system. | hep-th |
The effect of different regulators in the non-local field-antifield
quantization: Recently it was shown how to regularize the Batalin-Vilkovisky (BV)
field-antifield formalism of quantization of gauge theories with the non-local
regularization (NLR) method. The objective of this work is to make an analysis
of the behaviour of this NLR formalism, connected to the BV framework, using
two different regulators: a simple second order differential regulator and a
Fujikawa-like regulator. This analysis has been made in the light of the well
known fact that different regulators can generate different expressions for
anomalies that are related by a local couterterm, or that are equivalent after
a reparametrization. This has been done by computing precisely the anomaly of
the chiral Schwinger model. | hep-th |
Some views on monopoles and confinement: Aspects of the monopole condensation picture of confinement are discussed.
First, the nature of the monopole singularities in the abelian projection
approach is analysed. Their apparent gauge dependence is shown to have a
natural interpretation in terms of 't~Hooft-Polyakov-like monopoles in
euclidean SU(2) gauge theory. Next, the results and predictions of a
realization of confinement through condensation of such monopoles are
summarized and compared with numerical data. | hep-th |
The CP(n) Model on Noncommutative Plane: We construct the consistent CP(n) model on noncommutative plane. The
Bogomolny bound on the energy is saturated by (anti-)self-dual solitons with
integer topological charge, which is independent of their scaling and
orientation. This integer quantization is satisfied for our general solutions,
which turns out regular everywhere. We discuss the possible implication of our
result to the instanton physics in Yang-Mills theories on noncommutative R^4. | hep-th |
Superpotential of Three Dimensional ${\cal N}=1$ Heterotic Supergravity: We dimensionally reduce the ten dimensional heterotic action on spacetimes of
the form ${\cal M}_{(2,1)}\times Y$, where ${\cal M}_{(2,1)}$ is three
dimensional maximally symmetric Anti de Sitter or Minkowski space, and $Y$ is a
compact seven dimensional manifold with $G_2$ structure. In doing so, we derive
the real superpotential functional of the corresponding three dimensional
${\cal N}=1$ theory. We confirm that extrema of this functional precisely
correspond to supersymmetric heterotic compactifications on manifolds of $G_2$
structure. We make some comments on the role of the superpotential functional
with respect to the coupled moduli problem of instanton bundles over $G_2$
manifolds. | hep-th |
Building Quantum Field Theories Out of Neurons: An approach to field theory is studied in which fields are comprised of $N$
constituent random neurons. Gaussian theories arise in the infinite-$N$ limit
when neurons are independently distributed, via the Central Limit Theorem,
while interactions arise due to finite-$N$ effects or non-independently
distributed neurons. Euclidean-invariant ensembles of neurons are engineered,
with tunable two-point function, yielding families of Euclidean-invariant field
theories. Some Gaussian, Euclidean invariant theories are reflection positive,
which allows for analytic continuation to a Lorentz-invariant quantum field
theory. Examples are presented that yield dual theories at infinite-$N$, but
have different symmetries at finite-$N$. Landscapes of classical field
configurations are determined by local maxima of parameter distributions.
Predictions arise from mixed field-neuron correlators. Near-Gaussianity is
exhibited at large-$N$, potentially explaining a feature of field theories in
Nature. | hep-th |
Komar energy and Smarr formula for noncommutative Schwarzschild black
hole: We calculate the Komar energy $E$ for a noncommutative Schwarzschild black
hole. A deformation from the conventional identity $E=2ST_H$ is found in the
next to leading order computation in the noncommutative parameter $\theta$
(i.e. $\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})$) which is also consistent
with the fact that the area law now breaks down. This deformation yields a
nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes.
We then work out the Smarr formula, clearly elaborating the differences from
the standard result $M=2ST_H$, where the mass ($M$) of the black hole is
identified with the asymptotic limit of the Komar energy. Similar conclusions
are also shown to hold for a deSitter--Schwarzschild geometry. | hep-th |
Soft Supersymmetry Breaking in Anisotropic LARGE Volume
Compactifications: We study soft supersymmetry breaking terms for anisotropic LARGE volume
compactifications, where the bulk volume is set by a fibration with one small
four-cycle and one large two-cycle. We consider scenarios where D7s wrap either
a blow-up cycle or the small fibre cycle. Chiral matter can arise either from
modes parallel or perpendicular to the brane. We compute soft terms for this
matter and find that for the case where the D7 brane wraps the fibre cycle the
scalar masses can be parametrically different, allowing a possible splitting of
third-generation soft terms. | hep-th |
On the Lorentz Transformations of Momentum and Energy: Motivated by ultra-high-energy cosmic ray physics, we discuss all the
possible alternatives to the familiar Lorentz transformations of the momentum
and the energy of a particle. Starting from natural physical requirements, we
exclude all the possibilities, apart from the ones which arise from the usual
four-vector transformations by means of a change of coordinates in the
mass-shell. This result confirms the remark, given in a preceding paper, that,
in a theory without preferred inertial frames, one can always define a linearly
transforming energy parameter to which the GZK cutoff argument can be applied.
We also discuss the connections between the conservation and the transformation
properties of energy-momentum and the relation between energy-momentum and
velocity. | hep-th |
Behavior of Cosmological Perturbations in the Brane-World Mode: In this paper we present a gauge-invariant formalism for perturbations of the
brane-world model developed by the author, A. Ishibashi and O. Seto recently,
and analyze the behavior of cosmological perturbations in a spatially flat
expanding universe realized as a boundary 3-brane in AdS$^5$ in terms of this
formalism. For simplicity we restrict arguments to scalar perturbations. We
show that the behavior of cosmological perturbations on superhorizon scales in
the brane-world model is the same as that in the standard no-extradimension
model, irrespective of the initial condition for bulk perturbations, in the
late stage when the cosmic expansion rate $H$ is smaller than the inverse of
the bulk curvature scale $\ell$. Further, we give rough estimates which
indicate that in the early universe when $H$ is much larger than $1/\ell$,
perturbations in these two models behave quite differently, and the
conservation of the Bardeen parameter does not hold for superhorizon
perturbations in the brane-world model. | hep-th |
$q$-Virasoro/W Algebra at Root of Unity and Parafermions: We demonstrate that the parafermions appear in the $r$-th root of unity limit
of $q$-Virasoro/$W_n$ algebra. The proper value of the central charge of the
coset model $ \frac{\widehat{\mathfrak{sl}}(n)_r \oplus
\widehat{\mathfrak{sl}}(n)_{m-n}}{\widehat{\mathfrak{sl}}(n)_{m-n+r}}$ is given
from the parafermion construction of the block in the limit. | hep-th |
Ghost wave-function renormalization in Asymptotically Safe Quantum
Gravity: Motivated by Weinberg's asymptotic safety scenario, we investigate the
gravitational renormalization group flow in the Einstein-Hilbert truncation
supplemented by the wave-function renormalization of the ghost fields. The
latter induces non-trivial corrections to the beta-functions for Newton's
constant and the cosmological constant. The resulting ghost-improved phase
diagram is investigated in detail. In particular, we find a non-trivial
ultraviolet fixed point in agreement with the asymptotic safety conjecture,
which also survives in the presence of extra dimensions. In four dimensions the
ghost anomalous dimension at the fixed point is $\eta_c^* = -1.8$, supporting
space-time being effectively two-dimensional at short distances. | hep-th |
M-Theory, Torons and Confinement: We study the decompactification limit of M-theory superpotentials for N=1
four dimensional supersymmetric gauge theories. These superpotentials can be
interpreted as generated by toron configurations. The connection with the
confinement picture in the maximal abelian gauge is discussed. | hep-th |
Recurrent dynamical symmetry breaking and restoration by Wilson lines at
finite densities on a torus: In this paper we derive the general expression of a one-loop effective
potential of the nonintegrable phases of Wilson lines for an SU(N) gauge theory
with a massless adjoint fermion defined on the spactime manifold
$R^{1,d-3}\times T^2$ at finite temperature and fermion density. The Phase
structure of the vacuum is presented for the case with $d=4$ and N=2 at zero
temperature. It is found that gauge symmetry is broken and restored alternately
as the fermion density increases, a feature not found in the Higgs mechanism.
It is the manifestation of the quantum effects of the nonintegrable phases. | hep-th |
Higuchi Bound on Slow Roll Inflation and the Swampland: In this paper we study the implications of the generalized Higuchi bound on
massive spin-two fields for the derivative of the scalar potential within
bimetric theory. In contrast to the recent de Sitter swampland conjecture, an
upper bound on the derivate of the scalar potential follows from the
generalized Higuchi bound. In combination, this leaves a window for the
derivate of the scalar potential. We discuss this bound in several
representative bimetric models and parameter regions. | hep-th |
Classifying BPS bosonic Wilson loops in 3d ${\cal N}=4$
Chern-Simons-matter theories: We study the possible BPS Wilson loops in three-dimensional ${\cal N}=4$
Chern-Simons-matter theory which involve only the gauge field and bilinears of
the scalars. Previously known examples are the analogues of the Gaiotto-Yin
loops preserving four supercharges and "latitude" loops preserving two. We
carry out a careful classification and find, in addition, loops preserving
three supercharges, further inequivalent classes of loops preserving two
supercharges and loops preserving a single supercharge. For each of the classes
of loops, we present a representative example and analyse their full orbit
under the broken symmetries. | hep-th |
Momentum in Single-trace $T\bar T$ Holography: We extend the study of 2006.13249, 2303.12422 to black strings with general
momentum, and discuss their interpretation in single-trace $T\bar T$ deformed
$CFT_2$. | hep-th |
Matrix 3-Lie superalgebras and BRST supersymmetry: Given a matrix Lie algebra one can construct the 3-Lie algebra by means of
the trace of a matrix. In the present paper we show that this approach can be
extended to the infinite-dimensional Lie algebra of vector fields on a manifold
if instead of the trace of a matrix we consider a differential 1-form which
satisfies certain conditions. Then we show that the same approach can be
extended to matrix Lie superalgebras if instead of the trace of a matrix we
make use of the super trace of a matrix. It is proved that a graded triple
commutator of matrices constructed with the help of the graded commutator and
the super trace satisfies a graded ternary Filippov-Jacobi identity. In two
particular cases and we show that the Pauli and Dirac matrices generate the
matrix 3-Lie superalgebras, and we find the non-trivial graded triple
commutators of these algebras. We propose a Clifford algebra approach to 3-Lie
superalgebras induced by Lie superalgebras. We also discuss an application of
matrix 3-Lie superalgebras in BRST-formalism. | hep-th |
Strong coupling in extended Horava-Lifshitz gravity: An extension of Horava-Lifshitz gravity was recently proposed in order to
address the pathological behavior of the scalar mode all previous versions of
the theory exhibit. We show that even in this new extension the strong coupling
persists, casting doubts on whether such a model can constitute an interesting
alternative to general relativity (GR). | hep-th |
Fedosov Deformation Quantization as a BRST Theory: The relationship is established between the Fedosov deformation quantization
of a general symplectic manifold and the BFV-BRST quantization of constrained
dynamical systems. The original symplectic manifold $\mathcal M$ is presented
as a second class constrained surface in the fibre bundle ${{\mathcal
T}^*_\rho}{\mathcal M}$ which is a certain modification of a usual cotangent
bundle equipped with a natural symplectic structure. The second class system is
converted into the first class one by continuation of the constraints into the
extended manifold, being a direct sum of ${{\mathcal T}^*_\rho}{\mathcal M}$
and the tangent bundle $T {\mathcal M}$. This extended manifold is equipped
with a nontrivial Poisson bracket which naturally involves two basic
ingredients of Fedosov geometry: the symplectic structure and the symplectic
connection. The constructed first class constrained theory, being equivalent to
the original symplectic manifold, is quantized through the BFV-BRST procedure.
The existence theorem is proven for the quantum BRST charge and the quantum
BRST invariant observables. The adjoint action of the quantum BRST charge is
identified with the Abelian Fedosov connection while any observable, being
proven to be a unique BRST invariant continuation for the values defined in the
original symplectic manifold, is identified with the Fedosov flat section of
the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized
as a conventional product of the quantum BRST invariant observables. | hep-th |
Kerr-Bolt Black Hole Entropy and Soft Hair: Recently it has been speculated that a set of infinitesimal ${\rm
Virasoro_{\,L}}\otimes{\rm Virasoro_{\,R}}$ diffeomorphisms exist which act
non-trivially on the horizon of some black holes such as kerr and Kerr-Newman
black hole \cite{Haco:2018ske,Haco:2019ggi}. Using this symmetry in covariant
phase space formalism one can obtains Virasoro charges as surface integrals on
the horizon. Kerr-Bolt spacetime is well-known for its asymptotically topology
and has been studied widely in recent years. In this work we are interested to
find conserved charge associated to the Virosora symmetry of Kerr-Bolt geometry
using covariant phase space formalism. We will show right and left central
charge are $c_R=c_L=12 J$ respectively. Our results also show good agreement
with Kerr spacetime in the limiting behavior. | hep-th |
A Smooth Exit from Eternal Inflation?: The usual theory of inflation breaks down in eternal inflation. We derive a
dual description of eternal inflation in terms of a deformed Euclidean CFT
located at the threshold of eternal inflation. The partition function gives the
amplitude of different geometries of the threshold surface in the no-boundary
state. Its local and global behavior in dual toy models shows that the
amplitude is low for surfaces which are not nearly conformal to the round
three-sphere and essentially zero for surfaces with negative curvature. Based
on this we conjecture that the exit from eternal inflation does not produce an
infinite fractal-like multiverse, but is finite and reasonably smooth. | hep-th |
Reheating in small-field inflation on the brane: The Swampland Criteria
and observational constraints in light of the PLANCK 2018 results: We study cosmological inflation and its dynamics in the framework of the
Randall-Sundrum II brane model. In particular, we analyze in detail four
representative small-field inflationary potentials, namely Natural inflation,
Hilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each
characterized by two mass scales. We constrain the parameters for which a
viable inflationary Universe emerges using the latest PLANCK results.
Furthermore, we investigate whether or not those models in brane cosmology are
consistent with the recently proposed Swampland Criteria, and give predictions
for the duration of reheating as well as for the reheating temperature after
inflation. Our results show that (i) the distance conjecture is satisfied, (ii)
the de Sitter conjecture and its refined version may be avoided, and (iii) the
allowed range for the five-dimensional Planck mass, $M_5$, is found to be
between $10^5~\textrm{TeV}$ and $10^{12}~\textrm{TeV}$. Our main findings
indicate that non-thermal leptogenesis cannot work within the framework of
RS-II brane cosmology, at least for the inflationary potentials considered
here. | hep-th |
On the correspondence between the classical and quantum gravity: The relationship between the classical and quantum theories of gravity is
reexamined. The value of the gravitational potential defined with the help of
the two-particle scattering amplitudes is shown to be in disagreement with the
classical result of General Relativity given by the Schwarzschild solution. It
is shown also that the potential so defined fails to describe whatever
non-Newtonian interactions of macroscopic bodies. An alternative interpretation
of the $\hbar^0$-order part of the loop corrections is given directly in terms
of the effective action. Gauge independence of that part of the one-loop
radiative corrections to the gravitational form factors of the scalar particle
is proved, justifying the interpretation proposed. | hep-th |
Cosmology and the Fate of Dilatation Symmetry: We discuss the cosmological constant problem in the light of dilatation
symmetry and its possible anomaly. For dilatation symmetric quantum theories
realistic asymptotic cosmology is obtained provided the effective potential has
a non-trivial minimum. For theories with dilatation anomaly one needs as a
non-trivial "cosmon condition" that the energy-momentum tensor in the vacuum is
purely anomalous. Such a condition is related to the short-distance
renormalization group behavior of the fundamental theory. Observable deviations
from the standard hot big bang cosmology are possible. | hep-th |
The Dirac operator on hypersurfaces: Odd-dimensional Riemannian spaces that are non-orientable, but have a pin
structure, require the consideration of the twisted adjoint representation of
the corresponding pin group. It is shown here how the Dirac operator should be
modified, also on even-dimensional spaces, to make it equivariant with respect
to the action of that group when the twisted adjoint representation is used in
the definition of the pin structure. An explicit description of a pin structure
on a hypersurface, defined by its immersion in a Euclidean space, is used to
derive a "Schroedinger" transform of the Dirac operator in that case. This is
then applied to obtain - in a simple manner - the spectrum and eigenfunctions
of the Dirac operator on spheres and real projective spaces. | hep-th |
N-vaton: In general there are a large number of light scalar fields in the theories
going beyond standard model, such as string theory, and some of them can be
taken as the candidates of curvatons. For simplicity, we assume all of
curvatons have the same decay rate and suddenly decay into radiation at the
same time. In order to distinguish this scenario from the more general case, we
call it "N-vaton". We use $\delta {\cal N}$ formalism to calculate the
primordial power spectrum and bispectrum in N-vaton model and investigate
various bounds on the non-Gaussianity parameter $f_{NL}$. A red tilted
primordial power spectrum and a large value of $f_{NL}$ can be naturally
obtained if the curvature perturbation generated by inflaton also makes a
significant contribution to the primordial power spectrum. As a realistic
N-vaton model, we suppose that the axions in the KKLT compactifications of Type
IIB string theory are taken as curvatons and a rich phenomenology is obtained. | hep-th |
Light-front gauge invariant formulation and electromagnetic duality: The gauge invariant formulation of Maxwell's equations and the
electromagnetic duality transformations are given in the light-front (LF)
variables. The novel formulation of the LF canonical quantization, which is
based on the kinematic translation generator $P^{+}$ rather then on the
Hamiltonian $P^{-}$, is proposed. This canonical quantization is applied for
the free electromagnetic fields and for the fields generated by electric and
magnetic external currents. The covariant form of photon propagators, which
agrees with Schwinger's source theory, is achieved when the direct interaction
of external currents is properly chosen. Applying the path integral formalism,
the equivalent LF Lagrangian density, which depends on two Abelian gauge
potentials, is proposed. Some remarks on the Dirac strings and LF non local
structures are presented in the Appendix. | hep-th |
Stability and fluctuation modes of giant gravitons with NSNS B field: We study the stability of the giant gravitons in the string theory background
with NSNS B field. We consider the perturbation of giant gravitons formed by a
probe D$(8-p)$ brane in the background generated by D$(p-2)$-D$(p)$ branes for
$2 \le p \le 5$. We use the quadratic approximation to the brane action to find
the equations of motion. For $p=5$, giant graviton configurations are stable
independent of the size of the brane. For $p \ne 5$, we calculated the range of
the size of the brane where they are stable. We also present the mode
frequencies explicitly for some special cases. | hep-th |
Ground states of holographic superconductors: We investigate the ground states of the Abelian Higgs model in AdS_4 with
various choices of parameters, and with no deformations in the ultraviolet
other than a chemical potential for the electric charge under the Abelian gauge
field. For W-shaped potentials with symmetry-breaking minima, an analysis of
infrared asymptotics suggests that the ground state has emergent conformal
symmetry in the infrared when the charge of the complex scalar is large enough.
But when this charge is too small, the likeliest ground state has Lifshitz-like
scaling in the infrared. For positive mass quadratic potentials, Lifshitz-like
scaling is the only possible infrared behavior for constant nonzero values of
the scalar. The approach to Lifshitz-like scaling is shown in many cases to be
oscillatory. | hep-th |
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. | hep-th |
A Coherent State Path Integral for Anyons: We derive an $su(1,1)$ coherent state path integral formula for a system of
two one-dimensional anyons in a harmonic potential. By a change of variables we
transform this integral into a coherent states path integral for a harmonic
oscillator with a shifted energy. The shift is the same as the one obtained for
anyons by other methods. We justify the procedure by showing that the change of
variables corresponds to a $su(1,1)$ version of the Holstein-Primakoff
transformation. | hep-th |
Minkowski Conformal Blocks and the Regge Limit for SYK-like Models: We discuss scattering in a CFT via the conformal partial-wave analysis and
the Regge limit. The focus of this paper is on understanding an OPE with
Minkowski conformal blocks. Starting with a t-channel OPE, it leads to an
expansion for an s-channel scattering amplitude in terms of t-channel
exchanges. By contrasting with Euclidean conformal blocks we see a precise
relationship between conformal blocks in the two limits without preforming an
explicit analytic continuation. We discuss a generic feature for a CFT
correlation function having singular $F^{(M)}(u,v)\sim {u}^{-\delta}\,$,
$\delta>0$, in the limit $u \rightarrow 0$ and $v\rightarrow 1$. Here,
$\delta=(\ell_{eff}-1)/2$, with $\ell_{eff}$ serving as an effective spin and
it can be determined through an OPE. In particular, it is bounded from above,
$\ell_{eff} \leq 2$, for all CFTs with a gravity dual, and it can be associated
with string modes interpolating the graviton in AdS. This singularity is
historically referred to as the Pomeron. This bound is nearly saturated by
SYK-like effective $d=1$ CFT, and its stringy and thermal corrections have
piqued current interests. Our analysis has been facilitated by dealing with
Wightman functions. We provide a direct treatment in diagonalizing dynamical
equations via harmonic analysis over physical scattering regions. As an example
these methods are applied to the SYK model. | hep-th |
Eikonal phase matrix, deflection angle and time delay in effective field
theories of gravity: The eikonal approximation is an ideal tool to extract classical observables
in gauge theory and gravity directly from scattering amplitudes. Here we
consider effective theories of gravity where in addition to the
Einstein-Hilbert term we include non-minimal couplings of the type $R^3$, $R^4$
and $FFR$. In particular, we study the scattering of gravitons and photons of
frequency $\omega$ off heavy scalars of mass $m$ in the limit $m\gg \omega \gg
|\vec{q}\,|$, where $\vec{q}$ is the momentum transfer. The presence of
non-minimal couplings induces helicity-flip processes which survive the eikonal
limit, thereby promoting the eikonal phase to an eikonal phase matrix. We
obtain the latter from the relevant two-to-two helicity amplitudes that we
compute up to one-loop order, and confirm that the leading-order terms in
$\omega$ exponentiate \`{a} la Amati, Ciafaloni and Veneziano. From the
eigenvalues of the eikonal phase matrix we then extract two physical
observables, to 2PM order: the classical deflection angle and Shapiro time
delay/advance. Whenever the classical expectation of helicity conservation of
the massless scattered particle is violated, i.e. the eigenvalues of the
eikonal matrix are non-degenerate, causality violation due to time advance is a
generic possibility for small impact parameter. We show that for graviton
scattering in the $R^4$ and $FFR$ theories, time advance is circumvented if the
couplings of these interactions satisfy certain positivity conditions, while it
is unavoidable for graviton scattering in the $R^3$ theory and photon
scattering in the $FFR$ theory. The scattering processes we consider mimic the
deflection of photons and gravitons off spinless heavy objects such as
black~holes. | hep-th |
Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2): In this note we study worldsheet two- and four-point functions at the
one-loop level for the type IIA superstring in AdS(3) x S(3) x M(4) . We first
address the regularization ambiguity that appears in the dispersion relation
derived from integrability. We demonstrate that only the regulator treating all
fields equally respects worldsheet supersymmetry. This is done in an implicit
regularization scheme where all divergent terms are collected into master
tadpole-type integrals. We then investigate one-loop two-body scattering on the
string worldsheet and verify that a recent proposal for the dressing phase
reproduces explicit worldsheet computations. All calculations are done in a
near-BMN like expansion of the Green-Schwarz superstring equipped with quartic
fermions. | hep-th |
Gauge symmetry of unimodular gravity in Hamiltonian formalism: We work out the description of the gauge symmetry of unimodular gravity in
the constrained Hamiltonian formalism. In particular, we demonstrate how the
transversality conditions restricting the diffeomorphism parameters emerge from
the algebra of the Hamiltonian constraints. The alternative form is long known
as parametrizing the volume preserving diffeomorphisms by unrestricted
two-forms instead of the transverse vector fields. This gauge symmetry is
reducible. We work out the Hamiltonian description of this form of unimodular
gravity (UG) gauge symmetry.
Becchi-Rouet-Stora-Tyutin--Batalin-Fradkin-Vilkovisky (BFV-BRST) Hamiltonian
formalism is constructed for both forms of the UG gauge symmetry. These two
BRST complexes have a subtle inequivalence: Their BRST cohomology groups are
not isomorphic. In particular, for the first complex, which is related to the
restricted gauge parameters, the cosmological constant does not correspond to
any nontrivial BRST cocycle, while for the alternative complex it does. In the
wording of physics, this means $\Lambda$ is a fixed parameter defined by the
field asymptotics rather than the physical observable from the standpoint of
the first complex. The second formalism views $\Lambda$ as the observable with
unrestricted initial data. | hep-th |
Neutrino Majorana Masses from String Theory Instanton Effects: Finding a plausible origin for right-handed neutrino Majorana masses in
semirealistic compactifications of string theory remains one of the most
difficult problems in string phenomenology. We argue that right-handed neutrino
Majorana masses are induced by non-perturbative instanton effects in certain
classes of string compactifications in which the $U(1)_{B-L}$ gauge boson has a
St\"uckelberg mass. The induced operators are of the form $e^{-U}\nu_R\nu_R$
where $U$ is a closed string modulus whose imaginary part transforms
appropriately under $B-L$. This mass term may be quite large since this is not
a gauge instanton and $Re U$ is not directly related to SM gauge couplings.
Thus the size of the induced right-handed neutrino masses could be a few orders
of magnitude below the string scale, as phenomenologically required. It is also
argued that this origin for neutrino masses would predict the existence of
R-parity in SUSY versions of the SM. Finally we comment on other
phenomenological applications of similar instanton effects, like the generation
of a $\mu$-term, or of Yukawa couplings forbidden in perturbation theory. | hep-th |
Thirring Model as a Gauge Theory: We reformulate the Thirring model in $D$ $(2 \le D < 4)$ dimensions as a
gauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the
dynamical mass generation of the fermion through the Schwinger-Dyson (SD)
equation. By virtue of such a gauge symmetry we can greatly simplify the
analysis of the SD equation by taking the most appropriate gauge (``nonlocal
gauge'') for the HLS.
In the case of even-number of (2-component) fermions, we find the dynamical
fermion mass generation as the second order phase transition at certain fermion
number, which breaks the chiral symmetry but preserves the parity in (2+1)
dimensions ($D=3$). In the infinite four-fermion coupling (massless gauge
boson) limit in (2+1) dimensions, the result coincides with that of the
(2+1)-dimensional QED, with the critical number of the 4-component fermion
being $N_{\rm cr} = \frac{128}{3\pi^{2}}$. As to the case of odd-number
(2-component) fermion in (2+1) dimensions, the regularization ambiguity on the
induced Chern-Simons term may be resolved by specifying the regularization so
as to preserve the HLS.
Our method also applies to the (1+1) dimensions, the result being consistent
with the exact solution. The bosonization mechanism in (1+1) dimensional
Thirring model is also reproduced in the context of dual-transformed theory for
the HLS. | hep-th |
Finite Size Scaling in Quantum Hallography: At low temperatures observations of the Hall resistance for Quantum Hall
systems at the interface between two Hall plateaux reveal a power-law
behaviour, dR_xy/dB ~ T^(-p) (with p = 0.42 +/- 0.01); changing at still
smaller temperatures, T < T_s, to a temperature-independent value. Experiments
also show that the transition temperature varies with sample size, L, according
to T_s ~ 1/L. These experiments pose a potential challenge to the holographic
AdS/QHE model recently proposed in arXiv:1008.1917. This proposal, which was
motivated by the natural way AdS/CFT methods capture the emergent duality
symmetries exhibited by quantum Hall systems, successfully describes the
scaling exponent p by relating it to an infrared dynamical exponent z with p =
2/z. For a broad class of models z is robustly shown to be z = 5 in the regime
relevant to the experiments (though becoming z = 1 further in the ultraviolet).
By incorporating finite-size effects into these models we show that they
reproduce a transition to a temperature-independent regime, predicting a
transition temperature satisfying T_s ~ 1/L or ~ 1/L^5 in two separate regions
of parameter space, even though z = 5 governs the temperature dependence of the
conductivity in both cases. The possibility of a deviation from naive z = 5
scaling arises because the brane tension introduces a new scale, which alters
where the transition between UV and IR scaling occurs, in an L-dependent way.
The AdS/CFT calculation indicates the two regimes of temperature scaling are
separated by a first-order transition, suggesting new possibilities for testing
the picture experimentally. Remarkably, in this interpretation the gravity dual
of the transition from temperature scaling to temperature-independent
resistance is related to the Chandrashekar transition from a star to a black
hole with increasing mass. | hep-th |
Is it possible to recover information from the black-hole radiation?: In the framework of communication theory, we analyse the gedanken experiment
in which beams of quanta bearing information are flashed towards a black hole.
We show that stimulated emission at the horizon provides a correlation between
incoming and outgoing radiations consisting of bosons. For fermions, the
mechanism responsible for the correlation is the Fermi exclusion principle.
Each one of these mechanisms is responsible for the a partial transfer of the
information originally coded in the incoming beam to the black--hole radiation.
We show that this process is very efficient whenever stimulated emission
overpowers spontaneous emission (bosons). Thus, black holes are not `ultimate
waste baskets of information'. | hep-th |
Tachyon Perturbation on Two Dimensional Black Hole: We study the geometry of the two dimensional string theoretic black hole
under tachyonic perturbations. These perturbations are restricted to affect
only the metric and the dilaton, while other string theoretic excitations (like
the axion) are ignored. The metric and linearized dilaton perturbations are
determined to lowest non-trivial order of the tachyonic hair in the presence of
back reaction. We evaluate the Kretschmann scalar and argue that the horizon
does not become singular in the presence of tachyon perturbations (to the order
of our consideration). A closed-form solution of the allowed tachyon field and
that of the allowed tachyon potential emerges as a requirement of
self-consistency of our solution. | hep-th |
On the localization of fermions on thick D-branes: Hints on the possible localization of fermions on double thick D-branes
(Domain Walls) are found by analyzing the moduli space of parameters. Deeper
analysis toward this direction might help to select phenomenologically
plausible models. A new kind of condition for fermion localization is proposed.
This might be useful in multi-brane-world scenarios, which are important when
symmetry breaking is considered in the AdS/CFT formalism, as well as in curved
brane-worlds. | hep-th |
Conformal Symmetry for Black Holes in Four Dimensions and Irrelevant
Deformations: It has been argued several times in the past that the structure of the
entropy formula for general non-extremal asymptotically flat black holes in
four dimensions can be understood in terms of an underlying conformal symmetry.
A recent implementation of this idea, carried out by Cveti\v{c} and Larsen,
involves the replacement of a conformal factor in the original geometry by an
alternative conformal factor in such a way that the near-horizon behavior and
thermodynamic properties of the black hole remain unchanged, while only the
asymptotics or "environment" of the geometry are modified. The solution thus
obtained, dubbed "subtracted geometry", uplifts to an asymptotically
AdS$_{3}\times S^{2}$ black hole in five dimensions, and an AdS/CFT
interpretation is then possible. Building on this intuition we show that, at
least in the static case, the replacement of the conformal factor can be
implemented dynamically by means of an interpolating flow which we construct
explicitly. Furthermore, we show that this flow can be understood as the effect
of irrelevant perturbations from the point of view of the dual two-dimensional
CFT, and we identify the quantum numbers of the operators responsible for the
flow. This allows us to address quantitatively the validity of CFT computations
for these asymptotically flat black holes and provides a framework to
systematically compute corrections to the CFT results. | hep-th |
Comment on "Relativistic extension of shape-invariant potentials": This comment directs attention to some fails of the Alhaidari approach to
solve relativistic problems. It is shown that his gauge considerations are way
off the mark and that the class of exactly solvable relativistic problems is
not so enlarged as Alhaidari thinks it is. | hep-th |
D-branes on Calabi-Yau Manifolds and Superpotentials: We show how to compute terms in an expansion of the world-volume
superpotential for fairly general D-branes on the quintic Calabi-Yau using
linear sigma model techniques, and show in examples that this superpotential
captures the geometry and obstruction theory of bundles and sheaves on this
Calabi-Yau. | hep-th |
Particles creation from JNW quantum perturbed black holes by minimally
coupled Klein Gordon scalar free fields: In this work, we choose a minimal coupling interaction between massive Klein
Gordon (KG) quantum scalar free fields and Janis-Newman-Winicour (JNW)
spherically symmetric static black hole, to produce its Hawking temperature and
luminosity. This is done by calculating asymptotic wave solutions at near and
far from the black hole horizon. They are orthogonal mode solutions of local
Hilbert spaces. By using these mode solutions, we calculated Bogolubov
coefficients and then, we investigated number density matrix of created
particles. Mathematical calculations show that this is not exactly similar to
the Planck`s black body radiation energy density distribution but, it is "gray"
body radiation distribution depended to the emitted Hawking particles
frequency. Their difference is a non-vanishing absorptivity factor of
backscattered particles after to form horizon of a collapsing body. Our
motivation is determination of position of Hawking created pairs in which, two
different proposals are proposed, so called as "fairwall" and "quantum
atmosphere". | hep-th |
Supersymmetric WZW $σ$ Model on Full and Half Plane: We study classical integrability of the supersymmetric U(N) $\sigma$ model
with the Wess-Zumino-Witten term on full and half plane. We demonstrate the
existence of nonlocal conserved currents of the model and derive general
recursion relations for the infinite number of the corresponding charges in a
superfield framework. The explicit form of the first few supersymmetric charges
are constructed. We show that the considered model is integrable on full plane
as a concequence of the conservation of the supersymmetric charges. Also, we
study the model on half plane with free boundary, and examine the conservation
of the supersymmetric charges on half plane and find that they are conserved as
a result of the equations of motion and the free boundary condition. As a
result, the model on half plane with free boundary is integrable. Finally, we
conclude the paper and some features and comments are presented. | hep-th |
Classical W-symmetry and Grassmannian Manifold: Classical W-symmetry is globally parametrized by the Grassmannian Manifold
which is associated with the non-relativistic fermions. We give the
bosonization rule which defines the natural higher coordinates system to
describe the W-geometry. Generators of the W-algebra can be obtained from a
single tau-function by using vertex operators. | hep-th |
Fields in nonaffine bundles. III. Effective symmetries and conserved
currents in strings and higher branes: The principles of a previously developed formalism for the covariant
treatment of multi-scalar fields for which (as in a nonlinear sigma model) the
relevant target space is not of affine type -- but curved -- are recapitulated.
Their application is extended from ordinary harmonic models to a more general
category of "harmonious" field models, with emphasis on cases in which the
field is confined to a string or higher brane worldsheet, and for which the
relevant internal symmetry group is non Abelian, so that the conditions for
conservation of the corresponding charge currents become rather delicate,
particularly when the symmetry is gauged. Attention is also given to the
conditions for conservation of currents of a different kind -- representing
surface fluxes of generalised momentum or energy -- associated with symmetries
not of the internal target space but of the underlying spacetime background
structure, including the metric and any relevant gauge field. For the
corresponding current to be conserved the latter need not be manifestly
invariant: preservation modulo a gauge adjustment will suffice. The simplest
case is that of "strong" symmetry, meaning invariance under the action of an
effective Lie derivative (an appropriately gauge adjusted modification of an
ordinary Lie derivative). When the effective symmetry is of the more general
"weak" kind, the kinetic part of the current is not conserved by itself but
only after being supplemented by a suitable contribution from the background. | hep-th |
Deformation Theory of Holomorphic Vector Bundles, Extended Conformal
Symmetry and Extensions of 2D Gravity: Developing on the ideas of R. Stora and coworkers, a formulation of two
dimensional field theory endowed with extended conformal symmetry is given,
which is based on deformation theory of holomorphic and Hermitian spaces. The
geometric background consists of a vector bundle $E$ over a closed surface
$\Sigma$ endowed with a holomorphic structure and a Hermitian structure
subordinated to it. The symmetry group is the semidirect product of the
automorphism group ${\rm Aut}(E)$ of $E$ and the extended Weyl group ${\rm
Weyl}(E)$ of $E$ and acts on the holomorphic and Hermitian structures. The
extended Weyl anomaly can be shifted into an automorphism chirally split
anomaly by adding to the action a local counterterm, as in ordinary conformal
field theory. The dependence on the scale of the metric on the fiber of $E$ is
encoded in the Donaldson action, a vector bundle generalization of the
Liouville action. The Weyl and automorphism anomaly split into two
contributions corresponding respectively to the determinant and
projectivization of $E$. The determinant part induces an effective ordinary
Weyl or diffeomorphism anomaly and the induced central charge can be computed. | hep-th |
Super-renormalizable or Finite Lee-Wick Quantum Gravity: We propose a class of multidimensional higher derivative theories of gravity
without extra real degrees of freedom besides the graviton field. The
propagator shows up the usual real graviton pole and extra complex conjugates
poles that do not contribute to the absorptive part of the physical scattering
amplitudes. Indeed, they may consistently be excluded from the asymptotic
observable states of the theory making use of the Lee-Wick and Cutkoski,
Landshoff, Olive and Polkinghorne prescription for the construction of a
unitary S-matrix. Therefore, the spectrum consists on the graviton and short
lived elementary unstable particles that we named "anti-gravitons" because of
their repulsive contribution to the gravitational potential at short distance.
However, another interpretation of the complex conjugate pairs is proposed
based on the Calmet's suggestion, i.e. they could be understood as black hole
precursors long established in the classical theory. Since the theory is CPT
invariant, the complex conjugate of the micro black hole precursor has received
as a white hole precursor consistently with the t'Hooft complementary
principle. It is proved that the quantum theory is super-renormalizable in even
dimension, i.e. only a finite number of divergent diagrams survive, and finite
in odd dimension. Furthermore, turning on a local potential of the Riemann
tensor we can make the theory finite in any dimension. The singularity-free
Newtonian gravitational potential is explicitly computed for a range of higher
derivative theories. Finally, we propose a new super-reneromalizable or finite
Lee-Wick standard model of particle physics. | hep-th |
Bulk and brane radiative effects in gauge theories on orbifolds: We have computed one-loop bulk and brane mass renormalization effects in a
five-dimensional gauge theory compactified on the M_4 \times S^1/Z_2 orbifold,
where an arbitrary gauge group G is broken by the orbifold action to its
subgroup H. The space-time components of the gauge boson zero modes along the H
generators span the gauge theory on the orbifold fixed point branes while the
zero modes of the higher-dimensional components of the gauge bosons along the
G/H generators play the role of Higgs fields with respect to the gauge group H.
No quadratic divergences in the mass renormalization of the gauge and Higgs
fields are found either in the bulk or on the branes. All brane effects for the
Higgs field masses vanish (only wave function renormalization effects survive)
while bulk effects are finite and can trigger, depending on the fermionic
content of the theory, spontaneous Hosotani breaking of the brane gauge group
H. For the gauge fields we do find logarithmic divergences corresponding to
mass renormalization of their heavy Kaluza-Klein modes. Two-loop brane effects
for Higgs field masses are expected from wave function renormalization brane
effects inserted into finite bulk mass corrections. | hep-th |
Non-Higgsable clusters for 4D F-theory models: We analyze non-Higgsable clusters of gauge groups and matter that can arise
at the level of geometry in 4D F-theory models. Non-Higgsable clusters seem to
be generic features of F-theory compactifications, and give rise naturally to
structures that include the nonabelian part of the standard model gauge group
and certain specific types of potential dark matter candidates. In particular,
there are nine distinct single nonabelian gauge group factors, and only five
distinct products of two nonabelian gauge group factors with matter, including
$SU(3) \times SU(2)$, that can be realized through 4D non-Higgsable clusters.
There are also more complicated configurations involving more than two gauge
factors; in particular, the collection of gauge group factors with jointly
charged matter can exhibit branchings, loops, and long linear chains. | hep-th |
Critical Phenomena, Strings, and Interfaces: Some points concerning the relation of strings to interfaces in statistical
systems are discussed. | hep-th |
Superfield approach to symmetry invariance in QED with complex scalar
fields: We show that the Grassmannian independence of the super Lagrangian density,
expressed in terms of the superfields defined on a (4, 2)-dimensional
supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST)
and anti-BRST invariance of the corresoponding four (3 + 1)-dimensional (4D)
Lagrangian density that describes the interaction between the U(1) gauge field
and the charged complex scalar fields. The above 4D field theoretical model is
considered on a (4, 2)-dimensional supermanifold parametrized by the ordinary
four spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of
Grassmannian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,
\theta \bar\theta + \bar\theta \theta = 0). Geometrically, the (anti-)BRST
invariance is encoded in the translation of the super Lagrangian density along
the Grassmannian directions of the above supermanifold such that the outcome of
this shift operation is zero. | hep-th |
Gauged D=7 Supergravity on the S**1/Z_2 Orbifold: We construct the most general couplings of a bulk seven-dimensional
Yang-Mills-Einstein N=2 supergravity with a boundary six-dimensional chiral
N=(0,1) theory of vectors and charged hypermultiplets. The boundary consists of
two brane worlds sitting at the fixed points of an S^1/Z_2 compactification of
the seven-dimensional bulk supergravity. The resulting 6D massless spectrum
surviving the orbifold projection is anomalous. By introducing boundary fields
at the orbifold fixed points, we show that all anomalies are cancelled by a
Green-Schwarz mechanism. In addition, all couplings of the boundary fields to
the bulk are completely specified by supersymmetry. We emphasize that there is
no bulk Chern-Simons term to cancel the anomalies. The latter is traded for a
Green-Schwarz term which emerges in the boundary theory after a duality
transformation implemented to construct the bulk supergravity. | hep-th |
Anomalies on Orbifolds: We discuss the form of the chiral anomaly on an S1/Z2 orbifold with chiral
boundary conditions. We find that the 4-divergence of the higher-dimensional
current evaluated at a given point in the extra dimension is proportional to
the probability of finding the chiral zero mode there. Nevertheless the
anomaly, appropriately defined as the five dimensional divergence of the
current, lives entirely on the orbifold fixed planes and is independent of the
shape of the zero mode. Therefore long distance four dimensional anomaly
cancellation ensures the consistency of the higher dimensional orbifold theory. | hep-th |
Disc partition function of 2d $R^2$ gravity from DWG matrix model: We compute the sum over flat surfaces of disc topology with arbitrary number
of conical singularities. To that end, we explore and generalize a specific
case of the matrix model of dually weighted graphs (DWG) proposed and solved by
one of the authors, M. Staudacher and Th. Wynter. Namely, we compute the sum
over quadrangulations of the disc with certain boundary conditions, with
parameters controlling the number of squares (area), the length of the boundary
and the coordination numbers of vertices. The vertices introduce conical
defects with angle deficit given by a multiple of $\pi$, corresponding to
positive, zero or negative curvature. Our results interpolate between the
well-known 2d quantum gravity solution for the disc with fluctuating 2d metric
and the regime of 'almost flat' surfaces with all the negative curvature
concentrated on the boundary. We also speculate on possible ways to study the
fluctuating 2d geometry with $AdS_2$ background instead of the flat one. | hep-th |
Multi-Regge kinematics and the scattering equations: We study the solutions to the scattering equations in various
quasi-multi-Regge regimes where the produced particles are ordered in rapidity.
We observe that in all cases the solutions to the scattering equations admit
the same hierarchy as the rapidity ordering, and we conjecture that this
behaviour holds independently of the number of external particles. In
multi-Regge limit, where the produced particles are strongly ordered in
rapidity, we determine exactly all solutions to the scattering equations that
contribute to the Cachazo-He-Yuan (CHY) formula for gluon scattering in this
limit. When the CHY formula is localised on these solutions, it reproduces the
expected factorisation of tree-level amplitudes in terms of impact factors and
Lipatov vertices. We also investigate amplitudes in various quasi-MRK. While in
these cases we cannot determine the solutions to the scattering equations
exactly, we show that again our conjecture combined with the CHY formula
implies the factorisation of the amplitude into universal buildings blocks for
which we obtain a CHY-type representation. | hep-th |
Ultraviolet Behavior of N=8 Supergravity: In these lectures I describe the remarkable ultraviolet behavior of N=8
supergravity, which through four loops is no worse than that of N=4
super-Yang-Mills theory (a finite theory). I also explain the computational
tools that allow multi-loop amplitudes to be evaluated in this theory - the KLT
relations and the unitarity method - and sketch how ultraviolet divergences are
extracted from the amplitudes. | hep-th |
Running Shear Viscosities in Anisotropic Holographic Superfluids: We have examined holographic renormalization group($RG$) flows of the shear
viscosities in anisotropic holographic superfluids via their gravity duals,
Einstein-SU(2) Yang-Mills system. In anisotropic phase, below the critical
temperature $T_c$, the SO(3) isometry(spatial rotation) in the dual gravity
system is broken down to the residual SO(2). The shear viscosities in the
symmetry broken directions of the conformal fluids defined on $AdS$ boundary
present non-universal values which depend on the chemical potential $\mu$ and
temperature $T$ of the system and also satisfy non-trivial holographic
$RG$-flow equations. The shear viscosities flow down to the specific values in
$IR$ region, in fact which are given by the ratios of the metric components in
the symmetry unbroken direction to those in the broken directions, evaluated at
the black brane horizon in the dual gravity system. | hep-th |
Inequivalent Quantization in the Skyrme Model: Quantum mechanics on manifolds is not unique and in general infinite number
of inequivalent quantizations can be considered. They are specified by the
induced spin and the induced gauge structures on the manifold. The
configuration space of collective mode in the Skyrme model can be identified
with $S^{3}$ and thus the quantization is not unique. This leads to the
different predictions for the physical observables. | hep-th |
Inflation, Gravity Mediated Supersymmetry Breaking, and de Sitter Vacua
in Supergravity with a Kähler-Invariant FI Term: We use a new mechanism for generating a Fayet-Iliopoulos term in
supergravity, which is not associated to an R symmetry, to construct a
semi-realistic theory of slow-roll inflation for a theory with the same
K\"ahler potential and superpotential as the KKLT string background (without
anti-D3 branes). In our model, supersymmetry must be broken at a high scale in
a hidden sector to ensure that the cutoff of the effective field theory is
above the Hubble scale of inflation. The gravitino has a super-EeV mass and
supersymmetry breaking is communicated to the observable sector through gravity
mediation. Some mass scales of the supersymmetry-breaking soft terms in the
observable sector can be parametrically smaller than the SUSY breaking scale.
If a string realization of the new FI term were found, our model could be the
basis for a low energy effective supergravity description of realistic
superstring models of inflation. | hep-th |
Derived Categories and Zero-Brane Stability: We define a particular class of topological field theories associated to open
strings and prove the resulting D-branes and open strings form the bounded
derived category of coherent sheaves. This derivation is a variant of some
ideas proposed recently by Douglas. We then argue that any 0-brane on any
Calabi-Yau threefold must become unstable along some path in the Kahler moduli
space. As a byproduct of this analysis we see how the derived category can be
invariant under a birational transformation between Calabi-Yaus. | hep-th |
Magnetized Type I Orbifolds in Four Dimensions: I review the basic features of four dimensional Z_2 x Z_2 (shift)
orientifolds with internal magnetic fields, describing two examples with N=1
supersymmetry. As in the corresponding six-dimensional examples, D9-branes
magnetized along four internal directions can mimic D5-branes, even in presence
of multiplets of image branes localized on different fixed tori. Chiral
low-energy spectra can be obtained if the model also contains D5-branes
parallel to the magnetized directions. | hep-th |
On duality of the noncommutative extension of the Maxwell-Chern-Simons
model: We study issues of duality in 3D field theory models over a canonical
noncommutative spacetime and obtain the noncommutative extension of the
Self-Dual model induced by the Seiberg-Witten map. We apply the dual projection
technique to uncover some properties of the noncommutative Maxwell-Chern-Simons
theory up to first-order in the noncommutative parameter. A duality between
this theory and a model similar to the ordinary self-dual model is
estabilished. The correspondence of the basic fields is obtained and the
equivalence of algebras and equations of motion are directly verified. We also
comment on previous results in this subject. | hep-th |
Living on the walls of super-QCD: We study BPS domain walls in four-dimensional $\mathcal{N}=1$ massive SQCD
with gauge group $SU(N)$ and $F<N$ flavors. We propose a class of
three-dimensional Chern-Simons-matter theories to describe the effective
dynamics on the walls. Our proposal passes several checks, including the exact
matching between its vacua and the solutions to the four-dimensional BPS domain
wall equations, that we solve in the small mass regime. As the flavor mass is
varied, domain walls undergo a second-order phase transition, where multiple
vacua coalesce into a single one. For special values of the parameters, the
phase transition exhibits supersymmetry enhancement. Our proposal includes and
extends previous results in the literature, providing a complete picture of BPS
domain walls for $F<N$ massive SQCD. A similar picture holds also for SQCD with
gauge group $Sp(N)$ and $F < N+1$ flavors. | hep-th |
On quantization in background scalar fields: We consider (0+1) and (1+1) dimensional Yukawa theory in various scalar field
backgrounds, which are solving classical equations of motion: $\ddot{\phi}_{cl}
= 0$ or $\Box \phi_{cl} = 0$, correspondingly. The (0+1)--dimensional theory we
solve exactly. In (1+1)--dimensions we consider background fields of the form
$\phi_{cl} = E\, t$ and $\phi_{cl} = E\, x$, which are inspired by the constant
electric field. Here $E$ is a constant. We study the backreaction problem by
various methods, including the dynamics of a coherent state. We also calculate
loop corrections to the correlation functions in the theory using the
Schwinger--Keldysh diagrammatic technique. | hep-th |
Junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and
$Sp(N)/U(N)$ I: We construct on-shell ${\mathcal{N}}=2$ nonlinear sigma models on
$SO(2N)/U(N)$ and $Sp(N)/U(N)$ by holomorphically embedding the models in the
hyper-K\"{a}hler nonlinear sigma model on the cotangent bundle of the Grassmann
manifold $T^\ast G_{2N,N}$ in the ${\mathcal{N}}=1$ superspace formalism. We
apply the moduli matrix formalism to the mass-deformed nonlinear sigma models
on the quadrics to study three-pronged junctions by using a recently proposed
diagram method. | hep-th |
Affine and Yangian Symmetries in $SU(2)_1$ Conformal Field Theory: In these lectures, we study and compare two different formulations of
$SU(2)$, level $k=1$, Wess-Zumino-Witten conformal field theory. The first,
conventional, formulation employs the affine symmetry of the model; in this
approach correlation functions are derived from the so-called
Knizhnik-Zamolodchikov equations. The second formulation is based on an
entirely different algebraic structure, the so-called Yangian $Y(sl_2)$. In
this approach, the Hilbert space of the theory is obtained by repeated
application of modes of the so-called spinon field, which has $SU(2)$ spin
$j=\thalf$ and obeys fractional (semionic) statistics. We show how this new
formulation, which can be generalized to many other rational conformal field
theories, can be used to compute correlation functions and to obtain new
expressions for the Virasoro and affine characters in the theory. [Lectures
given at the 1994 Trieste Summer School on High Energy Physics and Cosmology,
Trieste, July 1994.] | hep-th |
Universality of low-energy scattering in three-dimensional field theory: Universal low-energy behaviour ${2 m c}\over{\ln |s-4m^2|}$ of the scattering
function of particles of positive mass m near the threshold $s=4m^2$, and
${\pi} \over {\ln |s-4m^2|}$ for the corresponding S-wave phase-shift, is
established for weakly coupled field theory models with a positive mass m in
space-time dimension 3; c is a numerical constant independent of the model and
couplings. This result is a non-perturbative property based on an exact
analysis of the scattering function in terms of a two-particle irreducible (or
Bethe-Salpeter) structure function. It also appears as generic by the same
analysis in the framework of general relativistic quantum field theory. | hep-th |
Tiny Graviton Matrix Theory/SYM Correspondence: Analysis of BPS States: In this paper we continue analysis of the Matrix theory describing the DLCQ
of type IIB string theory on AdS_5 x S^5 (and/or the plane-wave) background,
i.e. the Tiny Graviton Matrix Theory (TGMT)[hep-th/0406214]. We study and
classify 1/2, 1/4 and 1/8 BPS solutions of the TGMT which are generically of
the form of rotating three brane giants. These are branes whose shape are
deformed three spheres and hyperboloids. In lack of a classification of such
ten dimensional type IIb supergravity configurations, we focus on the dual N=4
four dimensional 1/2, 1/4 and one 1/8 BPS operators and show that they are in
one-to-one correspondence with the states of the same set of quantum numbers in
TGMT. This provides further evidence in support of the Matrix theory. | hep-th |
Surface defects and instanton partition functions: We study the superconformal index of five-dimensional SCFTs and the sphere
partition function of four-dimensional gauge theories with eight supercharges
in the presence of co-dimension two half-BPS defects. We derive a prescription
which is valid for defects which can be given a "vortex construction", i.e. can
be defined by RG flow from vortex configurations in a larger theory. We test
the prescription against known results and expected dualities. We employ our
prescription to develop a general computational strategy for defects defined by
coupling the bulk degrees of freedom to a Gauged Linear Sigma Model living in
co-dimension two. | hep-th |
Extremal Branes as Elementary Particles: The supersymmetric p-branes of Type II string theory can be interpreted after
compactification as extremal black holes with zero entropy and infinite
temperature. We show how the p-branes avoid this apparent, catastrophic
instability by developing an infinite mass gap. Equivalently, these black holes
behave like elementary particles: they are dressed by effective potentials that
prevent absorption of impinging particles. In contrast, configurations with 2,
3, and 4 intersecting branes and their nonextremal extensions, behave
increasingly like conventional black holes. These results extend and clarify
earlier work by Holzhey and Wilczek in the context of four dimensional dilaton
gravity. | hep-th |
New Instantons for Matrix Models: The complete, nonperturbative content of random matrix models is described by
resurgent-transseries -- general solutions to their corresponding
string-equations. These transseries include exponentially-suppressed
multi-instanton amplitudes obtained by eigenvalue tunneling, but they also
contain exponentially-enhanced and mixed instanton-like sectors with no known
matrix model interpretation. This work shows how these sectors can be also
described by eigenvalue tunneling in matrix models -- but on the non-physical
sheet of the spectral curve describing their large-N limit. This picture
further explains the full resurgence of random matrices via analysis of all
possible eigenvalue integration-contours. How to calculate these "anti"
eigenvalue-tunneling amplitudes is explained in detail and in various examples,
such as the cubic and quartic matrix models, and their double-scaling limit to
Painleve I. This further provides direct matrix-model derivations of their
resurgent Stokes data, which were recently obtained by different techniques. | hep-th |
Space-time Geometry in Exactly Solvable Quantum Dilaton Gravity: We describe in detail how one can extract space-time geometry in an exactly
solvable model of quantum dilaton gravity of the type proposed by Callan,
Giddings, Harvey and Strominger ( CGHS ). Based on our previous work, in which
a model with 24 massless matter scalars was quantized rigorously in BRST
operator formalism, we compute, without approximation, mean values of the
matter stress-energy tensor, the inverse metric and some related quantities in
a class of coherent physical states constructed in a specific gauge within the
conformal gauge. Our states are so designed as to describe a variety of
space-time in which in-falling matter energy distribution produces a black hole
with or without naked sigularity. In particular, we have been able to produce
the prototypical configuration first discovered by CGHS, in which a ( smeared )
matter shock wave produces a black hole without naked sigularity. | hep-th |
Unifying Constructions of Non-Invertible Symmetries: In the past year several constructions of non-invertible symmetries in
Quantum Field Theory in $d\geq 3$ have appeared. In this paper we provide a
unified perspective on these constructions. Central to this framework are
so-called theta defects, which generalize the notion of theta-angles, and allow
the construction of universal and non-universal topological symmetry defects.
We complement this physical analysis by proposing a mathematical framework
(based on higher-fusion categories) that converts the physical construction of
non-invertible symmetries into a concrete computational scheme. | hep-th |
Constraints for the existence of flat and stable non-supersymmetric
vacua in supergravity: We further develop on the study of the conditions for the existence of
locally stable non-supersymmetric vacua with vanishing cosmological constant in
supergravity models involving only chiral superfields. Starting from the two
necessary conditions for flatness and stability derived in a previous paper
(which involve the Kahler metric and its Riemann tensor contracted with the
supersymmetry breaking auxiliary fields) we show that the implications of these
constraints can be worked out exactly not only for factorizable scalar
manifolds, but also for symmetric coset manifolds. In both cases, the
conditions imply a strong restriction on the Kahler geometry and constrain the
vector of auxiliary fields defining the Goldstino direction to lie in a certain
cone. We then apply these results to the various homogeneous coset manifolds
spanned by the moduli and untwisted matter fields arising in string
compactifications, and discuss their implications. Finally, we also discuss
what can be said for completely arbitrary scalar manifolds, and derive in this
more general case some explicit but weaker restrictions on the Kahler geometry. | hep-th |
Scalar-Graviton Amplitudes and Celestial Holography: We compute scattering amplitudes involving one massive scalar and two, three,
or four gravitons. We show that when the conformal dimension of the massive
scalar is set to zero, the resulting celestial correlators depend {\it only} on
the coordinates of the gravitons. Such correlators of gravitons are
well-defined and do not suffer from divergences associated with the Mellin
transform of usual graviton amplitudes. Moreover, they are non-distributional
and take the form of standard CFT correlators. We show that they are consistent
with the usual OPEs but the statement of the soft theorem is modified. | hep-th |
Aspects of Spontaneous N=2 -> N=1 Breaking in Supergravity: We discuss some issues related to spontaneous N=2-> N=1 supersymmetry
breaking. In particular, we state a set of geometrical conditions which are
necessary that such a breaking occurs. Furthermore, we discuss the low energy
N=1 effective Lagrangian and show that it satisfies non-trivial consistency
conditions which can also be viewed as conditions on the geometry of the scalar
manifold. | hep-th |
Flat deformations of type IIB S-folds: Type IIB S-folds of the form $\textrm{AdS}_{4} \times \textrm{S}^1 \times
\textrm{S}^5$ have been shown to contain axion-like deformations parameterising
flat directions in the 4D scalar potential and corresponding to marginal
deformations of the dual S-fold CFT's. In this note we present a
group-theoretical characterisation of such flat deformations and provide a 5D
interpretation thereof in terms of $\mathfrak{so}(6)$-valued duality twists
inducing a class of Cremmer--Scherk--Schwarz flat gaugings in a reduction from
5D to 4D. In this manner we establish the existence of two flat deformations
for the $\mathcal{N}=4$ and $\textrm{SO}(4)$ symmetric S-fold causing a
symmetry breaking down to its $\textrm{U}(1)^2$ Cartan subgroup. The result is
a new two-parameter family of non-supersymmetric S-folds which are
perturbatively stable at the lower-dimensional supergravity level, thus
providing the first examples of such type IIB backgrounds. | hep-th |
The central charge in three dimensional anti-de Sitter space: This paper collects the various ways of computing the central charge
$c=3l/2G$ arising in 3d asymptotically anti-de Sitter spaces, in the
Chern-Simons formulation. Their similarities and differences are displayed. | hep-th |
Non-Unitary Holography: We propose gauge theory/gravity duality involving conformal theories based on
U(N+k|k) gauge groups. We show that to all orders in 1/N these non-unitary
theories based on supergroups are indistinguishable from the corresponding
unitary theories where the gauge group is replaced by U(N). This leads to
non-unitary gravity duals which to all orders in 1/N are indistinguishable from
their unitary cousins. They are distinguished by operators whose correlation
functions differ by O(exp(-aN)). The celebrated type IIB on AdS^5 x S^5 and
M-theory on AdS^4 x S^7 fall in this class and thus seem to also admit
non-unitary non-perturbative completions. It is tempting to conjecture that
this setup may provide a non-unitary model for black hole evaporation. | hep-th |
The web of swampland conjectures and the TCC bound: We consider the swampland distance and de Sitter conjectures, of respective
order one parameters $\lambda$ and $c$. Inspired by the recent Trans-Planckian
Censorship conjecture (TCC), we propose a generalization of the distance
conjecture, which bounds $\lambda$ to be a half of the TCC bound for $c$, i.e.
$\lambda \geq \frac{1}{2}\sqrt{\frac{2}{3}}$ in 4d. In addition, we propose a
correspondence between the two conjectures, relating the tower mass $m$ on the
one side to the scalar potential $V$ on the other side schematically as $m\sim
|V|^{\frac{1}{2}}$, in the large distance limit. These proposals suggest a
generalization of the scalar weak gravity conjecture, and are supported by a
variety of examples. The lower bound on $\lambda$ is verified explicitly in
many cases in the literature. The TCC bound on $c$ is checked as well on ten
different no-go theorems, which are worked-out in detail, and $V$ is analysed
in the asymptotic limit. In particular, new results on 4d scalar potentials
from type II compactifications are obtained. | hep-th |
Problems and Progress in Covariant High Spin Description: A universal description of particles with spins j greater or equal one ,
transforming in (j,0)+(0,j), is developed by means of representation specific
second order differential wave equations without auxiliary conditions and in
covariant bases such as Lorentz tensors for bosons, Lorentz-tensors with Dirac
spinor components for fermions, or, within the basis of the more fundamental
Weyl-Van-der-Waerden sl(2,C) spinor-tensors. At the root of the method, which
is free from the pathologies suffered by the traditional approaches, are
projectors constructed from the Casimir invariants of the spin-Lorentz group,
and the group of translations in the Minkowski space time. | hep-th |
Proper treatment of scalar and vector exponential potentials in the
Klein-Gordon equation: Scattering and bound states: We point out a misleading treatment in the literature regarding to
bound-state solutions for the $s$-wave Klein-Gordon equation with exponential
scalar and vector potentials. Following the appropriate procedure for an
arbitrary mixing of scalar and vector couplings, we generalize earlier works
and present the correct solution to bound states and additionally we address
the issue of scattering states. Moreover, we present a new effect related to
the polarization of the charge density in the presence of weak short-range
exponential scalar and vector potentials. | hep-th |
Primordial perturbations and non-Gaussianities in DBI and general
multi-field inflation: We study cosmological perturbations in general inflation models with multiple
scalar fields and arbitrary kinetic terms, with special emphasis on the
multi-field extension of Dirac-Born-Infeld (DBI) inflation. We compute the
second-order action governing the dynamics of linear perturbations in the most
general case. Specializing to DBI, we show that the adiabatic and entropy modes
propagate with a {\it common} effective sound speed and are thus amplified at
sound horizon crossing. In the small sound speed limit, we find that the
amplitude of the entropy modes is much higher than that of the adiabatic modes.
We also derive, in the general case, the third-order action which is useful for
studying primordial non-Gaussianities generated during inflation. In the DBI
case, we compute the dominant contributions to non-Gaussianities, which depend
on both the adiabatic and entropy modes. | hep-th |
Energy functionals from Conformal Gravity: We provide a new derivation of the Hawking mass and Willmore energy
functionals for asymptotically AdS spacetimes, by embedding Einstein-AdS
gravity in Conformal Gravity. By construction, the evaluation of the
four-dimensional Conformal Gravity action in a manifold with a conical defect
produces a codimension-2 conformal invariant functional $L_{\Sigma}$. The
energy functionals are then particular cases of $L_{\Sigma}$ for Einstein-AdS
and pure AdS ambient spaces, respectively. The bulk action is finite for AdS
asymptotics and both Hawking mass and Willmore energy are finite as well. The
result suggests a generic relation between conformal invariance and
renormalization, where the codimension-2 properties are inherited from the bulk
gravity action. | hep-th |
Classical BRST charge for nonlinear algebras: We study the construction of the classical nilpotent canonical BRST charge
for the nonlinear gauge algebras where a commutator (in terms of Poisson
brackets) of the constraints is a finite order polynomial of the constraints.
Such a polynomial is characterized by the coefficients forming a set of higher
order structure constraints. Assuming the set of constraints to be linearly
independent, we find the restrictions on the structure constraints when the
nilpotent BRST charge can be written in a simple and universal form. In the
case of quadratically nonlinear algebras we find the expression for third order
contribution in the ghost fields to the BRST charge without the use of any
additional restrictions on the structure constants. | hep-th |
Superstring Perturbation Theory Revisited: Perturbative superstring theory is revisited, with the goal of giving a
simpler and more direct demonstration that multi-loop amplitudes are
gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry
when expected, and have the expected infrared behavior. The main technical tool
is to make the whole analysis, including especially those arguments that
involve integration by parts, on supermoduli space, rather than after
descending to ordinary moduli space. | hep-th |
The large $N$ phase diagram of ${\cal N}=2$ $SU(N)$ Chern-Simons theory
with one fundamental chiral multiplet: We study the theory of a single fundamental fermion and boson coupled to
Chern-Simons theory at leading order in the large $N$ limit. Utilizing recent
progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we
compute the quantum effective potential that is exact to all orders in the 't
Hooft coupling for the lightest scalar operator of this theory at finite
temperature. Specializing to the zero temperature limit we use this potential
to determine the phase diagram of the large $N$ ${\cal N}=2$ supersymmetric
theory with this field content. This intricate two dimensional phase diagram
has four topological phases that are separated by lines of first and second
order phase transitions and includes special conformal points at which the
infrared dynamics is governed by Chern-Simons theory coupled respectively to
free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus
free fermions. We also describe the vacuum structure of the most general ${\cal
N} = 1$ supersymmetric theory with one fundamental boson and one fundamental
fermion coupled to an $SU(N)$ Chern-Simons gauge field, at arbitrary values of
the 't Hooft coupling. | hep-th |
Landau quantization for a neutral particle in presence of topological
defects: In this paper we study the Landau levels in the non-relativistic dynamics of
a neutral particle which possesses a permanent magnetic dipole moment
interacting with an external electric field in the curved spacetime background
with the presence or absence of a torsion field. The eigenfunction and
eigenvalues of Hamiltonian are obtained. We show that the presence of the
topological defect breaks the infinite degeneracy of the Landau levels arising
in this system. We also apply a duality transformation to discuss this same
quantization for a dynamics of a neutral particle with a permanent electric
dipole moment. | hep-th |
Massive Type IIA Theory on K3: In this paper we study K3 compactification of ten-dimensional massive type
IIA theory with all possible Ramond-Ramond background fluxes turned on. The
resulting six-dimensional theory is a new massive (gauged) supergravity with an
action that is manifestly invariant under an O(4,20) / (O(4) times O(20))
duality symmetry. We discover that this six-dimensional theory interpolates
between vacua of ten-dimensional massive IIA supergravity and vacua of massless
IIA supergravity with appropriate background fluxes turned on. This in turn
suggests a new 11-dimensional interpretation for the massive type IIA theory. | hep-th |
A new method for probing the late-time dynamics in the Lorentzian type
IIB matrix model: The type IIB matrix model has been investigated as a possible nonperturbative
formulation of superstring theory. In particular, it was found by Monte Carlo
simulation of the Lorentzian version that the 9-dimensional rotational symmetry
of the spatial matrices is broken spontaneously to the 3-dimensional one after
some "critical time". In this paper we develop a new simulation method based on
the effective theory for the submatrices corresponding to the late time. Using
this method, one can obtain the results for $N\times N$ matrices by simulating
matrices typically of the size $O(\sqrt{N})$. We confirm the validity of this
method and demonstrate its usefulness in simplified models. | hep-th |
Super Landau-Ginzburg mirrors and algebraic cycles: We investigate the super Landau-Ginzburg mirrors of gauged linear sigma
models which, in an appropriate low energy limit, reduce to nonlinear sigma
models with Kaehler supermanifold target spaces of nonnegative super-first
Chern class. | hep-th |
The extension of the massless fermion in the cosmic string spacetime: In this work, we have obtained the solutions of a massless fermion which is
under the external magnetic field around a cosmic string for specific three
potential models using supersymmetric quantum mechanics. The constant magnetic
field, energy dependent potentials and position dependent mass models are
investigated for the Dirac Hamiltonians and an extension of these three
potential models and their solutions are also obtained. The energy spectrum and
potential graphs for each case are discussed for the $\alpha$ deficit angle. | hep-th |
Radiative Corrections in Nonrelativistic Chern-Simons Theory: We present the one-loop scalar field effective potential for the $N=2$
supersymmetric nonrelativistic self-interacting matter fields coupled to an
Abelian Chern-Simons gauge field and for its generalization when bosonic matter
fields are coupled to non-Abelian Chern-Simons field. In both models, Gauss's
law linearly relates the magnetic field to the matter field densities; hence,
we also include radiative effects from the background gauge field. We compute
the scalar field effective potentials in two gauge families, a gauge
reminiscent of the $R_\xi$-gauge in the limit $\xi\rightarrow 0$ and in the
Coulomb family gauges. We regularize the theory with operator regularization
and a cutoff to demonstrate that the results are independent of the
regularization scheme. | hep-th |
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