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Quartic interaction vertex in the massive integer higher spin field
theory in a constant electromagnetic field: We consider the massive integer higher spin fields coupled to an external
constant electromagnetic field in flat space of arbitrary dimension and find a
gauge invariant quartic interaction vertex which is quadratic in dynamical
higher spin field and quadratic in external field. Construction of the vertex
is based on the BRST approach to higher spin filed theory where no off-shell
constraints on the fields and on the gauge parameters are imposed from the very
beginning (unconstrained formulation).
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Renormalization of Entanglement Entropy from topological terms: We propose a renormalization scheme for Entanglement Entropy of 3D CFTs with
a 4D asymptotically AdS gravity dual in the context of the gauge/gravity
correspondence. The procedure consists in adding the Chern form as a boundary
term to the area functional of the Ryu-Takayanagi minimal surface. We provide
an explicit prescription for the renormalized Entanglement Entropy, which is
derived via the replica trick. This is achieved by considering a Euclidean
gravitational action renormalized by the addition of the Chern form at the
spacetime boundary, evaluated in the conically-singular replica manifold. We
show that the addition of this boundary term cancels the divergent part of the
Entanglement Entropy, recovering the results obtained by Taylor and Woodhead.
We comment on how this prescription for renormalizing the Entanglement Entropy
is in line with the general program of topological renormalization in
asymptotically AdS gravity.
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The Casimir energy of a massive fermionic field confined in a d+1
dimensional slab-bag: We evaluate the fermionic Casimir effect associated with a massive fermion
confined within a planar (d+1) dimensional slab-bag, on which MIT bag model
boundary conditions of standard type, along a single spatial direction, are
imposed. A simple and effective method for adding up the zero-point energy
eigenvalues, corresponding to a quantum field under the influence of arbitrary
boundary conditions, imposed on the field on flat surfaces perpendicular to a
chosen spatial direction, is proposed. Using this procedure, an analytic result
is obtained, from which small and large fermion mass limits, valid for an
arbitrary number of dimensions, are derived. They match some known results in
particular cases. The method can be easily extended to other configurations.
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Vacuum Polarization and Energy Conditions at a Planar Frequency
Dependent Dielectric to Vacuum Interface: The form of the vacuum stress-tensor for the quantized scalar field at a
dielectric to vacuum interface is studied. The dielectric is modeled to have an
index of refraction that varies with frequency. We find that the stress-tensor
components, derived from the mode function expansion of the Wightman function,
are naturally regularized by the reflection and transmission coefficients of
the mode at the boundary. Additionally, the divergence of the vacuum energy
associated with a perfectly reflecting mirror is found to disappear for the
dielectric mirror at the expense of introducing a new energy density near the
surface which has the opposite sign. Thus the weak energy condition is always
violated in some region of the spacetime. For the dielectric mirror, the mean
vacuum energy density per unit plate area in a constant time hypersurface is
always found to be positive (or zero) and the averaged weak energy condition is
proven to hold for all observers with non-zero velocity along the normal
direction to the boundary. Both results are found to be generic features of the
vacuum stress-tensor and not necessarily dependent of the frequency dependence
of the dielectric.
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Is Holographic Entropy and Gravity the result of Quantum Mechanics?: In this paper we suggest a connection between quantum mechanics and
Verlinde's recently proposed entropic force theory for the laws of Newton. We
propose an entropy based on the quantum mechanical probability density
distribution. With the assumption that the holographic principle holds we
propose that our suggested quantum entropy generalizes the Bekenstein entropy
used by Verlinde in his approach. Based on this assumption we suggest that
Verlinde's entropic theory of gravity has a quantum mechanical origin. We
establish a reformulation of the Newtonian potential for gravity based on this
quantum mechanical entropy. We also discuss the notion of observation and the
correspondence to classical physics. Finally we give a discussion, a number of
open problems and some concluding remarks.
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Supersymmetric Lorentz-Covariant Hyperspaces and self-duality equations
in dimensions greater than (4|4): We generalise the notions of supersymmetry and superspace by allowing
generators and coordinates transforming according to more general Lorentz
representations than the spinorial and vectorial ones of standard lore. This
yields novel SO(3,1)-covariant superspaces, which we call hyperspaces, having
dimensionality greater than (4|4) of traditional super-Minkowski space. As an
application, we consider gauge fields on complexifications of these
superspaces; and extending the concept of self-duality, we obtain classes of
completely solvable equations analogous to the four-dimensional self-duality
equations.
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Finite temperature $0^{-+}$ glueball spectrum from non-susy D3 brane of
Type IIB string theory: Here, we calculate the pseudo-scalar glueball mass at finite temperature from
the holographic QCD in $3+1$ dimensions. The decoupled geometry of the
non-supersymmetric (non-susy) D$3$ brane at the finite temperature which is the
solution of the type-II supergravity is considered as the dual theory of QCD.
We calculate the mass spectrum from the axion fluctuation in this gravity
background using WKB approximations. Approximating the WKB equation for various
orders of mass, we derive the analytical expressions of the mass spectrum of
$0^{-+}$ at the finite temperature. Finally we evaluate the masses numerically
as $m_{-+}=2.5$GeV and $m_{-+}^*=3.8$GeV from the complete WKB equation. The
mass of a given state is found to decrease with increasing temperature and
becomes zero at confinement -deconfinement transition temperature which is
consistent with the idea of deconfinement and also matches with some recent
lattice results. From this temperature variation, the QCD transition point is
found to be about $186$MeV.
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Bulk Locality and Entanglement Swapping in AdS/CFT: Localized bulk excitations in AdS/CFT are produced by operators which modify
the pattern of entanglement in the boundary state. We show that simple
models--consisting of entanglement swapping operators acting on a qubit system
or a free field theory--capture qualitative features of gravitational
backreaction and reproduce predictions of the Ryu-Takayanagi formula. These
entanglement swapping operators naturally admit multiple representations
associated with different degrees of freedom, thereby reproducing the code
subspace structure emphasized by Almheiri, Dong, and Harlow. We also show that
the boundary Reeh-Schlieder theorem implies that equivalence of certain
operators on a code subspace necessarily breaks down when non-perturbative
effects are taken into account (as is expected based on bulk arguments).
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Combinatorics of Solitons in Noncritical String Theory: We study the combinatorics of solitons in $D<2$ (or $c<1$) string theory. The
weights in the summation over multi-solitons are shown to be automatically
determined if we further require that the partition function with soliton
background be a $\tau$ function of the KP hierarchy, in addition to the
$W_{1+\infty}$ constraint.
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Radiation from a charge circulating inside a waveguide with dielectric
filling: The emitted power of the radiation from a charged particle moving uniformly
on a circle inside a cylindrical waveguide is considered. The expressions for
the energy flux of the radiation passing through the waveguide cross-section
are derived for both TE and TM waves. The results of the numerical evaluation
are presented for the number of emitted quanta depending on the waveguide
radius, the radius of the charge rotation orbit and dielectric permittivity of
the filling medium. These results are compared with the corresponding
quantities for the synchrotron radiation in a homogeneous medium.
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Free harmonic oscillators, Jack polynomials and Calogero-Sutherland
systems: The algebraic structure and the relationships between the eigenspaces of the
Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are
investigated through the Cherednik operators. We find an exact connection
between the simultaneous non-symmetric eigenfunctions of the $A_{N-1}$
Cherednik operators, from which the eigenfunctions of the CSM and SM are
constructed, and the monomials. This construction, not only, allows one to
write down a harmonic oscillator algebra involving the Cherednik operators,
which yields the raising and lowering operators for both of these models, but
also shows the connection of the CSM with free oscillators and the SM with free
particles on a circle. We also point out the subtle differences between the
excitations of the CSM and the SM.
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New classes of solutions for Euclidean scalar field theories: This paper presents new classes of exact radial solutions to the nonlinear
ordinary differential equation that arises as a saddle-point condition for a
Euclidean scalar field theory in $D$-dimensional spacetime. These solutions are
found by exploiting the dimensional consistency of the radial differential
equation for a single {\it massless} scalar field, which allows one to
transform to an autonomous equation. For massive theories the radial equation
is not exactly solvable but the massless solutions provide useful
approximations to the results for the massive case. The solutions presented
here depend on the power of the interaction and on the spatial dimension, both
of which may be noninteger. Scalar equations arising in the study of conformal
invariance fit into this framework and classes of new solutions are found.
These solutions exhibit two distinct behaviours as $D\to2$ from above.
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q-Deformed Supersymmetry and Dynamic Magnon Representations: It was recently noted that the dispersion relation for the magnons of planar
N=4 SYM can be identified with the Casimir of a certain deformation of the
Poincare algebra, in which the energy and momentum operators are supplemented
by a boost generator J. By considering the relationship between J and su(2|2) x
R^2, we derive a q-deformed super-Poincare symmetry algebra of the kinematics.
Using this, we show that the dynamic magnon representations may be obtained by
boosting from a fixed rest-frame representation. We comment on aspects of the
coalgebra structure and some implications for the question of boost-covariance
of the S-matrix.
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Vacuum energy for Yang-Mills fields in $R^d\times S^1$: One-loop,
two-loop, and beyond: The vacuum energy is calculated for Yang-Mills (YM) system defined in $D$
dimensional space-time of $S^1\times R^d$ ($D=d+1$), where the possibility of
the YM fields to acquire the vacuum expectation values on $S^1$ is taken into
account. The vacuum energy has already been obtained to the order of one-loop
in many people. Here we calculate the vacuum energy in $D$ dimensions to
two-loop order. With an intention to reach higher loops, an approximation
method is proposed, which is especially effective in higher dimensions. By this
method, we can treat the higher-loop contributions of YM interactions as easily
as we treat one-loop effect. As a check, we show reproduction of the two-loop
contribution ($D$-dependence of the coefficient as well as the functional form)
when the coupling constant is small. This approximation method is useful not
only for the Kaluza-Klein theories but also for the finite temperature-density
system (as a quark-gluon plasma).
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The Shape of Branes Pulled by Strings: We examine the system where a string stretches between pair of D-branes, and
study the bending of the D-brane caused by the tension of the string. If the
distance between the pair of D-branes is sent to infinity, the tension of the
string stretching between them is strong enough to pull the spike all the way
to infinity. We study the shape of these spikes when the branes are finite
distance apart using two different methods. First, we consider a string
stretched between a pair of D2-branes in type IIA theory by going to the
M-theory limit in which all of these branes are M-theory 2-branes embedded
along a holomorphic curve. Second, we consider a D-string stretched between a
pair of D3-branes in type IIB theory and infer the geometry of the D3-brane
embeddings from the configuration of the adjoint scalar field in the magnetic
monopole solution of Prasad and Sommerfield. The case of fundamental string
stretching between a pair of D3-branes follows from S-duality. The energy of
these configurations matches the expected value based on fundamental string and
D-string tensions.
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Gauged WZW models and Non-abelian duality: We consider WZW models based on the non-semi-simple algebras that they were
recently constructed as contractions of corresponding algebras for semi-simple
groups. We give the explicit expression for the action of these models, as well
as for a generalization of them, and discuss their general properties.
Furthermore we consider gauged WZW models based on these non-semi-simple
algebras and we show that there are equivalent to non-abelian duality
transformations on WZW actions. We also show that a general non-abelian duality
transformation can be thought of as a limiting case of the non-abelian quotient
theory of the direct product of the original action and the WZW action for the
symmetry gauge group $H$. In this action there is no Lagrange multiplier term
that constrains the gauge field strength to vanish. A particular result is that
the gauged WZW action for the coset $(G_k \otimes H_l)/H_{k+l}$ is equivalent,
in the limit $l\to \infty$, to the dualized WZW action for $G_k$ with respect
to the subgroup $H$.
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Quiver Gauge Theory and Extended Electric-magnetic Duality: We construct N=1 A-D-E quiver gauge theory with the gauge kinetic term which
depends on the adjoint chiral superfields, as a low energy effective theory on
D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The
field-dependent gauge kinetic term can be engineered by introducing B-field
which holomorphically varies on the base space (complex plane) of Calabi-Yau.
We consider Weyl reflection on A-D-E node, which acts non-trivially on the
gauge kinetic term. It is known that Weyl reflection is related to N=1
electric-magnetic duality. Therefore, the non-trivial action implies an
extension of the electric-magnetic duality to the case with the field-dependent
gauge kinetic term. We show that this extended duality is consistent from the
field theoretical point of view. We also consider the duality map of the
operators.
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Dual Descriptions of Supersymmetry Breaking: Dynamical supersymmetry breaking is considered in models which admit
descriptions in terms of electric, confined, or magnetic degrees of freedom in
various limits. In this way, a variety of seemingly different theories which
break supersymmetry are actually inter-related by confinement or duality.
Specific examples are given in which there are two dual descriptions of the
supersymmetry breaking ground state.
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Principles and symmetries of complexity in quantum field theory: Based on general and minimal properties of the {\it discrete} circuit
complexity, we define the complexity in {\it continuous} systems in a
geometrical way. We first show that the Finsler metric naturally emerges in the
geometry of the complexity in continuous systems. Due to fundamental symmetries
of quantum field theories, the Finsler metric is more constrained and
consequently, the complexity of SU($n$) operators is uniquely determined as a
length of a geodesic in the Finsler geometry. Our Finsler metric is
bi-invariant contrary to the right-invariance of discrete qubit systems. We
clarify why the bi-invariance is relevant in quantum field theoretic systems.
After comparing our results with discrete qubit systems we show most results in
$k$-local right-invariant metric can also appear in our framework. Based on the
bi-invariance of our formalism, we propose a new interpretation for the
Schr\"{o}dinger's equation in isolated systems - the quantum state evolves by
the process of minimizing "computational cost."
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The Cosmological Constant and the Electroweak Scale: String theory has no parameter except the string scale, so a dynamically
compactified solution to 4 dimensional spacetime should determine both the
Planck scale and the cosmological constant $\Lambda$. In the racetrack K\"ahler
uplift flux compactification model in Type IIB theory, where the string theory
landscape is generated by scanning over discrete values of all the flux
parameters, a statistical preference for an exponentially small $\Lambda$ is
found to be natural (arXiv:1305.0753). Within this framework and matching the
median $\Lambda$ value to the observed $\Lambda$, a mass scale ${\bf m}\simeq
100$ GeV naturally appears. We explain how the electroweak scale can be
identified with this mass scale.
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Short Distance Repulsive Gravity as a Consequence of Non Trivial PPN
Parameters $β$ and $γ$: We look for a graviton-dilaton theory which can predict non trivial values of
the PPN parameters $\beta$ and/or $\gamma$ for a charge neutral point star,
without any naked singularity. With the potential for dilaton $\phi$ set to
zero, it contains one arbitrary function $\psi(\phi)$. Our requirements impose
certain constraints on $\psi$, which lead to the following generic and model
independent novel results: For a charge neutral point star, the gravitational
force becomes repulsive at distances of the order of, but greater than, the
Schwarzschild radius $r_0$. There is also no horizon for $r > r_0$. These
results suggest that black holes are unlikely to form in a stellar collapse in
this theory.
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Early Universe Evolution in Graviton-Dilaton Models: We present a class of graviton-dilaton models which leads to a singularity
free evolution of the universe. We study the evolution of a homogeneous
isotropic universe. We follow an approach which enables us to analyse the
evolution and obtain its generic features even in the absence of explicit
solutions, which are not possible in general. We describe the generic evolution
of the universe and show, in particular, that it is singularity free in the
present class of models. Such models may stand on their own as interesting
models for singularity free cosmology, and may be studied accordingly. They may
also arise from string theory. We discuss critically a few such possibilities.
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Dynamal (super)symmetries of monopoles and vortices: The dynamical (super)symmetries for various monopole systems are reviewed.
For a Dirac monopole, no smooth Runge-Lenz vector can exist; there is, however,
a spectrum-generating conformal $o(2,1)$ dynamical symmetry that extends into
$osp(1/1)$ or $osp(1/2)$ for spin 1/2 particles. Self-dual 't
Hooft-Polyakov-type monopoles admit an $su(2/2)$ dynamical supersymmetry
algebra, which allows us to reduce the fluctuation equation to the spin zero
case. For large $r$ the system reduces to a Dirac monopole plus an suitable
inverse-square potential considered before by McIntosh and Cisneros, and by
Zwanziger in the spin 0 case, and to the `dyon' of D'Hoker and Vinet for spin
1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a
`helicity-supersymmetry' analogous to the one Biedenharn found in the
relativistic Kepler problem. Similar results hold for the Kaluza-Klein monopole
of Gross-Perry-Sorkin. For the magnetic vortex, the N=2 supersymmetry of the
Pauli Hamiltonian in a static magnetic field in the plane combines with the
$o(2)\times o(2,1)$ bosonic symmetry into an $o(2)\times osp(1/2)$ dynamical
superalgebra.
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A QP perspective on topology change in Poisson-Lie T-duality: We describe topological T-duality and Poisson-Lie T-duality in terms of QP
(differential graded symplectic) manifolds and their canonical transformations.
Duality is mediated by a QP-manifold on doubled non-abelian "correspondence"
space, from which we can perform mutually dual symplectic reductions, where
certain canonical transformations play a vital role. In the presence of
spectator coordinates, we show how the introduction of "bibundle" structure on
correspondence space realises changes in the global fibration structure under
Poisson-Lie duality. Our approach can be directly translated to the worldsheet
to derive dual string current algebras. Finally, the canonical transformations
appearing in our reduction procedure naturally suggest a Fourier-Mukai integral
transformation for Poisson-Lie T-duality.
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Planck-Suppressed Operators: We show that the recent Planck limits on primordial non-Gaussianity impose
strong constraints on light hidden sector fields coupled to the inflaton via
operators suppressed by a high mass scale \Lambda. We study a simple effective
field theory in which a hidden sector field is coupled to a shift-symmetric
inflaton via arbitrary operators up to dimension five. Self-interactions in the
hidden sector lead to non-Gaussianity in the curvature perturbations. To be
consistent with the Planck limit on local non-Gaussianity, the coupling to any
hidden sector with light fields and natural cubic couplings must be suppressed
by a very high scale \Lambda > 10^5 H. Even if the hidden sector has Gaussian
correlations, nonlinearities in the mixing with the inflaton still lead to
non-Gaussian curvature perturbations. In this case, the non-Gaussianity is of
the equilateral or orthogonal type, and the Planck data requires \Lambda > 10^2
H.
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Definition of Magnetic Monopole Numbers for SU(N) Lattice Gauge-Higgs
Models: A geometric definition for a magnetic charge of Abelian monopoles in SU(N)
lattice gauge theories with Higgs fields is presented. The corresponding local
monopole number defined for almost all field configurations does not require
gauge fixing and is stable against small perturbations. Its topological content
is that of a 3-cochain. A detailed prescription for calculating the local
monopole number is worked out. Our method generalizes a magnetic charge
definition previously invented by Phillips and Stone for SU(2).
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SL(2,Z) S-duality of Super D-string Action in Type IIB Supergravity
Background: It is shown in a quantum-mechanically exact manner that a supersymmetric and
$\kappa$-symmetric D-string action in a general type IIB supergravity
background is transformed to a form of the type IIB Green-Schwarz superstring
action with the SL(2,Z) covariant tension through an S-duality transformation.
This result precisely proves a conjecture mentioned previously that the SL(2,Z)
S-duality of a super D-string action in a flat background is also valid even in
a curved IIB background geometry. We point further out the validity of the more
generalized conjecture that various duality relations of super D-brane and
M-brane actions originally found in a flat background also hold true in general
ten dimensional type II supergravity and eleven dimensional supergravity
background geometries by applying the present formalism to those cases.
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Space--Time Symmetry, CPT and Mirror Fermions: The motivations for the construction of an 8-component representation of
fermion fields based on a two dimensional representation of time reversal
transformation and CPT invariance are discussed. Some of the elementary
properties of the quantum field theory in the 8-component representation are
studied. It includes the space-time and charge conjugation symmetries, the
implementation of a reality condition, the construction of interaction
theories, the field theoretical imaginary- and real-time approach to
thermodynamics of fermionic systems, the quantization of fermion fields, their
particle content and the Feynman rules for perturbation theories. It is shown
that in the new presentation, a CPT violation can be formulated in principle.
The construction of interaction theories in the 8-component theory for fermions
is shown to be constrained by the CPT invariance. The short distance behavior
and relativistic covariance are studied. In the path integral representation of
the thermodynamical potential, the conventional imaginary-time approach is
shown to be smoothly connected to a real-time thermal field theory in the
8-component representation for fermion fields without any additional
subtraction of infinities. The metastability at zero density and the nature of
the spontaneous CP violation in color superconducting phases of strong
interaction ground states are clarified.
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On dynamical mass generation in three dimensional supersymmetric U(1)
gauge field theory: We investigate and contrast the non-perturbative infra red structure of N=1
and N=2 supersymmetric non-compact U(1) gauge field theory in three space-time
dimensions with N matter flavours. We study the Dyson-Schwinger equations in a
general gauge using superfield formalism; this ensures that supersymmetry is
kept manifest, though leads to spurious infra red divergences which we have to
avoid carefully. In the N=1 case the superfield formalism allows us to choose a
vertex which satisfies the U(1) Ward identity exactly, and we find the expected
critical behaviour in the wavefunction renormalization and strong evidence for
the existence of a gauge independent dynamically generated mass, but with no
evidence for a critical flavour number. We study the N=2 model by dimensional
reduction from four dimensional N=1 electrodynamics, and we refine the old
gauge dependence argument that there is no dynamical mass generation. We
recognize that the refinement only holds after dimensional reduction.
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Self-dual 6d 2-form fields coupled to non-abelian gauge field: quantum
corrections: We study a 6d model of a set of self-dual 2-form $B$-fields interacting with
a non-abelian vector $A$-field which is restricted to a 5d subspace. One
motivation is that if the gauge vector could be expressed in terms of the
$B$-field or integrated out, this model could lead to an interacting theory of
$B$-fields only. Treating the 5d gauge vector as a background field, we compute
the divergent part of the corresponding one-loop effective action which has the
$(DF)^2+F^3$ structure and compare it with similar contributions from other 6d
fields. We also discuss a 4d analog of the non-abelian self-dual model, which
turns out to be UV finite.
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Black hole microstates in AdS: We extend a recently derived higher-dimensional Cardy formula to include
angular momenta, which we use to obtain the Bekensten-Hawking entropy of AdS
black branes, compactified rotating branes, and large Schwarzschild/Kerr black
holes. This is the natural generalization of Strominger's microscopic
derivation of the BTZ black hole entropy to higher dimensions. We propose an
extension to include $U(1)$ charge, which agrees with the Bekenstein-Hawking
entropy of large Reissner-Nordstrom/Kerr-Newman black holes at high
temperature. We extend the results to arbitrary hyperscaling violation exponent
(this captures the case of black D$p$-branes as a subclass) and reproduce
logarithmic corrections.
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Fermions on lattice and chiral invariance: A model for lattice fermion is proposed which is, (i) free from doublers,
(ii) hermitian, and (iii) chirally invariant. The price paid is the loss of
hypercubic and reflection symmetries in the lattice action. Thanks to the
$\epsilon$-prescription, correlation functions are free from the ill effects
due to the loss of these symmetries. In weak coupling approximation, the U(1)
vector current of a gauge theory of lattice fermion in this model is conserved
in the continuum limit. As for the U(1) axial vector current, one obtains the
ABJ anomaly if the continuum limit is implemented before the chiral limit $m =
0$. The anomaly disappears, as in the Wilson model, if the order of the two
limits is reversed.
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Dynamics of Multiparticle Systems with non - Abelian Symmetry: We consider the dynamics governing the evolution of a many body system
constrained by an nonabelian local symmetry. We obtain explicit forms of the
global macroscopic condition assuring that at the microscopic level the
evolution respects the overall symmetry constraint. We demonstrate the
constraint mechanisms for the case of SU(2) system comprising particles in
fundamental, and adjoint representations (`nucleons' and `pions').
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Origin of Pure Spinor Superstring: The pure spinor formalism for the superstring, initiated by N. Berkovits, is
derived at the fully quantum level starting from a fundamental
reparametrization invariant and super-Poincare invariant worldsheet action. It
is a simple extension of the Green-Schwarz action with doubled spinor degrees
of freedom with a compensating local supersymmetry on top of the conventional
kappa-symmetry. Equivalence to the Green-Schwarz formalism is manifest from the
outset. The use of free fields in the pure spinor formalism is justified from
the first principle. The basic idea works also for the superparticle in 11
dimensions.
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Hamiltonian Cosmological Perturbation Theory: The Hamiltonian approach to cosmological perturbations in general relativity
in finite space-time is developed, where a cosmological scale factor is
identified with spatial averaging the metric determinant logarithm.
This identification preserves the number of variables and leads to a
cosmological perturbation theory with the scalar potential perturbations in
contrast to the kinetic perturbations in the Lifshitz version which are
responsible for the ``primordial power spectrum'' of CMB in the inflationary
model. The Hamiltonian approach enables to explain this ``spectrum'' in terms
of scale-invariant variables and to consider other topical problem of modern
cosmology in the context of quantum cosmological creation of both universes and
particles from the stable Bogoliubov vacuum.
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Gauged Hopfions: We discuss the $U(1)$ gauged version of the 3+1 dimensional Faddeev-Skyrme
model supplemented by the Maxwell term. We show that there exist axially
symmetric static solutions coupled to the non-integer toroidal flux of magnetic
field, which revert to the usual Hopfions ${\cal A}_{m,n}$ of lower degrees
$Q=mn$ in the limit of the gauge coupling constant vanishing. The masses of the
static gauged Hopfions are found to be less than the corresponding masses of
the usual ungauged solitons ${\cal A}_{1,1}$ and ${\cal A}_{2,1}$ respectively,
they become lighter as gauge coupling increases. The dependence of the
solutions on the gauge coupling is investigated. We find that in the strong
coupling regime the gauged Hopfion carries two magnetic fluxes, which are
quantized in units of $2\pi$, carrying $n$ and $m$ quanta respectively. The
first flux encircles the position curve and the second one is directed along
the symmetry axis. Effective quantization of the field in the gauge sector may
allow us to reconsider the usual arguments concerning the lower topological
bound in the Faddeev-Skyrme-Maxwell model.
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Anyons with anomalous gyromagnetic ratio & the Hall effect: Letting the mass depend on the spin-field coupling as
$M^2=m^2-(eg/2c^2)F_{\alpha\beta}S^{\alpha\beta}$, we propose a new set of
relativistic planar equations of motion for spinning anyons. Our model can
accommodate any gyromagnetic ratio $g$ and provides us with a novel version of
the Bargmann-Michel-Telegdi equations in 2+1 dimensions. The system becomes
singular when the field takes a critical value, and, for $g\neq2$, the only
allowed motions are those which satisfy the Hall law. For each $g\neq2,0$ a
secondary Hall effect arises also for another critical value of the field. The
non-relativistic limit of our equations yields new models which generalize our
previous ``exotic'' model, associated with the two-fold central extension of
the planar Galilei group.
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Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative
supergravity: We initiate a systematic study of supersymmetric backgrounds in 4d
$\mathcal{N}=2$ Euclidean supergravity in the presence of infinite towers of
higher derivative corrections. Adopting a Gibbons-Hawking view towards the
evaluation of the action in terms of nuts and bolts, we consider the two
maximally symmetric vacua $\mathbb{R}^4$ and $\mathbb{H}^4$ (Euclidean AdS$_4$)
and their unique supersymmetric deformations with (anti-) self-dual Maxwell
tensors corresponding to a single nut at the center. These are the Omega
background of Nekrasov-Okounkov, $\Omega\, \mathbb{R}^4$, and its
generalization with a cosmological constant of Martelli-Passias-Sparks, denoted
$\Omega\, \mathbb{H}^4$ (also known as the gravity dual of the $U(1) \times
U(1)$ squashed sphere). We write down the BPS configurations in the
superconformal formalism in the presence of vector multiplets and derive the
corresponding off- and on-shell actions. Our results provide a rigorous proof
for important parts of the conjecture in arXiv:2111.06903 and its holographic
corollary in arXiv:2204.02992, which we discuss in detail along with extensions
such as the addition of hypermultiplets and the presence of conical defects.
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Non-Pauli Effects from Noncommutative Spacetimes: Noncommutative spacetimes lead to nonlocal quantum field theories (qft's)
where spin-statistics theorems cannot be proved. For this reason, and also
backed by detailed arguments, it has been suggested that they get corrected on
such spacetimes leading to small violations of the Pauli principle. In a recent
paper \cite{Pauli}, Pauli-forbidden transitions from spacetime noncommutativity
were calculated and confronted with experiments. Here we give details of the
computation missing from this paper. The latter was based on a spacetime
$\mathcal{B}_{\chi\vec{n}}$ different from the Moyal plane. We argue that it
quantizes time in units of $\chi$. Energy is then conserved only mod
$\frac{2\pi}{\chi}$. Issues related to superselection rules raised by non-Pauli
effects are also discussed in a preliminary manner.
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BRST Analysis of the Supersymmetric Higher Spin Field Models: We develop the BRST approach for all massless integer and half-integer higher
spins in 4D Minkowski space, using the two component spinor nota- tion and
develop the Lagrangian formulation for supersymmetric higher spin models. It is
shown that the problem of second class constraints disappears and the BRST
procedure becomes much more simple than in tensorial nota- tion. Furthermore,
we demonstrate that the BRST procedure automatically provides extra auxiliary
components that belong in the set of supersymmetry auxiliary components.
Finally, we demonstrate how supersymmetry transfo- rmations are realized in
such an approach. As a result, we conclude that the BRST approach to higher
spin supersymmetric theories allows to derive both the Lagrangian and the
supersymmetry transformations. Although most part of the work is devoted to
massless component supersymmetric models, we also discuss generalization for
massive component supersymmetric models and for superfield models.
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Quantum symmetries of faces models and the double triangle algebra: Symmetries of trigonometric integrable two dimensional statistical face
models are considered. The corresponding symmetry operators on the Hilbert
space of states of the quantum version of these models define a weak *-Hopf
algebra isomorphic to the Ocneanu double triangle algebra.
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Extreme Kerr black hole microstates with horizon fluff: We present a one-function family of solutions to 4D vacuum Einstein
equations. While all diffeomorphic to the same extremal Kerr black hole, they
are labeled by well-defined conserved charges and are hence distinct
geometries. We show that this family of solutions forms a phase space the
symplectic structure of which is invariant under a $U(1)$ Kac-Moody algebra
generated by currents $\mathbb{J}_n$ and Virasoro generators $\mathbb{L}_n$
with central charge six times angular momentum of the black hole. This symmetry
algebra is well-defined everywhere in the spacetime, near the horizon or in the
asymptotic flat region. Out of the appropriate combination of $\mathbb{J}_n$
charges, we construct another Virasoro algebra at the same central charge.
Requiring that these two Virasoro algebras should describe the same system
leads us to a proposal for identifying extreme Kerr black hole microstates,
dubbed as extreme Kerr fluff. Counting these microstates, we not only correctly
reproduce the Bekenstein-Hawking entropy of extreme Kerr black hole, but also
its expected logarithmic corrections.
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UV Constraints on Massive Spinning Particles: Lessons from the Gravitino: Self-interacting massive particles with spin $\geq 1$ unavoidably violate
unitarity; the question is at what scale. For spin-$1$ the strong coupling
scale (at which perturbative unitarity is lost) cannot be raised by any finite
tuning of the interactions, while for spin-$2$ there exists a special tuning of
the Wilson coefficients which can raise this scale (and enjoys numerous special
properties such as ghost-freedom). Here, we fill in the missing piece by
describing how the self-interactions of a massive spin-$3/2$ field, or "massive
gravitino", become strongly coupled at high energies. We show that while
several different structures appear in the leading order potential, the strong
coupling scale cannot be raised (in the absence of additional fields). At the
level of the off-shell Lagrangian, it is always the non-linear symmetries of
the longitudinal Stuckelberg mode that dictate the strong coupling, and we show
that in general it is only possible to parametrically raise the strong coupling
scale if Wess-Zumino structures exist. We complement this off-shell approach
with a first analysis of positivity bounds for a massive spin-$3/2$ particle,
showing that any potential self-interaction which contributes to an on-shell
2-to-2 elastic process at tree level must vanish if this low-energy theory is
to have a standard UV completion. We identify the mixing between the
longitudinal mode and the transverse modes as the main obstacle to positivity,
and clarify how the non-Abelian nature of non-linear (dRGT) massive gravity
allows it to satisfy positivity where all known spin $\geq 3/2$ Abelian
theories fail. Our results imply that a massive gravitino cannot appear alone
in a controlled EFT---it must be accompanied by other particles, e.g.~as part
of a supermultiplet. Together with the spin-$1$ and spin-$2$ cases, we suggest
features which will persist in even higher spin massive theories.
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Localization of supergravity on the brane: A supersymmetric Randall-Sundrum brane-world demands that not merely the
graviton but the entire supergravity multiplet be trapped on the brane. To
demonstrate this, we present a complete ansatz for the reduction of (D=5,N=4)
gauged supergravity to (D=4,N=2) ungauged supergravity in the Randall-Sundrum
geometry. We verify that it is consistent to lowest order in fermion terms. In
particular, we show how the graviphotons avoid the `no photons on the brane'
result because they do not originate from Maxwell's equations in D=5 but rather
from odd-dimensional self-duality equations. In the case of the fivebrane, the
Randall-Sundrum mechanism also provides a new Kaluza-Klein way of obtaining
chiral supergravity starting from non-chiral.
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Skyrmions confined as beads on a vortex ring: A very simple, quadratic potential is used to construct vortex strings in a
generalized Skyrme model and an additional quadratic potential is used to embed
sine-Gordon-type halfkinks onto the string worldline, yielding half-Skyrmions
on a string. The strings are furthermore compactified onto a circle and the
halfkinks are forced to appear in pairs; in particular 2B halfkinks
(half-Skyrmions) will appear as beads on a ring with B being the number of
times the host vortex is twisted and also the baryon number (Skyrmion number)
from the bulk point of view. Finally, we construct an effective field theory on
the torus, describing the kinks living on the vortex rings.
|
Krylov Localization and suppression of complexity: Quantum complexity, suitably defined, has been suggested as an important
probe of late-time dynamics of black holes, particularly in the context of
AdS/CFT. A notion of quantum complexity can be effectively captured by
quantifying the spread of an operator in Krylov space as a consequence of time
evolution. Complexity is expected to behave differently in chaotic many-body
systems, as compared to integrable ones. In this paper we investigate Krylov
complexity for the case of interacting integrable models at finite size and
find that complexity saturation is suppressed as compared to chaotic systems.
We associate this behavior with a novel localization phenomenon on the Krylov
chain by mapping the theory of complexity growth and spread to an Anderson
localization hopping model with off-diagonal disorder, and find that
localization is enhanced in the integrable case due to a stronger disorder in
the hopping amplitudes, inducing an effective suppression of Krylov complexity.
We demonstrate this behavior for an interacting integrable model, the XXZ spin
chain, and show that the same behavior results from a phenomenological model
that we define: This model captures the essential features of our analysis and
is able to reproduce the behaviors we observe for chaotic and integrable
systems via an adjustable disorder parameter.
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Compatibility of Poisson--Lie transformations with symmetries of
Generalized Supergravity Equations: We investigate two types of transformations that keep NS-NS Generalized
Supergravity Equations satisfied : $\chi$-symmetry that shifts dilaton and
gauge transformations that change both dilaton and vector field $J$. Due to
these symmetries there is a large set of dilatons and vector fields $J$ that
(for a fixed metric and B-field) satisfy Generalized Supergravity Equations but
only some of them can be be used as input for Poisson--Lie transformations.
Conditions that define the admissible dilatons are given and examples are
presented.
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From Topological Field Theories to Covariant Matrix Strings: This paper is a shortened version of the previous work hep-th/9907099: We
propose a topological quantum field theory as a twisted candidate to formulate
covariant matrix strings. The model relies on the octonionic or complexified
instanton equations defined on an eight dimensional manifold with reduced
holonomy. To allow untwisting of the model without producing an anomaly, we
suggest (partially twisted) W-gravity as an "extended" 2d-gravity sector.
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Towards a Finite-$N$ Hologram: We suggest that holographic tensor models related to SYK are viable
candidates for exactly (ie., non-perturbatively in $N$) solvable holographic
theories. The reason is that in these theories, the Hilbert space is a spinor
representation, and the Hamiltonian (at least in some classes) can be arranged
to commute with the Clifford level. This makes the theory solvable level by
level. We demonstrate this for the specific case of the uncolored $O(n)^3$
tensor model with arbitrary even $n$, and reduce the question of determining
the spectrum and eigenstates to an algebraic equation relating Young tableaux.
Solving this reduced problem is conceptually trivial and amounts to matching
the representations on either side, as we demonstrate explicitly at low levels.
At high levels, representations become bigger, but should still be tractable.
None of our arguments require any supersymmetry.
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Correlators in superconformal quivers made QUICK: In this paper we conclude the program of 2012.15792 and 2105.00257 about
perturbative approaches for $\mathcal{N}=2$ superconformal quiver theories in
4D. We consider several classes of observables that involve multitrace local
operators and Wilson loops scattered in all the possible ways among the quiver.
We evaluate them exploiting the multi-matrix model arising from supersymmetric
localisation and we generalise the solution to both $SU(N)$ and $U(N)$ cases.
Moreover, we provide QUICK (QUIver Correlator Kit) a Wolfram Mathematica
package designed to automatise the perturbative solution of the $A_{q-1}$
multi-matrix model for all the observables mentioned above. Given the
interpolating nature of the superconformal quiver theories $A_{q-1}$, the
package is an efficient tool to compute correlators also in SCQCD,
$\mathcal{N}=4$ SYM and its $\mathbb{Z}_q$ orbifolds. This manuscript includes
a user guide and some pedagogical examples.
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Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline: We show that the propagators of gravitons and scalar fields seen by a static
patch observer in de Sitter spacetime are controlled by hidden SL(2,R)
symmetries, at all frequencies. The retarded Green's function is determined by
an SL(2,R) x SL(2,R) action generated by conformal Killing vectors of de Sitter
spacetime times a line. This observation uses the fact that the static patch of
dS_{d+1} x R is conformal to the hyperbolic patch of AdS_3 x S^{d-1}. The poles
of the propagators, the quasinormal frequencies, are generated by associated
SL(2,R) actions. The quasinormal mode generating algebras capture the conformal
weights more usually read off from the fields at future and past infinity. For
conformally coupled scalar fields, and for gravitons in four dimensions, this
SL(2,R) algebra has an enhanced supersymmetric structure and is generated by
particular conformal Killing vectors of de Sitter spacetime. We show how the
worldline de Sitter propagators can be reproduced from a `level matched' left
and right moving conformal quantum mechanics with an appropriate spectrum of
primary operators. Our observations are consistent with the notion that the
static patch of de Sitter spacetime is dually described by a (level matched)
large N worldline conformal quantum mechanics.
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Strong gauging or decoupling ghost matter: Gauging extra matter is a common way to couple two CFTs discontinuously. We
may consider gauging matter by strongly coupled gauge theories at criticality
rather than by weakly coupled (asymptotic free) gauge theories. It often
triggers relevant deformations and possibly leads to a non-trivial fixed point.
In many examples such as the IR limit of SQCDs (and their variants), the
relevant RG flow induced by this strong gauging makes the total central charge
$a$ increase rather than decrease compared with the sum of the original
decoupled CFTs. The dilaton effective field theory argument given by
Komargodski and Schwimmer does not apply because strong gauging is not a simple
deformation by operators in the original two decoupled CFTs and it may not be
UV complete. When the added matter is vector-like, one may emulate strong
gauging in a UV completed manner by decoupling of ghost matter. While the UV
completed description makes the dilaton effective field theory argument
possible, due to the non-unitarity, we cannot conclude the positivity of the
central charge difference in accordance with the observations in various
examples that show the contrary.
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Relation between large dimension operators and oscillator algebra of
Young diagrams: The operators with large scaling dimensions can be labelled by Young
diagrams. Among other bases, the operators using restricted Schur polynomials
have been known to have a large $N$ but nonplanar limit under which they map to
states of a system of harmonic oscillators. We analyze the oscillator algebra
acting on pairs of long rows or long columns in the Young diagrams of the
operators. The oscillator algebra can be reached by a Inonu-Wigner contraction
of the $u(2)$ algebra inside of the $u(p)$ algebra of $p$ giant gravitons. We
present evidences that integrability in this case can persist at higher loops
due to the presence of the oscillator algebra which is expected to be robust
under loop corrections in the nonplanar large $N$ limit.
|
Signals of a Quantum Universe: Structure in the Universe is widely believed to have originated from quantum
fluctuations during an early epoch of accelerated expansion. Yet, the patterns
we observe today do not distinguish between quantum or classical primordial
fluctuations; current cosmological data is consistent with either possibility.
We argue here that a detection of primordial non-Gaussianity can resolve the
present situation, and provide a litmus-test for the quantum origin of cosmic
structure. Unlike in quantum mechanics, vacuum fluctuations cannot arise in
classical theories and therefore long-range classical correlations must result
from (real) particles in the initial state. Similarly to flat-space scattering
processes, we show how basic principles require these particles to manifest
themselves as poles in the $n$-point functions, in the so-called folded
configurations. Following this observation, and assuming fluctuations are (i)
correlated over large scales, and (ii) generated by local evolution during an
inflationary phase, we demonstrate that: the absence of a pole in the folded
limit of non-Gaussian correlators uniquely identifies the quantum vacuum as the
initial state. In the same spirit as Bell's inequalities, we discuss how this
can be circumvented if locality is abandoned. We also briefly discuss the
implications for simulations of a non-Gaussian universe.
|
Higher spins in the symmetric orbifold of K3: The symmetric orbifold of K3 is believed to be the CFT dual of string theory
on AdS3 x S3 x K3 at the tensionless point. For the case when the K3 is
described by the orbifold T4/Z2, we identify a subsector of the symmetric
orbifold theory that is dual to a higher spin theory on AdS3. We analyse how
the BPS spectrum of string theory can be described from the higher spin
perspective, and determine which single-particle BPS states are accounted for
by the perturbative higher spin theory.
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Scalar perturbation of gravitating double-kink solutions: In this letter, a two-dimensional (2D) gravity-scalar model is studied. This
model supports interesting double-kink solutions, and the corresponding metric
solutions can be derived analytically. Depending on a tunable parameter $c$,
the metric can be symmetric or asymmetric. The Schr\"odinger-like equation for
normal modes of the physical linear perturbation is derived. As $c$ varies, the
effective potential can have one or two singular barriers. If $c$ is larger
than a critical value, the zero mode will be normalizable, despite of the
appearance of a strong repulsive singularity. The double-kink solution is
always stable against linear perturbations.
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On Grassmannian Heterotic Sigma Model: We study the non-minimal supersymmetric heterotically deformed
$\mathcal{N}=(0,2)$ sigma model with the Grassmannian target space
$\mathcal{G}_{M,N}$. To develop the appropriate superfield formalism, we begin
with a simplified model with flat target space, find its beta function up to
two loops, and prove a non-renormalization theorem. Then we generalize the
results to the full model with the Grassmannian target space. Using the
geometric formulation, we calculate the beta functions and discuss the 't Hooft
and Veneziano limits.
|
Mirror theories of 3d $\mathcal{N}=2$ SQCD: Using a recently proposed duality for $U(N)$ supersymmetric QCD (SQCD) in
three dimensions with monopole superpotential, in this paper we derive the
mirror dual description of $\mathcal{N}=2$ SQCD with unitary gauge group,
generalizing the known mirror dual description of abelian gauge theories. We
match the chiral ring of the dual theories and their partition functions on the
squashed sphere. We also conjecture a generalization for SQCD with orthogonal
and symplectic gauge groups.
|
Membrane and fivebrane instantons from quaternionic geometry: We determine the one-instanton corrections to the universal hypermultiplet
moduli space coming both from Euclidean membranes and NS-fivebranes wrapping
the cycles of a (rigid) Calabi-Yau threefold. These corrections are completely
encoded by a single function characterizing a generic four-dimensional
quaternion-Kahler metric without isometries. We give explicit solutions for
this function describing all one-instanton corrections, including the
fluctuations around the instanton to all orders in the string coupling
constant. In the semi-classical limit these results are in perfect agreement
with previous supergravity calculations.
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The appearence of the resolved singular hypersurface
{x_0}{x_1}-{{x_2}^n} =0 in the classical phase space of the Lie group SU(n): A classical phase space with a suitable symplectic structure is constructed
together with functions which have Poisson brackets algebraically identical to
the Lie algebra structure of the Lie group SU(n). In this phase space we show
that the orbit of the generators corresponding to the simple roots of the Lie
algebra give rise to fibres that are complex lines containing spheres. There
are n-1 spheres on a fibre and they intersect in exactly the same way as the
Cartan matrix of the Lie algebra. This classical phase space bundle,being
compact,has a description as a variety.Our construction shows that the variety
containing the intersecting spheres is exactly the one obtained by resolving
the singularities of the variety {x_0}{x_1}-{{x_2}^n}=0 in {C^3}. A direct
connection between this singular variety and the classical phase space
corresponding to the Lie group SU(n) is thus established.
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BRS Symmetry and Cohomology: The BRS symmetry determines physical states, Lagrange densities and candidate
anomalies. It renders gauge fixing unobservable in physical states and is
required if negative norm states are to decouple also in interacting models.
The relevant mathematical structures and the elementary cohomological
investigations are presented.
|
From AdS/CFT correspondence to hydrodynamics: We compute the correlation functions of R-charge currents and components of
the stress-energy tensor in the strongly coupled large-N finite-temperature N=4
supersymmetric Yang-Mills theory, following a recently formulated Minkowskian
AdS/CFT prescription. We observe that in the long-distance, low-frequency
limit, such correlators have the form dictated by hydrodynamics. We deduce from
the calculations the R-charge diffusion constant and the shear viscosity. The
value for the latter is in agreement with an earlier calculation based on the
Kubo formula and absorption by black branes.
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Consistent Off-Shell Tree String Amplitudes: We give a construction of off-shell tree bosonic string amplitudes, based on
the operatorial formalism of the $N$-string Vertex, with three external
massless states both for open and closed strings by requiring their being
projective invariant. In particular our prescription leads, in the low-energy
limit, to the three-gluon amplitude in the usual covariant gauge.
|
Cosmic Censorship for AdS$_5$-Kerr: We show that cosmic censorship takes an exceptionally complex and interesting
form in the case of five-dimensional AdS-Kerr black holes, due to the unusually
distant relation obtaining in that case between the black hole parameters and
the physical mass and angular momentum. One finds that, in this case,
censorship is less restrictive than one might hope: it apparently allows some
rather bizarre behaviour, and in particular does not prohibit arbitrarily large
angular momenta. We find however that most of the unwelcome geometries
permitted by censorship can be eliminated by requiring stability against
pair-production of branes. We suggest that the small set of surviving
problematic cases can be eliminated in a natural way by imposing a certain
(holographic) bound on the physical mass.
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Can negative bare couplings make sense? The $\vecφ^4$ theory at
large $N$: Scalar $\lambda\phi^4$ theory in 3+1D, for a positive coupling constant
$\lambda>0$, is known to have no interacting continuum limit, which is referred
to as quantum triviality. However, it has been recently argued that the theory
in 3+1D with an $N$-component scalar $\vec{\phi}$ and a
$(\vec{\phi}\cdot\vec{\phi})^{\,2}=\vec{\phi}^{\,4}$ interaction term does have
an interacting continuum limit at large $N$. It has been suggested that this
continuum limit has a negative (bare) coupling constant and exhibits asymptotic
freedom, similar to the $\mathcal{P}\mathcal{T}$-symmetric $-g\phi^4$ field
theory. In this paper I study the $\vec{\phi}^{\,4}$ theory in 3+1D at large
$N$ with a negative coupling constant $-g<0$, and with the scalar field taking
values in a $\mathcal{P}\mathcal{T}$-symmetric complex domain. The theory is
non-trivial, has asymptotic freedom, and has a Landau pole in the IR, and I
demonstrate that the thermal partition function matches that of the
positive-coupling $\lambda>0$ theory when the Landau poles of the two theories
(in the $\lambda>0$ case a pole in the UV) are identified with one another.
Thus the $\vec{\phi}^{\,4}$ theory at large $N$ appears to have a negative bare
coupling constant; the coupling only becomes positive in the IR, which in the
context of other $\mathcal{P}\mathcal{T}$-symmetric and large-$N$ quantum field
theories I argue is perfectly acceptable.
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Comment on ``Reduction of static field equation of Faddeev model to
first order PDE'', arXiv:0707.2207: The authors of the article Phys. Lett. B 652 (2007) 384, (arXiv:0707.2207),
propose an interesting method to solve the Faddeev model by reducing it to a
set of first order PDEs. They first construct a vectorial quantity $\bm \alpha
$, depending on the original field and its first derivatives, in terms of which
the field equations reduce to a linear first order equation. Then they find
vectors $\bm \alpha_1$ and $\bm \alpha_2$ which identically obey this linear
first order equation. The last step consists in the identification of the $\bm
\alpha_i$ with the original $\bm \alpha$ as a function of the original field.
Unfortunately, the derivation of this last step in the paper cited above
contains an error which invalidates most of its results.
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Some aspects of interaction amplitudes of D branes carrying worldvolume
fluxes: We report a systematic study of the stringy interaction between two sets of
Dp branes placed parallel at a separation in the presence of two worldvolume
fluxes for each set. We focus in this paper on that the two fluxes on one set
have the same structure as those on the other set but they in general differ in
values, which can be both electric or both magnetic or one electric and one
magnetic. We compute the respective stringy interaction amplitude and find that
the presence of electric fluxes gives rise to the open string pair production
while that of magnetic ones to the open string tachyon mode. The interplay of
these two leads to the open string pair production enhancement in certain cases
when one flux is electric and the other is magnetic. In particular, we find
that this enhancement occurs even when the electric flux and the magnetic one
share one common field strength index which is impossible in the one-flux case
studied previously by the present author and his collaborator in [17]. This
type of enhancement may have realistic physical applications, say, as a means
to explore the existence of extra dimensions.
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A bulk inflaton from large volume extra dimensions: The universe may have extra spatial dimensions with large volume that we
cannot perceive because the energy required to excite modes in the extra
directions is too high. Many examples are known of such manifolds with a large
volume and a large mass gap. These compactifications can help explain the
weakness of four-dimensional gravity and, as we show here, they also have the
capacity to produce reasonable potentials for an inflaton field. Modeling the
inflaton as a bulk scalar field, it becomes very weakly coupled in four
dimensions, and this enables us to build phenomenologically acceptable
inflationary models with tunings at the few per mil level. We speculate on dark
matter candidates and the possibility of braneless models in this setting.
|
Joule-Thomson expansion for noncommutative uncharged black holes: In this work we study the Joule-Thomson expansion for uncharged black holes
in a noncommutative scenario characterized by a parameter $\theta$, which is
present in the horizon function. We calculate the inversion temperature for
some values of $\theta$ and the isenthalpics for fixed masses. We find that the
uncharged noncommutative black hole behaves as a charged commutative one.
|
Casimir Effect for a Semitransparent Wedge and an Annular Piston: We consider the Casimir energy due to a massless scalar field in a geometry
of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge
is formed by $\delta$-function potentials, so-called semitransparent
boundaries. A finite expression for the Casimir energy corresponding to the arc
and the presence of both semitransparent potentials is obtained, from which the
torque on the sidewalls can be derived. The most interesting part of the
calculation is the nontrivial nature of the angular mode functions. Numerical
results are obtained which are closely analogous to those recently found for a
magnetodielectric wedge, with the same speed of light on both sides of the
wedge boundaries. Alternative methods are developed for annular regions with
radial semitransparent potentials, based on reduced Green's functions for the
angular dependence, which allows calculations using the multiple-scattering
formalism. Numerical results corresponding to the torque on the radial plates
are likewise computed, which generalize those for the wedge geometry. Generally
useful formulas for calculating Casimir energies in separable geometries are
derived.
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On the metric of the space of states in a modified QCD: The form of the resulting Feynman propagators in a proposed local and gauge
invariant QCD for massive fermions suggests the existence of indefinite metric
associated to quark states, a property that might relate it with the known
Lee-Wick theories. Thus, the nature of the asymptotic free quark states in the
theory is investigated here by quantizing the quadratic part of the quark
action. As opposite to the case in the standard QCD, the free theory does not
show Hamiltonian constraints. The propagation modes include a family of
massless waves and a complementary set of massive oscillations. The theory can
be quantized in a way that the massive modes show positive metric and the
massless ones exhibit negative norms. It is remarked that, since QCD is
expected to not exhibit gluon or quark asymptotic states, the presence of
negative metric massless modes does not constitute a definite drawback of the
theory. In addition, the fact that the positive metric quark states are
massive, seems to be a good feature of the model, being consistent with the
approximate existence of asymptotically free massive states in high energy
processes.
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Asymptotic freedom for $λφ^4_{\star}$ QFT in Snyder-de Sitter
space: We analyze the model of a self-interacting $\phi^4_{\star}$ scalar field
theory in Snyder-de Sitter space. After analytically computing the one-loop
beta functions {in the small noncommutativity and curvature limit}, we solve
numerically the corresponding system of differential equations, showing that in
this limit the model possesses at least one regime in which the theory is
asymptotically free. Moreover, in a given region of the parameter space we also
observe a peculiar running of the parameter associated to the curvature, which
changes its sign and therefore can be interpreted as a transition from an IR
de-Sitter space to and UV anti-de Sitter one.
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Bubble formation in phi^4 theory in the thin-wall limit and beyond: Scalar field theory with an asymmetric potential is studied at zero
temperature and high-temperature for phi^4 theory with both phi and phi^3
symmetry breaking. The equations of motion are solved numerically to obtain
O(4) symmetric and O(3) cylindrical symmetric bounce solutions. These solutions
control the rates for tunneling from the false vacuum to the true vacuum by
bubble formation. The range of validity of the thin-wall approximation (TWA) is
investigated. An analytical solution for the bounce is presented, which
reproduces the action in the thin-wall as well as the thick-wall limits.
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The gauge invariant quark Green's function in two-dimensional QCD: The gauge invariant quark Green's function, defined with a path-ordered phase
factor along a straight line, is studied in two-dimensional QCD in the
large-N_c limit by means of an exact integrodifferential equation. It is found
to be infrared finite with singularities represented by an infinite number of
threshold type branch points with a power of -3/2, starting at positive mass
squared values. The Green's function is analytically determined.
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Summation of diagrams in N=1 supersymmetric electrodynamics, regularized
by higher derivatives: For the massless N=1supersymmetric electrodynamics, regularized by higher
derivatives, the Feynman diagrams, which define the divergent part of the
two-point Green function and can not be found from Schwinger-Dyson equations
and Ward identities, are partially summed. The result can be written as a
special identity for Green functions.
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Worldline approach for spinor fields in manifolds with boundaries: The worldline formalism is a useful scheme in Quantum Field Theory which has
also become a powerful tool for numerical computations. It is based on the
first quantization of an auxiliary point-particle whose transition amplitudes
correspond to the heat-kernel of the operator of quantum fluctuations of the
field theory. However, to study a quantum field theory in a bounded manifold
one needs to restrict the path integration domain of the auxiliary
point-particle to a specific subset of worldlines enclosed by those boundaries.
In the present article it is shown how to implement this restriction for the
case of a spinor field in a two-dimensional curved half-plane under MIT bag
boundary conditions, and compute the first few heat-kernel coefficients as a
verification of the proposed construction. This construction admits several
generalisations.
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Localization of fermions in different domain wall models: Localization of fermions is studied in different gravitational domain wall
models. These are generalizations of the brane-world models considered by
Randall and Sundrum, but which also allow gravitational localization.
Therefore, they might be considered as possible realistic scenarios for
phenomenology.
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Flavor Superconductivity & Superfluidity: In these lecture notes we derive a generic holographic string theory
realization of a p-wave superconductor and superfluid. For this purpose we also
review basic D-brane physics, gauge/gravity methods at finite temperature, key
concepts of superconductivity and recent progress in distinct realizations of
holographic superconductors and superfluids. Then we focus on a D3/D7-brane
construction yielding a superconducting or superfluid vector-condensate. The
corresponding gauge theory is 3+1-dimensional N=2 supersymmetric Yang-Mills
theory with SU(N) color and SU(2) flavor symmetry. It shows a second order
phase transition to a phase in which a U(1) subgroup of the SU(2) symmetry is
spontaneously broken and typical superconductivity signatures emerge, such as a
conductivity (pseudo-)gap and the Meissner-Ochsenfeld effect. Condensates of
this nature are comparable to those recently found experimentally in p-wave
superconductors such as a ruthenate compound. A string picture of the pairing
mechanism and condensation is given using the exact knowledge of the
corresponding field theory degrees of freedom.
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Meson decays from string splitting: We discuss exclusive decays of large spin mesons into mesons in models of
large N_c quenched QCD at strong coupling using string theory. The rate of the
processes are calculated by studying the splitting of a macroscopic string on
the relevant dual gravity backgrounds. We study analytic formulas for the decay
rates of mesons made up of very heavy or very light quarks.
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On The Baxter's Q - Operator for the XXX Spin Chain: We discuss the construction of Baxter's Q-operator. The suggested approach
leads to the one-parametric family of Q-operators, satisfying to the
wronslian-type relations. Also we have found the generalization of Baxter
operators, with defines the nondiagonal part of the monodromy.
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Notes on Collective Field Theory of Matrix and Spin Calogero Models: Matrix models and related Spin-Calogero-Sutherland models are of major
relevance in a variety of subjects, ranging from condensed matter physics to
QCD and low dimensional string theory. They are characterized by integrability
and exact solvability. Their continuum, field theoretic representations are
likewise of definite interest. In this paper we describe various continuum,
field theoretic representations of these models based on bosonization and
collective field theory techniques. We compare various known representations
and describe some nontrivial applications.
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2+1 Gravity without dynamics: A three dimensional generally covariant theory is described that has a 2+1
canonical decomposition in which the Hamiltonian constraint, which generates
the dynamics, is absent. Physical observables for the theory are described and
the classical and quantum theories are compared with ordinary 2+1 gravity.
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Open superstring partition function in constant gauge field background
at finite temperature: We find the general expression for the open superstring partition function on
the annulus in a constant abelian gauge field background and at finite
temperature. We use the approach based on Green-Schwarz string path integral in
the light-cone gauge and compare it with NSR approach. We discuss the super
Yang-Mills theory limit and mention some D-brane applications.
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Functional integration and gauge ambiguities in generalized abelian
gauge theories: We consider the covariant quantization of generalized abelian gauge theories
on a closed and compact n-dimensional manifold whose space of gauge invariant
fields is the abelian group of Cheeger-Simons differential characters. The
space of gauge fields is shown to be a non-trivial bundle over the orbits of
the subgroup of smooth Cheeger-Simons differential characters. Furthermore each
orbit itself has the structure of a bundle over a multi-dimensional torus. As a
consequence there is a topological obstruction to the existence of a global
gauge fixing condition. A functional integral measure is proposed on the space
of gauge fields which takes this problem into account and provides a
regularization of the gauge degrees of freedom. For the generalized p-form
Maxwell theory closed expressions for all physical observables are obtained.
The Greens functions are shown to be affected by the non-trivial bundle
structure. Finally the vacuum expectation values of circle-valued
homomorphisms, including the Wilson operator for singular p-cycles of the
manifold, are computed and selection rules are derived.
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Asymptotic safety in the f(R) approximation: In the asymptotic safety programme for quantum gravity, it is important to go
beyond polynomial truncations. Three such approximations have been derived
where the restriction is only to a general function f(R) of the curvature R>0.
We confront these with the requirement that a fixed point solution be smooth
and exist for all non-negative R. Singularities induced by cutoff choices force
the earlier versions to have no such solutions. However, we show that the most
recent version has a number of lines of fixed points, each supporting a
continuous spectrum of eigen-perturbations. We uncover and analyse the first
five such lines. Sensible fixed point behaviour may be achieved if one
consistently incorporates geometry/topology change. As an exploratory example,
we analyse the equations analytically continued to R<0, however we now find
only partial solutions.We show how these results are always consistent with,
and to some extent can be predicted from, a straightforward analysis of the
constraints inherent in the equations.
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Open and Closed String Interpretation of SUSY CFT's on Branes with
Boundaries: We consider certain supersymmetric configurations of intersecting branes and
branes ending on branes and analyze the duality between their open and closed
string interpretation. The examples we study are chosen such that we have the
lower dimensional brane realizing an n+1 dimensional conformal field theory on
its worldvolume and the higher dimensional one introducing a conformal
boundary. We also consider two CFTs, possibly with different central charges,
interacting along a common conformal boundary. We show with a probe calculation
that the dual closed string description is in terms of gravity in an AdS_{n+2}
bulk with an AdS_{n+1} defect or two different AdS_{n+2} spaces joined along a
defect. We also comment briefly on the expected back-reaction.
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Point-splitting regularization of composite operators and anomalies: The point-splitting regularization technique for composite operators is
discussed in connection with anomaly calculation. We present a pedagogical and
self-contained review of the topic with an emphasis on the technical details.
We also develop simple algebraic tools to handle the path ordered exponential
insertions used within the covariant and non-covariant version of the
point-splitting method. The method is then applied to the calculation of the
chiral, vector, trace, translation and Lorentz anomalies within diverse
versions of the point-splitting regularization and a connection between the
results is described. As an alternative to the standard approach we use the
idea of deformed point-split transformation and corresponding Ward-Takahashi
identities rather than an application of the equation of motion, which seems to
save the complexity of the calculations.
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Membrane Paradigm and Holographic DC Conductivity for Nonlinear
Electrodynamics: Membrane paradigm is a powerful tool to study properties of black hole
horizons. We first explore the properties of the nonlinear electromagnetic
membrane of black holes. For a general nonlinear electrodynamics field, we show
that the conductivities of the horizon usually have off-diagonal components and
depend on the normal electric and magnetic fields on the horizon. Via the
holographic duality, we find a model-independent expression for the holographic
DC conductivities of the conserved current dual to a probe nonlinear
electrodynamics field in a neutral and static black brane background. It shows
that these DC conductivities only depend on the geometric and electromagnetic
quantities evaluated at the horizon. We can also express the DC conductivities
in terms of the temperature, charge density and magnetic field in the boundary
theory, as well as the values of the couplings in the nonlinear electrodynamics
at the horizon.
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Topological quantum field theory and crossing number: In this paper, we construct a new topological quantum field theory of
cohomological type and show that its partition function is a crossing number.
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Gauged Nambu-Jona-Lasinio Model at O(1/N) with and without a
Chern-Simons Term: We solve the gauged Nambu--Jona-Lasinio model at leading order in the large
$N$ expansion by computing the anomalous dimensions of all the fields of the
model and other gauge independent critical exponents by examining the scaling
behaviour of the Schwinger Dyson equation. We then restrict to the three
dimensional model and include a Chern Simons term to discover the
$\theta$-dependence of the same exponents where $\theta$ is the Chern Simons
coupling.
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The Phantom Divide in String Gas Cosmology: One of the main virtues of string gas cosmology is that it resolves
cosmological singularities. Since the Universe can be approximated by a locally
asymptotically de Sitter spacetime by the end of the inflationary era, a
singularity theorem implies that these cosmologies effectively violate the Null
Energy Condition [not just the Strong Energy Condition]. We stress that this is
an extremely robust result, which does not depend on assuming that the spatial
sections remain precisely flat in the early Universe. This means, however, that
it must be possible for string cosmologies to cross the recently much-discussed
"phantom divide" [from w < -1 to w > -1, where w is the equation-of-state
parameter]. This naturally raises the question as to whether the phantom divide
can be crossed again, to account for recent observations suggesting that w < -1
at the present time. We argue that non-perturbative string effects rule out
this possibility, even if the NEC violation in question is only "effective".
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Continuum Modes of Nonlocal Field Theories: A class of nonlocal Lorentzian quantum field theories is introduced in
arXiv:1502.01655 and arXiv:1411.6513, where the d'Alembertian operator $\Box$
is replaced by a non-analytic function of the d'Alembertian, $f(\Box)$. This is
inspired by the Causal Set program where such an evolution arises as the
continuum limit of a wave equation on causal sets. The spectrum of these
theories contains a continuum of massive excitations. This is perhaps the most
important feature which leads to distinct/interesting phenomenology. In this
paper, we study properties of the continuum massive modes in depth. We derive
the path integral formulation of these theories. Meanwhile, this derivation
introduces a dual picture in terms of local fields which clearly shows how
continuum massive modes of the nonlocal field interact. The dual picture, in
principle, provides a path to extension beyond scalar fields and addressing the
issue of renormalization.
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Bosonic Massless Higher Spin Fields from Matrix Model: We study matrix models as a new approach to formulate massless higher spin
gauge field theory. As a first step in this direction, we show that the free
equation of motion of bosonic massless higher spin gauge fields can be derived
from that of a matrix model.
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Non-Einstein geometries in Chiral Gravity: We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive
Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on
non-Einstein metrics. A class of such solutions admits curvature singularities
in the interior which are reflected as singularities or infinite bulk energy of
the corresponding linear solutions. A non-linear solution is found exactly. The
back-reaction induces a repulsion of geodesics and a shielding of the
singularity by an event horizon but also introduces closed timelike curves.
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Refined $E_n$ Chern-Simons theory: The partition function of refined Chern-Simons theory on 3d sphere for the
exceptional $E_n$ gauge algebras is presented in terms of multiple sine
functions. Gopakumar-Vafa (BPS) approximation is calculated and presented in
the form of some refined topological string partition function.
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Sources for Chern-Simons theories: The coupling between Chern-Simons theories and matter sources defined by
branes of different dimensionalities is examined. It is shown that the standard
coupling to membranes, such as the one found in supergravity or in string
theory, does not operate in the same way for CS theories; the only p-branes
that naturally couple seem to be those with p=2n; these p-branes break the
gauge symmetry (and supersymmetry) in a controlled and sensible manner.
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Notes on highest weight modules of the elliptic algebra ${\cal
A}_{q,p}\left(\widehat{sl}_2\right)$: We discuss a construction of highest weight modules for the recently defined
elliptic algebra ${\cal A}_{q,p}(\widehat{sl}_2)$, and make several conjectures
concerning them. The modules are generated by the action of the components of
the operator $L$ on the highest weight vectors. We introduce the vertex
operators $\Phi$ and $\Psi^*$ through their commutation relations with the
$L$-operator. We present ordering rules for the $L$- and $\Phi$-operators and
find an upper bound for the number of linearly independent vectors generated by
them, which agrees with the known characters of $\widehat{sl}_2$-modules.
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Minimal models of field theories: Chiral Higher Spin Gravity: There exists a unique class of local Higher Spin Gravities with propagating
massless fields in $4d$ - Chiral Higher Spin Gravity. Originally, it was
formulated in the light-cone gauge. We construct a covariant form of this
theory as a Free Differential Algebra up to NLO, i.e. at the level of equations
of motion. It also contains the recently discovered covariant forms of the
higher spin extensions of SDYM and SDGR, as well as SDYM and SDGR themselves.
From the mathematical viewpoint the result is equivalent to taking the minimal
model (in the sense of $L_\infty$-algebras) of the jet-space extension of the
BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also
information about (presymplectic AKSZ) action, counterterms, anomalies, etc.
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Gravity induced over a smooth soliton: I consider gravity induced over a smooth (finite thickness) soliton. Graviton
kinetic term is coupled to bulk scalar that develops solitonic vacuum
expectation value. Couplings of Kaluza-Klein modes to soliton-localized matter
are suppressed, giving rise to crossover distance $r_c=M_{P}^2/M_{*}^3$ between
4D and 5D behavior. This system can be viewed as a finite thickness brane
regularization of the model of Dvali, Gabadadze and Porrati.
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An Infinite Dimensional Symmetry Algebra in String Theory: Symmetry transformations of the space-time fields of string theory are
generated by certain similarity transformations of the stress-tensor of the
associated conformal field theories. This observation is complicated by the
fact that, as we explain, many of the operators we habitually use in string
theory (such as vertices and currents) have ill-defined commutators. However,
we identify an infinite-dimensional subalgebra whose commutators are not
singular, and explicitly calculate its structure constants. This constitutes a
subalgebra of the gauge symmetry of string theory, although it may act on
auxiliary as well as propagating fields. We term this object a {\it weighted
tensor algebra}, and, while it appears to be a distant cousin of the
$W$-algebras, it has not, to our knowledge, appeared in the literature before.
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Gluonic fields of a static particle to all orders in 1/N: We determine the expectation value of the gauge invariant operator Tr
[F^2+... ] for N=4 SU(N) SYM, in the presence of an infinitely heavy static
particle in the symmetric representation of SU(N). We carry out the computation
in the context of the AdS/CFT correspondence, by considering the perturbation
of the dilaton field caused by the presence of a D3 brane dual to such an
external probe. We find that the effective chromo-electric charge of the probe
has exactly the same expression as the one recently found in the computation of
energy loss by radiation.
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Strong coupling expansion for general relativity: Strong coupling expansion is computed for the Einstein equations in vacuum in
the Arnowitt-Deser-Misner (ADM) formalism. The series is given by the duality
principle in perturbation theory as presented in [M.Frasca, Phys. Rev. A 58,
3439 (1998)]. An example of application is also given for a two-dimensional
model of gravity expressed through the Liouville equation showing that the
expansion is not trivial and consistent with the exact solution, in agreement
with the general analysis. Application to the Einstein equations in vacuum in
the ADM formalism shows that the spacetime near singularities is driven by
space homogeneous equations.
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Worldline Instantons and Pair Production in Inhomogeneous Fields: We show how to do semiclassical nonperturbative computations within the
worldline approach to quantum field theory using ``worldline instantons''.
These worldline instantons are classical solutions to the Euclidean worldline
loop equations of motion, and are closed spacetime loops parametrized by the
proper-time. Specifically, we compute the imaginary part of the one loop
effective action in scalar QED using ``worldline instantons'', for a wide class
of inhomogeneous electric field backgrounds. We treat both time dependent and
space dependent electric fields, and note that temporal inhomogeneities tend to
shrink the instanton loops, while spatial inhomogeneities tend to expand them.
This corresponds to temporal inhomogeneities tending to enhance local pair
production, with spatial inhomogeneities tending to suppress local pair
production. We also show how the worldline instanton technique extends to
spinor QED.
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Quantum Interaction $φ^4_4$: the Construction of Quantum Field
defined as a Bilinear Form: We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation
$\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can
be expanded over Wick polynomials of the free $in$-field, and where
$:\!\phi^3(t,{\bf x})\!: $ is defined as the normal ordered product with
respect to the free $in$-field. The constructed solution is correctly defined
as a bilinear form on $D_{\theta}\times D_{\theta}$, where $D_{\theta}$ is a
dense linear subspace in the Fock space of the free $in$-field. On
$D_{\theta}\times D_{\theta}$ the diagonal Wick symbol of this bilinear form
satisfies the nonlinear classical wave equation.
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Noncommutative scalar fields in compact spaces: quantisation and
implications: In this paper we consider a two component scalar field theory, with
noncommutativity in its conjugate momentum space. We quantize such a theory in
a compact space with the help of dressing transformations and we reveal a
significant effect of introducing such noncommutativity as the splitting of the
energy levels of each individual mode that constitutes the whole system. We
further compute the thermal partition function exactly with predicted deformed
dispersion relations from noncommutative theories and compare the results with
usual results. It is found that thermodynamic quantities in noncommutative
models, irrespective of whether the model is more deformed in infrared/UV
region, show deviation from standard results in high temperature region.
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M-strings, Elliptic Genera and N=4 String Amplitudes: We study mass-deformed N=2 gauge theories from various points of view. Their
partition functions can be computed via three dual approaches: firstly,
(p,q)-brane webs in type II string theory using Nekrasov's instanton calculus,
secondly, the (refined) topological string using the topological vertex
formalism and thirdly, M theory via the elliptic genus of certain M-strings
configurations. We argue for a large class of theories that these approaches
yield the same gauge theory partition function which we study in detail. To
make their modular properties more tangible, we consider a fourth approach by
connecting the partition function to the equivariant elliptic genus of R^4
through a (singular) theta-transform. This form appears naturally as a specific
class of one-loop scattering amplitudes in type II string theory on T^2, which
we calculate explicitly.
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Matrix models for irregular conformal blocks and Argyres-Douglas
theories: As regular conformal blocks describe the N=2 superconformal gauge theories in
four dimensions, irregular conformal blocks are expected to reproduce the
instanton partition functions of the Argyres-Douglas theories. In this paper,
we construct matrix models which reproduce the irregular conformal conformal
blocks of the Liouville theory on sphere, by taking a colliding limit of the
Penner-type matrix models. The resulting matrix models have not only
logarithmic terms but also rational terms in the potential. We also discuss
their relation to the Argyres-Douglas type theories.
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Progress in classically solving ten dimensional supersymmetric reduced
Yang-Mills theories: It is shown that there exists an on-shell light cone gauge where half of the
fermionic components of the super vector potential vanish, so that part of the
superspace flatness conditions becomes linear. After reduction to $(1+1)$
space-time dimensions, the general solution of this subset of equations is
derived. The remaining non-linear equations are written in a form which is
analogous to Yang equations, albeit with superderivatives involving sixteen
fermionic coordinates. It is shown that this non-linear part may, nevertheless,
be solved by methods similar to powerful technics previously developed for the
(purely bosonic) self-dual Yang Mills equations in four dimensions.
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Damped Electromagnetic fluctuations in the early universe?: This short note considers the effects of quantum theory on the linear
evolution of the magnetic fields during and after inflation. The analysis
appears to show that the magnetic fields decay exponentially in the
high-temperature radiation era due to a combination of ohmic dissipation and
vacuum polarisation.
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An Alternative to Particle Dark Matter: We propose an alternative to particle dark matter that borrows ingredients of
MOdified Newtonian Dynamics (MOND) while adding new key components. The first
new feature is a dark matter fluid, in the form of a scalar field with small
equation of state and sound speed. This component is critical in reproducing
the success of cold dark matter for the expansion history and the growth of
linear perturbations, but does not cluster significantly on non-linear scales.
Instead, the missing mass problem on non-linear scales is addressed by a
modification of the gravitational force law. The force law approximates MOND at
large and intermediate accelerations, and therefore reproduces the empirical
success of MOND at fitting galactic rotation curves. At ultra-low
accelerations, the force law reverts to an inverse-square-law, albeit with a
larger Newton's constant. This latter regime is important in galaxy clusters
and is consistent with their observed isothermal profiles, provided the
characteristic acceleration scale of MOND is mildly varying with scale or mass,
such that it is ~12 times higher in clusters than in galaxies. We present an
explicit relativistic theory in terms of two scalar fields. The first scalar
field is governed by a Dirac-Born-Infeld action and behaves as a dark matter
fluid on large scales. The second scalar field also has single-derivative
interactions and mediates a fifth force that modifies gravity on non-linear
scales. Both scalars are coupled to matter via an effective metric that depends
locally on the fields. The form of this effective metric implies the equality
of the two scalar gravitational potentials, which ensures that lensing and
dynamical mass estimates agree. Further work is needed in order to make both
the acceleration scale of MOND and the fraction at which gravity reverts to an
inverse-square law explicitly dynamical quantities, varying with scale or mass.
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Staccato radiation from the decay of large amplitude oscillons: We study the decay of large amplitude, almost periodic breather-like states
in a deformed sine-Gordon model in one spatial dimension. We discover that
these objects decay in a staggered fashion via a series of transitions, during
which higher harmonics are released as short, staccato bursts of radiation.
Further, we argue that this phenomenon is not restricted to one particular
model, and that similar mechanisms of radiative decay of long-lived oscillating
states can be observed for a wide class of physical systems, including the
$\phi^6$ model.
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Adding subtractions: comparing the impact of different Regge behaviors: Dispersion relations let us leverage the analytic structure of scattering
amplitudes to derive constraints such as bounds on EFT coefficients.
An important input is the large-energy behavior of the amplitude. In this
paper, we systematically study how different large-energy behavior affects EFT
bounds for the $2 \to 2$ amplitude of complex scalars coupled to photons,
gravity, both, or neither. In many cases we find that singly-subtracted
dispersion relations (1SDRs) yield exactly the same bounds as doubly subtracted
relations (2SDRs). However, we identify another assumption, which we call
"$t$-channel dominance," that significantly strengthens the EFT bounds. This
assumption, which amounts to the requirement that the $++ \to ++$ amplitude has
no $s$-channel exchange, is justified in certain cases and is analogous to the
condition that the isospin-2 channel does not contribute to the pion amplitude.
Using this assumption in the absence of massless exchanges, we find that the
allowed region for the complex scalar EFT is identical to one recently
discussed for pion scattering at large-$N$. In the case of gravity and a gauge
field, we are able to derive a number of interesting bounds. These include an
upper bound for $G$ in terms of the gauge coupling $e^2$ and the leading
dispersive EFT coefficient, which is reminiscent of the weak gravity
conjecture. In the $e \to 0$ limit, we find that assuming smeared 1SDRs plus
$t$-channel dominance restores positivity on the leading EFT coefficient whose
positivity was spoiled by the inclusion of gravity. We interpret this to mean
that the negativity of that coefficient in the presence of gravity would imply
that the global $U(1)$ symmetry must be gauged.
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Gaugings and other supergravity tools of p-brane physics: In this series of lectures I present a review of the geometric structures of
supergravity in diverse dimensions mostly relevant to p-brane physics and to
pinpoint the correspondence between the macroscopic and microscopic description
of branes. In particular I review duality transformations, coset manifold
structures and the general steps involved by the process of gauging
supergravity lagrangians both with respect to compact, non compact and non
semisimple groups. I focus specifically on the issue of the Domain Wall field
theory correspondence and its relation with the gaugings of supergravity in p+2
dimensions. A complete review of the geometries involved by D=5, N=2
supergravity and of its most general form is given with emphasis on the problem
of finding smooth supersymmetric realizations of the Randall Sundrum scenarios.
I also give a general review of the algebraic machinery involved by the
Solvable Lie algebra description of the scalar manifolds of supergravity and I
emphasize its distinguished role in pinpointing the superstring interpretation
of supergravity p brane solutions and the macroscopic/microscopic
correspondence.
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A New Description of the E_6 Singularity: We discuss a new type of Landau-Ginzburg potential for the E_6 singularity of
the form $W=const+(Q_1(x)+P_1(x)\sqrt{P_2(x)})/x^3$ which featured in a recent
study of heterotic/typeII string duality. Here $Q_1,P_1$ and $P_2$ are
polynomials of degree 15,10 and 10, respectively. We study the properties of
the potential in detail and show that it gives a new and consistent description
of the E_6 singularity.
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String theory, $\mathcal{N}=4$ SYM and Riemann hypothesis: We discuss new relations among string theory, four-dimensional
$\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) and the Riemann
hypothesis. It is known that the Riemann hypothesis is equivalent to an
inequality for the sum of divisors function $\sigma (n)$. Based on previous
results in literature, we focus on the fact that $\sigma (n)$ appears in a
problem of counting supersymmetric states in the $\mathcal{N}=4$ SYM with
$SU(3)$ gauge group: the Schur limit of the superconformal index plays a role
of a generating function of $\sigma (n)$. Then assuming the Riemann hypothesis
gives bounds on information on the $1/8$-BPS states in the $\mathcal{N}=4$ SYM.
The AdS/CFT correspondence further connects the Riemann hypothesis to the type
IIB superstring theory on $AdS_5 \times S^5$. In particular, the Riemann
hypothesis implies a miraculous cancellation among Kaluza-Klein modes of the
supergravity multiplet and D3-branes wrapping supersymmetric cycles in the
string theory. We also discuss possibilities to gain new insights on the
Riemann hypothesis from the physics side.
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Mutual information on the fuzzy sphere: We numerically calculate entanglement entropy and mutual information for a
massive free scalar field on commutative (ordinary) and noncommutative (fuzzy)
spheres. We regularize the theory on the commutative geometry by discretizing
the polar coordinate, whereas the theory on the noncommutative geometry
naturally posseses a finite and adjustable number of degrees of freedom. Our
results show that the UV-divergent part of the entanglement entropy on a fuzzy
sphere does not follow an area law, while the entanglement entropy on a
commutative sphere does. Nonetheless, we find that mutual information (which is
UV-finite) is the same in both theories. This suggests that nonlocality at
short distances does not affect quantum correlations over large distances in a
free field theory.
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Entanglement entropies of an interval in the free Schrödinger field
theory at finite density: We study the entanglement entropies of an interval on the infinite line in
the free fermionic spinless Schr\"odinger field theory at finite density and
zero temperature, which is a non-relativistic model with Lifshitz exponent
$z=2$. We prove that the entanglement entropies are finite functions of one
dimensionless parameter proportional to the area of a rectangular region in the
phase space determined by the Fermi momentum and the length of the interval.
The entanglement entropy is a monotonically increasing function. By employing
the properties of the prolate spheroidal wave functions of order zero or the
asymptotic expansions of the tau function of the sine kernel, we find analytic
expressions for the expansions of the entanglement entropies in the asymptotic
regimes of small and large area of the rectangular region in the phase space.
These expansions lead to prove that the analogue of the relativistic entropic
$C$ function is not monotonous. Extending our analyses to a class of free
fermionic Lifshitz models labelled by their integer dynamical exponent $z$, we
find that the parity of this exponent determines the properties of the
bipartite entanglement for an interval on the line.
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Quantum mechanics in de Sitter space: We consider some possible phenomenological implications of the extended
uncertainty principle, which is believed to hold for quantum mechanics in de
Sitter spacetime. The relative size of the corrections to the standard results
is however of the order of the ratio between the length scale of the quantum
mechanical system and the de Sitter radius, and therefore exceedingly small.
Nevertheless, the existence of effects due to the large scale curvature of
spacetime in atomic experiments has a theoretical relevance.
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Gravitational Correction to Fuzzy String in Metastable Brane
Configuration: We study dynamics of a cosmic string in a metastable brane configuration in
Type IIA string theory. We first discuss a decay process of the cosmic string
via a fuzzy brane (equivalently bubble/string bound state) by neglecting
gravitational corrections in ten-dimension. We find that depending on the
strength of the magnetic field induced on the bubble, the decay rate can be
either larger or smaller than that of $O(4)$ symmetric bubble. Then, we
investigate gravitational corrections to the fuzzy brane by using the extremal
black $NS$-five brane solution, which makes the lifetime of the metastable
state longer.
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Baby Skyrmions on the Two-Sphere: We find the static multi-soliton solutions of the baby Skyrme model on the
two-sphere for topological charges 1 =< B =< 14. Numerical full-field results
show that the charge-one Skyrmion is spherical, the charge-two Skyrmion is
toroidal, and Skyrmions with higher charge all have point symmetries which are
subgroups of O(3). We find that a rational map ansatz yields very good
approximations to the full-field solutions. We point out a strong connection
between the discrete symmetries of our solutions and those of corresponding
solutions of the 3D Skyrme model.
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Construction of the Vacuum String Field Theory on a non-BPS Brane: In the framework of the Sen conjectures a construction of vacuum superstring
field theory on a non-BPS brane is discussed. A distinguished feature of this
theory is a presence of a ghost kinetic operator mixing GSO+/- sectors. A
candidate for such kinetic operator with zero cohomology is discussed.
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Introducing LambdaTensor1.0 - A package for explicit symbolic and
numeric Lie algebra and Lie group calculations: Due to the occurrence of large exceptional Lie groups in supergravity,
calculations involving explicit Lie algebra and Lie group element manipulations
easily become very complicated and hence also error-prone if done by hand.
Research on the extremal structure of maximal gauged supergravity theories in
various dimensions sparked the development of a library for efficient abstract
multilinear algebra calculations involving sparse and non-sparse higher-rank
tensors, which is presented here.
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Twistor action for general relativity: We reformulate Euclidean general relativity without cosmological constant as
an action governing the complex structure of twistor space. Extending Penrose's
non-linear graviton construction, we find a correspondence between twistor
spaces with partially integrable almost complex structures and four-dimensional
space-times with off-shell metrics. Using this, we prove that our twistor
action reduces to Plebanski's action for general relativity via the Penrose
transform. This should lead to new insights into the geometry of graviton
scattering as well as to the derivation of computational tools like
gravitational MHV rules.
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Towards a Unified Theory of Massless Superfields of All Superspins: We describe the ``universal'' action for massless superfields of all
superspins in N = 1, D = 4 anti-de Sitter superspace as a gauge theory of
unconstrained superfields taking their values in the commutative algebra of
analytic functions over a one-sheeted hyperboloid in $R^{3,1}$. The action is
invariant under N = 2 supersymmetry transformations which form a closed algebra
off the mass-shell.
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Deformations, Moduli Stabilisation and Gauge Couplings at One-Loop: We investigate deformations of $\mathbb{Z}_2$ orbifold singularities on the
toroidal orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_6)$ with discrete torsion
in the framework of Type IIA orientifold model building with intersecting
D6-branes wrapping special Lagrangian cycles. To this aim, we employ the
hypersurface formalism developed previously for the orbifold
$T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$ with discrete torsion and adapt it to
the $\mathbb{Z}_2\times\mathbb{Z}_6\times\Omega\mathcal{R}$ point group by
modding out the remaining $\mathbb{Z}_3$ subsymmetry and the orientifold
projection $\Omega\mathcal{R}$. We first study the local behaviour of the
$\mathbb{Z}_3\times\Omega\mathcal{R}$ invariant deformation orbits under
non-zero deformation and then develop methods to assess the deformation effects
on the fractional three-cycle volumes globally. We confirm that D6-branes
supporting USp(2N) or SO(2N) gauge groups do not constrain any deformation,
while deformation parameters associated to cycles wrapped by D6-branes with
U(N) gauge groups are constrained by D-term supersymmetry breaking. These
features are exposed in global prototype MSSM, Left-Right symmetric and
Pati-Salam models first constructed in arXiv:1509.00048 and arXiv:1409.1236,
for which we here count the number of stabilised moduli and study flat
directions changing the values of some gauge couplings. Finally, we confront
the behaviour of tree-level gauge couplings under non-vanishing deformations
along flat directions with the one-loop gauge threshold corrections at the
orbifold point and discuss phenomenological implications, in particular on
possible LARGE volume scenarios and the corresponding value of the string scale
$M_{\text{string}}$, for the same global D6-brane models.
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Dynamical solutions of warped six dimensional supergravity: We derive a new class of exact time dependent solutions in a warped six
dimensional supergravity model. Under the assumptions we make for the form of
the underlying moduli fields, we show that the only consistent time dependent
solutions lead to all six dimensions evolving in time, implying the eventual
decompactification or collapse of the extra dimensions. We also show how the
dynamics affects the quantization of the deficit angle.
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Gravity localization and mass hierarchy in scalar-tensor branes: We consider a braneworld model in the scalar-tensor gravity. In order to
solve the gauge hierarchy problem in this model, our world should be confined
on the positive tension brane rather than on the negative one. This is crucial
to reproduce a correct Friedmann-like equation on the brane. Interestingly, it
is found that the spacing of mass spectrum in this scenario is very tiny, but
the light gravitons cannot be observed individually in colliders because of
their sufficiently weak interaction with matter fields on the visible brane.
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Quantization of Field Theory on the Light Front: Canonical formulation of quantum field theory on the Light Front (LF) is
reviewed. The problem of constructing the LF Hamiltonian which gives the theory
equivalent to original Lorentz and gauge invariant one is considered. We
describe possible ways of solving this problem: (a) the limiting transition
from the equal-time Hamiltonian in a fast moving Lorentz frame to LF
Hamiltonian, (b) the direct comparison of LF perturbation theory in coupling
constant and usual Lorentz-covariant Feynman perturbation theory. The results
of the application of method (b) to QED-1+1 and QCD-3+1 are given. Gauge
invariant regularization of LF Hamiltonian via introducing a lattice in
transverse coordinates and imposing periodic boundary conditions in LF
coordinate x^- for gauge fields on the interval |x^-| smaller than L is also
considered.
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On confinement in a light-cone Hamiltonian for QCD: The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in
3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an
effective Hamiltonian which acts only in the Fock space of a quark and an
antiquark. Emphasis is put on the many-body aspects of gauge field theory, and
it is shown explicitly how the higher Fock-space amplitudes can be retrieved
self-consistently from solutions in the $q\bar q$-space. The approach is based
on the novel method of iterated resolvents and on discretized light-cone
quantization driven to the continuum limit. It is free of the usual
perturbative Tamm-Dancoff truncations in particle number and coupling constant
and respects all symmetries of the Lagrangian including covariance and gauge
invariance. Approximations are done to the non-truncated formalism. Together
with vertex as opposed to Fock-space regularization, the method allows to apply
the renormalization programme non-perturbatively to a Hamiltonian. The
conventional QCD scale is found arising from regulating the transversal
momenta. It conspires with additional mass scales to produce possibly
confinement.
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The $u$-plane integral, mock modularity and enumerative geometry: We revisit the low-energy effective $U(1)$ action of topologically twisted
$\mathcal N=2$ SYM theory with gauge group of rank one on a generic oriented
smooth 4-manifold $X$ with nontrivial fundamental group. After including a
specific new set of $\mathcal Q$-exact operators to the known action, we
express the integrand of the path integral of the low-energy $U(1)$ theory as
an anti-holomorphic derivative. This allows us to use the theory of mock
modular forms and indefinite theta functions for the explicit evaluation of
correlation functions of the theory, including but not restricted to those that
physically reproduce Donaldson invariants, thus facilitating the computations
compared to previously used methods. As an explicit check of our results, we
compute the path integral for the product ruled surfaces $X=\Sigma_g \times
\mathbb{CP}^1$ for the reduction on either factor and compare the results with
existing literature. In the case of reduction on the Riemann surface
$\Sigma_g$, via an equivalent topological A-model on $\mathbb{CP}^1$, we will
be able to express the generating function of genus zero Gromov-Witten
invariants of the moduli space of flat rank one connections over $\Sigma_g$ in
terms of an indefinite theta function, whence we would be able to make concrete
numerical predictions of these enumerative invariants in terms of modular data,
thereby allowing us to derive results in enumerative geometry from number
theory.
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Duality, Equivalence, Mass and The Quest For The Vacuum: I contemplate the possibility that the mismatch between the maximally
symmetric point (the free fermionic point) and the strictly self-dual point in
the Narain moduli space plays a role in the string vacuum selection. The role
of self-duality in the recent formulation of quantum mechanics from an
equivalence postulate, and the new perspective that it offers on the
foundations of quantum gravity and the origin of mass, are discussed.
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Emergent Cosmology from Matrix Theory: Matrix theory is a proposed non-perturbative definition of superstring theory
in which space is emergent. We begin a study of cosmology in the context of
matrix theory. Specifically, we show that matrix theory can lead to an emergent
non-singular cosmology which, at late times, can be described by an expanding
phase of Standard Big Bang cosmology. The horizon problem of Standard Big Bang
cosmology is automatically solved. We show that thermal fluctuations in the
emergent phase source an approximately scale-invariant spectrum of cosmological
perturbations and a scale-invariant spectrum of gravitational waves. Hence, it
appears that matrix theory can lead to a successful scenario for the origin of
perturbations responsible for the currently observed structure in the universe
while providing a consistent UV-complete description.
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Weyl Invariance and the Origins of Mass: By a uniform and simple Weyl invariant coupling of scale and matter fields,
we construct theories that unify massless, massive, and partially massless
excitations. Masses are related to tractor Weyl weights, and
Breitenlohner-Freedman stability bounds in anti de Sitter amount to reality of
these weights. The method relies on tractor calculus -- mathematical machinery
allowing Weyl invariance to be kept manifest at all stages. The equivalence
between tractor and higher spin systems with arbitrary spins and masses is also
considered.
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Boson Stars in a Theory of Complex Scalar Fields coupled to $U(1)$ Gauge
Field and Gravity: We study boson shells and boson stars in a theory of complex scalar field
coupled to the $U(1)$ gauge field $A_{\mu}$ and Einstein gravity with the
potential: $V(|\Phi|) := \frac{1}{2} m^{2} \left(|\Phi|+ a \right)^2$. This
could be considered either as a theory of massive complex scalar field coupled
to electromagnetic field and gravity in a conical potential or as a theory in
the presence of a potential which is an overlap of a parabolic and a conical
potential. Our theory has a positive cosmological constant $(\Lambda := 4 \pi G
m^2 a^2)$. Boson stars are found to come in two types, having either ball-like
or shell-like charge density. We have studied the properties of these solutions
and have also determined their domains of existence for some specific values of
the parameters of the theory. Similar solutions have also been obtained by
Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.
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Celestial double copy from the worldsheet: Using the ambitwistor string, we compute tree-level celestial amplitudes for
biadjoint scalars, Yang-Mills and gravity to all multiplicities. They are
presented in compact CHY-like formulas with operator-valued scattering
equations and numerators acting on a generalized hypergeometric function. With
these we extend the celestial double copy to tree-level amplitudes with
arbitrary number of external states. We also show how color-kinematics duality
is implemented in celestial amplitudes and its interpretation in terms of a
generalized twisted cohomology theory.
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New Asymptotic Conservation laws for Electromagnetism: We obtain the subleading tail to the memory term in the late time
electromagnetic radiative field generated due to a generic scattering of
charged bodies. We show that there exists a new asymptotic conservation law
which is related to the subleading tail term. The corresponding charge is made
of a mode of the asymptotic electromagnetic field that appears at
$\mathcal{O}(e^5)$ and we expect that it is uncorrected at higher orders. This
hints that the subleading tail arises from classical limit of a 2-loop soft
photon theorem. Building on the $m=1$ \cite{1903.09133, 1912.10229} and $m=2$
cases, we propose that there exists a conservation law for every $m$ such that
the respective charge involves an $\mathcal{O}(e^{2m+1})$ mode and is conserved
exactly. This would imply a hierarchy of an infinite number of $m$-loop soft
theorems. We also predict the structure of $m^{th}$ order tails to the memory
term that are tied to the classical limit of these soft theorems.
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Bifurcation of Plasma Balls and Black Holes to Lobed Configurations: At high energy densities any quantum field theory is expected to have an
effective hydrodynamic description. When combined with the gravity/gauge
duality an unified picture emerges, where gravity itself can have a formal
holographic hydrodynamic description. This provides a powerful tool to study
black holes in a hydrodynamic setup. We study the stability of plasma balls,
holographic duals of Scherck-Schwarz (SS) AdS black holes. We find that
rotating plasma balls are unstable against m-lobed perturbations for rotation
rates higher than a critical value. This unstable mode signals a bifurcation to
a new branch of non-axisymmetric stationary solutions which resemble a
"peanut-like" rotating plasma. The gravitational dual of the rotating plasma
ball must then be unstable and possibly decay to a non-axisymmetric long-lived
SS AdS black hole. This instability provides therefore a mechanism that bounds
the rotation of SS black holes. Our results are strictly valid for the SS AdS
gravity theory dual to a SS gauge theory. The latter is particularly important
because it shares common features with QCD, namely it is non-conformal,
non-supersymmetric and has a confinement/deconfinement phase transition. We
focus our analysis in 3-dimensional plasmas dual to SS AdS_5 black holes, but
many of our results should extend to higher dimensions and to other gauge
theory/gravity dualities with confined/deconfined phases and admitting a fluid
description.
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Three-dimensional black holes and descendants: We determine the most general three-dimensional vacuum spacetime with a
negative cosmological constant containing a non-singular Killing horizon. We
show that the general solution with a spatially compact horizon possesses a
second commuting Killing field and deduce that it must be related to the BTZ
black hole (or its near-horizon geometry) by a diffeomorphism. We show there is
a general class of asymptotically AdS$_3$ extreme black holes with arbitrary
charges with respect to one of the asymptotic-symmetry Virasoro algebras and
vanishing charges with respect to the other. We interpret these as descendants
of the extreme BTZ black hole.
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Quantum Hair in Electrodynamics and Gravity: We demonstrate the existence of quantum hair in electrodynamics and gravity
using effective action techniques. In the case of electrodynamics we use the
Euler-Heisenberg effective action while in the case of quantum gravity we use
the unique effective action. We give a general formulation of these effects
which applies to both theories and discuss analogies and differences between
them. Furthermore, we present a QED analog to black hole evaporation.
Spontaneous pair production in the external field of a ball of charge is
analogous to Hawking radiation from black holes. Assuming spherical symmetry,
the Gauss law prevents the external field from depending on the density profile
of the ball. Quantum corrections violate these expectations, showing that
quantum radiation can encode classically forbidden information about the
source.
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Holographic Walking Technicolor from D-branes: We investigate a model of dynamical electroweak symmetry breaking via a dual
gravitational description. The gravity dual is obtained by embedding a D7 -
anti-D7 pair of branes into a type IIB background that is dual to a walking
gauge theory. We develop further a previous study of this model. In particular,
we show that there is a nontrivial relation that needs to be satisfied in order
for axial-vector modes to exist. Furthermore, we compute explicitly the
electroweak S parameter. The result is positive-definite and, as was to be
expected, much smaller than in earlier QCD-like D-brane constructions. We also
find the masses and decay constants of the vector and axial-vector mesons in
this model. This allows us to obtain another estimate for S by summing the
contributions of the discrete states. It is noteworthy that, in contrast to
previous holographic studies, the sum of the first several lowest-lying states
does give a very good approximation to the full answer.
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DDF Construction and D-Brane Boundary States in Pure Spinor Formalism: Open string boundary conditions for non-BPS D-branes in type II string
theories discussed in hep-th/0505157 give rise to two sectors with integer (R
sector) and half-integer (NS sector) modes for the combined fermionic matter
and bosonic ghost variables in pure spinor formalism. Exploiting the manifest
supersymmetry of the formalism we explicitly construct the DDF (Del Giudice, Di
Vecchia, Fubini) states in both the sectors which are in one-to-one
correspondence with the states in light-cone Green-Schwarz formalism. We also
give a proof of validity of this construction. A similar construction in the
closed string sector enables us to define a physical Hilbert space in pure
spinor formalism which is used to project the covariant boundary states of both
the BPS and non-BPS instantonic D-branes. These projected boundary states take
exactly the same form as those found in light-cone Green-Schwarz formalism and
are suitable for computing the cylinder diagram with manifest open-closed
duality.
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Elusive Order Parameters for Non-Abelian Gauge Theories: In this Letter, we construct a set of order parameters for non-Abelian gauge
theories which probe directly the unbroken group and are free of the
deficiencies caused by quantum fluctuations and gauge fixing which have plagued
all previous attempts. These operators can be used to map out the phase diagram
of a non-Abelian gauge theory.
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Quantum Standard Clocks in the Primordial Trispectrum: We calculate the primordial trispectrum of curvature perturbation in
quasi-single field inflation, with general sound speeds for both the inflaton
and the massive scalar. Special attention is paid to various soft limits of the
trispectrum, where the shape function shows characteristic oscillatory pattern
(known as the quantum primordial standard clock signal) as a function of the
momentum ratio. Our calculation is greatly simplified by using the "mixed
propagator" developed under a diagrammatic representation of the in-in
formalism.
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Large N limit of O(N) vector models: Using a simple identity between various partial derivatives of the energy of
the vector model in 0+0 dimensions, we derive explicit results for the
coefficients of the large N expansion of the model. These coefficients are
functions in a variable $\rho^2$, which is the expectation value of the two
point function in the limit $N=\infty$. These functions are analytic and have
only one (multiple) pole in $\rho^2$. We show to all orders that these
expressions obey a given general formula. Using this formula it is possible to
derive the double scaling limit in an alternative way. All the results obtained
for the double scaling limit agree with earlier calculations. (to be published
in Physics Letters B)
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Holographic geometry for non-relativistic systems emerging from
generalized flow equations: An intriguing result presented by two of the present authors is that an anti
de Sitter space can be derived from a conformal field theory by considering a
flow equation. A natural expectation is that given a certain data on the
boundary system, the associated geometry would be able to emerge from a flow,
even beyond the conformal case. As a step along this line, we examine this
scenario for non-relativistic systems with anisotropic scaling symmetries, such
as Lifshitz field theories and Schr\"odinger invariant theories. In consequence
we obtain a new hybrid geometry of Lifshitz and Schr\"odinger spacetimes as a
general holographic geometry in this framework. We confirm that this geometry
reduces to each of them by considering special non-relativistic models.
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Discrete symmetries in the Kaluza-Klein-like theories: In theories of the Kaluza-Klein kind there are spins or total angular moments
in higher dimensions which manifest as charges in the observable $d=(3+1)$. The
charge conjugation requirement, if following the prescription in ($3+1$), would
transform any particle state out of the Dirac sea into the hole in the Dirac
sea, which manifests as an anti-particle having all the spin degrees of freedom
in $d$, except $S^{03}$, the same as the corresponding particle state. This is
in contradiction with what we observe for the anti-particle. In this paper we
redefine the discrete symmetries so that we stay within the subgroups of the
starting group of symmetries, while we require that the angular moments in
higher dimensions manifest as charges in $d=(3+1)$. We pay attention on spaces
with even $d$.
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Mott transition with Holographic Spectral function: We show that the Mott transition can be realized in a holographic model of a
fermion with bulk mass, $m$, and a dipole interaction of coupling strength $p$.
The phase diagram contains gapless, pseudo-gap and gapped phases and the first
one can be further divided into four sub-classes. We compare the spectral
densities of our holographic model with the Dynamical Mean Field Theory (DMFT)
results for Hubbard model as well as the experimental data of Vanadium Oxide
materials. Interestingly, single-site and cluster DMFT results of Hubbard model
share some similarities with the holographic model of different parameters,
although the spectral functions are quite different due to the asymmetry in the
holography part. The theory can fit the X-ray absorption spectrum (XAS) data
quite well, but once the theory parameters are fixed with the former it can fit
the photoelectric emission spectrum (PES) data only if we symmetrize the
spectral function.
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Two-dimensional black holes in the limiting curvature theory of gravity: In this paper we discuss modified gravity models in which growth of the
curvature is dynamically restricted. To illustrate interesting features of such
models we consider a modification of two-dimensional dilaton gravity theory
which satisfies the limiting curvature condition. We show that such a model
describes two-dimensional black holes which contain the de Sitter-like core
instead of the singularity of the original non-modified theory. In the second
part of the paper we study Vaidya type solutions of the model of the limiting
curvature theory of gravity and used them to analyse properties of black holes
which are created by the collapse of null fluid. We also apply these solutions
to study interesting features of a black hole evaporation.
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A Lie based 4-dimensional higher Chern-Simons theory: We present and study a model of 4-dimensional higher Chern-Simons theory,
special Chern-Simons (SCS) theory, instances of which have appeared in the
string literature, whose symmetry is encoded in a skeletal semistrict Lie
2-algebra constructed from a compact Lie group with non discrete center. The
field content of SCS theory consists of a Lie valued 2-connection coupled to a
background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge
symmetry organized in an infinite dimensional strict Lie 2-group. The partition
function of SCS theory is simply related to that of a topological gauge theory
localizing on flat connections with degree 3 second characteristic class
determined by the background 3-form. Finally, SCS theory is related to a
3-dimensional special gauge theory whose 2-connection space has a natural
symplectic structure with respect to which the 1-gauge transformation action is
Hamiltonian, the 2-curvature map acting as moment map.
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Singularity Free (Homogeneous Isotropic) Universe in Graviton-Dilaton
Models: We present a class of graviton-dilaton models in which a homogeneous
isotropic universe, such as our observed one, evolves with no singularity at
any time. Such models may stand on their own as interesting models for
singularity free cosmology, and may be studied further accordingly. They may
also arise from string theory. We discuss critically a few such possibilities.
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Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended
supersymmetric BMS$_{3}$ algebra: A new approach for obtaining the three-dimensional Chern-Simons supergravity
for the Poincar\'e algebra is presented. The $\mathcal{N}$-extended Poincar\'e
supergravity is obtained by expanding the super Lorentz theory. We extend our
procedure to their respective asymptotic symmetries and show that the
$\mathcal{N}=(1,2,4)$ super-BMS$_{3}$ appear as expansions of one Virasoro
superalgebra. Interestingly, the $\mathcal{N}$-extended super-BMS$_{3}$
obtained here are not only centrally extended but also endowed with internal
symmetry. We also show that the $\mathcal{N}$-extended super Poincar\'e
algebras with both central and automorphism generators are finite subalgebras.
|
Einstein spaces in five and seven dimensions and non-supersymmetric
gauge theories: A one-parameter family of new solutions representing Einstein spaces in
$d=5,7$ is presented, and used to construct non-supersymmetric backgrounds in
type IIB and M-theory that asymptotically approach $AdS_5\times S^5$ and
$AdS_7\times S^4$ . Upon dimensional reduction, the latter gives a type IIA
solution representing a 4-brane with Ramond-Ramond charge, which interpolates
between the "near-horizon" non-extremal D4 brane and a geometry connected by
T-duality to a new constant dilaton solution in type IIB. We discuss the
possibility that M-theory on this space may be related to a (0,2)
six-dimensional field theory on $S^1\times S^1$, with fermions obeying
antiperiodic boundary conditions in both circles.
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Rényi entanglement asymmetry in 1+1-dimensional conformal field
theories: In this paper, we consider the R\'enyi entanglement asymmetry of excited
states in the 1+1 dimensional free compact boson conformal field theory (CFT)
at equilibrium. We obtain a universal CFT expression written by correlation
functions for the charged moments via the replica trick. We provide detailed
analytic computations of the second R\'enyi entanglement asymmetry in the free
compact boson CFT for excited states $\Psi=V_{\beta}+V_{-\beta}$ and
$\Phi=V_{\beta}+J$ with $V_{\beta}$ and $J=i\partial\phi$ being the vertex
operator and current operator respectively. We make numerical tests of the
universal CFT computations using the XX spin chain model. Taking the
non-Hermite fake RDMs into consideration, we propose an effective way to test
them numerically, which can be applied to other excited states. The CFT
predictions are in perfect agreement with the exact numerical calculations.
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Rényi mutual information in quantum field theory, tensor networks, and
gravity: We explore a large class of correlation measures called the $\alpha-z$
R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI
involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are
positive semi-definite and monotonically decreasing under quantum operations,
making them sensible measures of total (quantum and classical) correlations.
This follows from their descendance from R\'enyi relative entropies. In
addition to upper bounding connected correlation functions between subsystems,
we prove the much stronger statement that for certain values of $\alpha$ and
$z$, the $\alpha-z$ RMIs also lower bound connected correlation functions. We
develop an easily implementable replica trick which enables us to compute the
$\alpha-z$ RMIs in a variety of many-body systems including conformal field
theories, free fermions, random tensor networks, and holography.
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Small Black Hole Constituents and Horizontal Symmetry: By exploiting the role of the horizontal symmetry SL(2,R), we extend the
analysis and classification of two-centered extremal black hole charge
configurations to the case of "small" single-centered constituents. These
latter are seen to decrease the number of independent horizontal-invariant
polynomials from four to one, depending on the rank of the charge orbit
supporting each of the two centers. Within U-duality groups of type E7, both
reducible and irreducible symmetric supergravity models in four space-time
dimensions are considered, thus encompassing N = 2 and N = 8 theories.
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A New Class of non-Hermitian Quantum Hamiltonians with PT Symmetry: In a remarkable development Bender and coworkers have shown that it is
possible to formulate quantum mechanics consistently even if the Hamiltonian
and other observables are not Hermitian. Their formulation, dubbed PT quantum
mechanics, replaces hermiticity by another set of requirements, notably that
the Hamiltonian should be invariant under the discrete symmetry PT, where P
denotes parity and T denotes time reversal. All prior work has focused on the
case that time reversal is even (T^2 = 1). We generalize the formalism to the
case of odd time reversal (T^2 = -1). We discover an analogue of Kramer's
theorem for PT quantum mechanics, present a prototypical example of a PT
quantum system with odd time reversal, and discuss potential applications of
the formalism. Odd time reversal symmetry applies to fermionic systems
including quarks and leptons and a plethora of models in nuclear, atomic and
condensed matter physics. PT quantum mechanics makes it possible to enlarge the
set of possible Hamiltonians that physicists could deploy to describe
fundamental physics beyond the standard model or for the effective description
of condensed matter phenomena.
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Ghost Kinetic Operator of Vacuum String Field Theory: Using the data of eigenvalues and eigenvectors of Neumann matrices in the
3-string vertex, we prove analytically that the ghost kinetic operator of
vacuum string field theory obtained by Hata and Kawano is equal to the ghost
operator inserted at the open string midpoint. We also comment on the values of
determinants appearing in the norm of sliver state.
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Wess-Zumino-Witten model off criticality: We study the renormalization group flow properties of the Wess-Zumino-Witten
model in the region of couplings between $g^2=0$ and $g^2=4\pi/k$, by
evaluating the two-loop Zamolodchikov's $c$-function. We also discuss the
region of negative couplings.
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An attempt to resolve the cosmological constant problem in the modified
Yang's noncommutative quantized space-time: We attempt to resolve the cosmological constant problem through the key
concept of the quantized number of spatial degrees of freedom in the modified
Yang's quantized space-time, $n_{\rm {dof}} (V_3^{R(\tau)})$.
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Thermodynamics in the NC disc: We study the thermodynamics of a scalar field on a noncommutative disc
implementing the boundary as the limit case of an interaction with an
appropriately chosen confining background. We explicitly obtain expressions for
thermodynamic potentials of gases of particles obeying different statistics. In
order to do that, we derive an asymptotic expansion for the density of the
zeros of Laguerre polynomials. As a result we prove that the Bose-Einstein
condensation in the noncommutative disc does not take place.
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Modifications of the Page Curve from correlations within Hawking
radiation: We investigate quantum correlations between successive steps of black hole
evaporation and investigate whether they might resolve the black hole
information paradox. 'Small' corrections in various models were shown to be
unable to restore unitarity. We study a toy qubit model of evaporation that
allows small quantum correlations between successive steps and reaffirm
previous results. Then, we relax the 'smallness' condition and find a
nontrivial upper and lower bound on the entanglement entropy change during the
evaporation process. This gives a quantitative measure of the size of the
correction needed to restore unitarity. We find that these entanglement entropy
bounds lead to a significant deviation from the expected Page curve.
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Nonperturbative Effects and the Large-Order Behavior of Matrix Models
and Topological Strings: This work addresses nonperturbative effects in both matrix models and
topological strings, and their relation with the large-order behavior of the
1/N expansion. We study instanton configurations in generic one-cut matrix
models, obtaining explicit results for the one-instanton amplitude at both one
and two loops. The holographic description of topological strings in terms of
matrix models implies that our nonperturbative results also apply to
topological strings on toric Calabi-Yau manifolds. This yields very precise
predictions for the large-order behavior of the perturbative genus expansion,
both in conventional matrix models and in topological string theory. We test
these predictions in detail in various examples, including the quartic matrix
model, topological strings on the local curve, and Hurwitz theory. In all these
cases we provide extensive numerical checks which heavily support our
nonperturbative analytical results. Moreover, since all these models have a
critical point describing two-dimensional gravity, we also obtain in this way
the large-order asymptotics of the relevant solution to the Painleve I
equation, including corrections in inverse genus. From a mathematical point of
view, our results predict the large-genus asymptotics of simple Hurwitz numbers
and of local Gromov-Witten invariants.
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Principal chiral model scattering and the alternating quantum spin chain: We consider the critical alternating quantum spin chain with ${q_{+}\over
2}$, ${q_{-} \over2}$ spins. Using the Bethe ansatz technique we find explicit
expressions for the $S$-matrix of the model. We show that in the limit that
$q_{\pm} \rightarrow \infty$ our results coincide with the ones obtained for
the principal chiral model level one, for the LL (RR) LR scattering. We also
study the scattering of the bound states of the model and we recover the
results of the XXZ (sine -Gordon) model.
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Dynamical Meson Melting in Holography: We discuss mesons in thermalizing gluon backgrounds in the N=2 supersymmetric
QCD using the gravity dual. We numerically compute the dynamics of a probe
D7-brane in the Vaidya-AdS geometry that corresponds to a D3-brane background
thermalizing from zero to finite temperatures by energy injection. In static
backgrounds, it has been known that there are two kinds of brane embeddings
where the brane intersects the black hole or not. They correspond to the phases
with melted or stable mesons. In our dynamical setup, we obtain three cases
depending on final temperatures and injection time scales. The brane stays
outside of the black hole horizon when the final temperature is low, while it
intersects the horizon and settles down to the static equilibrium state when
the final temperature is high. Between these two cases, we find the overeager
case where the brane dynamically intersects the horizon although the final
temperature is not high enough for a static brane to intersect the horizon. The
interpretation of this phenomenon in the dual field theory is meson melting due
to non-thermal effects caused by rapid energy injection. In addition, we
comment on the late time evolution of the brane and a possibility of its
reconnection.
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Internal magnetic fields and supersymmetry in orientifolds: Within the context of type I strings, we show the equivalence between BPS D9
branes with internal magnetic fluxes H_i in the three torii and non-BPS D3
branes with inverted internal magnetic fluxes 1/H_i. We then construct new
supersymmetric examples of Z_2 x Z_2 orientifolds with discrete torsion which
in the past had only non-supersymmetric solutions and emphasize the role of new
twisted tadpole cancellation conditions, arising in the presence of magnetic
fields, in order to get a consistent spectrum. In a second and independent part
of the paper, we construct a new nine-dimensional type IIB orientifold with
Scherk-Schwarz deformation which has the peculiarity of introducing a new type
of non-BPS O9 planes and which contains as top branes a Scherk-Schwarz
deformation of non-BPS D9 branes.The model contains charged D7 and D3 branes
with a soft supersymmetry breaking spectrum.
|
Green Function Method for Nonlinear Systems: We show that a Green function solution can be given for a class of
non-homogeneous nonlinear systems having relevance in quantum field theory.
This in turn means that a quantum field theory in the strong coupling limit can
be formulated and the spectrum obtained.
|
de Sitter Vacua in Type IIB String Theory: Classical Solutions and
Quantum Corrections: We revisit the classical theory of ten-dimensional two-derivative gravity
coupled to fluxes, scalar fields, D-branes, anti D-branes and
Orientifold-planes. We show that such set-ups do not give rise to a
four-dimensional positive curvature spacetime with the isometries of de Sitter
spacetime. We further argue that a de Sitter solution in type IIB theory may
still be achieved if the higher-order curvature corrections are carefully
controlled. Our analysis relies on the derivation of the de Sitter condition
from an explicit background solution by going beyond the supergravity limit of
type IIB theory. As such this also tells us how the background supersymmetry
should be broken and under what conditions D-term uplifting can be realized
with non self-dual fluxes.
|
Collective modes of polarizable holographic media in magnetic fields: We consider a neutral holographic plasma with dynamical electromagnetic
interactions in a finite external magnetic field. The Coulomb interactions are
introduced via mixed boundary conditions for the Maxwell gauge field. The
collective modes at finite wave-vector are analyzed in detail and compared to
the magneto-hydrodynamics results valid only at small magnetic fields.
Surprisingly, at large magnetic field, we observe the appearance of two
plasmon-like modes whose corresponding effective plasma frequency grows with
the magnetic field and is not supported by any background charge density.
Finally, we identify a mode collision which allows us to study the radius of
convergence of the linearized hydrodynamics expansion as a function of the
external magnetic field. We find that the radius of convergence in momentum
space, related to the diffusive transverse electromagnetic mode, increases
quadratically with the strength of the magnetic field.
|
On the computation of non-perturbative effective potentials in the
string theory landscape -- IIB/F-theory perspective: We discuss a number of issues arising when computing non-perturbative effects
systematically across the string theory landscape. In particular, we cast the
study of fairly generic physical properties into the language of
computability/number theory and show that this amounts to solving systems of
diophantine equations. In analogy to the negative solution to Hilbert's 10th
problem, we argue that in such systematic studies there may be no algorithm by
which one can determine all physical effects. We take large volume type IIB
compactifications as an example, with the physical property of interest being
the low-energy non-perturbative F-terms of a generic compactification. A
similar analysis is expected to hold for other kinds of string vacua, and we
discuss in particular the extension of our ideas to F-theory. While these
results imply that it may not be possible to answer systematically certain
physical questions about generic type IIB compactifications, we identify
particular Calabi-Yau manifolds in which the diophantine equations become
linear, and thus can be systematically solved. As part of the study of the
required systematics of F-terms, we develop technology for computing Z_2
equivariant line bundle cohomology on toric varieties, which determines the
presence of particular instanton zero modes via the Koszul complex. This is of
general interest for realistic IIB model building on complete intersections in
toric ambient spaces.
|
Higher-Derivative Quantum Gravity with Purely Virtual Particles:
Renormalizability and Unitarity: We review the formulation of quantum field theories with purely virtual
particles, a new type of degrees of freedom that can mediate interactions
without ever appear as external on-shell states. This property allows to solve
the problem of ghosts in higher-derivative quantum gravity, leading to a
renormalizable and unitary theory. The main steps for the BRST quantization of
gravity are recalled and renormalizability is discussed. Then, we introduce
purely virtual particles in a general quantum field theory and show the
derivation of the so-called spectral identities, which are a key ingredient to
prove unitarity. Finally, phenomenological consequences and predictions in
inflationary cosmology are presented.
|
${\cal N}{=}\,4$ supersymmetric Calogero-Sutherland models: Starting from the Hamiltonian formulation of supersymmetric Calogero models
associated with the classical $A_n$, $B_n$, $C_n$ and $D_n$ series we construct
the ${\cal N}{=}\,2$ and ${\cal N}{=}\,4$ supersymmetric extensions of the
their hyperbolic/trigonometric Calogero-Sutherland cousins. The bosonic core of
these models are the standard Calogero-Sutherland hyperbolic/trigonometric
systems.
|
The higher grading structure of the WKI hierarchy and the two-component
short pulse equation: A higher grading affine algebraic construction of integrable hierarchies,
containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is
proposed. We show that a two-component generalization of the Sch\" afer-Wayne
short pulse equation arises quite naturally from the first negative flow of the
WKI hierarchy. Some novel integrable nonautonomous models are also proposed.
The conserved charges, both local and nonlocal, are obtained from the Riccati
form of the spectral problem. The loop-soliton solutions of the WKI hierarchy
are systematically constructed through gauge followed by reciprocal B\" acklund
transformation, establishing the precise connection between the whole WKI and
AKNS hierarchies. The connection between the short pulse equation with the
sine-Gordon model is extended to a correspondence between the two-component
short pulse equation and the Lund-Regge model.
|
Massless Spectra of Three Generation U(N) Heterotic String Vacua: We provide the methods to compute the complete massless spectra of a class of
recently introduced supersymmetric E8 x E8 heterotic string models which invoke
vector bundles with U(N) structure group on simply connected Calabi-Yau
manifolds and which yield flipped SU(5) and MSSM string vacua of potential
phenomenological interest. We apply Leray spectral sequences in order to derive
the localisation of the cohomology groups H^i(X,V_a \times V_b),
H^i(X,\bigwedge^2 V) and H^i(X,{\bf S}^2 V) for vector bundles defined via
Fourier-Mukai transforms on elliptically fibered Calabi-Yau manifolds. By the
method of bundle extensions we define a stable U(4) vector bundle leading to
the first flipped SU(5) model with just three generations, i.e. without any
vector-like matter. Along the way, we propose the notion of Lambda-stability
for heterotic bundles.
|
Universality of Loop Corrected Soft Theorems in 4d: In \cite{1808.03288}, logarithmic correction to subleading soft photon and
soft graviton theorems have been derived in four spacetime dimensions from the
ratio of IR-finite S-matrices. This has been achieved after factoring out
IR-divergent components from the traditional electromagnetic and gravitational
S-matrices using Grammer-Yennie prescription. Although the loop corrected
subleading soft theorems are derived from one-loop scattering amplitudes
involving scalar particles in a minimally coupled theory with scalar contact
interaction, it has been conjectured that the soft factors are universal
(theory independent) and one-loop exact (don't receive corrections from higher
loops).
This paper extends the analysis conducted in \cite{1808.03288} to encompass
general spinning particle scattering with non-minimal couplings permitted by
gauge invariance and general coordinate invariance. By re-deriving the
$\ln\omega$ soft factors in this generic setup, we establish their universal
nature. Furthermore, we summarize the results of loop corrected soft photon and
graviton theorems up to sub-subleading order, which follows from the analysis
of one and two loop QED and quantum gravity S-matrices. While the classical
versions of these soft factors have already been derived in the literature, we
put forth conjectures regarding the quantum soft factors and outline potential
strategies for their derivation.
|
The Triumph And Limitations Of Quantum Field Theory: Talk presented at the conference ``Historical and Philosophical Reflections
on the Foundations of Quantum Field Theory,'' at Boston University, March 1996.
It will be published in the proceedings of this conference.
|
Cold planar horizons are floppy: Extremal planar black holes of four dimensional Einstein-Maxwell theory with
a negative cosmological constant have an AdS$_2 \times \R^2$ near horizon
geometry. We show that this near horizon geometry admits a deformation to a two
parameter family of extremal geometries with inhomogeneous, spatially periodic
horizons. At a linear level, static inhomogeneous perturbations of AdS$_2
\times \R^2$ decay towards the horizon and thus appear irrelevant under the
holographic RG flow. However we have found numerically that nonlinear effects
lead to inhomogeneous near horizon geometries. A consequence of these
observations is that an arbitrarily small periodic deformation of the boundary
theory at nonzero charge density does not flow to AdS$_2 \times \R^2$ in the
IR, but rather to an inhomogeneous horizon. These results shed light on
existing numerical studies of low temperature periodically modulated black
holes and also offer a new mechanism for holographic metal-insulator crossovers
or transitions.
|
Chiral transition in the probe approximation from an
Einstein-Maxwell-dilaton gravity model: We refine an earlier introduced 5-dimensional gravity solution capable of
holographically capturing several qualitative aspects of (lattice) QCD in a
strong magnetic background such as the anisotropic behaviour of the string
tension, inverse catalysis at the level of the deconfinement transition or
sensitivity of the entanglement entropy to the latter. Here, we consistently
modify our solution of the considered Einstein-Maxwell-dilaton system to not
only overcome an unphysical flattening at large distances in the
quark-antiquark potential plaguing earlier work, but also to encapsulate
inverse catalysis for the chiral transition in the probe approximation. This
brings our dynamical holographic QCD model yet again closer to a stage at which
it can be used to predict magnetic QCD quantities not directly computable via
lattice techniques.
|
Non-Abelian T-duality for open strings: In the first part of the talk we discuss T-duality for a free boson on a
world sheet with boundary in a setting suitable for the generalization to
non-trivial backgrounds. The gauging method as well as the canonical
transformation are considered. In both cases Dirichlet strings as T-duals of
Neumann strings arise in a generic way. In the second part the gauging method
is employed to construct the T-dual of a model with non-Abelian isometries.
|
Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the
de Sitter/CFT Correspondence: We investigate a recent proposal for defining a conserved mass in
asymptotically de Sitter spacetimes that is based on a conjectured holographic
duality between such spacetimes and Euclidean conformal field theory. We show
that an algorithm for deriving such terms in asymptotically anti de Sitter
spacetimes has an asymptotically de Sitter counterpart, and derive the explicit
form for such terms up to 9 dimensions. We show that divergences of the
on-shell action for de Sitter spacetime are removed in any dimension in
inflationary coordinates, but in covering coordinates a linear divergence
remains in odd dimensions that cannot be cancelled by local terms that are
polynomial in boundary curvature invariants. We show that the class of
Schwarzschild-de Sitter black holes up to 9 dimensions has finite action and
conserved mass, and construct a definition of entropy outside the cosmological
horizon by generalizing the Gibbs-Duhem relation in asymptotically dS
spacetimes. The entropy is agreement with that obtained from CFT methods in
$d=2$. In general our results provide further supporting evidence for a dS/CFT
correspondence, although some important interpretive problems remain.
|
Coulomb gauge ghost propagator and the Coulomb potential: The ghost propagator and the Coulomb potential are evaluated in Coulomb gauge
on the lattice, using an improved gauge fixing scheme which includes the
residual symmetry. This setting has been shown to be essential in order to
explain the scaling violations in the instantaneous gluon propagator. We find
that both the ghost propagator and the Coulomb potential are insensitive to the
Gribov problem or the details of the residual gauge fixing, even if the Coulomb
potential is evaluated from the A0--propagator instead of the Coulomb kernel.
In particular, no signs of scaling violations could be found in either
quantity, at least to well below the numerical accuracy where these violations
were visible for the gluon propagator. The Coulomb potential from the
A0-propagator is shown to be in qualitative agreement with the (formally
equivalent) expression evaluated from the Coulomb kernel.
|
A Monopole Index for N=4 Chern-Simons Theories: We compute a certain index for an N=4 Chern-Simons theory with gauge group
U(N)^r in the large N limit with taking account of monopole contribution, and
compare it to the corresponding multi-particle index for M-theory in the dual
geometry AdS_4 x X_7. The internal space X_7 has non-trivial two-cycles, and
M2-branes wrapped on them contribute to the multi-particle index. We establish
one-to-one map between r-1 independent magnetic charges on the gauge theory
side and the same number of charges on the gravity side: the M-momentum and r-2
(=b_2(X_7)) wrapping numbers. With a certain assumption for the wrapped
M2-brane contribution, we confirm the agreement of the indices for many sectors
specified by the r-1 charges by using analytic and numerical methods.
|
Quantum Spherical Spins with Local Symmetry: We construct a quantum system of spherical spins with a continuous local
symmetry. The model is exactly soluble in the thermodynamic limit and exhibits
a number of interesting properties. We show that the local symmetry is
spontaneously broken at finite as well as zero temperatures, implying the
existence of classical and quantum phase transitions with a nontrivial critical
behavior. The dynamical generation of gauge fields and the equivalence with the
$CP^{(\mathcal{N}-1)}$ model in the limit $\mathcal{N}\rightarrow\infty$ are
investigated. The dynamical generation of gauge fields is a consequence of the
restoration of the local symmetry.
|
Hessian geometry and the holomorphic anomaly: We present a geometrical framework which incorporates higher derivative
corrections to the action of N = 2 vector multiplets in terms of an enlarged
scalar manifold which includes a complex deformation parameter. This enlarged
space carries a deformed version of special Kahler geometry which we
characterise. The holomorphic anomaly equation arises in this framework from
the integrability condition for the existence of a Hesse potential.
|
Fat Gravitons, the Cosmological Constant and Sub-millimeter Tests: We revisit the proposal that the resolution of the Cosmological Constant
Problem involves a sub-millimeter breakdown of the point-particle approximation
for gravitons. No fundamental description of such a breakdown, which
simultaneously preserves the point-particle nature of matter particles, is yet
known. However, basic aspects of the self-consistency of the idea, such as
preservation of the macroscopic Equivalence Principle while satisfying quantum
naturalness of the cosmological constant, are addressed in this paper within a
Soft Graviton Effective Theory. It builds on Weinberg's analysis of soft
graviton couplings and standard heavy particle effective theory, and minimally
encompasses the experimental regime of soft gravity coupled to hard matter. A
qualitatively distinct signature for short-distance tests of gravity is
discussed, bounded by naturalness to appear above approximately 20 microns.
|
Geometric conservation in curved spacetime and entropy: We provide an improved definition of new conserved quantities derived from
the energy-momentum tensor in curved spacetime by introducing an additional
scalar function. We find that the conserved current and the associated
conserved charge become geometric under a certain initial condition of the
scalar function, and show that such a conserved geometric current generally
exists in curved spacetime. Furthermore, we demonstrate that the geometric
conserved current agrees with the entropy current for the perfect fluid, thus
the conserved charge is the total entropy of the system. While the geometric
charge can be regarded as the entropy for non-dissipative fluid, its physical
meaning should be investigated for more general cases.
|
$SU_q(2)$ Lattice Gauge Theory: We reformulate the Hamiltonian approach to lattice gauge theories such that,
at the classical level, the gauge group does not act canonically, but instead
as a Poisson-Lie group. At the quantum level, it then gets promoted to a
quantum group gauge symmetry. The theory depends on two parameters - the
deformation parameter $\lambda$ and the lattice spacing $a$. We show that the
system of Kogut and Susskind is recovered when $\lambda \rightarrow 0$, while
QCD is recovered in the continuum limit (for any $\lambda$). We thus have the
possibility of having a two parameter regularization of QCD.
|
Four-dimensional Lattice Gauge Theory with ribbon categories and the
Crane-Yetter state sum: Lattice Gauge Theory in 4-dimensional Euclidean space-time is generalized to
ribbon categories which replace the category of representations of the gauge
group. This provides a framework in which the gauge group becomes a quantum
group while space-time is still given by the `classical' lattice. At the
technical level, this construction generalizes the Spin Foam Model dual to
Lattice Gauge Theory and defines the partition function for a given
triangulation of a closed and oriented piecewise-linear 4-manifold. This
definition encompasses both the standard formulation of d=4 pure Yang-Mills
theory on a lattice and the Crane-Yetter invariant of 4-manifolds. The
construction also implies that a certain class of Spin Foam Models formulated
using ribbon categories are well-defined even if they do not correspond to a
Topological Quantum Field Theory.
|
Charged Black Holes with Scalar Hair: We consider a class of Einstein-Maxwell-Dilaton theories, in which the
dilaton coupling to the Maxwell field is not the usual single exponential
function, but one with a stationary point. The theories admit two charged black
holes: one is the Reissner-Nordstr{\o}m (RN) black hole and the other has a
varying dilaton. For a given charge, the new black hole in the extremal limit
has the same AdS$_2\times$Sphere near-horizon geometry as the RN black hole,
but it carries larger mass. We then introduce some scalar potentials and obtain
exact charged AdS black holes. We also generalize the results to black
$p$-branes with scalar hair.
|
5 loops in 24/5 dimensions: A first quantised approach to loop amplitudes based on the pure spinor
particle is applied to the systematics of four-particle amplitudes in maximally
supersymmetric field theories. Counting of fermionic zero modes allows the
identification of momentum factors multiplying R**4 in the case of supergravity
(and F**4 in the Yang--Mills case) thereby making manifest their ultraviolet
properties as a function of dimension, D. For L=2,3,4 loops the leading
supergravity divergence is in D=4+6/L dimensions and proportional to d*2L R**4,
in line with earlier field theory calculations. However, at five loops there is
a radical change in the systematics, suggesting the presence of a contribution
with an explicit L=5 logarithmic ultraviolet divergence when D=24/5 that is
proportional to d*8 R**4. We further argue that d*8 R**4 should receive
contributions from all loops, which would imply that N=8 supergravity (with
D=4) is not protected by supersymmetry from a seven-loop divergence.
|
A compendium of logarithmic corrections in AdS/CFT: We study the logarithmic corrections to various CFT partition functions in
the context of the AdS$_4$/CFT$_3$ correspondence for theories arising on the
worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and
heat kernel methods and present general expressions for the logarithmic
corrections to the gravitational on-shell action and black hole entropy for a
number of different supergravity backgrounds. We outline several subtle
features of these calculations and contrast them with a similar analysis of
logarithmic corrections performed directly in the eleven-dimensional uplift of
a given four-dimensional supergravity background. We find results consistent
with AdS/CFT provided that the infinite sum over KK modes on the internal space
is regularized in a specific manner. This analysis leads to an explicit
expression for the logarithmic correction to the Bekenstein-Hawking entropy of
large Kerr-Newmann and Reissner-Nordstr\"om black holes in AdS$_4$. Our results
also have important implications for effective field theory coupled to gravity
in AdS$_4$ and for the existence of scale-separated AdS$_4$ vacua in string
theory, which come in the form of new constraints on the field content and mass
spectrum of matter fields.
|
Deformed Cauchy random matrix ensembles and large $N$ phase transitions: We study a new hermitian one-matrix model containing a logarithmic Penner's
type term and another term, which can be obtained as a limit from logarithmic
terms. For small coupling, the potential has an absolute minimum at the origin,
but beyond a certain value of the coupling the potential develops a double
well. For a higher critical value of the coupling, the system undergoes a large
$N$ third-order phase transition.
|
Strong Brane Gravity and the Radion at Low Energies: For the 2-brane Randall-Sundrum model, we calculate the bulk geometry for
strong gravity, in the low matter density regime, for slowly varying matter
sources. This is relevant for astrophysical or cosmological applications. The
warped compactification means the radion can not be written as a homogeneous
mode in the orbifold coordinate, and we introduce it by extending the
coordinate patch approach of the linear theory to the non-linear case. The
negative tension brane is taken to be in vacuum. For conformally invariant
matter on the positive tension brane, we solve the bulk geometry as a
derivative expansion, formally summing the `Kaluza-Klein' contributions to all
orders. For general matter we compute the Einstein equations to leading order,
finding a scalar-tensor theory with $\omega(\Psi) \propto \Psi / (1 - \Psi)$,
and geometrically interpret the radion. We comment that this radion scalar may
become large in the context of strong gravity with low density matter.
Equations of state allowing $(\rho - 3 P)$ to be negative, can exhibit behavior
where the matter decreases the distance between the 2 branes, which we
illustrate numerically for static star solutions using an incompressible fluid.
For increasing stellar density, the branes become close before the upper mass
limit, but after violation of the dominant energy condition. This raises the
interesting question of whether astrophysically reasonable matter, and initial
data, could cause branes to collide at low energy, such as in dynamical
collapse.
|
Gauge dependence of the one-loop divergences in $6D$, ${\cal N} = (1,0)$
abelian theory: We study the gauge dependence of the one-loop effective action for the
abelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated in
harmonic superspace. We introduce the superfield $\xi$-gauge, construct the
corresponding gauge superfield propagator, and calculate the one-loop two-and
three-point Green functions with two external hypermultiplet legs. We
demonstrate that in the general $\xi$-gauge the two-point Green function of the
hypermultiplet is divergent, as opposed to the Feynman gauge $\xi =1$. The
three-point Green function with two external hypermultiplet legs and one leg of
the gauge superfield is also divergent. We verified that the Green functions
considered satisfy the Ward identity formulated in ${\cal N}=(1,0)$ harmonic
superspace and that their gauge dependence vanishes on shell. Using the result
for the two- and three-point Green functions and arguments based on the gauge
invariance, we present the complete divergent part of the one-loop effective
action in the general $\xi$-gauge.
|
Worldsheet Instanton Corrections to Five-branes and Waves in Double
Field Theory: We make a comprehensive study on the string winding corrections to
supergravity solutions in double field theory (DFT). We find five-brane and
wave solutions of diverse codimensions in which the winding coordinates are
naturally included. We discuss a physical interpretation of the winding
coordinate dependence. The analysis based on the geometric structures behind
the solutions leads to an interpretation of the winding dependence as string
worldsheet instanton corrections. We also give a brief discussion on the
origins of these winding corrections in gauged linear sigma model. Our analysis
reveals that for every supergravity solution, one has DFT solutions that
include string winding corrections.
|
Quark contribution to the reggeon-reggeon-gluon vertex in QCD: The quark loop contribution to the reggeon-reggeon-gluon vertex is calculated
in QCD, where the reggeon is the reggeized gluon. Compared with the vertex in
the Born approximation, this contribution exhibits a new spin structure as well
as the gluon loop one. A remarkable but not complete cancellation between gluon
and quark contributions to this new spin structure takes place for the case of
three massless quark flavours.
|
Two-loop beta-function from the exact renormalization group: We calculate the two-loop renormalization group (RG) beta-function of a
massless scalar field theory from the irreducible version of Polchinski's exact
RG flow equation. To obtain the correct two-loop result within this method, it
is necessary to take the full momentum-dependence of the irreducible four-point
vertex and the six-point vertex into account. Although the same calculation
within the orthodox field theory method is less tedious, the flow equation
method makes no assumptions about the renormalizability of the theory, and
promises to be useful for performing two-loop calculations for
non-renormalizable condensed-matter systems. We pay particular attention to the
problem of the field rescaling and the effect of the associated exponent eta on
the RG flow.
|
W-algebras arising as chiral algebras of conformal field theory: It is argued that chiral algebras of conformal field theory possess a
W-algebra structure. A survey of explicitly known W-algebras and their
constructions is given. (Talk given at the XIX International Colloquium on
``Group Theoretical Methods in Physics'', Salamanca, Spain, June 29 -- July 4,
1992)
|
On Domain-Wall/QFT Dualities in Various Dimensions: We investigate domain-wall/quantum field theory correspondences in various
dimensions. Our general analysis does not only cover the well-studied cases in
ten and eleven dimensions but also enables us to discuss new cases like a Type
I/Heterotic 6-brane in ten dimensions and domain wall dualities in lower than
ten dimensions. The examples we discuss include `d-branes' in six dimensions
preserving 8 supersymmetries and extreme black holes in various dimensions. In
the latter case we construct the quantum mechanics Hamiltonian and discuss
several limits.
|
Chiral Symmetry on ${\bf S}^2_F$: In this talk we give a brief description of the formulation of chiral and
gauge symmetries on the fuzzy sphere . In particular fermion doublers are shown
to be absent and the correct anomaly equation in two dimensions is obtained in
the corresponding continuum limit .
|
Black Hole Information: Hawking's 1974 calculation of thermal emission from a classical black hole
led to his 1976 proposal that information may be lost from our universe as a
pure quantum state collapses gravitationally into a black hole, which then
evaporates completely into a mixed state of thermal radiation. Another
possibility is that the information is not lost, but is stored in a remnant of
the evaporating black hole. A third idea is that the information comes out in
nonthermal correlations within the Hawking radiation, which would be expected
to occur at too slow a rate, or be too spread out, to be revealed by any
nonperturbative calculation.
|
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