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Monodromy methods for torus conformal blocks and entanglement entropy at
large central charge: We compute the entanglement entropy in a two dimensional conformal field
theory at finite size and finite temperature in the large central charge limit
via the replica trick. We first generalize the known monodromy method for the
calculation of conformal blocks on the plane to the torus. Then, we derive a
monodromy method for the zero-point conformal blocks of the replica partition
function. We explain the differences between the two monodromy methods before
applying them to the calculation of the entanglement entropy. We find that the
contribution of the vacuum exchange dominates the entanglement entropy for a
large class of CFTs, leading to universal results in agreement with holographic
predictions from the RT formula. Moreover, we determine in which regime the
replica partition function agrees with a correlation function of local twist
operators on the torus.
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Differential Geometry of the Vortex Filament Equation: Differential calculus on the space of asymptotically linear curves is
developed. The calculus is applied to the vortex filament equation in its
Hamiltonian description. The recursion operator generating the infinite
sequence of commuting flows is shown to be hereditary. The system is shown to
have a description with a Hamiltonian pair. Master symmetries are found and are
applied to deriving an expression of the constants of motion in involution. The
expression agrees with the inspection of Langer and Perline.
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Brane Dynamics and Chiral non-Chiral Transitions: We study brane realizations of chiral matter in N=1 supersymmetric gauge
theories in four dimensions. A "cross" configuration which leads to "flavor
doubling" is found to have a superpotential. The main example is realized using
a special "fork" configuration. Many of the results are found by studying a SU
times SU product gauge group first. The chiral theory is then an orientifold
projection of the product gauge group. An interesting observation in the brane
picture is that there are transitions between chiral and non chiral models.
These transitions are closely related to small instanton transitions in six
dimensions.
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Solving RG equations with the Lambert W function: It has been known for some time that 2-loop renormalization group (RG)
equations of a dimensionless parameter can be solved in a closed form in terms
of the Lambert W function. We apply the method to a generic theory with a
Gaussian fixed point to construct RG invariant physical parameters such as a
coupling constant and a physical squared mass. As a further application, we
speculate a possible exact effective potential for the O(N) linear sigma model
in four dimensions.
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Exact Results in N_c=2 IIB Matrix Model: We investigate N_c=2 case of IIB matrix model, which is exactly soluble. We
calculate the partition function exactly and obtain a finite result without
introducing any cut-off. We also evaluate some correlation functions consisting
of Wilson loops.
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On Large N Solution of N=3 Chern-Simons-adjoint Theories: The planar resolvent for N=3 U(N)_k Chern-Simons theory coupled to an
arbitrary number of adjoint matters is determined. Analytic continuation of the
't Hooft coupling t is analyzed. The eigenvalue distribution turns out to be
confined in a finite region even for a large t. The vev of a Wilson loop does
not exhibit an exponential growth although such a behavior would be expected
for theories with classical gravity duals.
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N-dimensional sl(2)-coalgebra spaces with non-constant curvature: An infinite family of ND spaces endowed with sl(2)-coalgebra symmetry is
introduced. For all these spaces the geodesic flow is superintegrable, and the
explicit form of their common set of integrals is obtained from the underlying
sl(2)-coalgebra structure. In particular, ND spherically symmetric spaces with
Euclidean signature are shown to be sl(2)-coalgebra spaces. As a byproduct of
this construction we present ND generalizations of the classical Darboux
surfaces, thus obtaining remarkable superintegrable ND spaces with non-constant
curvature.
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Conservation laws in the teleparallel theory of gravity: We study the conservation laws associated with the asymptotic Poincare
symmetry of spacetime in the general teleparallel theory of gravity. Demanding
that the canonical Poincare generators have well defined functional derivatives
in a properly defined phase space, we obtain the improved form of the
generators, containing certain surface terms. These terms are shown to
represent the values of the related conserved charges: energy-momentum and
angular momentum.
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Finite Cutoff CFT's and Composite Operators: Recently a conformally invariant action describing the Wilson-Fischer fixed
point in $D=4-\epsilon$ dimensions in the presence of a {\em finite} UV cutoff
was constructed \cite{Dutta}. In the present paper we construct two composite
operator perturbations of this action with definite scaling dimension also in
the presence of a finite cutoff. Thus the operator (as well as the fixed point
action) is well defined at all momenta $0\leq p\leq \infty$ and at low energies
they reduce to $\int_x \phi^2$ and $\int _x \phi^4$ respectively. The
construction includes terms up to $O(\lamda^2)$. In the presence of a finite
cutoff they mix with higher order irrelevant operators. The dimensions are also
calculated to this order and agree with known results.
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Self-consistency in relativistic theory of infinite statistics fields: Infinite statistics in which all representations of the symmetric group can
occur is known as a special case of quon theory. Our previous work has built a
relativistic quantum field theory which allows interactions involving infinite
statistics particles. In this paper, a more detailed analysis of this theory is
available. Topics discussed include cluster decomposition, CPT symmetry and
renormalization.
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Stationary $D=4$ Black Holes in Supergravity: The Issue of Real
Nilpotent Orbits: The complete classification of the nilpotent orbits of ${\rm SO}(2,2)^2$ in
the representation ${\bf (2,2,2,2)}$, achieved in \cite{Dietrich:2016ojx}, is
applied to the study of multi-center, asymptotically flat, extremal black hole
solutions to the STU model. These real orbits provide an intrinsic
characterization of regular single-center solutions, which is invariant with
respect to the action of the global symmetry group ${\rm SO}(4,4)$, underlying
the stationary solutions of the model, and provide stringent regularity
constraints on multi-centered solutions. The known \emph{almost-BPS} and
\emph{composite non-BPS} solutions are revisited in this setting. We
systematically provide, for the relevant ${\rm SO}(2,2)^2$-nilpotent orbits of
the global Noether charge matrix, regular representatives thereof. This
analysis unveils a composition law of the orbits according to which those
containing regular multi-centered solutions can be obtained as combinations of
specific single-center orbits defining the constituent black holes. Some of the
${\rm SO}(2,2)^2$-orbits of the total Noether charge matrix are characterized
as "intrinsically singular" in that they cannot contain any regular solution.
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Loop Variables and Gauge Invariance in (Open) Bosonic String Theory: We give a simplified and more complete description of the loop variable
approach for writing down gauge invariant equations of motion for the fields of
the open string. A simple proof of gauge invariance to all orders is given. In
terms of loop variables, the interacting equations look exactly like the free
equations, but with a loop variable depending on an extra parameter, thus
making it a band of finite width. The arguments for gauge invariance work
exactly as in the free case. We show that these equations are Wilsonian RG
equations with a finite world-sheet cutoff and that in the infrared limit,
equivalence with the Callan-Symanzik $\beta$-functions should ensure that they
reproduce the on-shell scattering amplitudes in string theory. It is applied to
the tachyon-photon system and the general arguments for gauge invariance can be
easily checked to the order calculated. One can see that when there is a finite
world sheet cutoff in place, even the U(1) invariance of the equations for the
photon, involves massive mode contributions. A field redefinition involving the
tachyon is required to get the gauge transformations of the photon into
standard form.
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d-objects kinematics on smooth manifolds: The kinematical part of general theory of deformational structures on smooth
manifolds is developed. We introduce general concept of d-objects deformation,
then within the set of all such deformations we develop some special algebra
and investigate group and homotopical properties of the set. In case of proper
deformations some propositions, generalizing isometry theory on Riemannian
manifolds are formulated.
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Anomaly Freedom and Realisations for Super-$W_3$ Strings: We construct new multi-field realisations of the $N=2$ super-$W_3$ algebra,
which are important for building super-$W_3$ string theories. We derive the
structure of the ghost vacuum for such theories, and use the result to
calculate the intercepts. These results determine the conditions for physical
states in the super-$W_3$ string theory.
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On the Connection between Pauli-Villars and Higher Derivative
Regularizations: It is shown that in some cases higher (covariant) derivative regularization
for spinor field is equivalent to the gauge invariant Pauli-Villars one.
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Moduli Space for Conifolds as Intersection of Orthogonal D6 branes: We show that a system of parallel D3 branes near a conifold singularity can
be mapped onto an intersecting configuration of orthogonal branes in type IIA
string theory. Using this brane configuration, we analyze the Higgs moduli
space of the associated field theory. The dimension of the Higgs moduli space
is computed from a geometrical analysis of the conifold singularity. Our
results provide evidence for an extended s-rule. In addition, a discrepancy
between the prediction of the brane configuration and the result obtained from
a geometrical anaysis is noted. This discrepancy is traced back to worldsheet
instanton effects.
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Holographic RG flows on Squashed $S^3$: Holographic RG flows dual to QFTs on a squashed $S^3$ are considered in the
framework of Einstein dilaton gravity in four dimensions. A general dilaton
potential is used and flows are driven by a scalar relevant operator. The
general properties of such flows are analysed and the UV and IR asymptotics are
computed. Exotic asymptotics are found, that are different from the standard
Fefferman-Graham asymptotics.
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Celestial Amplitudes as AdS-Witten Diagrams: Both celestial and momentum space amplitudes in four dimensions are beset by
divergences resulting from spacetime translation and sometimes scale
invariance. In this paper we consider a (linearized) marginal deformation of
the celestial CFT for Yang-Mills theory which preserves 2D conformal invariance
but breaks both spacetime translation and scale invariance and involves a
chirally coupled massive scalar. The resulting celestial amplitudes are
completely finite (apart from the usual soft and collinear divergences) and
take the canonical CFT form. Moreover, we show they can be simply rewritten in
terms of AdS$_3$-Witten contact diagrams which evaluate to the well-known
$D$-functions, thereby forging a direct connection between flat and AdS
holography.
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On the N=1 beta-function from the conifold: We obtain the correct all-loop beta-function of pure N=1 super Yang-Mills
theory from the supergravity solution of the warped deformed conifold,
including also some nonperturbative corrections. The crucial ingredient is the
gauge-gravity relation that can be inferred by taking into account the
phenomenon of gaugino condensation.
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Central charges, black-hole entropy and geometrical structure of
N-extended supergravities in D=4: The derivation of absolute (moduli-independent) U-invariants for all N>2
extended supergravities at D=4 in terms of (moduli-dependent) central and
matter charges is reported. These invariants give a general definition of the
``topological'' Bekenstein-Hawking entropy formula for extremal black-holes and
reduce to the square of the black-hole ADM mass for ``fixed scalars'' which
extremize the black-hole ``potential'' energy.
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Two dimensional black-hole as a topological coset model of c=1 string
theory: We show that a special superconformal coset (with $\hat c =3$) is equivalent
to $c=1$ matter coupled to two dimensional gravity. This identification allows
a direct computation of the correlation functions of the $c=1$ non-critical
string to all genus, and at nonzero cosmological constant, directly from the
continuum approach. The results agree with those of the matrix model. Moreover
we connect our coset with a twisted version of a Euclidean two dimensional
black hole, in which the ghost and matter systems are mixed.
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Color Confinement in Perturbation Theory from a Topological Model,: Color confinement by the mechanism of Kugo and Ojima can treat confinement of
any quantized color carrying fields including dynamical quarks. However, the
non-perturbative condition for this confinement has been known to be satisfied
only in the pure-gauge model (PGM), which is a topological model without
physical degrees of freedom. Here we analyze the Yang-Mills theory by adding
physical degrees of freedom as perturbation to PGM. We find that quarks and
gluons are indeed confined in this perturbation theory.
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Parametrised Homotopy Theory and Gauge Enhancement: We review a first-principles derivation of Type IIA D-brane charges from
M-theory degrees of freedom in the approximation of super rational homotopy
theory.
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Pulsating strings from two dimensional CFT on $(T^4)^N/S(N)$: We propose a state from the two-dimensional conformal field theory on the
orbifold $(T^4)^N/S(N)$ as a dual description for a pulsating string moving in
$AdS_3$. We show that, up to first order in the deforming parameter, the energy
in both descriptions has the same dependence on the mode number, but with a
non-trivial function of the coupling.
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A Black Hole Levitron: We study the problem of spatially stabilising four dimensional extremal black
holes in background electric/magnetic fields. Whilst looking for stationary
stable solutions describing black holes kept in external fields we find that
taking a continuum limit of Denef et al's multi-center solutions provides a
supergravity description of such backgrounds within which a black hole can be
trapped in a given volume. This is realised by levitating a black hole over a
magnetic dipole base. We comment on how such a construction resembles a
mechanical Levitron.
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Extended Dualization: a method for the Bosonization of Anomalous Fermion
Systems in Arbitrary Dimension: The technique of extended dualization developed in this paper is used to
bosonize quantized fermion systems in arbitrary dimension $D$ in the low energy
regime. In its original (minimal) form, dualization is restricted to models
wherein it is possible to define a dynamical quantized conserved charge. We
generalize the usual dualization prescription to include systems with dynamical
non--conserved quantum currents. Bosonization based on this extended
dualization requires the introduction of an additional rank $0$ (scalar) field
together with the usual antisymmetric tensor field of rank $(D-2)$. Our
generalized dualization prescription permits one to clearly distinguish the
arbitrariness in the bosonization from the arbitrariness in the quantization of
the system. We study the bosonization of four--fermion interactions with large
mass in arbitrary dimension. First, we observe that dualization permits one to
formally bosonize these models by invoking the bosonization of the free massive
Dirac fermion and adding some extra model--dependent bosonic terms. Secondly,
we explore the potential of extended dualization by considering the particular
case of \underbar{chiral} four--fermion interactions. Here minimal dualization
is inadequate for calculating the extra bosonic terms. We demonstrate the
utility of extended dualization by successfully completing the bosonization of
this chiral model. Finally, we consider two examples in two dimensions which
illuminate the utility of using extended dualization by showing how
quantization ambiguities in a fermionic theory propagate into the bosonized
version. An explicit parametrization of the quantization ambiguities of the
chiral current in the Chiral Schwinger model is obtained. Similarly, for the
sine--Gordon interaction in the massive Thirring model the quantization
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Chiral Symmetry Breaking and Dual Gluon Mass in the Confining Region of
QCD: The Dual Meissner Effect description of QCD in the confining region provides
$\frac{1}{q^4}$ behaviour for the gluon propagator and involves the dual gluon
mass $m$ as a parameter. This is used in the Schwinger-Dyson equation for the
quarks in the infrared region to exhibit chiral symmetry breaking for light
quarks. Using the light quark condensate as input, the dual gluon mass is
determined and its importance in showing the asymptotic free behaviour of the
extrinsic curvature coupling in the rigid QCD string is discussed.
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Holographic complexity of the disk subregion in (2+1)-dimensional gapped
systems: Using the volume of the space enclosed by the Ryu-Takayanagi (RT) surface, we
study the complexity of the disk-shape subregion (with radius R) in various
(2+1)-dimensional gapped systems with gravity dual. These systems include a
class of toy models with singular IR and the bottom-up models for quantum
chromodynamics and fractional quantum Hall effects. Two main results are: i) in
the large-R expansion of the complexity, the R-linear term is always absent,
similar to the absence of topological entanglement entropy; ii) when the
entanglement entropy exhibits the classic `swallowtail' phase transition, the
complexity is sensitive but reacts differently.
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The symmetry, connecting the processes in 2- and 4-dimensional
space-times, and the value $α_0 = 1/4π$ for the bare fine structure
constant: Defined by Bogoliubov coefficients the spectra of pairs of Bose (Fermi)
massless quanta, emitted by point mirror in 1+1-space, coincide up to
multiplier $e^2/ \hbar c$ with the spectra of photons (scalar quanta), emitted
by point electric (scalar) charge in 3+1-space for any common trajectory of the
sources. The integral connection of the propagator of a pair in 1+1-space with
the propagator of a single particle in 3+1-space leads to equality of the
vacuum-vacuum amplitudes for charge and mirror if the mean number of created
particles is small and the charge $e=\sqrt{\hbar c}$. Due to the symmetry the
mass shifts of electric and scalar charges, the sources of Bose-fields with
spin 1 and 0 in 3+1-space, for the trajectories with subluminal relative
velocity $\beta_{12}$ of the ends and maximum proper acceleration $w_0$ are
expressed in terms of heat capacity (or energy) spectral densities of Bose and
Fermi massless particle gases with temperature $w_0/2\pi$ in 1+1-space. The
energy of one-dimensional proper field oscillations is partly deexcited in the
form of real quanta and partly remains in the field. As a result, the mass
shift of accelerated electric charge is nonzero and negative, while that of
scalar charge is zero. The traces of the Bogoliubov coefficients $\alpha^{B,F}$
describe the vector and scalar interactions of accelerated mirror with a
uniformly moving detector and were found in analytical form. The symmetry
predicts one and the same value $e_0=\sqrt{\hbar c}$ for electric and scalar
charges in 3+1-space. The arguments are adduced in favour of that this value
and the corresponding value $\alpha_0=1/4\pi$ for fine structure constant are
the bare, nonrenormalized values.
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q-deformed superconformal algebra on quantum superspace: A quantum deformation of 4-dimensional superconformal algebra realized on
quantum superspace is investigated. We study the differential calculus and the
action of the quantum generators corresponding to $sl_q(1|4)$ which act on the
quantum superspace. We derive deformed $su(1|2,2)$ algebras from the deformed
$sl(1|4)$ algebra. Through a contraction procedure we obtain a deformed
super-Poincar{\'e} algebra.
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Open Gromov-Witten Invariants from the Augmentation Polynomial: A conjecture of Aganagic and Vafa relates the open Gromov-Witten theory of
$X=\mathcal{O}_{\mathbb{P}^{1}}(-1,-1)$ to the augmentation polynomial of
Legendrian contact homology. We describe how to use this conjecture to compute
genus zero, one boundary component open Gromov-Witten invariants for Lagrangian
submanifolds $L_{K}\subset X$ obtained from the conormal bundles of knots
$K\subset S^{3}$. This computation is then performed for two non-toric examples
(the figure-eight and three-twist knots). For $(r,s)$ torus knots, the open
Gromov-Witten invariants can also be computed using Atiyah-Bott localization.
Using this result for the unknot and the $(3,2)$ torus knot, we show that the
augmentation polynomial can be derived from these open Gromov-Witten
invariants.
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Marginal deformations and the Higgs phenomenon in higher spin AdS_3
holography: Recently, a 2d coset model with N=3 superconformal symmetry was proposed to
be holographic dual to a higher spin supergravity on AdS_3 and the relation to
superstring theory was discussed. However, away from the tensionless limit,
there is no higher spin symmetry and the higher spin states are massive. In
this paper, we examine the deformations of the coset model which preserve N=3
superconformal symmetry, but break generic higher spin symmetry. We focus on
double-trace type deformations which are dual to changes of boundary conditions
for the bulk matter fields. In the bulk theory, the symmetry breaking will
generate mass for the higher spin fields. As a concrete example, we compute the
Higgs mass of a spin 2 field both from the bulk and the boundary theory.
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Induced Rigid String Action From Fermions: From the Dirac action on the world sheet, an effective action is obtained by
integrating over the 4-dimensional fermion fields pulled back to the world
sheet. This action consists of the Nambu-Goto area term with right dimensionful
constant in front, extrinsic curvature action and the topological Euler
characteristic term.
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Holographic Description of M-branes via AdS$_2$: We study $\textrm{AdS}_2\times S^4 \times S^2 \times \Sigma_2$ solutions in
type IIB string theory arising from D1 -- D3 -- NS5 brane intersections. These
backgrounds enjoy sixteen supercharges and the corresponding internal geometry
is non-compact due to the specific form of the warping w.r.t. the Riemann
surface $\Sigma_2$. Even though a direct computation of the holographic free
energy of the would-be dual CFT$_1$ yields a divergent behaviour, it reveals
the typical $N^3$ scaling of a 6d theory upon introducing a hard cut-off. We
claim that such geometries may be interpreted as the gravity duals of M(atrix)
models describing an IR phase of the $(2,0)$ theory of M5 branes, in presence
of momentum and NUT charges. We discuss parallel $\textrm{AdS}_2$ geometries
describing longitudinal M2 branes in the UV, where the counting of the number
of degrees of freedom correctly reproduces the expected $N^{3/2}$ behaviour of
the dual field theory. These geometries provide explicit examples where
deconstructed extra dimensions yield well-defined UV descriptions in terms of
higher-dimensional CFTs.
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Z(2) monopoles in SU(n) Yang-Mills-Higgs theories: Z(n) monopoles are important for the understanding of Goddard-Nuyts-Olive
duality when the scalar field is not in the adjoint representation. We analyze
the Z(2) monopole solutions in a SU(n) Yang-Mills-Higgs theory spontaneously
broken to Spin(n)/Z(2) by a scalar in the n x n representation. We construct a
Z(2) monopole asymptotic form for each of the weights of the defining
representation of the algebra dual to so(n).
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Holography for Heavy Quarks and Mesons at Finite Chemical Potential: We study the properties of heavy quarks as probes of strongly coupled plasmas
with and without chemical potential by means of the gauge/gravity (AdS/CFT)
duality. We compute the screening distance of a heavy quark-antiquark pair, its
free energy, and the running coupling in large classes of non-conformal models
arising as deformations of pure AdS space. We further investigate the energy
loss of a heavy quark moving on a circular orbit as an example of an
accelerated motion. These observables exhibit universal features independent of
the deformation, pointing to strong-coupling universality. Our results should
be relevant for processes involving heavy quarks and their bound states in the
quark-gluon plasma, including the case of finite net baryon density.
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Zero point energy on extra dimension: Noncommutative Torus: In this paper we calculate the zero point energy density experienced by
observers on M^4 due to a massless scalar field defined throughout M^4 x T^2_F,
where T^2_F are fuzzy extra dimensions. Using the Green's function approach we
calculate the energy density for the commutative torus and the fuzzy torus. We
calculate then the energy density for the fuzzy torus using the Hamiltonian
approach. Agreement is shown between Green's function and Hamiltonian
approaches.
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Instanton corrections to circular Wilson loops in N=4 Supersymmetric
Yang-Mills: It is argued that whereas supersymmetry requires the instanton contribution
to the expectation value of a straight Wilson line in the N=4 supersymmetric
SU(2) Yang-Mills theory to vanish, it is not required to vanish in the case of
a circular Wilson loop. A non-vanishing value can arise from a subtle interplay
between a divergent integral over bosonic moduli and a vanishing integral over
fermionic moduli. The one-instanton contribution to such Wilson loops is
explicitly evaluated in semi-classical approximation. The method utilizes the
symmetries of the problem to perform the integration over the bosonic and
fermionic collective coordinates of the instanton. The integral is singular for
small instantons touching the loop and is regularized by introducing a cutoff
at the boundary of the (euclidean) AdS_5 moduli space. In the case of a
circular loop a nonzero finite result is obtained when the cutoff is removed
and a perimeter divergence subtracted. This is contrasted with the case of the
straight line where the result is zero after subtraction of an identical
divergence per unit length. The linear divergence is an artifact of our non
supersymmetric regulator that deserves further consideration. The
generalization to gauge group SU(N) with arbitrary N is straightforward in the
limit of small 't Hooft coupling. The extension to strong 't Hooft coupling is
more challenging and only a qualitative discussion is given of the AdS/CFT
correspondence
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Gluing I: Integrals and Symmetries: We review some aspects of the cutting and gluing law in local quantum field
theory. In particular, we emphasize the description of gluing by a path
integral over a space of polarized boundary conditions, which are given by
leaves of some Lagrangian foliation in the phase space. We think of this path
integral as a non-local $(d-1)$-dimensional gluing theory associated to the
parent local $d$-dimensional theory. We describe various properties of this
procedure and spell out conditions under which symmetries of the parent theory
lead to symmetries of the gluing theory. The purpose of this paper is to set up
a playground for the companion paper where these techniques are applied to
obtain new results in supersymmetric theories.
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On Non-Critical Superstring/Black Hole Transition: An interesting case of string/black hole transition occurs in two-dimensional
non-critical string theory dressed with a compact CFT. In these models the high
energy densities of states of perturbative strings and black holes have the
same leading behavior when the Hawking temperature of the black hole is equal
to the Hagedorn temperature of perturbative strings. We compare the first
subleading terms in the black hole and closed string entropies in this setting
and argue that the entropy interpolates between these expressions as the energy
is varied. We compute the subleading correction to the black hole entropy for a
specific simple model.
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Moduli stability in type I string orbifold models: We analyze the stability of the moduli at the quantum level in an open-string
model realizing the $\mathcal{N}=2\to \mathcal{N}=0$ spontaneous breaking of
supersymmetry in four-dimensional Minkowski spacetime. In the region of moduli
space where the supersymmetry breaking scale is lower than the other scales, we
identify vanishing minima of the one-loop effective potential, up to
exponentially small corrections. In these backgrounds, the spectrum satisfies
Bose-Fermi degeneracy at the massless level.
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Distinquishing 4d N=2 SCFTs: We construct a family of examples of pairs of 4d N=2 SCFTs whose graded
Coulomb branch dimensions, Weyl-anomaly coefficients and flavour symmetry
algebras and levels coincide, but which are nonetheless distinct SCFTs. The
difference (detectable by the superconformal index) can occur at arbitrarily
high order. We argue that it is, however, reflected in a difference in the
global form of the flavour symmetry groups.
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Probing F-theory With Multiple Branes: We study multiple 3-branes on an F theory orientifold. The world-volume
theory of the 3-branes is d=4, N=2 Sp(2k) gauge theory with an antisymmetric
tensor and four flavors of matter in the fundamental. The solution of this
gauge theory is found for vanishing bare mass of the antisymmetric tensor
matter, and massive fundamental matter. The integrable system underlying this
theory is constructed.
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A temperature correction to the tachyon, using the Casimir effect: We find the free energy of the string by applying the known Matsubara
formalism. Then through the Casimir effect we offer a temperature correction to
the tachyon mass of the string. We see that for the fermionic part the
temperature correction is precisely the opposite of that of bosonic part, so
the quantum ground state of the superstring would remain massless, as expected.
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BRS symmetry versus supersymmetry in Yang-Mills-Chern-Simons theory: We prove that three-dimensional $N=1$ supersymmetric Yang-Mills-Chern-Simons
theory is finite to all loop orders. In general this leaves open the
possibility that different regularization methods lead to different finite
effective actions. We show that in this model dimensional regularization and
regularization by dimensional reduction yield the same effective action.
Consequently, the superfield approach preserves BRS invariance for this model.
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Self-Dual Gravity Revisited: Reconsidering the harmonic space description of the self-dual Einstein
equations, we streamline the proof that all self-dual pure gravitational fields
allow a local description in terms of an unconstrained analytic prepotential in
harmonic space. Our formulation yields a simple recipe for constructing
self-dual metrics starting from any explicit choice of such prepotential; and
we illustrate the procedure by producing a metric related to the Taub-NUT
solution from the simplest monomial choice of prepotential.
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R^4 counterterm and E7(7) symmetry in maximal supergravity: The coefficient of a potential R^4 counterterm in N=8 supergravity has been
shown previously to vanish in an explicit three-loop calculation. The R^4 term
respects N=8 supersymmetry; hence this result poses the question of whether
another symmetry could be responsible for the cancellation of the three-loop
divergence. In this article we investigate possible restrictions from the coset
symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as
well as a double-soft scalar limit relation derived recently by Arkani-Hamed et
al. We implement these relations for the matrix elements of the R^4 term that
occurs in the low-energy expansion of closed-string tree-level amplitudes. We
find that the matrix elements of R^4 that we investigated all obey the
double-soft scalar limit relation, including certain
non-maximally-helicity-violating six-point amplitudes. However, the single-soft
limit does not vanish for this latter set of amplitudes, which suggests that
the E7(7) symmetry is broken by the R^4 term.
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Towards Holographic Spintronics: We study transport phenomena of total angular momentum in holography, as a
first step toward holographic understanding of spin transport phenomena. Spin
current, which has both the local Lorentz index for spins and the space-time
vector index for current, couples naturally to the bulk spin connection.
Therefore the bulk spin connection becomes the source for the boundary spin
current. This allows us to evaluate the spin current holographically, with a
relation to the stress tensor and metric fluctuations in the bulk. We examine
the spin transport coefficients and the thermal spin Hall conductivity in a
simple holographic setup.
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The Wu-Yang Ambiguity Revisited: Several examples are given of continuous families of SU(2) vector potentials
$A_i^a(x)$ in 3 space dimensions which generate the same magnetic field
$B^{ai}(x)$ (with det $B\neq 0$). These Wu-Yang families are obtained from the
Einstein equation $R_{ij}=-2G_{ij}$ derived recently via a local map of the
gauge field system into a spatial geometry with $2$-tensor $G_{ij}=B^a{}_i
B^a{}_j\det B$ and connection $\Gamma_{jk}^i$ with torsion defined from gauge
covariant derivatives of $B$.
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Nonassociativity, Dirac monopoles and Aharonov-Bohm effect: The Aharonov-Bohm (AB) effect for the singular string associated with the
Dirac monopole carrying an arbitrary magnetic charge is studied. It is shown
that the emerging difficulties in explanation of the AB effect may be removed
by introducing nonassociative path-dependent wave functions. This provides the
absence of the AB effect for the Dirac string of magnetic monopole with an
arbitrary magnetic charge.
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On the baryon-color-flavor (BCF) anomaly in vector-like theories: We consider the most general fractional background fluxes in the color,
flavor, and baryon number directions, compatible with the faithful action of
the global symmetry of a given theory. We call the obstruction to gauging
symmetries revealed by such backgrounds the baryon-color-flavor (BCF) 't Hooft
anomaly. We apply the BCF anomaly to vector-like theories, with fermions in
higher-dimensional representations of arbitrary N-ality, and derive non-trivial
constraints on their IR dynamics. In particular, this class of theories enjoys
an independent discrete chiral symmetry and one may ask about the fate of this
symmetry in the background of BCF fluxes. We show that, under certain
conditions, an anomaly between the chiral symmetry and the BCF background rules
out massless composite fermions as the sole player in the IR: either the
composites do not form or additional contributions to the matching of the BCF
anomaly are required. We can also give a flavor-symmetric mass to the fermions,
smaller than or of order the strong scale of the theory, and examine the
$\theta$-angle periodicity of the theory in the BCF background. Interestingly,
we find that the conditions that rule out the composites are the exact same
conditions that lead to an anomaly of the $\theta$ periodicity: the massive
theory will experience a phase transition as we vary $\theta$ from $0$ to
$2\pi$.
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Onset of Quantum Chaos in Random Field Theories: We study the quantum Lyapunov exponent $\lambda_L$ in theories with
spacetime-independent disorder. We first derive self-consistency equations for
the two- and four-point functions for products of $N$ models coupled by
disorder at large $N$, generalizing the equations appearing in SYK-like models.
We then study families of theories in which the disorder coupling is an exactly
marginal deformation, allowing us to follow $\lambda_L$ from weak to strong
coupling. We find interesting behaviors, including a discontinuous transition
into chaos, mimicking classical KAM theory.
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Causality Constraints on Black Holes beyond GR: We derive causality constraints on the simplest scalar-tensor theories in
which black holes differ from what General Relativity predicts, a scalar
coupled to the Gauss-Bonnet or the Chern-Simons terms. Demanding that time
advances are unobservable within the regime of validity of these effective
field theories, we find their cutoff must be parametrically of the same size as
the inverse Schwarzschild radius of the black holes for which the non-standard
effects are of order one. For astrophysical black holes within the range of
current gravitational wave detectors, this means a cutoff length at the km. We
further explore the leading additional higher-dimensional operators potentially
associated with the scale of UV completion and discuss their phenomenological
implications for gravitational wave science.
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Large Volume Perspective on Branes at Singularities: In this paper we consider a somewhat unconventional approach for deriving
worldvolume theories for D3 branes probing Calabi-Yau singularities. The
strategy consists of extrapolating the calculation of F-terms to the large
volume limit. This method circumvents the inherent limitations of more
traditional approaches used for orbifold and toric singularities. We illustrate
its usefulness by deriving quiver theories for D3 branes probing singularities
where a Del Pezzo surface containing four, five or six exceptional curves
collapses to zero size. In the latter two cases the superpotential depends
explicitly on complex structure parameters. These are examples of probe
theories for singularities which can currently not be computed by other means.
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GLSMs for non-Kahler Geometries: We identify a simple mechanism by which H-flux satisfying the modified
Bianchi identity arises in garden-variety (0,2) gauged linear sigma models.
Taking suitable limits leads to effective gauged linear sigma models with
Green-Schwarz anomaly cancellation. We test the quantum-consistency of a class
of such effective theories by constructing an off-shell superconformal algebra,
providing evidence that these models run to good CFTs in the deep IR.
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AdS/CFT for Four-Point Amplitudes involving Gravitino Exchange: In this paper we compute the tree-level four-point scattering amplitude of
two dilatini and two axion-dilaton fields in type IIB supergravity in AdS5 x
S5. A special feature of this process is that there is an "exotic" channel in
which there are no singleparticle poles. Another novelty is that this process
involves the exchange of a bulk gravitino. The amplitude is interpreted in
terms of N = 4 supersymmetric Yang-Mills theory at large 't Hooft coupling.
Properties of the Operator Product Expansion are used to analyze the various
contributions from single- and double-trace operators in the weak and strongly
coupled regimes, and to determine the anomalous dimensions of semi-short
operators. The analysis is particularly clear in the exotic channel, given the
absence of BPS states.
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Membrane solutions in M-theory: Motivated by the recent achievements in the framework of the semiclassical
limit of the M-theory/field theory correspondence, we propose an approach for
obtaining exact membrane solutions in general enough M-theory backgrounds,
having field theory dual description. As an application of the derived general
results, we obtain several types of membrane solutions in AdS_4xS^7 M-theory
background.
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Integrable Chain Model with Additional Staggered Model Parameter: The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2
grading along both chain and time directions is presented. The XXZ model with
staggered disposition along a chain of both, the anisotropy \pm\Delta, as well
as shifts of the spectral parameters are considered and the corresponding
integrable model is constructed. The Hamiltonian of the model is computed in
fermionic and spin formulations. It involves three neighbour site interactions
and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe
Ansatz technique is applied and the eigenstates, along with eigenvalues of the
transfer matrix of the model are found. The model has a free fermionic limit at
\Delta=0 and the integrable boundary terms are found in this case.
This construction is quite general and can be applied to other known
integrable models.
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Oscillons in $φ^6$-theories: Possible occurrence in MHD: In this work, we report on the possibility of occurrence of oscillon
configurations in the fourth state of matter. Oscillons are extremely
long-lived, time-periodic, spatially-localised scalar field structures.
Starting from a scalar field theory in 1+1 space-time dimensions, we find out
that small-amplitude oscillons can be obtained in the framework of a $\phi^6$
self-interacting potential. A connection between our results and ideal MHD
theory is established. Perspectives for a development of the present work are
pointed out.
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A duality web of linear quivers: We show that applying the Bailey lemma to elliptic hypergeometric integrals
on the $A_n$ root system leads to a large web of dualities for $\mathcal{N} =
1$ supersymmetric linear quiver theories. The superconformal index of Seiberg's
SQCD with $SU(N_c)$ gauge group and $SU(N_f)\times SU(N_f)\times U(1)$ flavour
symmetry is equal to that of $N_f-N_c-1$ distinct linear quivers. Seiberg
duality further enlarges this web by adding new quivers. In particular, both
interacting electric and magnetic theories with arbitrary $N_c$ and $N_f$ can
be constructed by quivering an $s$-confining theory with $N_f=N_c+1$.
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Strong-Weak Coupling Duality in Quantum Mechanics: We present a strong-weak coupling duality for quantum mechanical potentials.
Similarly to what happens in quantum field theory, it relates two problems with
inverse couplings, leading to a mapping of the strong coupling regime into the
weak one, giving information from the nonperturbative region of the parameters
space. It can be used to solve exactly power-type potentials and to extract
deep information about the energy spectra of polynomial ones.
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General Rotating Five Dimensional Black Holes of Toroidally Compactified
Heterotic String: We present the most general rotating black hole solution of five-dimensional
N=4 superstring vacua that conforms to the ``no hair theorem''. It is chosen to
be parameterized in terms of massless fields of the toroidally compactified
heterotic string. The solutions are obtained by performing a subset of O(8,24)
transformations, i.e., symmetry transformations of the effective
three-dimensional action for stationary solutions, on the five-dimensional
(neutral) rotating solution parameterized by the mass m and two rotational
parameters $l_1$ and $l_2$. The explicit form of the generating solution is
determined by three $SO(1,1)\subset O(8,24)$ boosts, which specify two electric
charges $Q_1^{(1)}, Q_{2}^{(2)}$ of the Kaluza-Klein and two-form U(1) gauge
fields associated with the same compactified direction, and the charge Q
(electric charge of the vector field, whose field strength is dual to the field
strength of the five-dimensional two-form field). The general solution,
parameterized by 27 charges, two rotational parameters and the ADM mass
compatible with the Bogomol'nyi bound, is obtained by imposing $[SO(5)\times
SO(21)]/[SO(4)\times SO(20)]\subset O(5,21)$ transformations, which do not
affect the five-dimensional space-time. We also analyze the deviations from the
BPS-saturated limit.
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The General Decomposition Theory of SU(2) Gauge Potential, Topological
Structure and Bifurcation of SU(2) Chern Density: By means of the geometric algebra the general decomposition of SU(2) gauge
potential on the sphere bundle of a compact and oriented 4-dimensional manifold
is given. Using this decomposition theory the SU(2) Chern density has been
studied in detail. It shows that the SU(2) Chern density can be expressed in
terms of the $\delta -$function $\delta (\phi) $. And one can find that the
zero points of the vector fields $\phi$ are essential to the topological
properties of a manifold. It is shown that there exists the crucial case of
branch process at the zero points. Based on the implicit function theorem and
the taylor expansion, the bifurcation of the Chern density is detailed in the
neighborhoods of the bifurcation points of $\phi$. It is pointed out that,
since the Chren density is a topological invariant, the sum topological
chargers of the branches will remain constant during the bifurcation process.
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Generalized asymptotics for gauge fields: An interesting question is to characterize the general class of allowed
boundary conditions for gauge theories, including gravity, at spatial and null
infinity. This has played a role in discussions of soft charges, where
antipodal symmetry has typically been assumed. However, the existence of
electric and gravitational line operators, arising from gauge-invariant dressed
observables, for example associated to axial or Fefferman-Graham like gauges,
indicates the existence of non-antipodally symmetric initial data. This note
studies aspects of the solutions corresponding to such non-symmetric initial
data. The explicit evolution can be found, via a Green function, and bounds can
be given on the asymptotic behavior of such solutions, evading arguments for
singular behavior. Likewise, objections to such solutions based on infinite
symplectic form are also avoided, although these solutions may be
superselected. Soft charge conservation laws, and their modification, are
briefly examined for such solutions. This discussion strengthens (though is not
necessary for) arguments that soft charges characterize gauge field degrees of
freedom, but not necessarily the degrees of freedom associated to the matter
sourcing the field.
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Weyl Gravity in Covariant Hamiltonian Formalism: We find covariant canonical formalism for Weyl invariant gravity. We discuss
constraint structure of this theory and its gauge fixed form.
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Integrability, spin-chains and the AdS3/CFT2 correspondence: Building on arXiv:0912.1723, in this paper we investigate the AdS3/CFT2
correspondence using integrability techniques. We present an all-loop Bethe
Ansatz (BA) for strings on AdS_3 x S^3 x S^3 x S^1, with symmetry
D(2,1;alpha)^2, valid for all values of alpha. This construction relies on a
novel, alpha-dependent generalisation of the Zhukovsky map. We investigate the
weakly-coupled limit of this BA and of the all-loop BA for strings on AdS_3 x
S^3 x T^4. We construct integrable short-range spin-chains and Hamiltonians
that correspond to these weakly-coupled BAs. The spin-chains are alternating
and homogenous, respectively. The alternating spin-chain can be regarded as
giving some of the first hints about the unknown CFT2 dual to string theory on
AdS_3 x S^3 x S^3 x S^1. We show that, in the alpha to 1 limit, the integrable
structure of the D(2,1;alpha) model is non-singular and keeps track of not just
massive but also massless modes. This provides a way of incorporating massless
modes into the integrability machinery of the AdS3/CFT2 correspondence.
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Chaotic strings in a near Penrose limit of AdS$_5\times T^{1,1}$: We study chaotic motions of a classical string in a near Penrose limit of
AdS$_5\times T^{1,1}$. It is known that chaotic solutions appear on $R\times
T^{1,1}$, depending on initial conditions. It may be interesting to ask whether
the chaos persists even in Penrose limits or not. In this paper, we show that
sub-leading corrections in a Penrose limit provide an unstable separatrix, so
that chaotic motions are generated as a consequence of collapsed
Kolmogorov-Arnold-Moser (KAM) tori. Our analysis is based on deriving a reduced
system composed of two degrees of freedom by supposing a winding string ansatz.
Then, we provide support for the existence of chaos by computing Poincare
sections. In comparison to the AdS$_5\times T^{1,1}$ case, we argue that no
chaos lives in a near Penrose limit of AdS$_5\times$S$^5$, as expected from the
classical integrability of the parent system.
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Yukawas and discrete symmetries in F-theory compactifications without
section: In the case of F-theory compactifications on genus-one fibrations without
section there are naturally appearing discrete symmetries, which we argue to be
associated to geometrically massive U(1) gauge symmetries. These discrete
symmetries are shown to induce non-trivial selection rules for the allowed
Yukawa couplings in SU(N) gauge theories. The general discussion is exemplified
using a concrete Calabi-Yau fourfold realizing an SU(5) GUT model. We observe
that M2 instanton effects appear to play a key role in the generation of new
superpotential terms and in the dynamics close to phase transition loci.
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Composition of many spins, random walks and statistics: The multiplicities of the decomposition of the product of an arbitrary number
$n$ of spin $s$ states into irreducible $SU(2)$ representations are computed.
Two complementary methods are presented, one based on random walks in
representation space and another based on the partition function of the system
in the presence of a magnetic field. The large-$n$ scaling limit of these
multiplicities is derived, including nonperturbative corrections, and related
to semiclassical features of the system. A physical application of these
results to ferromagnetism is explicitly worked out. Generalizations involving
several types of spins, as well as spin distributions, are also presented. The
corresponding problem for (anti-)symmetric composition of spins is also
considered and shown to obey remarkable duality and bosonization relations and
exhibit qualitatively different large-$n$ scaling properties.
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Integrable boundary states in D3-D5 dCFT: beyond scalars: A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the
gauge group jumps by k units across a domain wall. The one-point functions of
local operators in this set-up map to overlaps between on-shell Bethe states in
the underlying spin chain and a boundary state representing the D5 brane.
Focussing on the k=1 case, we extend the construction to gluonic and fermionic
sectors, which was prohibitively difficult to achieve for k>1. As a byproduct,
we test an all-loop proposal for the one-point functions in the su(2) sector at
the half-wrapping order of perturbation theory.
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No triangles on the moduli space of maximally supersymmetric gauge
theory: Maximally supersymmetric gauge theory in four dimensions has a remarkably
simple S-matrix at the origin of its moduli space at both tree and loop level.
This leads to the question what, if any, of this structure survives at the
complement of this one point. Here this question is studied in detail at one
loop for the branch of the moduli space parameterized by a vacuum expectation
value for one complex scalar. Motivated by the parallel D-brane picture of
spontaneous symmetry breaking a simple relation is demonstrated between the
Lagrangian of broken super Yang-Mills theory and that of its higher dimensional
unbroken cousin. Using this relation it is proven both through an on- as well
as an off-shell method there are no so-called triangle coefficients in the
natural basis of one-loop functions at any finite point of the moduli space for
the theory under study. The off-shell method yields in addition absence of
rational terms in a class of theories on the Coulomb branch which includes the
special case of maximal supersymmetry. The results in this article provide
direct field theory evidence for a recently proposed exact dual conformal
symmetry motivated by the AdS/CFT correspondence.
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Finite-difference representations of the degenerate affine Hecke algebra: The representations of the degenerate affine Hecke algebra in which the
analogues of the Dunkl operators are given by finite-difference operators are
introduced. The non-selfadjoint lattice analogues of the spin
Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The $
sl(m)$-Yangian representations arising from the finite-difference
representations of the degenerate affine Hecke algebra are shown to be related
to the Yangian representation of the 1-d Hubbard Model.
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Noncompact Gepner Models with Discrete Spectra: We investigate a noncompact Gepner model, which is composed of a number of
SL(2,R)/U(1) Kazama-Suzuki models and N=2 minimal models. The SL(2,R)/U(1)
Kazama-Suzuki model contains the discrete series among the SL(2,R) unitary
representations as well as the continuous series. We claim that the discrete
series contain the vanishing cohomology and the vanishing cycles of the
associated noncompact Calabi-Yau manifold. We calculate the Elliptic genus and
the open string Witten indices. In the A_{N-1} ALE models, they actually agree
with the vanishing cohomology and the intersection form of the vanishing
cycles.
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Little Groups of Preon Branes: Little groups for preon branes (i.e. configurations of branes with maximal
(n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are
calculated for all massless, and partially for massive orbits. For massless
orbits little groups are semidirect product of d-2 translational group
$T_{d-2}$ on a subgroup of (SO(d-2) $\times$ R-invariance) group. E.g. at d=9
the subgroup is exceptional $G_2$ group. It is also argued, that 11d Majorana
spinor invariants, which distinguish orbits, are actually invariant under
d=2+10 Lorentz group. Possible applications of these results include
construction of field theories in generalized space-times with brane charges
coordinates, different problems of group's representations decompositions,
spin-statistics issues.
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Deformed boson-fermion correspondence, Q-bosons, and topological strings
on the conifold: We consider two different physical systems for which the basis of the Hilbert
space can be parametrized by Young diagrams: free complex fermions and the
phase model of strongly correlated bosons. Both systems have natural,
well-known deformations parametrized by a parameter Q: the former one is
related to the deformed boson-fermion correspondence introduced by N. Jing,
while the latter is the so-called Q-boson, arising also in the context of
quantum groups. These deformations are equivalent and can be realized in the
same way in the algebra of Hall-Littlewood symmetric functions. Without a
deformation, these reduce to Schur functions, which can be used to construct a
generating function of plane partitions, reproducing a topological string
partition function on $C^3$. We show that a deformation of both systems leads
then to a deformed generating function, which reproduces topological string
partition function of the conifold, with the deformation parameter Q identified
with the size of $P^1$. Similarly, a deformation of the fermion one-point
function results in the A-brane partition function on the conifold.
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Operadic formulation of topological vertex algebras and Gerstenhaber or
Batalin-Vilkovisky algebras: We give the operadic formulation of (weak, strong) topological vertex
algebras, which are variants of topological vertex operator algebras studied
recently by Lian and Zuckerman. As an application, we obtain a conceptual and
geometric construction of the Batalin-Vilkovisky algebraic structure (or the
Gerstenhaber algebra structure) on the cohomology of a topological vertex
algebra (or of a weak topological vertex algebra) by combining this operadic
formulation with a theorem of Getzler (or of Cohen) which formulates
Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology
of the framed little disk operad (or of the little disk operad).
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Fixed scalar greybody factors in five and four dimensions: We perform the classical gravity calculations of the fixed scalar absorption
cross-sections by D=5 black holes with three charges and by D=4 black holes
with four charges. We obtain analytic results for the cases where the energy
and the left and right moving temperatures are sufficiently low but have
arbitrary ratios. In D=5 the greybody factor is in perfect agreement with the
recent calculation performed in the context of the effective string model for
black holes. In D=4 the formula for the greybody factor in terms of the energy
and the temperatures differs from that in D=5 only by the overall
normalization. This suggests that the fixed scalar coupling to the effective
string in D=4 is identical to that in D=5.
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Supergravity as a constrained BF theory: In this paper we formulate ${\cal N}=1$ supergravity as a constrained $BF$
theory with $OSp(4|1)$ gauge superalgebra. We derive the modified supergravity
Lagrangian that, apart from the standard supergravity with negative
cosmological constant, contains terms proportional to the (inverse of) Immirzi
parameter. Although these terms do not change classical field equations, they
might be relevant in quantum theory. We briefly discuss the perturbation theory
around the supersymmetric topological vacuum.
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Embeddings of the "New Massive Gravity": Using different types of embeddings of equations of motion we investigate the
existence of generalizations of the "New Massive Gravity" (NMG) model with the
same particle content (massive gravitons). By using the Weyl symmetry as a
guiding principle for the embeddings we show that the Noether gauge embedding
approach leads us to a sixth order model in derivatives with either a massive
or a massless ghost. If the Weyl symmetry is implemented by means of a
Stueckelberg field we obtain a new scalar-tensor model for massive gravitons.
It is ghost free and Weyl invariant at linearized level. The model can be
nonlinearly completed into a scalar field coupled to the NMG theory. The
elimination of the scalar field leads to a nonlocal modification of the NMG.
We also prove to all orders in derivatives that there is no local, ghost free
embedding of the linearized NMG equations of motion around Minkowski space when
written in terms of one symmetric tensor. Regarding that point, NMG differs
from the Fierz-Pauli theory, since in later case we can replace the
Einstein-Hilbert action by specific $f(R,\Box\, R)$ generalizations and still
keep the theory ghost free at linearized level.
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Resumming the string perturbation series: We use the AdS/CFT correspondence to study the resummation of a perturbative
genus expansion appearing in the type II superstring dual of ABJM theory.
Although the series is Borel summable, its Borel resummation does not agree
with the exact non-perturbative answer due to the presence of complex
instantons. The same type of behavior appears in the WKB quantization of the
quartic oscillator in Quantum Mechanics, which we analyze in detail as a toy
model for the string perturbation series. We conclude that, in these examples,
Borel summability is not enough for extracting non-perturbative information,
due to non-perturbative effects associated to complex instantons. We also
analyze the resummation of the genus expansion for topological string theory on
local $\mathbb P^1 \times \mathbb P^1$, which is closely related to ABJM
theory. In this case, the non-perturbative answer involves membrane instantons
computed by the refined topological string, which are crucial to produce a
well-defined result. We give evidence that the Borel resummation of the
perturbative series requires such a non-perturbative sector.
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Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop: We study the wall-crossing phenomena of D4-D2-D0 bound states with two units
of D4-brane charge on the resolved conifold. We identify the walls of marginal
stability and evaluate the discrete changes of the BPS indices by using the
Kontsevich-Soibelman wall-crossing formula. In particular, we find that the
field theories on D4-branes in two large radius limits are properly connected
by the wall-crossings involving the flop transition of the conifold. We also
find that in one of the large radius limits there are stable bound states of
two D4-D2-D0 fragments.
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Bosonization and Current Algebra of Spinning Strings: We write down a general geometric action principle for spinning strings in
$d$-dimensional Minkowski space, which is formulated without the use of
Grassmann coordinates. Instead, it is constructed in terms of the pull-back of
a left invariant Maurer-Cartan form on the $d$-dimensional Poincar\'e group to
the world sheet. The system contains some interesting special cases. Among them
are the Nambu string (as well as, null and tachyionic strings) where the spin
vanishes, and also the case of a string with a spin current - but no momentum
current. We find the general form for the Virasoro generators, and show that
they are first class constraints in the Hamiltonian formulation of the theory.
The current algebra associated with the momentum and angular momentum densities
are shown, in general, to contain rather complicated anomaly terms which
obstruct quantization. As expected, the anomalies vanish when one specializes
to the case of the Nambu string, and there one simply recovers the algebra
associated with the Poincar\'e loop group. We speculate that there exist other
cases where the anomalies vanish, and that these cases give the bosonization of
the known pseudoclassical formulations of spinning strings.
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Line discontinuities, local action with both the field and its dual, and
spin from no spin in two-dimensional scalar theory: We consider a local action with both the real scalar field and its dual in
two Euclidean dimensions. The role of singular line discontinuities is
emphasized. Exotic properties of the correlation of the field with its dual,
the generation of spin from scalar fields, and quantization of dual charges are
pointed out. Wick's theorem and rotation properties of fermions are recovered
for half-integer quantization.
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Dual gravity with $R$ flux from graded Poisson algebra: We suggest a new action for a ``dual'' gravity in a stringy $R$, $Q$ flux
background. The construction is based on degree-$2$ graded symplectic geometry
with a homological vector field. The structure we consider is non-canonical and
features a curvature-free connection. It is known that the data of Poisson
structures of degree $2$ with a Hamiltonian correspond to a Courant algebroid
on $TM \oplus T^{*}M$, the bundle of generalized geometry. With the bracket for
the Courant algebroid and a further bracket which resembles the Lie bracket of
vector fields, we get a connection with non-zero curvature for the bundle of
generalized geometry. The action is the (almost) Hilbert-Einstein action for
that connection.
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Low-energy electron-electron bound states in planar QED: In this talk, we present a parity-preserving QED3 model with spontaneous
breaking of a local U(1)-symmetry. The breaking is accomplished by a potential
of the phi^6-type. It is shown that a net attractive interaction appears in the
Moeller scattering (s- and p-wave scatterings between two electrons) as
mediated by the gauge field and a Higgs scalar. We show, by solving numerically
the Schroedinger equation for both the scattering potentials (s- and p-wave),
that in the weak-coupling regime only s-wave bound states appear, whereas in
the strong-coupling regime s- and p-wave bound states show up. Also, we discuss
possible applications of the model to the phenomenology of high-Tc
superconductors and to the re-entrant superconductivity effect.
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NDIM achievements: Massive, Arbitrary tensor rank and N-loop insertions
in Feynman integrals: One of the main difficulties in studying Quantum Field Theory, in the
perturbative regime, is the calculation of D-dimensional Feynman integrals. In
general, one introduces the so-called Feynman parameters and associated with
them the cumbersome parametric integrals. Solving these integrals beyond the
one-loop level can be a difficult task. Negative dimensional integration method
(\ndim{}) is a technique whereby such problem is dramatically reduced. In this
work we present the calculation of two-loop integrals in three diferent cases:
scalar ones with three diferent masses, massless with arbitrary tensor rank,
with N-insertions of a 2-loop diagram.
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(m,n)-Strings In IIB Matrix Model: By adding gauge fields to the D-string classical solution, which have
non-zero contribution to commutators in continuum limit (extreme large $N$), we
introduced $(m,n)$-strings in IIB matrix model. It is found that the size of
matrices depends on the value of the electric field. The tension of these
strings appears in $SL(2,Z)$ invariant form. The interaction for parallel and
angled strings are found in agreement with the string theory for small electric
fields.
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Anomalies, equivalence and renormalization of cosmological frames: We study the question of whether two frames of a given physical theory are
equivalent or not in the presence of quantum corrections. By using field theory
arguments we claim that equivalence is broken in the presence of anomalous
symmetries in one of the frames. This is particularized to the case of the
relation between the Einstein and Jordan frames in scalar-tensor theories used
to describe early Universe dynamics. Although in this case a regularization
that cancels the anomaly exists, the renormalized theory always develop a
non-vanishing contribution to the S-matrix that is present only in the Jordan
frame, promoting the different frames to different physical theories that must
be UV completed in a different way.
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High-energy asymptotics of D-brane decay amplitudes from Coulomb gas
electrostatics: We study the high-energy limit of tree-level string production amplitudes
from decaying D-branes in bosonic string theory, interpreting the vertex
operators as external charges interacting with a Coulomb gas corresponding to
the rolling tachyon background, and performing an electrostatic analysis. In
particular, we consider two open string - one closed string amplitudes and four
open string amplitudes, and calculate explicit formulas for the leading
exponential behavior.
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Codimension-2 Brane-Bulk Matching: Examples from Six and Ten Dimensions: Experience with Randall-Sundrum models teaches the importance of following
how branes back-react onto the bulk geometry, since this can dramatically
affect the system's low-energy properties. Yet the practical use of this
observation for model building is so far mostly restricted to branes having
only one transverse dimension (codimension-1) in the bulk space, since this is
where tools for following back-reaction are well-developed. This is likely a
serious limitation since experience also tells us that one dimension is rarely
representative of what happens in higher dimensions. We here summarize recent
progress on developing the matching conditions that describe how codimension-2
branes couple to bulk metric, gauge and scalar fields. These matching
conditions are then applied to three situations: D7-branes in F-theory
compactifications of 10D Type IIB string vacua; 3-branes coupled to bulk axions
in unwarped and non-supersymmetric 6D systems; and 3-branes coupled to chiral,
gauged 6D supergravity. For each it is shown how the resulting brane-bulk
dynamics is reproduced by the scalar potential for the low-energy moduli in the
dimensionally reduced, on-brane effective theory. For 6D supergravity we show
that the only 4D-maximally symmetric bulk geometries supported by
positive-tension branes are flat.
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Conformal Gauge-Yukawa Theories away From Four Dimensions: We present the phase diagram and associated fixed points for a wide class of
Gauge-Yukawa theories in $d=4+\epsilon$ dimensions. The theories we investigate
involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten
limit. The analysis is performed in steps, we start with QCD$_d$ and then we
add Yukawa interactions and scalars which we study at next-to- and
next-to-next-to-leading order. Interacting infrared fixed points naturally
emerge in dimensions lower than four while ultraviolet ones appear above four.
We also analyse the stability of the scalar potential for the discovered fixed
points. We argue for a very rich phase diagram in three dimensions while in
dimensions higher than four certain Gauge-Yukawa theories are ultraviolet
complete because of the emergence of an asymptotically safe fixed point.
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Abelian Duality at Higher Genus: In three dimensions, a free, periodic scalar field is related by duality to
an abelian gauge field. Here I explore aspects of this duality when both
theories are quantized on a Riemann surface of genus g. At higher genus,
duality involves an identification of winding with momentum on the Jacobian
variety of the Riemann surface. I also consider duality for monopole and loop
operators on the surface and exhibit the operator algebra, a refinement of the
Wilson-'t Hooft algebra.
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Generalized Geometry and M theory: We reformulate the Hamiltonian form of bosonic eleven dimensional
supergravity in terms of an object that unifies the three-form and the metric.
For the case of four spatial dimensions, the duality group is manifest and the
metric and C-field are on an equal footing even though no dimensional reduction
is required for our results to hold. One may also describe our results using
the generalized geometry that emerges from membrane duality. The relationship
between the twisted Courant algebra and the gauge symmetries of eleven
dimensional supergravity are described in detail.
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Asymptotic Dynamics in Perturbative Quantum Gravity and BMS
Supertranslations: Recently it has been shown that infrared divergences in the conventional
S-matrix elements of gauge and gravitational theories arise from a violation of
the conservation laws associated with large gauge symmetries. These infrared
divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as
the basis for S-matrix elements. Motivated by this connection, we study the
action of BMS supertranslations on the FK asymptotic states of perturbative
quantum gravity. We compute the BMS charge of the FK states and show that it
characterizes the superselection sector to which the state belongs.
Conservation of the BMS charge then implies that there is no transition between
different superselection sectors, hence showing that the FK graviton clouds
implement the necessary vacuum transition induced by the scattering process.
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Wilson loop on a sphere: We give the formula for a simple Wilson loop on a sphere which is valid for
an arbitrary QCD$_2$ saddle-point $\rho(x)$: \mbox{$W(A_1,A_2)=\oint
\frac{dx}{2\pi i} \exp(\int dy \frac{\rho(y)}{y-x}+A_2x)$}. The
strong-coupling-phase solution is investigated.
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Superconformal Vortex Strings: We study the low-energy dynamics of semi-classical vortex strings living
above Argyres-Douglas superconformal field theories. The worldsheet theory of
the string is shown to be a deformation of the CP^N model which flows in the
infra-red to a superconformal minimal model. The scaling dimensions of chiral
primary operators are determined and the dimensions of the associated relevant
perturbations on the worldsheet and in the four dimensional bulk are found to
agree. The vortex string thereby provides a map between the A-series of N=2
superconformal theories in two and four dimensions.
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Semiclassical Calculation of Photon-Stimulated Schwinger Pair Creation: We consider the electron-positron pair creation by a photon in an external
constant electric field. The presented treatment is based on a purely
quasiclassical calculation of the imaginary part of the on-shell photon
polarization operator. By using this approach we find the pair production rate
for photons with polarization parallel as well as orthogonal to the external
electric field in the leading order in the parameter $eE / m ^ 2$, which has
been recently found by other methods. For the orthogonal polarization we also
find a new contribution to the rate, which is leading in the ratio of the
photon energy to the electron mass $\omega/m$. We also reproduce by a purely
geometrical calculation the exponential factor in the probability of the
stimulated pair creation at arbitrary energy of the photon.
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Hamilton-Jacobi treatment of a non-relativistic particle on a curved
space: In this paper a non-relativistic particle moving on a hypersurface in a
curved space and the multidimensional rotator are investigated using the
Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism
is demonstrated in both Cartesian and curvilinear coordinates. The energy
spectrum of the multidimensional rotator is equal to that of a pure
Laplace-Beltrami operator with no additional constant arising from the
curvature of the sphere.
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Infrared dynamics in de Sitter space from Schwinger-Dyson equations: We study the two-point correlator of an O(N) scalar field with quartic
self-coupling in de Sitter space. For light fields in units of the expansion
rate, perturbation theory is plagued by large logarithmic terms for
superhorizon momenta. We show that a proper treatment of the infinite series of
self-energy insertions through the Schwinger-Dyson equations resums these
infrared logarithms into well defined power laws. We provide an exact
analytical solution of the Schwinger-Dyson equations for infrared momenta when
the self-energy is computed at two-loop order. The obtained correlator exhibits
a rich structure with a superposition of free-field-like power laws. We extract
mass and field-strength renormalization factors from the asymptotic infrared
behavior. The latter are nonperturbative in the coupling in the case of a
vanishing tree-level mass.
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CFT driven cosmology and the DGP/CFT correspondence: We present a dual 5D braneworld picture of a recently suggested model for a
microcanonical description of a 4D cosmology driven by a conformal field theory
with a large number of quantum fields. The 5D side of the duality relation is
represented by a generalized brane induced gravity model in a Schwarzschild-de
Sitter bulk. The values of the bulk cosmological and the induced 4D
cosmological constants are determined by requiring the absence of conical
singularity at the de Sitter horizon of the Euclidean Schwarzschild-de Sitter
bulk. Those values belong to the vicinity of the upper bound of a range of
admissible values for the cosmological constant. This upper bound is enforced
by the 4D CFT and coincides with the natural gravitational cutoff in a theory
with many quantum species. The resulting DGP/CFT duality suggests the
possibility of a new type of {\em background independent} correspondence. A
mechanism for inverting the sign of the effective cosmological constant is
found, which might reconcile a negative value of the primordial cosmological
constant compatible with supersymmetry with the one required by inflationary
cosmology.
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On (non-Hermitian) Lagrangeans in (particle) physics and their dynamical
generation: On the basis of a new method to derive the effective action the
nonperturbative concept of "dynamical generation" is explained. A non-trivial,
non-Hermitian and PT-symmetric solution for Wightman's scalar field theory in
four dimensions is dynamically generated, rehabilitating Symanzik's precarious
phi**4-theory with a negative quartic coupling constant as a candidate for an
asymptotically free theory of strong interactions. Finally it is shown making
use of dynamically generation that a Symanzik-like field theory with scalar
confinement for the theory of strong interactions can be even suggested by
experiment.
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General bound-state structure of the massive Schwinger model: Within the Euclidean path integral and mass perturbation theory we derive,
from the Dyson-Schwinger equations of the massive Schwinger model, a general
formula that incorporates, for sufficiently small fermion mass, all the
bound-state mass poles of the massive Schwinger model. As an illustration we
perturbatively compute the masses of the three lowest bound states.
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Invariance of interaction terms in new representation of self-dual
electrodynamics: A new representation of Lagrangians of 4D nonlinear electrodynamics is
considered. In this new formulation, in parallel with the standard Maxwell
field strength F, an auxiliary bispinor (tensor) field V is introduced. The
gauge field strength appears only in bilinear terms of the full Lagrangian,
while the interaction Lagrangian E depends on the auxiliary fields, E = E(V).
Two types of self-duality inherent in the nonlinear electrodynamics models
admit a simple characterization in terms of the function E. The continuous
SO(2) duality symmetry between nonlinear equations of motion and Bianchi
identities amounts to requiring E to be a function of the SO(2) invariant
quartic combination |V|^4. The discrete self-duality (or self-duality under
Legendre transformation) amounts to a weaker condition E(V)= E(iV). This
approach can be generalized to a system of n Abelian gauge fields exhibiting
U(n) duality. The corresponding interaction Lagrangian should be U(n) invariant
function of n bispinor auxiliary fields.
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A Class of FRT Quantum Groups and Fun$_q$(G$_2$) as a Special Case: Citations are updated; referred papers are increased. An error right after
the eq.~(27) is corrected, and several chages (not serious) are made.
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A solution manual for Polchinski's "String Theory": We present detailed solutions to 81 of the 202 problems in J. Polchinski's
two-volume textbook "String Theory".
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The Perils of `Soft' SUSY Breaking: We consider a two dimensional SU(N) gauge theory coupled to an adjoint
Majorana fermion, which is known to be supersymmetric for a particular value of
fermion mass. We investigate the `soft' supersymmetry breaking of the discrete
light cone quantization (DLCQ) of this theory. There are several DLCQ
formulations of this theory currently in the literature and they naively appear
to behave differently under `soft' supersymmetry breaking at finite resolution.
We show that all these formulations nevertheless yield identical bound state
masses in the decompactification limit of the light-like circle. Moreover, we
are able to show that the supersymmetry-inspired version of DLCQ (so called
`SDLCQ') provides the best rate of convergence of DLCQ bound state masses
towards the actual continuum values, except possibly near or at the critical
fermion mass. In this last case, we discuss improved extrapolation schemes that
must supplement the DLCQ algorithm in order to obtain correct continuum bound
state masses. Interestingly, when we truncate the Fock space to two particles,
the SDLCQ prescription presented here provides a scheme for improving the rate
of convergence of the massive t'Hooft model. Thus the supersymmetry-inspired
SDLCQ prescription is applicable to theories without supersymmetry.
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Tri-Sasaki 7-metrics fibered over the QK limit of the
Plebanski-Demianski metrics: We consider a family of conical hyperkahler 8-metrics and we find the
corresponding tri-Sasaki 7-metrics. We find in particular, a 7-dimensional
fibration over the AdS-Kerr-Newmann-Taub-Nut solutions which is tri-Sasaki, and
we consider several limits of the parameters of this solution. We also find an
squashed version of these metrics, which is of weak $G_2$ holonomy.
Construction of supergravity backgrounds is briefly discussed, in particular
examples which do not possess $AdS_4$ near horizon limit.
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The energy of the high-temperature quark-gluon plasma: For the quark-gluon plasma, an energy-momentum tensor is found corresponding
to the high-temperature Braaten-Pisarski effective action. The tensor is found
by considering the interaction of the plasma with a weak gravitational field
and the positivity of the energy is studied. In addition, the complete
effective action in curved spacetime is written down.
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On $α'$-effects from $D$-branes in $4d \; \mathcal{N} = 1$: In this work we study type IIB Calabi-Yau orientifold compactifications in
the presence of space-time filling D7-branes and O7-planes. In particular, we
conclude that $\alpha'^2 g_s$-corrections to their DBI actions lead to a
modification of the four-dimensional $\mathcal{N}=1$ K\"ahler potential and
coordinates. We focus on the one-modulus case of the geometric background i.e.
$h^{1,1}=1$ where we find that the $\alpha'^2 g_s$-correction is of topological
nature. It depends on the first Chern form of the four-cycle of the Calabi-Yau
orientifold which is wrapped by the D7-branes and O7-plane. This is in
agreement with our previous F-theory analysis and provides further evidence for
a potential breaking of the no-scale structure at order $\alpha'^2 g_s$.
Corrected background solutions for the dilaton, the warp-factor as well as the
internal space metric are derived. Additionally, we briefly discuss
$\alpha'$-corrections from other D$p$-branes.
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Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions: We use localization techniques to calculate the Euclidean partition functions
for $\mathcal{N}=1$ theories on four-dimensional manifolds $M$ of the form $S^1
\times M_3$, where $M_3$ is a circle bundle over a Riemann surface. These are
generalizations of the $\mathcal{N}=1$ indices in four-dimensions including the
lens space index. We show that these generalized indices are holomorphic
functions of the complex structure moduli on $M$. We exhibit the deformation by
background flat connections.
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When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid: We analyze the behavior of quarks coupled to a $SU(N_c)$ gauge theory in 1+1
dimensions. In the limit of strong coupling, the model reduces to a
Wess-Zumino-Novikov-Witten (WZNW) model. At nonzero density, excitations near
the Fermi surface form a non-Fermi liquid. With $N_f$ flavors, the finite
density of quarks reduce to a free $U(1)$ field, which governs fluctuations in
baryon number, together with a WZNW $SU(N_f)$ nonlinear sigma model at level
$N_c$, from the pion/kaon modes. We compute the singularity in the charge
susceptibility at the Fermi surface and the attendant power law correlations.
We suggest that this is relevant to the quarkyonic regime of cold, dense QCD in
3+1 dimensions, in the limit that the Fermi surface is covered by many small
patches, and the theory is effectively one dimensional. In this regime the
dominant excitations near the Fermi surface are not baryons, but gapless
bosonic modes.
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The black hole behind the cut: We study the analytic structure of the heavy-heavy-light-light holographic
correlators in the supergravity approximation of the AdS$_3 \times S^3$/CFT$_2$
duality. As an explicit example, we derive the correlator where the heavy
operator is a classical microstate of the 5D supersymmetric black hole and its
dual geometry interpolates as a function of a continuous parameter between
global AdS$_3$ and the extremal BTZ black hole. The simplest perturbation of
this interpolating geometry by a light field is described by the Heun equation
and we exploit the relation of its connection coefficients to the Liouville CFT
to analytically compute the correlator in the two limits, focusing in
particular on the black hole regime. In this limit we find that the real poles
of the correlator become dense and can be approximated by a cut. We show that,
when the charges of the heavy state are in the black hole regime, the
discontinuity across the cut has complex poles corresponding to the
quasi-normal modes of BTZ. This behaviour is qualitatively similar to what is
expected for the large central charge limit of a typical black hole microstate
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Spin Foam Models of Quantum Gravity: We give a short review of the spin foam models of quantum gravity, with an
emphasis on the Barret-Crane model. After explaining the shortcomings of the
Barret-Crane model, we briefly discuss two new approaches, one based on the 3d
spin foam state sum invariants for the embedded spin networks, and the other
based on representing the string scattering amplitudes as 2d spin foam state
sum invariants.
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Current Interactions and Holography from the 0-Form Sector of Nonlinear
Higher-Spin Equations: The form of higher-spin current interactions in $AdS_4$ is derived from the
full nonlinear higher-spin equations in the sector of Weyl 0-forms. The
coupling constant in front of spin-one currents built from scalars and spinors
as well as Yukawa coupling are determined explicitly. Couplings of all other
higher-spin current interactions are determined implicitly. All couplings are
shown to be independent of the phase parameter of the nonlinear higher-spin
theory. The proper holographic dependence of the vertex on the higher-spin
phase parameter is shown to result from the boundary conditions on the bulk
fields.
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The particle-hole transformation, supersymmetry and achiral boundaries
of the open Hubbard model: We show that the particle-hole transformation in the Hubbard model has a
crucial role in relating Shastry's R-matrix to the AdS/CFT S-matrix. In
addition, we construct an achiral boundary for the open Hubbard chain which
possesses twisted Yangian symmetry.
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Curvature Induced Phase Transition in a Four-Fermion Theory Using the
Weak Curvature Expansion: Curvature induced phase transition is thoroughly investigated in a four-
fermion theory with $N$ components of fermions for arbitrary space-time
dimensions $(2 \leq D < 4)$. We adopt the $1/N$ expansion method and calculate
the effective potential for a composite operator $\bar{\psi}\psi$. The
resulting effective potential is expanded asymptotically in terms of the
space-time curvature $R$ by using the Riemann normal coordinate. We assume that
the space-time curves slowly and keep only terms independent of $R$ and terms
linear in $R$. Evaluating the effective potential it is found that the
first-order phase transition is caused and the broken chiral symmetry is
restored for a large positive curvature. In the space-time with a negative
curvature the chiral symmetry is broken down even if the coupling constant of
the four-fermion interaction is sufficiently small. We present the behavior of
the dynamically generated fermion mass. The critical curvature, $R_{cr}$, which
divides the symmetric and asymmetric phases is obtained analytically as a
function of the space-time dimension $D$. At the four-dimensional limit our
result $R_{cr}$ agrees with the exact results known in de Sitter space and
Einstein universe.
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Modified Gravity on the Brane and Dark Energy: We analyze the dynamics of an AdS5 braneworld with matter fields when gravity
is allowed to deviate from the Einstein form on the brane. We consider exact
5-dimensional warped solutions which are associated with conformal bulk fields
of weight -4 and describe on the brane the following three dynamics: those of
inhomogeneous dust, of generalized dark radiation, and of homogeneous
polytropic dark energy. We show that, with modified gravity on the brane, the
existence of such dynamical geometries requires the presence of non-conformal
matter fields confined to the brane.
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State of the Unification Address: After reviewing how M-theory subsumes string theory, I report on some new and
interesting developments, focusing on the ``brane-world'': circumventing no-go
theorems for supersymmetric brane-worlds, complementarity of the Maldacena and
Randall-Sundrum pictures; self-tuning of the cosmological constant. I conclude
with the top ten unsolved problems.
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Four-dimensional greybody factors and the effective string: Recently Maldacena and Strominger found that the calculation of greybody
factors for $D=5$ black holes carrying three U(1) charges gives striking new
evidence for their description as multiply wound effective strings. Here we
show that a similar result holds for $D=4$ black holes with four $U(1)$
charges. In this case the effective string may be thought of as the triple
intersection of the 5-branes in M-theory compactified on $T^7$.
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Kink scattering in a hybrid model: In this work we consider a model where the potential has two topological
sectors connecting three adjacent minima, as occurs with the $\phi^6$ model. In
each topological sector, the potential is symmetric around the local maximum.
For $\phi>0$ there is a linear map between the model and the $\lambda\phi^4$
model. For $\phi<0$ the potential is reflected. Linear stability analysis of
kink and antikink lead to discrete and continuum modes related by a linear
coordinate transformation to those known analytically for the $\lambda\phi^4$
model. Fixing one topological sector, the structure of antikink-kink scattering
is related to the observed in the $\lambda\phi^4$ model. For kink-antikink
collisions a new structure of bounce windows appear. Depending on the initial
velocity, one can have oscillations of the scalar field at the center of mass
even for one bounce, or a change of topological sector. We also found a
structure of one-bounce, with secondary windows corresponding to the changing
of the topological sector accumulating close to each one-bounce windows. The
kink-kink collisions are characterized by a repulsive interaction and there is
no possibility of forming a bound state.
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Full mass range analysis of the QED effective action for an O(2)xO(3)
symmetric field: An interesting class of background field configurations in quantum
electrodynamics (QED) are the O(2)xO(3) symmetric fields, originally introduced
by S.L. Adler in 1972. Those backgrounds have some instanton-like properties
and yield a one-loop effective action that is highly nontrivial, but amenable
to numerical calculation. Here, we use the recently developed
"partial-wave-cutoff method" for a full mass range numerical analysis of the
effective action for the "standard" O(2)xO(3) symmetric field, modified by a
radial suppression factor. At large mass, we are able to match the asymptotics
of the physically renormalized effective action against the leading two mass
levels of the inverse mass expansion. For small masses, with a suitable choice
of the renormalization scheme we obtain stable numerical results even in the
massless limit. We analyze the N - point functions in this background and show
that, even in the absence of the radial suppression factor, the two-point
contribution to the effective action is the only obstacle to taking its
massless limit. The standard O(2)xO(3) background leads to a chiral anomaly
term in the effective action, and both our perturbative and nonperturbative
results strongly suggest that the small-mass asymptotic behavior of the
effective action is, after the subtraction of the two-point contribution,
dominated by this anomaly term as the only source of a logarithmic mass
dependence. This confirms a conjecture by M. Fry.
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Asymptotic symmetries and thermodynamics of higher spin black holes in
AdS3: We study black holes carrying higher spin charge in AdS3 within the framework
of SL(N, R) x SL(N, R) Chern-Simons theory. Focussing attention on the N=4
case, we explicitly analyze the asymptotic symmetry algebra of black hole
solutions with a chemical potential for spin-four charge. We demonstrate that
the background describes an RG flow between an IR fixed point with W_4 symmetry
and a UV fixed point with W-symmetry associated to a non-principal embedding of
sl(2) in sl(4). Matching Chern-Simons equations with Ward identities of the
deformed CFT, we show that the UV stress tensor is twisted by a certain U(1)
current, and the flow is triggered by an operator with dimension 4/3 at the UV
fixed point. We find independent confirmation of this picture via a consistent
formulation of thermodynamics with respect to this UV fixed point. We further
analyze the thermodynamics of multiple branches of black hole solutions for
N=4,5 and find that the BTZ-branch, dominant at low temperatures, ceases to
exist at higher temperatures following a merger with a thermodynamically
unstable branch. We also point out an interesting connection between the RG
flows and generalized KdV hierarchies.
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Quantum quenches during inflation: We propose a new technique to study fast transitions during inflation, by
studying the dynamics of quantum quenches in an $O(N)$ scalar field theory in
de Sitter spacetime. We compute the time evolution of the system using a
non-perturbative large-$N$ limit approach. We derive the self-consistent mass
equation for several physically relevant transitions of the parameters of the
theory, in a slow motion approximation. Our computations reveal that the
effective mass after the quench evolves in the direction of recovering its
value before the quench, but stopping at a different asymptotic value, in which
the mass squared is strictly positive. Furthermore, we tentatively find
situations in which the effective mass squared can be temporarily negative,
thus breaking the $O(N)$ symmetry of the system for a certain time, only to
then come back to a positive value, restoring the symmetry. We argue the
relevance of our new method in a cosmological scenario.
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Distribution of instanton sizes in a simplified instanton gas model: We investigate the distribution of instanton sizes in the framework of a
simplified model for ensembles of instantons. This model takes into account the
non-diluteness of instantons. The infrared problem for the integration over
instanton sizes is dealt with in a self-consistent manner by approximating
instanton interactions by a repulsive hard core potential. This leads to a
dynamical suppression of large instantons. The characteristic features of the
instanton size distribution are studied by means of analytic and Monte Carlo
methods. In one dimension exact results can be derived. In any dimension we
find a power law behaviour for small sizes, consistent with the semi-classical
results. At large instanton sizes the distribution decays exponentially. The
results are compared with those from lattice simulations.
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Double Field Theory for Generalized $λ$-deformation: We embed the geometries of the generalized $\lambda$-deformations into the
framework of the Double Field Theory.
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On non-supersymmetric stable marginal deformations in AdS$_3$/CFT$_2$: We discuss a continuous family of non-supersymmetric AdS$_3\times
S^3\times{\rm T^4}$ vacua in heterotic and type II supergravities whose
complete Kaluza-Klein spectrum is computed and found to be free from
instabilities. This family is protected as well against some non-perturbative
decay channels, and as such it provides the first candidate for a
non-supersymmetric holographic conformal manifold in 2$d$. We also describe the
operators realising the deformations in the worldsheet and boundary CFT's.
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Manifestly T-Duality Symmetric Matrix Models: We present a new class of matrix models which are manifestly symmetric under
the T-duality transformation of the target space. The models may serve as a
nonperturbative regularization for the T-duality symmetry in continuum string
theory. In particular, it now becomes possible to extract winding modes
explicitly in terms of extended matrix variables.
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Generating Generalized $G_{D-2}$ solutions: We show how one can systematically construct vacuum solutions to Einstein
field equations with $D-2$ commuting Killing vectors in $D>4$ dimensions. The
construction uses Einstein-scalar field seed solutions in 4 dimensions and is
performed both for the case when all the Killing directions are spacelike, as
well as when one of the Killing vectors is timelike. The later case corresponds
to generalizations of stationary axially symmetric solutions to higher
dimensions. Some examples representing generalizations of known higher
dimensional stationary solutions are discussed in terms of their rod structure
and horizon locations and deformations.
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Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with
$SU(2)\times U(1)$ Isometry: We study $N=2$ supersymmetric gauge theories on a large family of squashed
4-spheres preserving $SU(2)\times U(1)\subset SO(4)$ isometry and determine the
conditions under which this background is supersymmetric. We then compute the
partition function of the theories by using localization technique. The results
indicate that for $N=2$ SUSY, including both vector-multiplets and
hypermultiplets, the partition function is independent of the arbitrary
squashing functions as well as of the other supergravity background fields.
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Supersymmetry and deterministic chaos: We show that the fluctuations of the periodic orbits of deterministically
chaotic systems can be captured by supersymmetry, in the sense that they are
repackaged in the contribution of the absolute value of the determinant of the
noise fields, defined by the equations of motion.
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Construction of $θ$-Poincaré Algebras and their Invariants on
$\mathcal{M}_θ$: In the present paper we construct deformations of the Poincar\'e algebra as
representations on a noncommutative spacetime with canonical commutation
relations. These deformations are obtained by solving a set of conditions by an
appropriate ansatz for the deformed Lorentz generator. They turn out to be Hopf
algebras of quantum universal enveloping algebra type with nontrivial
antipodes. In order to present a notion of $\theta$-deformed Minkowski space
$\mathcal{M}_\theta$, we introduce Casimir operators and spacetime invariants
for all deformations obtained.
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Two-loop superstring five-point amplitudes I: Construction via chiral
splitting and pure spinors: The full two-loop amplitudes for five massless states in Type~II and
Heterotic superstrings are constructed in terms of convergent integrals over
the genus-two moduli space of compact Riemann surfaces and integrals of Green
functions and Abelian differentials on the surface. The construction combines
elements from the BRST cohomology of the pure spinor formulation and from
chiral splitting with the help of loop momenta and homology invariance. The
$\alpha' \to 0$ limit of the resulting superstring amplitude is shown to be in
perfect agreement with the previously known amplitude computed in Type~II
supergravity. Investigations of the $\alpha'$ expansion of the Type~II
amplitude and comparisons with predictions from S-duality are relegated to a
first companion paper. A construction from first principles in the RNS
formulation of the genus-two amplitude with five external NS states is
relegated to a second companion paper.
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New higher-spin curvatures in flat space: It was shown that the Lie algebra underlying higher-spin holography admits a
contraction including a Poincar\'e subalgebra in any space-time dimensions. The
associated curvatures, however, do not reproduce upon linearisation those that
are usually employed to formulate the equations of motion of free massless
particles in Minkowski space. We show that, despite this mismatch, the new
linearised curvatures can also be used to describe massless higher-spin fields.
This suggests a new way to build interacting higher-spin gauge theories in
Minkowski space that may admit a holographic description.
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Perturbative decay of anti-branes in flux backgrounds due to space time
instabilities: In this paper we suggest a new source of perturbative decay of the KPV-state,
which might have consequences for the viability of the KKLT-construction. The
results do not rely on any direct enhancement of the decay due to flux
accumulating on the anti-brane in transverse space. Instead, we note that the
system can lower its energy through a sequence of NS5-configurations all the
way to the true vacuum, without encountering a barrier, if we allow for
clumping of screened charge in space time. The clumping can possibly be a
parallel to the Gregory-Laflamme instability of black branes. The results are
obtained at large $p$, but for $p/M$ arbitrarily small. It is furthermore
argued that the results extend to cases of few or single anti-branes where
quantization becomes important. We believe that it is important to investigate
this possible effect further to judge whether there are any fatal consequences.
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TASI Lectures: Introduction to the AdS/CFT Correspondence: This is an introductory review of the AdS/CFT correspondence and of the ideas
that led to its formulation. We show how comparison of stacks of D3-branes with
corresponding supergravity solutions leads to dualities between conformal large
$N$ gauge theories in 4 dimensions and string backgrounds of the form
$AdS_5\times X_5$ where $X_5$ is an Einstein manifold. The gauge invariant
chiral operators of the field theory are in one-to-one correspondence with the
supergravity modes, and their correlation functions at strong `t Hooft coupling
are determined by the dependence of the supergravity action on AdS boundary
conditions. The simplest case is when $X_5$ is a 5-sphere and the dual gauge
theory is the ${\cal N}=4$ supersymmetric SU(N) Yang-Mills theory. We also
discuss D3-branes on the conifold corresponding to $X_5$ being a coset space
$T^{1,1}=(SU(2)\times SU(2))/U(1)$. This background is dual to a certain ${\cal
N}=1$ superconformal field theory with gauge group $SU(N)\times SU(N)$.
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Three-dimensional flux vacua from IIB on co-calibrated G2 orientifolds: We derive the 3D N=1 superpotential for the closed string sector of type IIB
supergravity on toroidal O5 orientifolds with co-calibrated G2 structure and RR
background flux. We find that such compactifications can provide full closed
string moduli stabilization on supersymmetric AdS$_3$ vacua, and once we
include brane-supersymmetry-breaking we also find indication for the existence
of classical 3D de Sitter solutions. The latter however are rather difficult to
reconcile with the shape moduli stabilization and flux quantization. We also
discuss the possibility of achieving scale separation in AdS$_3$ and dS$_3$
vacua, but such effects seems to be hindered by the geometric flux
quantization.
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Non-gaussianity from the trispectrum in general single field inflation: We compute the fourth order action in perturbation theory for scalar and
second order tensor perturbations for a minimally coupled single field
inflationary model, where the inflaton's lagrangian is a general function of
the field's value and its kinetic energy. We obtain the fourth order action in
two gauges, the comoving gauge and the uniform curvature gauge. Using the
comoving gauge action we calculate the trispectrum at leading order in
slow-roll, finding agreement with a previously known result in the literature.
We point out that in general to obtain the correct leading order trispectrum
one cannot ignore second order tensor perturbations as previously done by
others. The next-to-leading order corrections may become detectable depending
on the shape and we provide the necessary formalism to calculate them.
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Wigner's $D$-matrix elements for $SU(3)$ - A Generating Function
Approach: A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is
derived. From this an explicit expression for the individual matrix elements is
obtained in a closed form.
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Topological classes of thermodynamics of the static multi-charge AdS
black holes in gauged supergravities: We investigate, in the framework of the topological approach to black hole
thermodynamics, using the generalized off-shell Helmholtz free energy, the
topological numbers of the static multi-charge AdS black holes in the four- and
five-dimensional gauged supergravities. We find that the topological number of
static charged AdS black holes in gauged supergravity theories are
significantly affected by the number of the electric charge parameters. We also
show that, from the perspective of the thermodynamic topology, the
single-charge AdS black hole in four-dimensional gauged supergravity and the
four-dimensional Reissner-Nordstr\"om-AdS (RN-AdS) black hole belong to
different classes, even though they are both four-dimensional static
single-charge AdS black holes. Moreover, for the four-dimensional static
two-charge AdS black hole and the five-dimensional static single-charge AdS
black hole in gauged supergravity theory, we find a new property unique to
them, namely that different values of the electric charge parameters can
influence their topological number. In addition, we demonstrate that, in gauged
supergravity theory, for the four-dimensional two-charge static AdS black hole
when both two electric charge parameters take smaller values and the
five-dimensional single-charge static AdS black hole when the electric charge
parameter takes a smaller value, have two different topological numbers at
different fixed temperatures, which constitute the first two counterexamples to
the conjecture that a black hole can only have one definite topological number.
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Reparametrising the Skyrme Model using the Lithium-6 Nucleus: The minimal energy B=6 solution of the Skyrme model is a static soliton with
$D_{4d}$ symmetry. The symmetries of the solution imply that the quantum
numbers of the ground state are the same as those of the Lithium-6 nucleus.
This identification is considered further by obtaining expressions for the mean
charge radius and quadrupole moment, dependent only on the Skyrme model
parameters $e$ (a dimensionless constant) and $F_\pi$ (the pion decay
constant). The optimal values of these parameters have often been deliberated
upon, and we propose, for $B>2$, changing them from those which are most
commonly accepted. We obtain specific values for these parameters for B=6, by
matching with properties of the Lithium-6 nucleus. We find further support for
the new values by reconsidering the $\alpha$-particle and deuteron as quantized
B=4 and B=2 Skyrmions.
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Higher order contributions to the effective action of N=4 super
Yang-Mills: The one-loop low-energy effective action for non-Abelian N=4 supersymmetric
Yang-Mills theory is computed to order $F^6$ by use of heat kernel techniques
in N=1 superspace. At the component level, the $F^5$ terms are found to be
consistent with the form of the non-Abelian Born-Infeld action computed to this
order by superstring methods. The $F^6$ terms will be of importance for
comparison with superstring calculations.
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The $\mathcal{N}=3$ Weyl Multiplet in Four Dimensions: The main ingredient for local superconformal methods is the multiplet of
gauge fields: the Weyl multiplet. We construct the transformations of this
multiplet for $\mathcal{N}=3$, $D = 4$. The construction is based on a
supersymmetry truncation from the $\mathcal{N}=4$ Weyl multiplet, on coupling
with a current multiplet, and on the implementation of a soft algebra at the
nonlinear level, extending su$(2, 2|3)$. This is the first step towards a
superconformal calculus for $\mathcal{N}=3$, $D = 4$.
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On Scalar Electromagnetism in Phase Space: In this paper the interaction of a scalar field and the electromagnetic field
in phase space is analyzed. The scattering process is calculated up to first
order in the Planck constant which is obtained by an expansion of the Moyal
product in phase space. The transition amplitude is calculated in the same
context.
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How to Succeed at Witten Diagram Recursions without Really Trying: Witten diagrams are basic objects for studying dynamics in AdS space, and
also play key roles in the analytic functional bootstrap. However, these
diagrams are notoriously hard to evaluate, making it extremely difficult to
search for recursion relations among them. In this note, we present simple
methods to obtain recursion relations for exchange Witten diagrams from
conformal block recursion relations. We discover a variety of new relations,
including the dimensional reduction formulae for exchange Witten diagrams. In
particular, we find a five-term recursion relation relating exchange Witten
diagrams in $d$ and $d-2$ dimensions. This gives the holographic analogue of a
similar formula for conformal blocks due to Parisi-Sourlas supersymmetry. We
also extend the analysis to two-point functions in CFTs with conformal
boundaries, and obtain similar results.
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BPS states in (2,0) theory on R x T5: We consider $(2, 0)$ theory on a space-time of the form $R \times T^5$, where
the first factor denotes time, and the second factor is a flat spatial
five-torus. In addition to their energy, quantum states are characterized by
their spatial momentum, 't Hooft flux, and $Sp (4)$ $R$-symmetry
representation. The momentum obeys a shifted quantization law determined by the
't Hooft flux. By supersymmetry, the energy is bounded from below by the
magnitude of the momentum. This bound is saturated by BPS states, that are
annihilated by half of the supercharges. The spectrum of such states is
invariant under smooth deformations of the theory, and can thus be studied by
exploiting the interpretation of $(2, 0)$ theory as an ultra-violet completion
of maximally supersymmetric Yang-Mills theory on $R \times T^4$. Our main
example is the $A$-series of $(2,0)$ theories, where such methods allow us to
study the spectrum of BPS states for many values of the momentum and the 't
Hooft flux. In particular, we can describe the $R$-symmetry transformation
properties of these states by determining the image of their $Sp (4)$
representation in a certain quotient of the $Sp (4)$ representation ring.
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Getting superstring amplitudes by degenerating Riemann surfaces: We explicitly show how the chiral superstring amplitudes can be obtained
through factorisation of the higher genus chiral measure induced by suitable
degenerations of Riemann surfaces. This powerful tool also allows to derive, at
any genera, consistency relations involving the amplitudes and the measure. A
key point concerns the choice of the local coordinate at the node on degenerate
Riemann surfaces that greatly simplifies the computations. As a first
application, starting from recent ansaetze for the chiral measure up to genus
five, we compute the chiral two-point function for massless Neveu-Schwarz
states at genus two, three and four. For genus higher than three, these
computations include some new corrections to the conjectural formulae appeared
so far in the literature. After GSO projection, the two-point function vanishes
at genus two and three, as expected from space-time supersymmetry arguments,
but not at genus four. This suggests that the ansatz for the superstring
measure should be corrected for genus higher than four.
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Catalysis of Black Holes/Wormholes Formation in High Energy Collisions: We discuss various mechanisms of catalysis of black holes/wormholes (BH/WH)
formation in particles collisions. The current paradigm suggests that BH/WH
formation in particles collisions will happen when center of mass energies of
colliding particles is sufficiently above the Planck scale (the transplanckian
region). To estimate the BH/WH production we use the classical geometrical
cross section. We confirm the classical geometrical cross section of the BH
production reconsidering the process of two transplanckian particles collision
in the rest frame of one of incident particles. This consideration permits to
use the standard Thorne's hoop conjecture for a matter compressed into a region
to prove a variant of the conjecture dealing with a total amount of compressed
energy in the case of colliding particles. We calculate geometrical cross
sections for different processes and for different background, in particular,
for (A)dS. We show that results are in agreement with closed trapped surface
(CTS) estimations though there are no general theorems providing that the BH
formation follows from CTS's formation. We show that the process of BH
formation is catalyzed by the negative cosmological constant and by a
particular scalar matter, namely dilaton, while it is relaxed by the positive
cosmological constant and at a critical value just turns off. Also we note that
the cross section is sensible to the compactification of extra dimensions and
to the particular brane model.
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Seiberg-Witten theory as a Fermi gas: We explore a new connection between Seiberg-Witten theory and quantum
statistical systems by relating the dual partition function of SU(2) Super
Yang-Mills theory in a self-dual Omega-background to the spectral determinant
of an ideal Fermi gas. We show that the spectrum of this gas is encoded in the
zeroes of the Painleve III tau function. In addition we find that the Nekrasov
partition function on this background can be expressed as an O(2) matrix model.
Our construction arises as a four-dimensional limit of a recently proposed
conjecture relating topological strings and spectral theory. In this limit, we
provide a mathematical proof of the conjecture for the local P1xP1 geometry.
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T-Dual Cosmological Solutions of Double Field Theory II: In this paper we present cosmological solutions of Double Field Theory in the
supergravity frame and in the winding frame which are related via T-duality. In
particular, we show that the solutions can be viewed without the need of
complexifying the cosmological scale factor.
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From Form Factors to Correlation Functions: The Ising Model: Using exact expressions for the Ising form factors, we give a new very simple
proof that the spin-spin and disorder-disorder correlation functions are
governed by the Painlev\'e III non linear differential equation. We also show
that the generating function of the correlation functions of the descendents of
the spin and disorder operators is a $N$-soliton, $N\to\infty$, $\tau$-function
of the sinh-Gordon hierarchy. We discuss a relation of our approach to
isomonodromy deformation problems, as well as further possible generalizations.
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Thermodynamics and Stability of Hyperbolic Charged Black Holes: In AdS space the black hole horizon can be a hypersurface with a positive,
zero or negative constant curvature, resulting in different horizon topology.
Thermodynamics and stability of black holes in AdS spaces are quite different
for different horizon curvatures. In this paper we study thermodynamics and
stability of hyperbolic charged black holes with negative constant curvature
horizon in the grand canonical ensemble and canonical ensemble, respectively.
They include hyperbolic Reissner-Nordstr\"om black holes in arbitrary
dimensions and hyperbolic black holes in the D=5,4,7 gauged supergravities. It
is found that the associated Gibbs free energies are always negative, which
implies that these black hole solutions are globally stable and black hole
phase is dominant in the grand canonical ensemble, but there is a region in the
phase space where black hole is not locally thermodynamical stable with a
negative heat capacity for a given gauge potential. In the canonical ensemble,
the Helmholtz free energies are not always negative and heat capacities with
fixed electric charge are not always positive, which indicates that the
Hawking-Page phase transition may happen and black holes are not always locally
thermodynamical stable.
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Upper bound of the charge diffusion constant in holography: We investigate the upper bound of charge diffusion constant in holography.
For this purpose, we apply the conjectured upper bound proposal related to the
equilibration scales ($\omega_{\text{eq}}, k_{\text{eq}}$) to the
Einstein-Maxwell-Axion model. ($\omega_{\text{eq}}, k_{\text{eq}}$) is defined
as the collision point between the diffusive hydrodynamic mode and the first
non-hydrodynamic mode, giving rise to the upper bound of the diffusion constant
$D$ at low temperature $T$ as $D = \omega_{\text{eq}}/k_{\text{eq}}^2$. We show
that the upper bound proposal also works for the charge diffusion and
($\omega_{\text{eq}}, k_{\text{eq}}$), at low $T$, is determined by $D$ and the
scaling dimension $\Delta(0)$ of an infra-red operator as $(\omega_{\text{eq}},
\, k_{\text{eq}}^2) \,=\, (2 \pi T \Delta(0) \,, \omega_{\text{eq}}/D)$, as for
other diffusion constants. However, for the charge diffusion, we find that the
collision occurs at real $k_{\text{eq}}$, while it is complex for other
diffusions. In order to examine the universality of the conjectured upper
bound, we also introduce a higher derivative coupling to the
Einstein-Maxwell-Axion model. This coupling is particularly interesting since
it leads to the violation of the \textit{lower} bound of the charge diffusion
constant so the correction may also have effects on the \textit{upper} bound of
the charge diffusion. We find that the higher derivative coupling does not
affect the upper bound so that the conjectured upper bound would not be easily
violated.
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Scalar mass stability bound in a simple Yukawa-theory from
renormalisation group equations: Functional Renormalisation Group (FRG) equations are constructed for a simple
Yukawa-model with discrete chiral symmetry, including also the effect of a
nonzero composite fermion background beyond the conventional scalar condensate.
The evolution of the effective potential of the model, generically depending on
two invariants, is explored with help of power series expansions. Systematic
investigation of the effect of a class of irrelevant operators on the lower
(stability) bound allows a non-perturbative extension of the maximal cut-off
value consistent with any given mass of the scalar field.
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Kaluza-Klein towers for spinors in warped spaces: All the boundary conditions compatible with the reduction of a five
dimensional spinor field of bulk mass $M$ in a compactified warped space to a
four dimensional brane are derived from the hermiticity conditions of the
relevant operator. The possible presence of metric singularities is taken into
account. Examples of resulting Kaluza-Klein spinor towers are given for a
representative set of values for the basic parameters of the model and of the
parameters describing the allowed boundary conditions, within the hypothesis
that there exists one-mass-scale-only, the Planck mass. In many cases, the
lowest mass in the tower is small and very sensitive to the parameters while
the other masses are much higher and become more regularly spaced. In these
cases, if a basic fermion of the standard model (lepton or quark) happens to be
the lowest mass of a Kaluza-Klein tower, the other masses would be much larger
and weakly dependent on the fermion which defines the tower.
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A Note on the evolution of cosmic string/superstring networks: In the context of brane world scenario, cosmic superstrings can be formed in
D-brane annihilation at the end of the brane inflationary era. The cosmic
superstring network has a scaling solution and the characteristic scale of the
network is proportional to the square root of the reconnection probability.
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Noether Identities, $β$-functions and symmetries in DFT: Given the $\beta$ functions of the closed string sigma model up to one loop
in $\alpha'$, the effective action implement the condition $\beta=0$ to
preserve conformal symmetry at quantum level. One of the more powerful and
striking results of string theory is that this effective action contains
Einstein gravity as an emergent dynamics in space-time. We show from the
$\beta$ functions and its relation with the equations of motion of the
effective action, that the differential identities [1] are the Noether
identities associated with the effective action and its gauge symmetries. From
here, we reconstruct the gauge and space time symmetries of the effective
action. In turn, we can show that the differential identities are the
contracted Bianchi identities of the the field strength $H$ and Riemann tensor
$R$. Next, we apply the same ideas to DFT. Taking as starting point that the
generalized $\beta$ functions in DFT are proportional to the equations of
motion, we construct the generalized differential identities in DFT. Relating
the Noether identities with the contracted Bianchi identities of DFT, we were
able to reconstruct the generalized gauge and space time symmetries. Finally,
we recover the original $\beta$ functions, effective action, differential
identities, and symmetries when we turn off the $\tilde x$ space time
coordinates from DFT.
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Generating asymptotically plane wave spacetimes: In an attempt to study asymptotically plane wave spacetimes which admit an
event horizon, we find solutions to vacuum Einstein's equations in arbitrary
dimension which have a globally null Killing field and rotational symmetry. We
show that while such solutions can be deformed to include ones which are
asymptotically plane wave, they do not posses a regular event horizon. If we
allow for additional matter, such as in supergravity theories, we show that it
is possible to have extremal solutions with globally null Killing field, a
regular horizon, and which, in addition, are asymptotically plane wave. In
particular, we deform the extremal M2-brane solution in 11-dimensional
supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane
wave times a real line.
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Non-Supersymmetric Vacua and Self-Adjoint Extensions: Internal intervals spanned by finite ranges of a conformal coordinate $z$ and
terminating at a pair of singularities are a common feature of many string
compactifications with broken supersymmetry. The squared masses emerging in
lower-dimensional Minkowski spaces are then eigenvalues of Schr\"odinger-like
operators, whose potentials have double poles at the ends of the intervals. For
one-component systems, the possible self-adjoint extensions of Schr\"odinger
operators are described by points in $AdS_3 \times S^1$, and those
corresponding to independent boundary conditions at the ends of the intervals
by points on the boundary of $AdS_3$. The perturbative stability of
compactifications to Minkowski space time depends, in general, on these choices
of self-adjoint extensions. We apply this setup to the orientifold vacua driven
by the ``tadpole potential'' $V=T \ e^{\,\frac{3}{2}\,\phi}$ and find, in nine
dimensions, a massive scalar spectrum, a unique choice of boundary conditions
with stable tensor modes and a massless graviton, and a wide range of choices
leading to massless and/or massive vector modes.
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Quantum theory of three-dimensional de Sitter space: We sketch the construction of a quantum model of 3 dimensional de Sitter
space, based on the Covariant Entropy Principle and the observation that
semi-classical physics suggests the possibility of a consistent theory of a
finite number of unstable massive particles with purely gravitational
interactions. Our model is holographic, finite, unitary, causal, plausibly
exhibits fast scrambling, and qualitatively reproduces features of
semi-classical de Sitter physics. In an appendix we outline some calculations
that might lead to further tests of the model.
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On General Off-Shell Representations of Worldline (1D) Supersymmetry: Every finite-dimensional unitary representation of the N-extended worldline
supersymmetry without central charges may be obtained by a sequence of
differential transformations from a direct sum of minimal Adinkras, simple
supermultiplets that are identifiable with representations of the Clifford
algebra. The data specifying this procedure is a sequence of subspaces of the
direct sum of Adinkras, which then opens an avenue for classification of the
continuum of so constructed off-shell supermultiplets.
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Binary Cosmic Strings: The properties of cosmic strings have been investigated in detail for their
implications in early-universe cosmology. Although many variations of the basic
structure have been discovered, with implications for both the microscopic and
macroscopic properties of cosmic strings, the cylindrical symmetry of the
short-distance structure of the string is generally unaffected. In this paper
we describe some mechanisms leading to an asymmetric structure of the string
core, giving the defects a quasi-two-dimensional character. We also begin to
investigate the consequences of this internal structure for the microscopic and
macroscopic physics.
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Horndeski genesis: consistency of classical theory: Genesis within the Horndeski theory is one of possible scenarios for the
start of the Universe. In this model, the absence of instabilities is obtained
at the expense of the property that coefficients, serving as effective Planck
masses, vanish in the asymptotics $t\rightarrow -\infty$, which signalizes the
danger of strong coupling and inconsistency of the classical treatment. We
investigate this problem in a specific model and extend the analysis of cubic
action for perturbations (arXiv:2003.01202) to arbitrary order. Our study is
based on power counting and dimensional analysis of the higher order terms. We
derive the latter, find characteristic strong coupling energy scales and obtain
the conditions for the validity of the classical description. Curiously, we
find that the strongest condition is the same as that obtained in already
examined cubic case.
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Indispensability of Ghost Fields and Extended Hamiltonian Formalism in
Axial Gauge Quantization of Gauge Fields: It is shown that ghost fields are indispensable in deriving well-defined
antiderivatives in pure space-like axial gauge quantizations of gauge fields.
To avoid inessential complications we confine ourselves to noninteracting
abelian fields and incorporate their quantizations as a continuous deformation
of those in light-cone gauge. We attain this by constructing an axial gauge
formulation in auxiliary coordinates $x^{\mu}= (x^+,x^-,x^1,x^2)$, where
$x^+=x^0{\rm sin}{\theta}+x^3{\rm cos}{\theta}, x^-=x^0{\rm
cos}{\theta}-x^3{\rm sin}{\theta}$ and $x^+$ and $A_-=A^0{\rm cos}
{\theta}+A^3{\rm sin}{\theta}=0$ are taken as the evolution parameter and the
gauge fixing condition, respectively. We introduce $x^-$-independent residual
gauge fields as ghost fields and accomodate them to the Hamiltonian formalism
by applying McCartor and Robertson's method. As a result, we obtain conserved
translational generators $P_{\mu}$, which retain ghost degrees of freedom
integrated over the hyperplane $x^-=$ constant. They enable us to determine
quantization conditions for the ghost fields in such a way that commutation
relations with $P_{\mu}$ give rise to the correct Heisenberg equations. We show
that regularizing singularities arising from the inversion of a hyperbolic
Laplace operator as principal values, enables us to cancel linear divergences
resulting from $({\partial}_-)^{-2}$ so that the Mandelstam- Leibbrandt form of
gauge field propagator can be derived. It is also shown that the pure
space-like axial gauge formulation in ordinary coordinates can be derived in
the limit ${\theta}\to\frac{\pi}{2}-0$ and that the light-cone axial gauge
formulation turns out to be the case of ${\theta}=\frac{\pi}{4}$.
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Veneziano Amplitude of Vasiliev Theory: We compute the four-point function of scalar operators in CFTs with weakly
broken higher spin symmetry at arbitrary 't Hooft coupling. We use the known
three-point functions in these theories, the Lorentzian OPE inversion formula
and crossing to fix the result up to the addition of three functions of the
cross ratios. These are given by contact Witten diagrams in AdS and manifest
non-analyticity of the OPE data in spin. We use Schwinger-Dyson equations to
show that such terms are absent in the large $N$ Chern-Simons matter theories.
The result is that the OPE data is analytic in spin up to $J=0$.
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From state distinguishability to effective bulk locality: We provide quantitative evidence that the emergence of an effective notion of
spacetime locality in black hole physics is due to restricting to the subset of
observables that are unable to resolve black hole microstates from the maxi-
mally entangled state. We identify the subset of observables in the full
quantum theory that can distinguish microstates, and argue that any measurement
of such observables involves either long times or large energies, both
signaling the breaking down of effective field theory where locality is
manifest. We discuss some of the implications of our results for black hole
complementarity and the existence of black hole interiors.
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On the zero of the fermion zero mode: We argue that the fermionic zero mode in non-trivial gauge field backgrounds
must have a zero. We demonstrate this explicitly for calorons where its
location is related to a constituent monopole. Furthermore a topological
reasoning for the existence of the zero is given which therefore will be
present for any non-trivial configuration. We propose the use of this property
in particular for lattice simulations in order to uncover the topological
content of a configuration.
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Solitons on Branes: We examine the possibility that gauge field configurations on stacks of
parallel Dp branes support topological solitons. We give an exhaustive list of
possible soliton charges for p<7. We also discuss how configurations carrying
the soliton charges can be constructed from intersecting branes.
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Type II and heterotic one loop string effective actions in four
dimensions: We analyze the reduction to four dimensions of the R^4 terms which are part
of the ten-dimensional string effective actions, both at tree level and one
loop. We show that there are two independent combinations of R^4 present, at
one loop, in the type IIA four dimensional effective action, which means they
both have their origin in M-theory. The d=4 heterotic effective action also has
such terms. This contradicts the common belief thathere is only one R^4 term in
four-dimensional supergravity theories, given by the square of the Bel-Robinson
tensor. In pure N=1 supergravity this new R^4 combination cannot be directly
supersymmetrized, but we show that, when coupled to a scalar chiral multiplet
(violating the U(1) $R$-symmetry), it emerges in the action after elimination
of the auxiliary fields.
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A Counter-Example to a Putative Classification of 1-Dimensional,
N-extended Supermultiplets: We present a counter-example to the recent claim that supermultiplets of
N-extended supersymmetry with no central charge and in 1-dimension are
specified unambiguously by providing the numbers of component fields in all
available engineering dimensions within the supermultiplet.
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The moduli space of hyper-K{ä}hler four-fold compactifications: I discuss some aspects of the moduli space of hyper-K{\"a}hler four-fold
compactifications of type II and ${\cal M}$- theories. The dimension of the
moduli space of these theories is strictly bounded from above. As an example I
study Hilb$^2(K3)$ and the generalized Kummer variety $K^2(T^4)$. In both cases
RR-flux (or $G$-flux in ${\cal M}$-theory) must be turned on, and we show that
they give rise to vacua with ${\cal N}=2$ or ${\cal N}=3$ supersymmetry upon
turning on appropriate fluxes. An interesting subtlety involving the symmetric
product limit $S^2(K3)$ is pointed out.
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Narain CFTs and error-correcting codes on finite fields: We construct Narain CFTs from self-dual codes on the finite field $F_p$
through even self-dual lattices for any prime $p>2$. Using this correspondence,
we can relate the spectral gap and the partition function of the CFT to the
error correction capability and the extended enumerator polynomial of the code.
In particular, we calculate specific spectral gaps of CFTs constructed from
codes and compare them with the largest spectral gap among all Narain CFTs.
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On tree amplitudes with gluons coupled to gravitons: In this paper, we study the tree amplitudes with gluons coupled to gravitons.
We first study the relations among the mixed amplitudes. With BCFW on-shell
recursion relation, we will show the color-order reversed relation,
$U(1)$-decoupling relation and KK relation hold for tree amplitudes with gluons
coupled to gravitons. We then study the disk relation which expresses mixed
amplitudes by pure gluon amplitudes. More specifically we will prove the disk
relation for mixed amplitudes with gluons coupled to one graviton. Using the
disk relation and the properties of pure gluon amplitudes, the color-order
reversed relation, $U(1)$-decoupling relation and KK relation for mixed
amplitudes can also be proved. Finally, we give some brief discussions on
BCJ-like relation for mixed amplitudes.
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The deconfinement phase transition as an Aharonov-Bohm effect: A subjective and incomplete list of interesting and unique features of the
deconfinement phase transition is presented. Furthermore a formal similarity of
the density matrix of the Aharonov-Bohm system and QCD is mentioned, as well.
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Small Schwarzschild de Sitter black holes, quantum extremal surfaces and
islands: We study 4-dimensional Schwarzschild de Sitter black holes in the regime
where the black hole mass is small compared with the de Sitter scale. Then the
de Sitter temperature is very low compared with that of the black hole and we
study the black hole, approximating the ambient de Sitter space as a frozen
classical background. We consider distant observers in the static diamond, far
from the black hole but within the cosmological horizon. Using 2-dimensional
tools, we find that the entanglement entropy of radiation exhibits linear
growth in time, indicative of the information paradox for the black hole.
Self-consistently including an appropriate island emerging at late times near
the black hole horizon leads to a reasonable Page curve. There are close
parallels with flat space Schwarzschild black holes in the regime we consider.
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Study of Asymptotic Free Scalar Field Theories from Adaptive
Perturbation Method: We focus on the behavior of (2+1)d $\lambda\phi^4$ and (5+1)d $\lambda\phi^3$
or $\lambda|\phi|^3$ theories in different regimes and compare the results
obtained from the adaptive perturbation method with those obtained from lattice
simulation. These theories are simple models that exhibit asymptotic freedom,
which is a property that is also observed in more complex theories such as QCD,
which describes the strong interaction between quarks and gluons. Asymptotic
freedom is an important feature of these theories because it allows for a
perturbative treatment of interactions at high energies. However, the standard
perturbation scheme breaks down in the presence of strong interactions, and the
adaptive perturbation method, which involves resuming the Feynman diagrams, is
more suitable for studying these interactions. Our research involves comparing
the perturbation result to lattice simulation. In the case of the $\phi^3$
theory, there is no stable vacuum, so we explore evidence from the $|\phi|^3$
theory instead. Our results appear to show that resummation improves the strong
coupling result for both the $\lambda\phi^4$ and $\lambda|\phi|^3$ theories.
Additionally, we improve the resummation method for the three-point coupling
vertex and study the RG flow to analyze the resummation contribution and
theoretical properties.
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Quantum Gravity with Minimal Assumptions: The purpose is to construct the quantum field theory including gravity, based
on physical assumptions as few as possible. Up to now, the work by Prof. Steven
Weinberg probably suits this purpose the most. Though the purpose is difficult
to reach, my recent preprint was interested in an exceptional case caused by
singularity. Therefore, I'd like to explain the motivations and possible
applications of the preprint.
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Some Features of Blown-Up Nonlinear $σ$-Models: In terms of the gauged nonlinear $\sigma$-models, we describe some results
and implications of solving the following problem: Given a smooth symplectic
manifold as target space with a quasi-free Hamiltonian group action, perform
the symplectic blowing up of the point singularity and identify the blow-up
modes in the corresponding (gauged) $\sigma$-model. Both classical and quantum
aspects of the construction are explained, along with illustrating examples
from the toric projective space and the K\"ahler manifold. We also discuss
related problems such as the origin of Mirror symmetry and the quantum
cohomologies.(Talk to be given at ICHEP94, Glasgow, July 20-27.)
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Physical states of dyons: It is shown that physical states of a non-abelian Yang-Mills-Higgs dyon are
invariant under large gauge transformations that do not commute with its
magnetic field. This result is established within an enlarged Hamiltonian
formalism where surface terms are kept as dynamical variables. These additional
variables are parameters of large gauge transformations, and are potential
collective coordinates for the quantization of the monopole. Our result implies
that there are no physical effects associated to some large gauge
transformations and therefore their parameters should not be counted as
collective coordinates.
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Universal chaotic dynamics from Krylov space: Krylov complexity measures the spread of the wavefunction in the Krylov
basis, which is constructed using the Hamiltonian and an initial state. We
investigate the evolution of the maximally entangled state in the Krylov basis
for both chaotic and non-chaotic systems. For this purpose, we derive an
Ehrenfest theorem for the Krylov complexity, which reveals its close relation
to the spectrum. Our findings suggest that neither the linear growth nor the
saturation of Krylov complexity is necessarily associated with chaos. However,
for chaotic systems, we observe a universal rise-slope-ramp-plateau behavior in
the transition probability from the initial state to one of the Krylov basis
states. Moreover, a long ramp in the transition probability is a signal for
spectral rigidity, characterizing quantum chaos. Also, this ramp is directly
responsible for the late-time peak of Krylov complexity observed in the
literature. On the other hand, for non-chaotic systems, this long ramp is
absent. Therefore, our results help to clarify which features of the wave
function time evolution in Krylov space characterize chaos. We exemplify this
by considering the Sachdev-Ye-Kitaev model with two-body or four-body
interactions.
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Building Blocks for Generalized Heterotic/F-theory Duality: In this note we propose a generalization of heterotic/F-theory duality. We
introduce a set of non-compact building blocks which we glue together to reach
compact examples of generalized duality pairs. The F-theory building blocks
consist of non-compact elliptically fibered Calabi-Yau fourfolds which also
admit a K3 fibration. The compact elliptic model obtained by gluing need not
have a globally defined K3 fibration. By replacing the K3 fiber of each
F-theory building block with a T^2, we reach building blocks in a heterotic
dual vacuum which includes a position dependent dilaton and three-form flux.
These building blocks are glued together to reach a heterotic flux background.
We argue that in these vacua, the gauge fields of the heterotic string become
localized, and remain dynamical even when gravity decouples. This enables a
heterotic dual for the hyperflux GUT breaking mechanism which has recently
figured prominently in F-theory GUT models. We illustrate our general proposal
with some explicit examples.
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Defects and Quantum Seiberg-Witten Geometry: We study the Nekrasov partition function of the five dimensional U(N) gauge
theory with maximal supersymmetry on R^4 x S^1 in the presence of codimension
two defects. The codimension two defects can be described either as monodromy
defects, or by coupling to a certain class of three dimensional quiver gauge
theories on R^2 x S^1. We explain how these computations are connected with
both classical and quantum integrable systems. We check, as an expansion in the
instanton number, that the aforementioned partition functions are
eigenfunctions of an elliptic integrable many-body system, which quantizes the
Seiberg-Witten geometry of the five-dimensional gauge theory.
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Spacetime and Fields, a Quantum Texture: We report on joint work, past and in progress, with K.Fredenhagen and with
J.E,Roberts, on the quantum structure of spacetime in the small which is
dictated by the principles of Quantum Mechanics and of General Relativity; we
comment on how these principles point to a deep link between coordinates and
fields. This is an expanded version of a lecture delivered at the 37th Karpacz
School in Theoretical Physics, February 2001.
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Self-Dual Effective Action of N=4 Super-Yang Mills: The full low energy effective action of N=4 SYM is believed to be self-dual.
Starting with the first two leading terms in a momentum expansion of this
effective action, we perform a duality transformation and find the conditions
for self-duality. These determine some of the higher order terms. We compare
the effective action of N=4 SYM with the probe-source description of type II_B
D3-branes in the AdS_5 \times S_5 background. We find agreement up to six
derivative terms if we identify the separation of the 3-branes with a
redefinition of the gauge scalar that involves the gauge field strength.
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The Cosmological Constant Problem: Why it's hard to get Dark Energy from
Micro-physics: These notes present a brief introduction to `naturalness' problems in
cosmology, and to the Cosmological Constant Problem in particular. The main
focus is the `old' cosmological constant problem, though the more recent
variants are also briefly discussed. Several notions of naturalness are
defined, including the closely related ideas of technical naturalness and `t
Hooft naturalness, and it is shown why these naturally arise when cosmology is
embedded within a framework --- effective field theories --- that efficiently
captures what is consistent with what is known about the physics of smaller
distances. Some care is taken to clarify conceptual issues, such as the
relevance or not of quadratic divergences, about which some confusion has
arisen over the years. A set of minimal criteria are formulated against which
proposed solutions to the problem can be judged, and a brief overview made of
the general limitations of most of the approaches. A somewhat more in-depth
discussion is provided of what I view as the most promising approach. These
notes are aimed at graduate students with a basic working knowledge of quantum
field theory and cosmology, but with no detailed knowledge of particle physics.
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Mixed (open/closed) N=(2,2) string theory as an integrable deformation
of self-duality: The exact effective field equations of motion, corresponding to the
perturbative mixed theory of open and closed (2,2) world-sheet supersymmetric
strings, are investigated. It is shown that they are only integrable in the
case of an abelian gauge group. The gravitational equations are then stationary
with respect to the Born-Infeld-type effective action.
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Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs: By applying the recently proposed (3D rank-0 $\mathcal{N}$=4
SCFT)/(non-unitary TQFTs) correspondence to S-fold SCFTs, we construct an
exotic class of non-unitary TQFTs labelled by an integer $k\geq 3$. The SCFTs
are obtained by gauging diagonal $SU(2)$ subgroup of $T[SU(2)]$ theory with
Chern-Simons level $k$. We give the explicit expression for modular data, $S$
and $T$ matrices, of the TQFTs. When $k=4m^2+4m+3$ with an integer $m\geq 1$,
the modular data (modulo a decoupled semion) is identical to a non-unitary
Haagerup-Izumi modular data. Thus, we give a physical realization of the exotic
non-unitary modular data as well as its generalization using an exotic class of
SCFTs.
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Magnetic Monopoles, Duality, and Supersymmetry: These notes present a pedagogical introduction to magnetic monopoles and
exact electromagnetic duality in supersymmetric gauge theories. They are based
on lectures given at the 1995 Trieste Summer School in High Energy Physics and
Cosmology and at the 1995 Busstepp Summer School at Cosener's House.
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Invariants and divergences in half-maximal supergravity theories: The invariants in half-maximal supergravity theories in D=4,5 are discussed
in detail up to dimension eight (e.g. R^4). In D=4, owing to the anomaly in the
rigid SL(2,R) duality symmetry, the restrictions on divergences need careful
treatment. In pure N=4 supergravity, this anomalous symmetry still implies
duality invariance of candidate counterterms at three loops. Provided one makes
the additional assumption that there exists a full 16-supercharge off-shell
formulation of the theory, counterterms at L>1 loops would also have to be
writable as full-superspace integrals. At the three-loop order such a
duality-invariant full-superspace integral candidate counterterm exists, but
its duality invariance is marginal in the sense that the full-superspace
counter-Lagrangian is not itself duality-invariant. We show that such marginal
invariants are not allowable as counterterms in a 16-supercharge off-shell
formalism. It is not possible to draw the same conclusion when vector
multiplets are present because of the appearance of F^4 terms in the SL(2,R)
anomaly. In D=5 there is no one-loop anomaly in the shift invariance of the
dilaton, and we argue that this implies finiteness at two loops, again subject
to the assumption that 16 supercharges can be preserved off-shell.
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Black holes with halos: We present new AdS4 black hole solutions in N = 2 gauged supergravity coupled
to vector and hypermultiplets. We focus on a particular consistent truncation
of M-theory on the homogeneous Sasaki-Einstein seven-manifold M111,
characterized by the presence of one Betti vector multiplet. We numerically
construct static and spherically symmetric black holes with electric and
magnetic charges, corresponding to M2 and M5 branes wrapping non-contractible
cycles of the internal manifold. These configurations have nonzero temperature
and are moreover surrounded by a massive vector field halo. For these solutions
we verify the first law of black hole mechanics and we analyze the
thermodynamics and phase transitions in the canonical ensemble, interpreting
the process in the corresponding dual field theory.
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Sigma models with off-shell N=(4,4) supersymmetry and noncommuting
complex structures: We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric
nonlinear sigma models written in terms of semichiral superfields. We find that
some of these models have additional off-shell supersymmetry. The (4,4)
supersymmetry introduces geometrical structures on the target-space which are
conveniently described in terms of Yano f-structures and Magri-Morosi
concomitants. On-shell, we relate the new structures to the known
bi-hypercomplex structures.
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Dashen's Phenomenon in Gauge Theories with Spontaneously Broken Chiral
Symmetries: We examine Dashen's phenomenon in the Leutwyler--Smilga regime of QCD with
any number of colors and quarks in either the fundamental or adjoint
representations of the gauge group. In this limit, the theories only depend on
simple combinations of quark masses, volume, chiral condensate and vacuum
angle. Based upon this observation, we derive simple expressions for the chiral
condensate and the topological density and show that they are in fact related.
By examining the zeros of the various partition functions, we elucidate the
mechanism leading to Dashen's phenomena in QCD.
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Toward NS5 Branes on the Resolved Cone over Y^{p,q}: Motivated by recent developments in the understanding of the connection
between five branes on resolved geometries and the corresponding
generalizations of complex deformations in the context of the warped resolved
deformed conifold, we consider the construction of five branes solutions on the
resolved cone over Y^{p,q} spaces. We establish the existence of supersymmetric
five branes solutions wrapped on two-cycles of the resolved cone over Y^{p,q}
in the probe limit. We then use calibration techniques to begin the
construction of fully back-reacted five branes; we present an Ansatz and the
corresponding equations of motion. Our results establish a detailed framework
to study back-reacted five branes wrapped on the resolved cone over Y^{p,q} and
as a first step we find explicit solutions and construct an asymptotic
expansion with the expected properties.
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Generalized Schroedinger representation in BRST-quantization: An analysis of the state space in the BRST--quantization in the Schroedinger
representation is performed on the basis of the results obtained earlier in the
framework of the Fock space representation. It is shown that to get
satisfactory results it is necessary to have from the very beginning a
meaningful definition of the total state space.
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Schwarzschild-AdS Black Holes in N=2 Geometric Flux Compactification: We present AdS black hole solutions in four-dimensional N=2 gauged
supergravity with the universal hypermultiplet. Here the axion field in this
multiplet is dualized to a two-form field. This system is derived from
ten-dimensional massive type IIA theory compactified on nearly-Kahler manifold
in the presence of geometric fluxes and RR-fluxes. In this work we focus on the
simplest coset space G_2/SU(3). Imposing the covariantly constant condition on
all scalar fields, we obtain AdS black hole solutions with vanishing
electromagnetic charges and arbitrary mass parameter.
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Dynamical supersymmetry analysis of conformal invariance for
superstrings in type IIB R-R plane-wave: In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet
conformal invariance for superstrings in type IIB R-R plane-wave in
semi-light-cone gauge. Here we give further justification to the results found
in that work through alternative arguments using dynamical supersymmetries. We
show that by using the susy algebra the same quantum definition of the
energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi
identities we indirectly compute the Virasoro anomaly terms by calculating
second order susy variation of the EM tensor. Certain integrated form of all
such terms are shown to vanish. In order to deal with various divergences that
appear in such computations we take a point-split definition of the same EM
tensor. The final results are shown not to suffer from the ordering ambiguity
as noticed in the previous work provided the coincidence limit is taken before
sending the regularization parameter to zero at the end of the computation.
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Ricci flow, quantum mechanics and gravity: It has been argued that, underlying any given quantum-mechanical model, there
exists at least one deterministic system that reproduces, after
prequantisation, the given quantum dynamics. For a quantum mechanics with a
complex d-dimensional Hilbert space, the Lie group SU(d) represents classical
canonical transformations on the projective space CP^{d-1} of quantum states.
Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and
let P denote the projection from the Hopf bundle onto its base CP^{d-1}. Then
the underlying deterministic model we propose here is the Lie group SU(d),
acted on by the operation PR. Finally we comment on some possible consequences
that our model may have on a quantum theory of gravity.
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Dirac Operator on a disk with global boundary conditions: We compute the functional determinant for a Dirac operator in the presence of
an Abelian gauge field on a bidimensional disk, under global boundary
conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the
connection between our result and the index theorem.
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Spectral action on noncommutative torus: The spectral action on noncommutative torus is obtained, using a
Chamseddine--Connes formula via computations of zeta functions. The importance
of a Diophantine condition is outlined. Several results on holomorphic
continuation of series of holomorphic functions are obtained in this context.
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Comment on ``Anyon in an External Eletromagnetic Field: Hamiltonian and
Lagrangian Formulations'': We comment on a recent paper by Chaichian et al. (Phys.Rev.Lett.
71(1993)3405).
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Exploring Vacuum Structure around Identity-Based Solutions: We explore the vacuum structure in bosonic open string field theory expanded
around an identity-based solution parameterized by $a(>=-1/2)$. Analyzing the
expanded theory using level truncation approximation up to level 20, we find
that the theory has the tachyon vacuum solution for $a>-1/2$. We also find
that, at $a=-1/2$, there exists an unstable vacuum solution in the expanded
theory and the solution is expected to be the perturbative open string vacuum.
These results reasonably support the expectation that the identity-based
solution is a trivial pure gauge configuration for $a>-1/2$, but it can be
regarded as the tachyon vacuum solution at $a=-1/2$.
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