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Twisted Noncommutative Field Theory: Wick-Voros vs Moyal: We present a comparison of the noncommutative field theories built using two
different star products: Moyal and Wick-Voros (or normally ordered). We compare
the two theories in the context of the noncommutative geometry determined by a
Drinfeld twist, and the comparison is made at the level of Green's functions
and S-matrix. We find that while the Green's functions are different for the
two theories, the S-matrix is the same in both cases, and is different from the
commutative case. | Statistical Mechanics of Multiply Wound D-Branes: The D-brane counting of black hole entropy is commonly understood in terms of
excitations carrying fractional charges living on long, multiply-wound branes
(e.g. open strings with fractional Kaluza-Klein momentum). This paper addresses
why the branes become multiply wound. Since multiply wound branes are T-dual to
branes evenly spaced around the compact dimension, this tendency for branes to
become multiply wound can be seen as an effective repulsion between branes in
the T-dual picture. We also discuss how the fractional charges on multiply
wound branes conspire to always form configurations with integer charge. |
Additional analytically exact solutions for three-anyons: We present new family of exact analytic solutions for three anyons in a
harmonic potential (or in free space) in terms of generalized harmonics on
$S^3$, which supplement the known solutions. The new solutions satisfy the
hard-core condition when $\alpha={1\over 3},1$ ($\alpha$ being the statistical
parameter) but otherwise, have finite non-vanishing two-particle colliding
probability density, which is consistent with self-adjointness of the
Hamiltonian. These solutions, however, do not have one-to-one mapping property
between bosonic and fermionic spectra. | DGP brane cosmology and quark-hadron phase transition: In the standard picture of cosmology it is predicted that a phase transition,
associated with chiral symmetry breaking after the electroweak transition, has
occurred at approximately 10 \mu seconds after the Big Bang to convert a plasma
of free quarks and gluons into hadrons. We consider the quark-hadron phase
transition in a DGP brane world scenario within an effective model of QCD. We
study the evolution of the physical quantities useful for the study of the
early universe, namely, the energy density, temperature and the scale factor
before, during, and after the phase transition. Also, due to the high energy
density in the early universe, we consider the quadratic energy density term
that appears in the Friedmann equation. In DGP brane models such a term
corresponds to the negative branch (\epsilon=-1) of the Friedmann equation when
the Hubble radius is much smaller than the crossover length in 4D and 5D
regimes. We show that for different values of the cosmological constant on a
brane, \lambda, phase transition occurs and results in decreasing the effective
temperature of the quark-gluon plasma and of the hadronic fluid. We then
consider the quark-hadron transition in the smooth crossover regime at high and
low temperatures and show that such a transition occurs along with decreasing
the effective temperature of the quark-gluon plasma during the process of the
phase transition. |
The light asymptotic limit of conformal blocks in Toda field theory: We compute the light asymptotic limit of $A_{n-1}$ Toda conformal blocks by
using the AGT correspondence. We show that for certain class of CFT blocks the
corresponding Nekrasov partition functions in this limit are simplified
drastically being represented as a sum of a restricted class of Young diagrams.
In the particular case of $A_{2}$ Toda we also compute the corresponding
conformal blocks using conventional CFT techniques finding a perfect agreement
with the results obtained from the Nekrasov partition functions. | Deformed Lorentz Symmetry and High-Energy Astrophysics (III): Lorentz symmetry violation (LSV) can be generated at the Planck scale, or at
some other fundamental length scale, and naturally preserve Lorentz symmetry as
a low-energy limit (deformed Lorentz symmetry, DLS). DLS can have important
implications for ultra-high energy cosmic-ray physics (see papers
physics/0003080 - hereafter referred to as I -, astro-ph/0011181 and
astro-ph/0011182, and references quoted in these papers). A crucial question is
how DLS can be extended to a deformed Poincar\'e symmetry (DPS), and what can
be the dynamical origin of this phenomenon. In a recent paper (hep-th/0208064,
hereafter referred to as II), we started a discussion of proposals to identify
DPS with a symmetry incorporating the Planck scale (like doubly special
relativity, DSR) and suggested new ways in similar directions. Implications for
models of quadratically deformed relativistic kinematics (QDRK) and linearly
deformed relativistic kinematics (LDRK) were also discussed. We pursue here our
study of these basic problems, focusing on the possibility to relate deformed
relativistic kinematics (DRK) to new space-time dimensions and compare our QDRK
model, in the form proposed since 1997, which the Kirzhnits-Chechin (KCh) and
Sato-Tati (ST) models. It is pointed out that, although the KCh model does not
seem to work such as it was formulated, our more recent proposals can be
related to suitable extensions of this model generalizing the Finsler algebras
(even to situations where a preferred physical inertial frame exists) and using
the Magueijo-Smolin transformation as a technical tool. |
Anyonic Chains, Topological Defects, and Conformal Field Theory: Motivated by the three-dimensional topological field theory / two-dimensional
conformal field theory (CFT) correspondence, we study a broad class of
one-dimensional quantum mechanical models, known as anyonic chains, that can
give rise to an enormously rich (and largely unexplored) space of
two-dimensional critical theories in the thermodynamic limit. One remarkable
feature of these systems is the appearance of non-local microscopic
"topological symmetries" that descend to topological defects of the resulting
CFTs. We derive various model-independent properties of these theories and of
this topological symmetry / topological defect correspondence. For example, by
studying precursors of certain twist and defect fields directly in the anyonic
chains, we argue that (under mild assumptions) the two-dimensional CFTs
correspond to particular modular invariants with respect to their maximal
chiral algebras and that the topological defects descending from topological
symmetries commute with these maximal chiral algebras. Using this map, we apply
properties of defect Hilbert spaces to show how topological symmetries give a
handle on the set of allowed relevant deformations of these theories.
Throughout, we give a unified perspective that treats the constraints from
discrete symmetries on the same footing as the constraints from topological
ones. | Finite Temperature Effect on Wilson Loop Mechanism: We evaluate the energy splitting of vacua appearing in the gauge theory in
the space $M_4\times S^N/Z_2$ ($N=2,3,4,5,6$ and $7$). One-loop quantum effects
which come from scalar and gauge fields are considered. We calculate them at
zero temperature as well as in high-temperature limit. We find that in these
situations there is no breakdown of the gauge symmetry. |
Soap bubble hadronic states in a QCD-motivated Nambu-Jona-Lasinio model: Inhomogeneous solutions of the gap equation in the mean field approach to
Nambu-Jona-Lasinio model are studied. An approximate Ginzburg-Landau-like gap
equation is obtained and the domain wall solution is found. Binding of fermions
to the domain wall is demonstrated. Compact domain wall with bound fermions is
studied and stabilisation by fermion pressure is demonstrated which opens a
possibility for existence of "soap bubble" hadronic states. | Five-dimensional gauge theories on spheres with negative couplings: We consider supersymmetric gauge theories on $S^5$ with a negative Yang-Mills
coupling in their large $N$ limits. Using localization we compute the partition
functions and show that the pure ${\mathrm{SU}}(N)$ gauge theory descends to an
${\mathrm{SU}}(N/2)_{+N/2}\times {\mathrm{SU}}(N/2)_{-N/2}\times
{\mathrm{SU}}(2)$ Chern-Simons gauge theory as the inverse 't Hooft coupling is
taken to negative infinity for $N$ even. The Yang-Mills coupling of the
${\mathrm{SU}}(N/2)_{\pm N/2}$ is positive and infinite, while that on the
${\mathrm{SU}}(2)$ goes to zero. We also show that the odd $N$ case has
somewhat different behavior. We then study the ${\mathrm{SU}}(N/2)_{N/2}$ pure
Chern-Simons theory. While the eigenvalue density is only found numerically, we
show that its width equals $1$ in units of the inverse sphere radius, which
allows us to find the leading correction to the free energy when turning on the
Yang-Mills term. We then consider ${\mathrm{USp}}(2N)$ theories with an
antisymmetric hypermultiplet and $N_f<8$ fundamental hypermultiplets and carry
out a similar analysis. Along the way we show that the one-instanton
contribution to the partition function remains exponentially suppressed at
negative coupling for the ${\mathrm{SU}}(N)$ theories in the large $N$ limit. |
On Marginal Operators in Boundary Conformal Field Theory: The presence of a boundary (or defect) in a conformal field theory allows one
to generalize the notion of an exactly marginal deformation. Without a
boundary, one must find an operator of protected scaling dimension $\Delta$
equal to the space-time dimension $d$ of the conformal field theory, while with
a boundary, as long as the operator dimension is protected, one can make up for
the difference $d-\Delta$ by including a factor $z^{\Delta-d}$ in the
deformation where $z$ is the distance from the boundary. This coordinate
dependence does not lead to a reduction in the underlying $SO(d,1)$ global
conformal symmetry group of the boundary conformal field theory. We show that
such terms can arise from boundary flows in interacting field theories.
Ultimately, we would like to be able to characterize what types of boundary
conformal field theories live on the orbits of such deformations. As a first
step, we consider a free scalar with a conformally invariant mass term $z^{-2}
\phi^2$, and a fermion with a similar mass. We find a connection to double
trace deformations in the AdS/CFT literature. | Radiative corrections to the Casimir effect for the massive scalar field: We compute the $O(\lambda)$ correction to the Casimir energy for the massive
$\lambda\phi^4$ model confined between a pair of parallel plates. The
calculations are made with Dirichlet and Neumann boundary conditions. The
correction is shown to be sensitive to the boundary conditions, except in the
zero mass limit, in which case our results agree with those found in the
literature. |
Bootstrapping SCFTs with Four Supercharges: We study the constraints imposed by superconformal symmetry, crossing
symmetry, and unitarity for theories with four supercharges in spacetime
dimension $2\leq d\leq 4$. We show how superconformal algebras with four
Poincar\'{e} supercharges can be treated in a formalism applicable to any, in
principle continuous, value of $d$ and use this to construct the superconformal
blocks for any $d\leq 4$. We then use numerical bootstrap techniques to derive
upper bounds on the conformal dimension of the first unprotected operator
appearing in the OPE of a chiral and an anti-chiral superconformal primary. We
obtain an intriguing structure of three distinct kinks. We argue that one of
the kinks smoothly interpolates between the $d=2$, $\mathcal N=(2,2)$ minimal
model with central charge $c=1$ and the theory of a free chiral multiplet in
$d=4$, passing through the critical Wess-Zumino model with cubic superpotential
in intermediate dimensions. | On a family of $α'$-corrected solutions of the Heterotic
Superstring effective action: We compute explicitly the first-order in $\alpha'$ corrections to a family of
solutions of the Heterotic Superstring effective action that describes
fundamental strings with momentum along themselves, parallel to solitonic
5-branes with Kaluza-Klein monopoles (Gibbons-Hawking metrics) in their
transverse space. These solutions correspond to 4-charge extremal black holes
in 4 dimensions upon dimensional reduction on $\mathrm{T}^{6}$. We show that
some of the $\alpha'$ corrections can be cancelled by introducing solitonic
$\mathrm{SU}(2)\times \mathrm{SU}(2)$ Yang-Mills fields, and that this family
of $\alpha'$-corrected solutions is invariant under $\alpha'$-corrected
T-duality transformations. We study in detail the mechanism that allows us to
compute explicitly these $\alpha'$ corrections for the ansatz considered here,
based on a generalization of the 't Hooft ansatz to hyperK\"ahler spaces. |
Sur un système intégrable à bord: [French] We develop new applications of Sklyanin's $K$-matrix formalism to
the study of periodic solutions of the sinh-Gordon equation. | An Action for Extended String Newton-Cartan Gravity: We construct an action for four-dimensional extended string Newton-Cartan
gravity which is an extension of the string Newton-Cartan gravity that
underlies nonrelativistic string theory. The action can be obtained as a
nonrelativistic limit of the Einstein-Hilbert action in General Relativity
augmented with a term that contains an auxiliary two-form and one-form gauge
field that both have zero flux on-shell. The four-dimensional extended string
Newton-Cartan gravity is based on a central extension of the algebra that
underlies string Newton-Cartan gravity.
The construction is similar to the earlier construction of a
three-dimensional Chern-Simons action for extended Newton-Cartan gravity, which
is based on a central extension of the algebra that underlies Newton-Cartan
gravity. We show that this three-dimensional action is naturally obtained from
the four-dimensional action by a reduction over the spatial isometry direction
longitudinal to the string followed by a truncation of the extended string
Newton-Cartan gravity fields. Our construction can be seen as a special case of
the construction of an action for extended p-brane Newton-Cartan gravity in p+3
dimensions. |
BKM Lie superalgebra for the Z_5 orbifolded CHL string: We study the Z_5-orbifolding of the CHL string theory by explicitly
constructing the modular form tilde{Phi}_2 generating the degeneracies of the
1/4-BPS states in the theory. Since the additive seed for the sum form is a
weak Jacobi form in this case, a mismatch is found between the modular forms
generated from the additive lift and the product form derived from threshold
corrections. We also construct the BKM Lie superalgebra, tilde{G}_5,
corresponding to the modular form tilde{Delta}_1 (Z) = tilde{Phi}_2 (Z)^{1/2}
which happens to be a hyperbolic algebra. This is the first occurrence of a
hyperbolic BKM Lie superalgebra. We also study the walls of marginal stability
of this theory in detail, and extend the arithmetic structure found by Cheng
and Dabholkar for the N=1,2,3 orbifoldings to the N=4,5 and 6 models, all of
which have an infinite number of walls in the fundamental domain. We find that
analogous to the Stern-Brocot tree, which generated the intercepts of the walls
on the real line, the intercepts for the N >3 cases are generated by linear
recurrence relations. Using the correspondence between the walls of marginal
stability and the walls of the Weyl chamber of the corresponding BKM Lie
superalgebra, we propose the Cartan matrices for the BKM Lie superalgebras
corresponding to the N=5 and 6 models. | The classical double copy for Taub-NUT spacetime: The double copy is a much-studied relationship between gauge theory and
gravity amplitudes. Recently, this was generalised to an infinite family of
classical solutions to Einstein's equations, namely stationary Kerr-Schild
geometries. In this paper, we extend this to the Taub-NUT solution in gravity,
which has a double Kerr-Schild form. The single copy of this solution is a
dyon, whose electric and magnetic charges are related to the mass and NUT
charge in the gravity theory. Finally, we find hints that the classical double
copy extends to curved background geometries. |
The Sen Limit: F-theory compactifications on elliptic Calabi-Yau manifolds may be related to
IIb compactifications by taking a certain limit in complex structure moduli
space, introduced by A. Sen. The limit has been characterized on the basis of
SL(2,Z) monodromies of the elliptic fibration. Instead, we introduce a stable
version of the Sen limit. In this picture the elliptic Calabi-Yau splits into
two pieces, a P^1-bundle and a conic bundle, and the intersection yields the
IIb space-time. We get a precise match between F-theory and perturbative type
IIb. The correspondence is holographic, in the sense that physical quantities
seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as
expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds
to summing up the D(-1)-instanton corrections to the IIb theory. | Seiberg-Witten Theories, Integrable Models and Perturbative
Prepotentials: This is a very brief review of relations between Seiberg-Witten theories and
integrable systems with emphasis on the perturbative prepotentials presented at
the E.S.Fradkin Memorial Conference. |
On Hybrid (Topologically) Massive Supergravity in Three Dimensions: A class of hybrid (topologically) massive off-shell supergravities coupled to
an on-shell matter scalar multiplet was recently constructed. The auxiliary
field in the off-shell multiplet is dynamical for generic values of the eight
parameters. We find that by choosing the parameters appropriately, it remains
non-dynamical. We perform linearized analysis around the supersymmetric AdS3
vacuum and its Minkowski limit. The ghost-free condition for the Minkowski
vacuum is explored. For the AdS3 vacuum, we obtain the criticality condition
and find that at the critical points, one of the two massive gravitons becomes
pure gauge and decouples from the bulk physics, whilst the other has positive
energy. We demonstrate that the mass of the BTZ black hole is non-negative at
the critical points. We also investigate general BPS solutions. For certain
parameter choices, we obtain exact solutions. In particular, we present the BPS
string (domain-wall) solution that is dual to certain two-dimensional quantum
field theory with an ultra-violet conformal fixed point. | Hyperkahler Metrics from Monopole Walls: We present ALH hyperkahler metrics induced from well-separated SU(2) monopole
walls which are equivalent to monopoles on T^2 x R. The metrics are explicitly
obtained due to Manton's observation by using explicit monopole solutions.
These are doubly-periodic and have the modular invariance with respect to the
complex structure of the complex torus T^2. We also derive metrics from
monopole walls with Dirac-type singularities. |
Small Black Hole Explosions: Small black holes are a powerful tool to explore infinite distances in moduli
spaces. However, we show that in 4d theories with a scalar potential growing
fast enough at infinity, it is energetically too costly for scalars to diverge
at the core, and the small black hole puffs up into a regular black hole, or
follows a runaway behaviour.
We derive a critical exponent characterizing the occurrence or not of such
small black hole explosions, both from a 4d perspective, and in the 2d theory
after an $\bf{S}^2$ truncation. The latter setup allows a unified discussion of
fluxes, domain walls and black holes, solving an apparent puzzle in the
expression of their potentials in the 4d $\cal{N}=2$ gauged supergravity
context.
We discuss the realization of these ideas in 4d $\cal{N}=2$ gauged
supergravities. Along the way we show that many regular black hole supergravity
solutions in the literature in the latter context are incomplete, due to
Freed-Witten anomalies (or duals thereof), and require the emission of strings
by the black hole.
From the 2d perspective, small black hole solutions correspond to dynamical
cobordisms, with the core describing an end of the world brane. Small black
hole explosions represent obstructions to completing the dynamical cobordism.
We study the implications for the Cobordism Distance Conjecture, which states
that in any theory there should exist dynamical cobordisms accessing all
possible infinite distance limits in scalar field space. The realization of
this principle using small black holes leads to non-trivial constraints on the
4d scalar potential of any consistent theory; in the 4d $\cal{N}=2$ context,
they allow to recover from a purely bottom-up perspective, several non-trivial
properties of vector moduli spaces near infinity familiar from CY$_3$
compactifications. | Deep Inelastic Scattering off a Plasma with a Background Magnetic Field: Using holography, we analyse deep inelastic scattering of a flavor current
from a strongly coupled quark-gluon plasma with a background magnetic field.
The aim is to show how the magnetic field affects the partonic picture of the
plasma. The flavored constituents of the plasma are described using D3-D7 brane
model at finite temperature. We find that the presence of a background magnetic
field makes it harder to detect the plasma constituents. Our calculations are
in agreement with those calculated from other approaches. Besides the resulting
changes for plasma structure functions a criteria will be obtained for the
possibility of deep inelastic process in the presence of magnetic field. |
Extremal black string with Kalb-Ramond field via $α^{\prime}$
corrections: In this paper, we obtain the three-dimensional regular extremal black string
solution incorporating $\alpha'$ corrections and a non-trivial Kalb-Ramond
field. The difficulty in considering the Kalb-Ramond field lies in the fact
that it transforms the original equations of motion into an infinite summation
form involving matrices, making it difficult to calculate the matrix
differential equations. To solve this problem, we introduce a new method that
transforms the infinite summation of matrix differential equations into a
simple trace of the matrix. As a result, we are able to obtain a
non-perturbative and non-singular extremal black string solution. Indeed, this
work serves as a good example for studying more complicated non-perturbative
solutions that incorporate the Kalb-Ramond field via complete $\alpha'$
corrections. | Do gauge fields really contribute negatively to black hole entropy?: Quantum fluctuations of matter fields contribute to the thermal entropy of
black holes. For free minimally-coupled scalar and spinor fields, this
contribution is precisely the entanglement entropy. For gauge fields, Kabat
found an extra negative divergent "contact term" with no known statistical
interpretation. We compare this contact term to a similar term that arises for
nonminimally-coupled scalar fields. Although both divergences may be
interpreted as terms in the Wald entropy, we point out that the contact term
for gauge fields comes from a gauge-dependent ambiguity in Wald's formula.
Revisiting Kabat's derivation of the contact term, we show that it is sensitive
to the treatment of infrared modes. To explore these infrared issues, we
consider two-dimensional compact manifolds, such as Euclidean de Sitter space,
and show that the contact term arises from an incorrect treatment of zero
modes. In a manifestly gauge-invariant reduced phase space quantization, the
gauge field contribution to the entropy is positive, finite, and equal to the
entanglement entropy. |
Effective action approach to dynamical generation of fermion mixing: In this paper we discuss a mechanism for the dynamical generation of flavor
mixing, in the framework of the Nambu--Jona Lasinio model. Our approach is
illustrated both with the conventional operatorial formalism and with
functional integral and ensuing one-loop effective action. The results obtained
are briefly discussed. | Towards Supergravity Duals of Chiral Symmetry Breaking in
Sasaki-Einstein Cascading Quiver Theories: We construct a first order deformation of the complex structure of the cone
over Sasaki-Einstein spaces Y^{p,q} and check supersymmetry explicitly. This
space is a central element in the holographic dual of chiral symmetry breaking
for a large class of cascading quiver theories. We discuss a solution
describing a stack of N D3 branes and M fractional D3 branes at the tip of the
deformed spaces. |
Bound States of the Hydrogen Atom in the Presence of a Magnetic Monopole
Field and an Aharonov-Bohm Potential: In the present article we analyze the bound states of an electron in a
Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole
are present. We solve, via separation of variables, the Schr\"odinger equation
in spherical coordinates and we show how the Hydrogen energy spectrum depends
on the Aharonov-Bohm and the magnetic monopole strengths. In passing, the
Klein-Gordon equation is solved. | ABJ Triality: from Higher Spin Fields to Strings: We demonstrate that a supersymmetric and parity violating version of
Vasiliev's higher spin gauge theory in AdS$_4$ admits boundary conditions that
preserve ${\cal N}=0,1,2,3,4$ or 6 supersymmetries. In particular, we argue
that the Vasiliev theory with U(M) Chan-Paton and ${\cal N}=6$ boundary
condition is holographically dual to the 2+1 dimensional $U(N)_k\times
U(M)_{-k}$ ABJ theory in the limit of large $N,k$ and finite $M$. In this
system all bulk higher spin fields transform in the adjoint of the U(M) gauge
group, whose bulk t'Hooft coupling is $\frac{M}{N}$. Analysis of boundary
conditions in Vasiliev theory allows us to determine exact relations between
the parity breaking phase of Vasiliev theory and the coefficients of two and
three point functions in Chern-Simons vector models at large $N$. Our picture
suggests that the supersymmetric Vasiliev theory can be obtained as a limit of
type IIA string theory in AdS$_4\times \mathbb{CP}^3$, and that the non-Abelian
Vasiliev theory at strong bulk 't Hooft coupling smoothly turn into a string
field theory. The fundamental string is a singlet bound state of Vasiliev's
higher spin particles held together by U(M) gauge interactions. This is
illustrated by the thermal partition function of free ABJ theory on a two
sphere at large $M$ and $N$ even in the analytically tractable free limit. In
this system the traces or strings of the low temperature phase break up into
their Vasiliev particulate constituents at a U(M) deconfinement phase
transition of order unity. At a higher temperature of order
$T=\sqrt{\frac{N}{M}}$ Vasiliev's higher spin fields themselves break up into
more elementary constituents at a U(N) deconfinement temperature, in a process
described in the bulk as black hole nucleation. |
Supersymmetry Breaking, Moduli Stabilization and Hidden U(1) Breaking in
M-Theory: We calculate and explore the moduli potential for M-Theory compactified on
G_2-manifolds in which the superpotential is dominated by a single membrane
instanton term plus one from an asymptotically free hidden sector gauge
interaction. We show that all moduli can be stabilized and that hidden sector
gauge symmetries can be Higgsed at a high scale. We then compute the spectrum
of superpartner masses at the GUT scale and evolve it to the electroweak scale.
We find a spectrum which is very similar to the G_2-MSSM with light gauginos -
accessible at the LHC - and a neutral wino dark matter candidate. | Singular hypersurfaces and thin shells in cosmology: We analyse spherically symmetric geometries, combining a cosmological patch
and a Schwarzschild black hole patch joined via a singular co-dimension 1
hypersurface. In a general analysis applicable to dimensions greater than
three, assuming an arbitrary homogeneous and isotropic cosmology, we derive the
stress-energy tensor of the hypersurface in terms of the cosmological energy
density. This analysis reveals a novel exact solution featuring radiation
within the cosmology and a shell composed of pressureless dust. Exploring the
parameter space yields twenty-two distinct solution families, including `bubble
of cosmology' and `Swiss cheese' spacetimes. Notably, solutions with a negative
cosmological constant exhibit a holographic dual. Additionally, we provide a
pedagogical introduction to hypersurfaces in general relativity and a practical
approach for constructing thin shell spacetimes. |
Comments on Non-Supersymmetric Orientifolds at Strong Coupling: We consider several properties of a set of anti-D$p$-branes in the presence
of orientifold $p$-planes in type II theory. This system breaks all the
supersymmetries of the theory, but is free of tachyons. In particular, we
center on the case of a single anti-D$p$-brane stuck at a negatively charged
orientifold $p$-plane, and study its strong coupling behaviour for $p=2,3,4$.
Interestingly enough, as the coupling increases the system undergoes a phase
transition where an additional antibrane is created. We conclude with some
remarks on the limit of large number of antibranes on top of orientifold
planes. | Weaving the Exotic Web: String and M-theory contain a family of branes forming U-duality multiplets.
In particular, standard branes with codimension higher than or equal to two,
can be explicitly found as supergravity solutions. However, whether domain-wall
branes and space-filling branes can be found as supergravity solutions is still
unclear. In this paper, we firstly provide a full list of exotic branes in type
II string theory or M-theory compactified to three or higher dimensions. We
show how to systematically obtain backgrounds of exotic domain-wall branes and
space-filling branes as solutions of the double field theory or the exceptional
field theory. Such solutions explicitly depend on the winding coordinates and
cannot be given as solutions of the conventional supergravity theories.
However, as the domain-wall solutions depend linearly on the winding
coordinates, we describe them as solutions of deformed supergravities such as
the Romans massive IIA supergravity or lower-dimensional gauged supergravities.
We establish explicit relations among the domain-wall branes, the
mixed-symmetry potentials, the locally non-geometric fluxes, and deformed
supergravities. |
Free field realisation of boundary vertex algebras for Abelian gauge
theories in three dimensions: We study the boundary vertex algebras of $A$-twisted $\mathcal{N}=4$ Abelian
gauge theories in three dimensions. These are identified with the BRST quotient
(semi-infinite cohomology) of collections of symplectic bosons and free
fermions that reflect the matter content of the corresponding gauge theory. We
develop various free field realisations for these vertex algebras which we
propose to interpret in terms of their localisation on their associated
varieties. We derive the free field realisations by bosonising the elementary
symplectic bosons and free fermions and then calculating the relevant
semi-infinite cohomology, which can be done systematically. An interesting
feature of our construction is that for certain preferred free field
realisations, the outer automorphism symmetry of the vertex algebras in
question (which are identified with the symmetries of the Coulomb branch in the
infrared) are made manifest. | Non-perturbative membrane spin-orbit couplings in M/IIA theory: Membrane source-probe dynamics is investigated in the framework of the finite
N-sector DLCQ M theory compactified on a transverse two-torus for an arbitrary
size of the longitudinal dimension. The non-perturbative two fermion terms in
the effective action of the matrix theory, the (2+1)-dimensional supersymmetric
Yang-Mills theory, that are related to the four derivative F^4 terms by the
supersymmetry transformation are obtained, including the one-loop term and full
instanton corrections. On the supergravity side, we compute the classical probe
action up to two fermion terms based on the classical supermembrane formulation
in an arbitrary curved background geometry produced by source membranes
satisfying the BPS condition; two fermion terms correspond to the spin-orbit
couplings for membranes. We find precise agreement between two approaches when
the background space-time is chosen to be that of the DLCQ M theory, which is
asymptotically locally Anti-de Sitter. |
Holography as Cutoff: a proposal for measure of inflationary universes: We propose the holographic principle as a dynamical cutoff for any quantum
theory of gravity with a geometric description at low energies, incorporating
ideas of effective field theory. We illustrate the proposal by revisiting the
problem of defining a measure for homogeneous and isotropic spacetimes coupled
to a scalar field and conclude by discussing the implications to the
inflationary model. | A Color Dual Form for Gauge-Theory Amplitudes: Recently a duality between color and kinematics has been proposed, exposing a
new unexpected structure in gauge theory and gravity scattering amplitudes.
Here we propose that the relation goes deeper, allowing us to reorganize
amplitudes into a form reminiscent of the standard color decomposition in terms
of traces over generators, but with the role of color and kinematics swapped.
By imposing additional conditions similar to Kleiss-Kuijf relations between
partial amplitudes, the relationship between the earlier form satisfying the
duality and the current one is invertible. We comment on extensions to loop
level. |
Splitting of folded strings in AdS_3: In this paper we present semiclassical computations of the splitting of
folded spinning strings in AdS_3, which may be of interest in the context of
AdS/CFT duality. We start with a classical closed string and assume that it can
split on two closed string fragments, if at a given time two points on it
coincide in target space and their velocities agree. First we consider the case
of the folded string with large spin. Assuming the formal large-spin
approximation of the folded string solution in AdS_3, we can completely
describe the process of splitting: compute the full set of charges and obtain
the string solutions describing the evolution of the final states. We find
that, in this limit, the world surface does not change in the process and the
final states are described by the solutions of the same type as the initial
string, i.e. the formal large-spin approximation of the folded string in AdS_3.
Then we consider the general case --- splitting of string given by the exact
folded string solution. We find the expressions for the charges of the final
fragments, the coordinate transformations diagonalizing them and, finally,
their energies and spins. Due to the complexity of the initial string profile,
we cannot find the solutions describing the evolution of the final fragments,
but we can predict their qualitative behavior. We also generalize the results
to include circular rotations and windings in S^5. | Reconstruction of Type II Supergravities via $O(d) \times O(d)$ Duality
Invariants: We reconstruct type II supergravities by using building blocks of $O(d)
\times O(d)$ invariants.These invariants are obtained by explicitly analyzing
$O(d) \times O(d)$ transformations of 10 dimensional massless fields. Similar
constructions are done by employing double field theory or generalized
geometry, but we completed the reconstruction within the framework of the
supergravities. |
Quasi-exactly solvable quasinormal modes: We consider quasinormal modes with complex energies from the point of view of
the theory of quasi-exactly solvable (QES) models. We demonstrate that it is
possible to find new potentials which admit exactly solvable or QES quasinormal
modes by suitable complexification of parameters defining the QES potentials.
Particularly, we obtain one QES and four exactly solvable potentials out of the
five one-dimensional QES systems based on the $sl(2)$ algebra. | Initial Kaluza-Klein fluctuations and inflationary gravitational waves
in braneworld cosmology: We study the spectrum of gravitational waves generated from inflation in the
Randall-Sundrum braneworld. Since the inflationary gravitational waves are of
quantum-mechanical origin, the initial configuration of perturbations in the
bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the
zero mode. We show, however, that the initial fluctuations in Kaluza-Klein
modes have no significant effect on the late time spectrum, irrespective of the
energy scale of inflation and the equation of state parameter in the
post-inflationary stage. This is done numerically, using the Wronskian
formulation. |
Restricted sine-Gordon Theory in the Repulsive Regime as Perturbed
Minimal CFTs: We construct the restricted sine-Gordon theory by truncating the sine-Gordon
multi-soliton Hilbert space for the repulsive coupling constant due to the
quantum group symmetry $SL_q(2)$ which we identify from the Korepin's
$S$-matrices. We connect this restricted sine-Gordon theory with the minimal
($c<1$) conformal field theory ${\cal M}_{p/p+2}$ ($p$ odd) perturbed by the
least relevent primary field $\Phi_{1,3}$. The exact $S$-matrices are derived
for the particle spectrum of a kink and neutral particles. As a consistency
check, we compute the central charge of the restricted theory in the UV limit
using the thermodynamic Bethe ansatz analysis and show that it is equal to that
of ${\cal M}_{p/p+2}$. | Symmetric space sigma-model dynamics: Current formalism: After explicitly constructing the symmetric space sigma model lagrangian in
terms of the coset scalars of the solvable Lie algebra gauge in the current
formalism we derive the field equations of the theory. |
Holomorphic Couplings in String Theory: In these lectures we review the properties of holomorphic couplings in the
effective action of four-dimensional N=1 and N=2 closed string vacua. We
briefly outline their role in establishing a duality among (classes of)
different string vacua. (Lectures presented by J. Louis at the Trieste Spring
School 1996.) | A Comment on Entropy and Area: For an arbitrary quantum field in flat space with a planar boundary, an
entropy of entanglement, associated with correlations across the boundary, is
present when the field is in its vacuum state. The vacuum state of the same
quantum field appears thermal in Rindler space, with an associated thermal
entropy. We show that the density matrices describing the two situations are
identical, and therefore that the two entropies are equal. We comment on the
generality and significance of this result, and make use of it in analyzing the
area and cutoff dependence of the entropy. The equivalence of the density
matrices leads us to speculate that a planar boundary in Minkowski space has a
classical entropy given by the Bekenstein--Hawking formula. |
The spectrum of strings on BTZ black holes and spectral flow in the
SL(2,R) WZW model: We study the spectrum of bosonic string theory on rotating BTZ black holes,
using a SL(2,R) WZW model. Previously, Natsuume and Satoh have analyzed strings
on BTZ black holes using orbifold techniques. We show how an appropriate
spectral flow in the WZW model can be used to generate the twisted sectors,
emphasizing how the spectral flow works in the hyperbolic basis natural for the
BTZ black hole. We discuss the projection condition which leads to the
quantization condition for the allowed quantum numbers for the string
excitations, and its connection to the anomaly in the corresponding conserved
Noether current. | On stability of false vacuum in supersymmetric theories with cosmic
strings: We study the stability of supersymmetry breaking vacuum in the presence of
cosmic strings arising in the messenger sector. For certain ranges of the
couplings, the desired supersymmetry breaking vacua become unstable against
decay into phenomenologically unacceptable vacua. This sets constraints on the
range of allowed values of the coupling constants appearing in the models and
more generally on the chosen dynamics of gauge symmetry breaking. |
Advances in Inflation in String Theory: We provide a pedagogical overview of inflation in string theory. Our theme is
the sensitivity of inflation to Planck-scale physics, which we argue provides
both the primary motivation and the central theoretical challenge for the
subject. We illustrate these issues through two case studies of inflationary
scenarios in string theory: warped D-brane inflation and axion monodromy
inflation. Finally, we indicate how future observations can test scenarios of
inflation in string theory. | Quasinormal modes and thermodynamic phase transitions: It has recently been suggested that scalar, Dirac and Rarita-Schwinger
perturbations are related to thermodynamic phase transitions of charged
(Reissner-Nordstr\"om) black holes. In this note we show that this result is
probably a numerical coincidence, and that the conjectured correspondence does
not straightforwardly generalize to other metrics, such as Kerr or
Schwarzschild (anti-)de Sitter. Our calculations do not rule out a relation
between dynamical and thermodynamical properties of black holes, but they
suggest that such a relation is non-trivial. |
Supersymmetric quantum theory, non-commutative geometry, and
gravitation. Lecture Notes Les Houches 1995: This is an expanded version of the notes to a course taught by the first
author at the 1995 Les Houches Summer School. Constraints on a tentative
reconciliation of quantum theory and general relativity are reviewed. It is
explained what supersymmetric quantum theory teaches us about differential
topology and geometry. Non-commutative differential topology and geometry are
developed in some detail. As an example, the non-commutative torus is studied.
An introduction to string theory and $M$(atrix) models is provided, and it is
outlined how tools of non-commutative geometry can be used to explore the
geometry of string theory and conformal field theory. | The covariant and on-shell statistics in kappa-deformed spacetime: It has been a long-standing issue to construct the statistics of identical
particles in $\kappa$-deformed spacetime. In this letter, we investigate
different ideas on this problem. Following the ideas of Young and Zegers, we
obtain the covariant and on-shell kappa two-particle state in 1+1 D in a
simpler way. Finally, a procedure to get such state in higher dimension is
proposed. |
Twist decomposition of nonlocal light-ray operators and harmonic tensor
functions: For arbitrary spacetime dimension a systematic procedure is carried on to
uniquely decompose nonlocal light-cone operators into harmonic operators of
well defined twist. Thereby, harmonic tensor polynomials up to rank 2 are
introduced. Symmetric tensor operators of rank 2 are considered as an example. | 3d Conformal Higher Spin Symmetry in 2+1 Dimensional Matter Systems: The symmetry algebra of massless fields living on the 3-dimensional conformal
boundary of AdS(4) is shown to be isomorphic to 3d conformal higher spin
algebra (AdS(4) higher spin algebra). A simple realization of this algebra on
the free flat 3d massless matter fields is given in terms of an auxiliary Fock
module. |
Review of W Strings: We review some of the recent developments in the construction of $W$-string
theories. These are generalisations of ordinary strings in which the
two-dimensional ``worldsheet'' theory, instead of being a gauging of the
Virasoro algebra, is a gauging of a higher-spin extension of the Virasoro
algebra---a $W$ algebra. Despite the complexity of the (non-linear) $W$
algebras, it turns out that the spectrum can be computed completely and
explicitly for more or less any $W$ string. The result is equivalent to a set
of spectra for Virasoro strings with unusual central charge and intercepts. | Nonrelativistic Lee model in three dimensional Riemannian manifolds: In this work, we construct the non-relativistic Lee model on some class of
three dimensional Riemannian manifolds by following a novel approach introduced
by S. G. Rajeev hep-th/9902025. This approach together with the help of heat
kernel allows us to perform the renormalization non-perturbatively and
explicitly. For completeness, we show that the ground state energy is bounded
from below for different classes of manifolds, using the upper bound estimates
on the heat kernel. Finally, we apply a kind of mean field approximation to the
model for compact and non-compact manifolds separately and discover that the
ground state energy grows linearly with the number of bosons n. |
String Theory in Polar Coordinates and the Vanishing of the One-Loop
Rindler Entropy: We analyze the string spectrum of flat space in polar coordinates, following
the small curvature limit of the $SL(2,\mathbb{R})/U(1)$ cigar CFT. We first
analyze the partition function of the cigar itself, making some clarifications
of the structure of the spectrum that have escaped attention up to this point.
The superstring spectrum (type 0 and type II) is shown to exhibit an involution
symmetry, that survives the small curvature limit. We classify all marginal
states in polar coordinates for type II superstrings, with emphasis on their
links and their superconformal structure. This classification is confirmed by
an explicit large $\tau_2$ analysis of the partition function. Next we compare
three approaches towards the type II genus one entropy in Rindler space: using
a sum-over-fields strategy, using a Melvin model approach and finally using a
saddle point method on the cigar partition function. In each case we highlight
possible obstructions and motivate that the correct procedures yield a
vanishing result: $S=0$. We finally discuss how the QFT UV divergences of the
fields in the spectrum disappear when computing the free energy and entropy
using Euclidean techniques. | Gauge-invariant spectral description of the $U(1)$ Higgs model from
local composite operators: The spectral properties of a set of local gauge-invariant composite operators
are investigated in the $U(1)$ Higgs model quantized in the 't Hooft $R_{\xi}$
gauge. These operators enable us to give a gauge-invariant description of the
spectrum of the theory, thereby surpassing certain incommodities when using the
standard elementary fields. The corresponding two-point correlation functions
are evaluated at one-loop order and their spectral functions are obtained
explicitly. As expected, the above mentioned correlation functions are
independent from the gauge parameter $\xi$, while exhibiting positive spectral
densities as well as gauge-invariant pole masses corresponding to the massive
photon and Higgs physical excitations. |
Branes at Orbifolded Conifold Singularities and Supersymmetric Gauge
Field Theories: We consider D3 branes at orbifolded conifold singularities which are not
quotient singularities. We use toric geometry and gauged linear sigma model to
study the moduli space of the gauge theories on the D3 branes. We find that
topologically distinct phases are related by a flop transition. It is also
shown that an orbifold singularity can occur in some phases if we give
expectation values to some of the chiral fields. | Higher order corrections to beyond-all-order effects in a fifth order
Korteweg-de Vries equation: A perturbative scheme is applied to calculate corrections to the leading,
exponentially small (beyond-all-orders) amplitude of the ``trailing'' wave
asymptotics of weakly localized solitons. The model considered is a Korteweg-de
Vries equation modified by a fifth order derivative term,
$\epsilon^2\partial_x^5$ with $\epsilon\ll1$ (fKdV). The leading order
corrections to the tail amplitude are calculated up to ${\cal{O}}(\epsilon^5)$.
An arbitrary precision numerical code is implemented to solve the fKdV equation
and to check the perturbative results. Excellent agreement is found between the
numerical and analytical results. Our work also clarifies the origin of a
long-standing disagreement between the ${\cal{O}}(\epsilon^2)$ perturbative
result of Grimshaw and Joshi [SIAM J. Appl. Math. 55, 124 (1995)] and the
numerical results of Boyd [Comp. Phys. 9, 324 (1995)]. |
Lagrangian and Covariant Field Equations for Supersymmetric Yang-Mills
Theory in 12D: We present a lagrangian formulation for recently-proposed supersymmetric
Yang-Mills theory in twelve dimensions. The field content of our multiplet has
an additional auxiliary vector field in the adjoint representation. The usual
Yang-Mills field strength is modified by a Chern-Simons form containing this
auxiliary vector field. This formulation needs no constraint imposed on the
component field from outside, and a constraint on the Yang-Mills field is
generated as the field equation of the auxiliary vector field. The invariance
check of the action is also performed without any reference to constraints by
hand. Even though the total lagrangian takes a simple form, it has several
highly non-trivial extra symmetries. We couple this twelve-dimensional
supersymmetric Yang-Mills background to Green-Schwarz superstring, and confirm
fermionic kappa-invariance. As another improvement of this theory, we present a
set of fully Lorentz-covariant and supercovariant field equations with no use
of null-vectors. This system has an additional scalar field, whose gradient
plays a role of the null-vector. This system exhibits spontaneous breaking of
the original Lorentz symmetry SO(10,2) for twelve-dimensions down to SO(9,1)
for ten-dimensions. | Relations Between Closed String Amplitudes at Higher-order Tree Level
and Open String Amplitudes: KLT relations almost factorize closed string amplitudes on $S_2$ by two open
string tree amplitudes which correspond to the left- and the right- moving
sectors. In this paper, we investigate string amplitudes on $D_2$ and $RP_2$.
We find that KLT factorization relations do not hold in these two cases. The
relations between closed and open string amplitudes have new forms. On $D_2$
and $RP_2$, the left- and the right- moving sectors are connected into a single
sector. Then an amplitude with closed strings on $D_2$ or $RP_2$ can be given
by one open string tree amplitude except for a phase factor. The relations
depends on the topologies of the world-sheets.Under T-duality, the relations on
$D_2$ and $RP_2$ give the amplitudes between closed strings scattering from
D-brane and O-plane respectively by open string partial amplitudes.In the low
energy limits of these two cases, the factorization relations for graviton
amplitudes do not hold. The amplitudes for gravitons must be given by the new
relations instead. |
Fractional Conformal Descendants and Correlators in General 2D $S_N$
Orbifold CFTs at Large $N$: We consider correlation functions in symmetric product ($S_N$) orbifold CFTs
at large $N$ with arbitrary seed CFT. Specifically, we consider correlators of
descendant operators constructed using both the full Virasoro generators
$L_{m}$ and fractional Virasoro generators $\ell_{m/n_i}$. Using covering space
techniques, we show that correlators of descendants may be written entirely in
terms of correlators of ancestors, and further that the appropriate set of
ancestors are those operators that lift to conformal primaries on the cover. We
argue that the covering space data should cancel out in such calculations. To
back this claim, we provide some example calculations by considering a
three-point function of the form (4-cycle)-(2-cycle)-(5-cycle) that lifts to a
three-point function of arbitrary primaries on the cover, and descendants
thereof. In these examples we show that while the covering space is used for
the calculation, the final descent relations do not depend on covering space
data, nor on the details of which seed CFT is used to construct the orbifold,
making these results universal. | Relativistic and nonrelativistic Landau levels for the noncommutative
quantum Hall effect with anomalous magnetic moment in a conical Gödel-type
spacetime: In this paper, we analyze the relativistic and nonrelativistic energy spectra
(fermionic Landau levels) for the noncommutative quantum Hall effect with
anomalous magnetic moment in the conical G\"odel-type spacetime in
(2+1)-dimensions, where such spacetime is the combination of the flat
G\"odel-type spacetime with a cosmic string (conical gravitational topological
defect). To analyze these energy spectra, we start from the noncommutative
Dirac equation with minimal and nonminimal couplings in polar coordinates.
Using the tetrads formalism, we obtain a second-order differential equation.
Next, we solve exactly this differential equation, where we obtain a
generalized Laguerre equation, and also a quadratic polynomial equation for the
total relativistic energy. By solving this polynomial equation, we obtain the
relativistic energy spectrum of the fermion and antifermion. Besides, we also
analyze the nonrelativistic limit of the system, where we obtain the
nonrelativistic energy spectrum. In both cases (relativistic and
nonrelativistic), we discuss in detail the characteristics of each spectrum as
well as the influence of all parameters and physical quantities in such
spectra. Comparing our problem with other works, we verified that our results
generalize several particular cases in the literature. |
Thermal gravity, black holes and cosmological entropy: Taking seriously the interpretation of black hole entropy as the logarithm of
the number of microstates, we argue that thermal gravitons may undergo a phase
transition to a kind of black hole condensate. The phase transition proceeds
via nucleation of black holes at a rate governed by a saddlepoint configuration
whose free energy is of order the inverse temperature in Planck units. Whether
the universe remains in a low entropy state as opposed to the high entropy
black hole condensate depends sensitively on its thermal history. Our results
may clarify an old observation of Penrose regarding the very low entropy state
of the universe. | Quantum Curves, Resurgence and Exact WKB: We study the non-perturbative quantum geometry of the open and closed
topological string on the resolved conifold and its mirror. Our tools are
finite difference equations in the open and closed string moduli and the
resurgence analysis of their formal power series solutions. In the closed
setting, we derive new finite difference equations for the refined partition
function as well as its Nekrasov-Shatashvili (NS) limit. We write down a
distinguished analytic solution for the refined difference equation that
reproduces the expected non-perturbative content of the refined topological
string. We compare this solution to the Borel analysis of the free energy in
the NS limit. We find that the singularities of the Borel transform lie on
infinitely many rays in the Borel plane and that the Stokes jumps across these
rays encode the associated Donaldson-Thomas invariants of the underlying
Calabi-Yau geometry. In the open setting, the finite difference equation
corresponds to a canonical quantization of the mirror curve. We analyze this
difference equation using Borel analysis and exact WKB techniques and identify
the 5d BPS states in the corresponding exponential spectral networks. We
furthermore relate the resurgence analysis in the open and closed setting. This
guides us to a five-dimensional extension of the Nekrasov-Rosly-Shatashvili
proposal, in which the NS free energy is computed as a generating function of
$q$-difference opers in terms of a special set of spectral coordinates.
Finally, we examine two spectral problems describing the corresponding quantum
integrable system. |
D-brane Configurations and Nicolai Map in Supersymmetric Yang-Mills
Theory: We discuss some properties of a supersymmetric matrix model that is the
dimensional reduction of supersymmetric Yang-Mills theory in ten dimensions and
which has been recently argued to represent the short-distance structure of M
theory in the infinite momentum frame. We describe a reduced version of the
matrix quantum mechanics and derive the Nicolai map of the simplified
supersymmetric matrix model. We use this to argue that there are no phase
transitions in the large-N limit, and hence that S-duality is preserved in the
full eleven dimensional theory. | Linearized supergravity from Matrix theory: We show that the linearized supergravity potential between two objects
arising from the exchange of quanta with zero longitudinal momentum is
reproduced to all orders in 1/r by terms in the one-loop Matrix theory
potential. The essential ingredient in the proof is the identification of the
Matrix theory quantities corresponding to moments of the stress tensor and
membrane current. We also point out that finite-N Matrix theory violates the
equivalence principle. |
1/8 BPS States in Ads/CFT: We study a class of exact supersymmetric solutions of type IIB Supergravity.
They have an SO(4) x SU(2) x U(1) isometry and preserve generically 4 of the 32
supersymmetries of the theory. Asymptotically AdS_5 x S^5 solutions in this
class are dual to 1/8 BPS chiral operators which preserve the same symmetries
in the N=4 SYM theory. They are parametrized by a set of four functions that
satisfy certain differential equations. We analyze the solutions to these
equations in a large radius asymptotic expansion: they carry charges with
respect to two U(1) KK gauge fields and their mass saturates the expected BPS
bound. | The zeros of the QCD partition function: We establish a relationship between the zeros of the partition function in
the complex mass plane and the spectral properties of the Dirac operator in
QCD. This relation is derived within the context of chiral Random Matrix Theory
and applies to QCD when chiral symmetry is spontaneously broken. Further, we
introduce and examine the concept of normal modes in chiral spectra. Using this
formalism we study the consequences of a finite Thouless energy for the zeros
of the partition function. This leads to the demonstration that certain
features of the QCD partition function are universal. |
Transgression Forms and Abelian Semigroups in Supergravity: Two main themes populate this Thesis's pages: transgression forms as
Lagrangians for gauge theories and the Abelian semigroup expansion of Lie
algebras.
A transgression form is a function of two gauge connections whose main
property is its full invariance under gauge transformations. From this form a
Lagrangian is built, and equations of motion, boundary conditions and
associated Noether currents are derived. A subspace separation method, based on
the extended Cartan homotopy formula, is proposed, which allows to (i) split
the Lagrangian in 'bulk' and 'boundary' contributions and (ii) separate the
bulk term in sublagrangians corresponding to the subspaces of the gauge
algebra.
Use is made of Abelian semigroups to develop an expansion method for Lie
(super)algebras, based on the work by de Azcarraga, Izquierdo, Picon and
Varela. The main idea consists in considering the direct product between an
Abelian semigroup S and a Lie (super)algebra g. General conditions under which
smaller algebras can be extracted from S \otimes g are given. It is shown how
to recover the known expansion cases in this new context. Several d=11
superalgebras are obtained as examples of the application of the method.
General theorems that allow to find an invariant tensor for the expanded
algebra from an invariant tensor for the original algebra are formulated.
Finally, a d=11 gauge theory for the M Algebra is considered by using the
ideas developed in the Thesis. The dynamical properties of this theory are
briefly analyzed. | Geometric Models of Matter: Inspired by soliton models, we propose a description of static particles in
terms of Riemannian 4-manifolds with self-dual Weyl tensor. For electrically
charged particles, the 4-manifolds are non-compact and asymptotically fibred by
circles over physical 3-space. This is akin to the Kaluza-Klein description of
electromagnetism, except that we exchange the roles of magnetic and electric
fields, and only assume the bundle structure asymptotically, away from the core
of the particle in question. We identify the Chern class of the circle bundle
at infinity with minus the electric charge and the signature of the 4-manifold
with the baryon number. Electrically neutral particles are described by compact
4-manifolds. We illustrate our approach by studying the Taub-NUT manifold as a
model for the electron, the Atiyah-Hitchin manifold as a model for the proton,
CP^2 with the Fubini-Study metric as a model for the neutron, and S^4 with its
standard metric as a model for the neutrino. |
3d $\mathcal{N}=3$ Generalized Giveon-Kutasov Duality: We generalize the Giveon-Kutasov duality for the 3d $\mathcal{N}=3$
$U(N)_{k,k+nN}$ Chern-Simons matter gauge theory with $F$ fundamental
hypermultiplets by introducing $SU(N)$ and $U(1)$ Chern-Simons levels
differently. We study the supersymmetric partition functions and the
superconformal indices of the duality, which supports the validity of the
duality proposal. From the duality, we can map out the low-energy phases: For
example, confinement appears for $F+k-N=-n=1$ or $N=2F=k=-n=2$. For $F+k-N<0$,
supersymmetry is spontaneously broken, which is in accord with the fact that
the partition function vanishes. In some cases, the theory shows supersymmetry
enhancement to 3d $\mathcal{N}=4$. For $k=0$, we comment on the magnetic
description dual to the so-called "ugly" theory, where the usual decoupled
sector is still interacting with others for $n \neq 0$. We argue that the
$SU(N)_0$ "ugly-good" duality (which corresponds to the $n \rightarrow \infty$
limit in our setup) is closely related to the S-duality of the 4d
$\mathcal{N}=2$ $SU(N)$ superconformal gauge theory with $2N$ fundamental
hypermultiplets. By reducing the number of flavors via real masses, we suggest
possible ways to flow to the "bad" theories. | Charged black holes from near extremal black holes: We recover the properties of a wide class of far from extremal charged black
branes from the properties of near extremal black branes, generalizing the
results of Danielsson, Guijosa and Kruczenski. |
$q$-Poincaré supersymmetry in $AdS_5/CFT_4$: We consider the exact S-matrix governing the planar spectral problem for
strings on $AdS_5\times S^5$ and $\mathcal N=4$ super Yang-Mills, and we show
that it is invariant under a novel "boost" symmetry, which acts as a
differentiation with respect to the particle momentum. This generator leads us
also to reinterpret the usual centrally extended $\mathfrak{psu}(2|2)$
symmetry, and to conclude that the S-matrix is invariant under a $q$-Poincar\'e
supersymmetry algebra, where the deformation parameter is related to the 't
Hooft coupling. We determine the two-particle action (coproduct) that turns out
to be non-local, and study the property of the new symmetry under crossing
transformations. We look at both the strong-coupling (large tension in the
string theory) and weak-coupling (spin-chain description of the gauge theory)
limits; in the former regime we calculate the cobracket utilising the universal
classical r-matrix of Beisert and Spill. In the eventuality that the boost has
higher partners, we also construct a quantum affine version of 2D Poincar\'e
symmetry, by contraction of the quantum affine algebra
$U_q(\widehat{\mathfrak{sl}_2})$ in Drinfeld's second realisation. | Traversable Asymptotically Flat Wormholes with Short Transit Times: We construct traversable wormholes by starting with simple four-dimensional
classical solutions respecting the null energy condition and containing a pair
of oppositely charged black holes connected by a non-traversable wormhole. We
then consider the perturbative back-reaction of bulk quantum fields in
Hartle-Hawking states. Our geometries have zero cosmological constant and are
asymptotically flat except for a cosmic string stretching to infinity that is
used to hold the black holes apart. Another cosmic string wraps the
non-contractible cycle through the wormhole, and its quantum fluctuations
provide the negative energy needed for traversability. Our setting is closely
related to the non-perturbative construction of Maldacena, Milekhin, and Popov
(MMP), but the analysis is complementary. In particular, we consider cases
where back-reaction slows, but fails to halt, the collapse of the wormhole
interior, so that the wormhole is traversable only at sufficiently early times.
For non-extremal backgrounds, we find the integrated null energy along the
horizon of the classical background to be exponentially small, and thus
traversability to be exponentially fragile. Nevertheless, if there are no
larger perturbations, and for appropriately timed signals, a wormhole with
mouths separated by a distance $d$ becomes traversable with a minimum transit
time $t_{\text{min transit}} = d + \text{logs}$. Thus $\frac{t_{\text{min
transit}}}{d}$ is smaller than for the eternally traversable MMP wormholes by
more than a factor of 2, and approaches the value that, at least in higher
dimensions, would be the theoretical minimum. For contrast we also briefly
consider a `cosmological wormhole' solution where the back-reaction has the
opposite sign, so that negative energy from quantum fields makes the wormhole
harder to traverse. |
A note on the functional determinant of higher-derivative scalar fields
on sphere products: It is shown that the functional determinant ($\sim$ effective action) for a
scalar field propagating on the mixed signature product of unit spheres,
S$^q\times$S$^p$, according to the GJMS operator, depends, if $d$ is odd, only
on $d=p+q$ and on whether $p$ is even or odd. In the first case the effective
action equals twice the standard quantity on S$^d$ and vanishes in the second. | Phases of kinky holographic nuclear matter: Holographic QCD at finite baryon number density and zero temperature is
studied within the five-dimensional Sakai-Sugimoto model. We introduce a new
approximation that models a smeared crystal of solitonic baryons by assuming
spatial homogeneity to obtain an effective kink theory in the holographic
direction. The kink theory correctly reproduces a first order phase transition
to lightly bound nuclear matter. As the density is further increased the kink
splits into a pair of half-kink constituents, providing a concrete realization
of the previously suggested dyonic salt phase, where the bulk soliton splits
into constituents at high density. The kink model also captures the phenomenon
of baryonic popcorn, in which a first order phase transition generates an
additional soliton layer in the holographic direction. We find that this
popcorn transition takes place at a density below the dyonic salt phase, making
the latter energetically unfavourable. However, the kink model predicts only
one pop, rather than the sequence of pops suggested by previous approximations.
In the kink model the two layers produced by the single pop form the surface of
a soliton bag that increases in size as the baryon chemical potential is
increased. The interior of the bag is filled with abelian electric potential
and the instanton charge density is localized on the surface of the bag. The
soliton bag may provide a holographic description of a quarkyonic phase. |
Pure Spinor Formalism for Osp(N|4) backgrounds: We start from the Maurer-Cartan (MC) equations of the Osp(N|4) superalgebras
satisfied by the left-invariant super-forms realized on supercoset manifolds of
the corresponding supergroups and we derive some new pure spinor constraints.
They are obtained by "ghostifying" the MC forms and extending the differential
d to a BRST differential. From the superalgebras G =Osp(N|4) we single out
different subalgebras H contained in G associated with the different cosets
G/H: each choice of H leads to a different weakening of the pure spinor
constraints. In each case, the number of parameter is counted and we show that
in the cases of Osp(6|4)/U(3) x SO(1,3), Osp(4|4)/SO(3) x SO(1,3) and finally
Osp(4|4) U(2)} x SO(1,3) the bosonic and fermionic degrees of freedom match in
order to provide a c=0 superconformal field theory. We construct both the
Green-Schwarz and the pure spinor sigma model for the case Osp(6|4)/U(3)x
SO(1,3) corresponding to AdS_4 x P^3. The pure spinor sigma model can be
consistently quantized. | Quantum Mechanically Induced Wess-Zumino Term in the Principal Chiral
Model: It is argued that, in the two dimensional principal chiral model, the
Wess-Zumino term can be induced quantum mechanically, allowing the model with
the critical value of the coupling constant $\lambda^2 = 8\pi/|k|$ to turn into
the Wess-Zumino-Novikov-Witten model at the quantum level. The Wess-Zumino term
emerges from the inequivalent quantizations possible on a sphere hidden in the
configuration space of the original model. It is shown that the Dirac monopole
potential, which is induced on the sphere in the inequivalent quantizations,
turns out to be the Wess-Zumino term in the entire configuration space. |
Towards a Classification of Charge-3 Monopoles with Symmetry: We classify all possible charge-3 monopole spectral curves with non-trivial
automorphism group and within these identify those with elliptic quotients. By
focussing on elliptic quotients the transcendental constraints for a monopole
spectral curve become ones regarding periods of elliptic functions. We
construct the Nahm data and new monopole spectral curves with $D_6$ and $V_4$
symmetry, the latter based on an integrable complexification of Euler's
equations, and for which energy density isosurfaces are plotted. Extensions of
our approach to higher charge and hyperbolic monopoles are discussed. | Evolution of Pure States into Mixed States: In the formulation of Banks, Peskin and Susskind, we show that one can
construct evolution equations for the quantum mechanical density matrix $\rho$
with operators which do not commute with hamiltonian which evolve pure states
into mixed states, preserve the normalization and positivity of $\rho$ and
conserve energy. Furthermore, it seems to be different from a quantum
mechanical system with random sources. |
Black Hole Hair Removal: Macroscopic entropy of an extremal black hole is expected to be determined
completely by its near horizon geometry. Thus two black holes with identical
near horizon geometries should have identical macroscopic entropy, and the
expected equality between macroscopic and microscopic entropies will then imply
that they have identical degeneracies of microstates. An apparent
counterexample is provided by the 4D-5D lift relating BMPV black hole to a four
dimensional black hole. The two black holes have identical near horizon
geometries but different microscopic spectrum. We suggest that this discrepancy
can be accounted for by black hole hair, -- degrees of freedom living outside
the horizon and contributing to the degeneracies. We identify these degrees of
freedom for both the four and the five dimensional black holes and show that
after their contributions are removed from the microscopic degeneracies of the
respective systems, the result for the four and five dimensional black holes
match exactly. | Quantization of Second Order Fermions: The quantization of a massive spin $1/2$ field that satisfies the
Klein-Gordon equation is studied. The framework is consistent, provided it is
formulated as a pseudo-hermitian quantum field theory by the redefinition of
the field dual and the identification of an operator that modifies the internal
product of states in Hilbert space to preserve a real energy spectrum and
unitary evolution. Since the fermion field has mass dimension one, the theory
admits renormalizable fermion self-interactions. |
Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field
Theory: Recently, the theory of renormalization in perturbative quantum field theory
underwent some exciting new developments. Kreimer discovered an organization of
Feynman graphs into combinatorial Hopf algebras. The process of renormalization
is captured by a factorization theorem for regularized Hopf algebra characters.
In this context the notion of Rota-Baxter algebras enters the scene. We review
several aspects of Rota-Baxter algebras as they appear in other sectors also
relevant to perturbative renormalization, for instance multiple-zeta-values and
matrix differential equations. | Comments on Higher Loop Integrability in the $su(1|1)$ Sector of $\cal
N$=4 $SYM$: Lessons From the $su(2)$ Sector: An analysis of two loop integrability in the $su(1|1)$ sector of
$\cal{N}$=4$SYM$ is presented from the point of view of Yangian symmetries. The
analysis is carried out in the scaling limit of the dilatation operator which
is shown to have a manifest $su(1|1)$ invariance. After embedding the scaling
limit of the dilatation operator in a general (Inozemtsev like) integrable long
ranged supersymmetric spin chain, the perturbative Yangian symmetry of the two
loop dilatation operator is also made evident. The explicit formulae for the
two loop gauge theory transfer matrix and Yangian charges are presented.
Comparisons with recent results for the effective Hamiltonians for fast moving
strings in the same sector are also carried out. Apart from this, a review of
the corresponding results in the $su(2)$ sector obtained by Beisert, Dippel,
Serban and Staudacher is also presented. |
Glueballs vs. Gluinoballs: Fluctuation Spectra in Non-AdS/Non-CFT: Building on earlier results on holographic bulk dynamics in confining gauge
theories, we compute the spin-0 and spin-2 spectra of gauge theories dual to
the non-singular Maldacena-Nunez and Klebanov-Strassler supergravity
backgrounds. We construct and apply a numerical recipe for computing mass
spectra from certain determinants. In the Klebanov-Strassler case, states
containing the glueball and gluinoball obey "quadratic confinement", i.e. their
mass-squareds depend on consecutive number as m^2 ~ n^2 for large n, with a
universal proportionality constant. The hardwall approximation appears to work
poorly when compared to the unique spectra we find in the full theory with a
smooth cap-off in the infrared. | Solitonic fullerene structures in light atomic nuclei: The Skyrme model is a classical field theory which has topological soliton
solutions. These solitons are candidates for describing nuclei, with an
identification between the numbers of solitons and nucleons. We have computed
numerically, using two different minimization algorithms, minimum energy
configurations for up to 22 solitons. We find, remarkably, that the solutions
for seven or more solitons have nucleon density isosurfaces in the form of
polyhedra made of hexagons and pentagons. Precisely these structures arise,
though at the much larger molecular scale, in the chemistry of carbon shells,
where they are known as fullerenes. |
Lagrangian formulation, generalizations and quantization of null
Maxwell's knots: Knotted solutions to electromagnetism are investigated as an independent
subsector of the theory. We write down a Lagrangian and a Hamiltonian
formulation of Bateman's construction for the knotted electromagnetic
solutions. We introduce a general definition of the null condition and
generalize the construction of Maxwell's theory to massless free complex
scalar, its dual two form field, and to a massless DBI scalar. We set up the
framework for quantizing the theory both in a path integral approach, as well
as the canonical Dirac method for a constrained system. We make several
observations about the semi-classical quantization of systems of null
configurations. | Universal critical coupling constants for the three-dimensional n-vector
model from field theory: The field-theoretical renormalization group approach in three dimensions is
used to estimate the universal critical values of renormalized coupling
constants g_6 and g_8 for the O(n)-symmetric model. The RG series for g_6 and
g_8 are calculated in the four-loop and three-loop approximations respectively
and then resummed by means of the Pade-Borel-Leroy technique. Under the optimal
value of the shift parameter b providing the fastest convergence of the
iteration procedure numerical estimates for the universal critical values
g_6^*(n) are obtained for n = 1, 2, 3,...40 with the accuracy no worse than
0.3%. The RG expansion for g_8 demonstrates stronger divergence and results in
considerably cruder numerical estimates. They are found to be consistent with
the values of g_8^* deduced from the exact RG equations and, for n > 8, with
those given by a constrained analysis of corresponding \epsilon-expansion. |
Aspects of Flavour and Supersymmetry in F-theory GUTs: We study the constraints of supersymmetry on flavour in recently proposed
models of F-theory GUTs. We relate the topologically twisted theory to the
canonical presentation of eight-dimensional super Yang-Mills and provide a
dictionary between the two. We describe the constraints on Yukawa couplings
implied by holomorphy of the superpotential in the effective 4-dimensional
supergravity theory, including the scaling with \alpha_{GUT}. Taking D-terms
into account we solve explicitly to second order for wavefunctions and Yukawas
due to metric and flux perturbations and find a rank-one Yukawa matrix with no
subleading corrections. | A bi-invariant Einstein-Hilbert action for the non-geometric string: Inspired by recent studies on string theory with non-geometric fluxes, we
develop a differential geometry calculus combining usual diffeomorphisms with
what we call beta-diffeomorphisms. This allows us to construct a manifestly
bi-invariant Einstein-Hilbert type action for the graviton, the dilaton and a
dynamical (quasi-)symplectic structure. The equations of motion of this
symplectic gravity theory, further generalizations and the relation to the
usual form of the string effective action are discussed. The Seiberg-Witten
limit, known for open strings to relate commutative with non-commutative
theories, makes an interesting appearance. |
Characters for Coset Conformal Field Theories: We solve the Kac-Moody branching equation to obtain explicit formulae for the
characters of coset conformal field theories and then apply these to specific
examples to determine the integer shift of the conformal weights of primary
fields. We also present an example of coset conformal field theory which cannot
be described by the identification current method. | Alternative approach to the regularization of odd dimensional AdS
gravity: In this paper I present an action principle for odd dimensional AdS gravity
which consists of introducing another manifold with the same boundary and a
very specific boundary term. This new action allows and alternative approach to
the regularization of the theory, yielding a finite euclidean action and finite
conserved charges. The choice of the boundary term is justified on the grounds
that an enhanced 'almost off-shell' local AdS/Conformal symmetry arises for
that very special choice. One may say that the boundary term is dictated by a
guiding symmetry principle. Two sets of boundary conditions are considered,
which yield regularization procedures analogous to (but different from) the
standard 'background substraction' and 'counterterms' regularization methods.
The Noether charges are constructed in general. As an application it is shown
that for Schwarszchild-AdS black holes the charge associated to the time-like
Killing vector is finite and is indeed the mass. The Euclidean action for
Schwarzschild-AdS black holes is computed, and it turns out to be finite, and
to yield the right thermodynamics. The previous paragraph may be interpreted in
the sense that the boundary term dictated by the symmetry principle is the one
that correctly regularizes the action. |
The twelve dimensional super (2+2)-brane: We discuss supersymmetry in twelve dimensions and present a covariant
supersymmetric action for a brane with worldsheet signature (2,2), called a
super (2+2)-brane, propagating in the osp(64,12) superspace. This superspace is
explicitly constructed, and is trivial in the sense that the spinorial part is
a trivial bundle over spacetime, unlike the twisted superspace of usual
Poincare supersymmetry. For consistency, it is necessary to take a projection
of the superspace. This is the same as the projection required for worldvolume
supersymmetry. Upon compactification of this superspace, a torsion is naturally
introduced and we produce the membrane and type IIB string actions in 11 and 10
dimensional Minkowski spacetimes. In addition, the compactification of the
twelve dimensional supersymmetry algebra produces the correct algebras for
these theories, including central charges. These considerations thus give the
type IIB string and M-theory a single twelve dimensional origin. | Chaotic string dynamics in Bosonic $η$-deformed $AdS_5 \times T^{
1,1}$ background: We investigate a new class of $\eta$-deformed $AdS_5 \times T^{1,1}$
backgrounds produced by $r$-matrices that satisfy the modified classical
Yang-Baxter equation [Jour. High Ener. Phys. 03 (2022) 094]. We examine the
classical phase space of these (semi)classical strings by numerically studying
the dynamics of the string sigma models over this deformed background, and we
compute several chaos signals. These involve figuring out the Poincar'e section
and computing the Lyapunov exponents. In the (semi)classical limit, we discover
evidence that supports a non-integrable phase space dynamics. |
Fermionic Casimir effect in toroidally compactified de Sitter spacetime: We investigate the fermionic condensate and the vacuum expectation values of
the energy-momentum tensor for a massive spinor field in de Sitter spacetime
with spatial topology $\mathrm{R}^{p}\times (\mathrm{S}^{1})^{q}$. Both cases
of periodicity and antiperiodicity conditions along the compactified dimensions
are considered. By using the Abel-Plana formula, the topological parts are
explicitly extracted from the vacuum expectation values. In this way the
renormalization is reduced to the renormalization procedure in uncompactified
de Sitter spacetime. It is shown that in the uncompactified subspace the
equation of state for the topological part of the energy-momentum tensor is of
the cosmological constant type. Asymptotic behavior of the topological parts in
the expectation values is investigated in the early and late stages of the
cosmological expansion. In the limit when the comoving length of a compactified
dimension is much smaller than the de Sitter curvature radius the topological
part in the expectation value of the energy-momentum tensor coincides with the
corresponding quantity for a massless field and is conformally related to the
corresponding flat spacetime result. In this limit the topological part
dominates the uncompactified de Sitter part. In the opposite limit, for a
massive field the asymptotic behavior of the topological parts is damping
oscillatory for both fermionic condensate and the energy-momentum tensor. | Pole Inflation - Shift Symmetry and Universal Corrections: An appealing explanation for the Planck data is provided by inflationary
models with a singular non-canonical kinetic term: a Laurent expansion of the
kinetic function translates into a potential with a nearly shift-symmetric
plateau in canonical fields. The shift symmetry can be broken at large field
values by including higher-order poles, which need to be hierarchically
suppressed in order not to spoil the inflationary plateau. The herefrom
resulting corrections to the inflationary dynamics and predictions are shown to
be universal at lowest order and possibly to induce power loss at large angular
scales. At lowest order there are no corrections from a pole of just one order
higher and we argue that this phenomenon is related to the well-known extended
no-scale structure arising in string theory scenarios. Finally, we outline
which other corrections may arise from string loop effects. |
Planck Scale Effect in the Entropic Force Law: In this note we generalize the quantum uncertainty relation proposed by
Vancea and Santos [7] in the entropic force law, by introducing Planck scale
modifications. The latter is induced by the Generalized Uncertainty Principle.
We show that the proposed uncertainty relation of [7], involving the entropic
force and the square of particle position, gets modified from the consideration
of a minimum measurable length, (which can be the Planck length). | Aether SUSY breaking: Can aether be alternative to F-term SUSY breaking?: We investigate supersymmetry (SUSY) breaking scenarios where both SUSY and
Lorentz symmetry are broken spontaneously. For concreteness, we propose models
in which scalar fluid or vector condensation breaks Lorentz symmetry and
accordingly SUSY. Then, we examine whether such scenarios are viable for
realistic model buildings. We find, however, that the scalar fluid model
suffers from several issues. Then, we extend it to a vector condensation model,
which avoids the issues in the scalar fluid case. We show that accelerated
expansion and soft SUSY breaking in matter sector can be achieved. In our
simple setup, the soft SUSY breaking is constrained to be less than
$\mathcal{O}(100)$TeV from the constraints on modification of gravity. |
Transverse Fierz-Pauli symmetry: We consider some flat space theories for spin 2 gravitons, with less
invariance than full diffeomorphisms. For the massless case, classical
stability and absence of ghosts require invariance under transverse
diffeomorphisms (TDiff). Generic TDiff invariant theories contain a propagating
scalar, which disappears if the symmetry is enhanced in one of two ways. One
possibility is to consider full diffeomorphisms (Diff). The other (which we
denote WTDiff) adds a Weyl symmetry, by which the Lagrangian becomes
independent of the trace. The first possibility corresponds to General
Relativity, whereas the second corresponds to "unimodular" gravity (in a
certain gauge). Phenomenologically, both options are equally acceptable. For
massive gravitons, the situation is more restrictive. Up to field
redefinitions, classical stability and absence of ghosts lead directly to the
standard Fierz-Pauli Lagrangian. In this sense, the WTDiff theory is more rigid
against deformations than linearized GR, since a mass term cannot be added
without provoking the appearance of ghosts. | String Theories on Flat Supermanifolds: We construct bosonic string theories, RNS string theories and heterotic
string theories on flat supermanifolds. For these string theories, we show
cancellations of the central charges and modular invariance. Bosonic string
theories on supermanifolds have dimensions (D_B,D_F)=(26,0),(28,2),(30,4),...,
where D_B and D_F are the numbers of bosonic coordinates and fermionic
coordinates, respectively. We show that in type II string theories the one loop
vacuum amplitudes vanish. From this result, we can suggest the existence of
supersymmetry on supermanifolds. As examples of the heterotic string theories,
we construct those whose massless spectra are related to N=1 supergravity
theories and N=1 super Yang-Mills theories with orthosymplectic supergroups on
the bosonic flat 10 dimensional Minkowski space. Also, we construct D-branes on
supermanifolds and compute tensions of the D-branes. We show that the number of
fermionic coordinates contributes to the tensions of the D-branes as an inverse
power of the contribution of bosonic coordinates. Moreover, we find some
configurations of two D-branes which satisfy the BPS-like no-force conditions
if \nu_B - \nu_F = 0,4 and 8, where \nu_B and \nu_F are the numbers of
Dirichlet-Neumann directions in the bosonic coordinates and in the fermionic
coordinates, respectively. |
Path integrals for awkward actions: Time derivatives of scalar fields occur quadratically in textbook actions. A
simple Legendre transformation turns the lagrangian into a hamiltonian that is
quadratic in the momenta. The path integral over the momenta is gaussian. Mean
values of operators are euclidian path integrals of their classical
counterparts with positive weight functions. Monte Carlo simulations can
estimate such mean values.
This familiar framework falls apart when the time derivatives do not occur
quadratically. The Legendre transformation becomes difficult or so intractable
that one can't find the hamiltonian. Even if one finds the hamiltonian, it
usually is so complicated that one can't path-integrate over the momenta and
get a euclidian path integral with a positive weight function. Monte Carlo
simulations don't work when the weight function assumes negative or complex
values.
This paper solves both problems. It shows how to make path integrals without
knowing the hamiltonian. It also shows how to estimate complex path integrals
by combining the Monte Carlo method with parallel numerical integration and a
look-up table. This "Atlantic City method" lets one estimate the energy
densities of theories that, unlike those with quadratic time derivatives, may
have finite energy densities. It may lead to a theory of dark energy.
The approximation of multiple integrals over weight functions that assume
negative or complex values is the long-standing sign problem. The Atlantic City
method solves it for problems in which numerical integration leads to a
positive weight function. | Topology and Signature Changes in Braneworlds: It has been believed that topology and signature change of the universe can
only happen accompanied by singularities, in classical, or instantons, in
quantum, gravity. In this note, we point out however that in the braneworld
context, such an event can be understood as a classical, smooth event. We
supply some explicit examples of such cases, starting from the
Dirac-Born-Infeld action. Topology change of the brane universe can be realised
by allowing self-intersecting branes. Signature change in a braneworld is made
possible in an everywhere Lorentzian bulk spacetime. In our examples, the
boundary of the signature change is a curvature singularity from the brane
point of view, but nevertheless that event can be described in a completely
smooth manner from the bulk point of view. |
Lax Pair Formulation of the W-gravity Theories in two Dimensions: The Lax pair formulation of the two dimensional induced gravity in the
light-cone gauge is extended to the more general $w_N$ theories. After
presenting the $w_2$ and $w_3$ gravities, we give a general prescription for an
arbitrary $w_N$ case. This is further illustrated with the $w_4$ gravity to
point out some peculiarities. The constraints and the possible presence of the
cosmological constants are systematically exhibited in the zero-curvature
condition, which also yields the relevant Ward identities. The restrictions on
the gauge parameters in presence of the constraints are also pointed out and
are contrasted with those of the ordinary 2d-gravity. | The Quantum Effective Action, Wave Functions and Yang-Mills (2+1): We explore the relationship between the quantum effective action and the
ground state (and excited state) wave functions of a field theory. Applied to
the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the
effective action from the ground state wave function previously obtained in the
Hamiltonian formalism by solving the Schrodinger equation. |
Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy: In an earlier short paper [Phys.\ Rev.\ Lett.\ 120 (2018) 101301,
arXiv:1702.04439], I argued that the horizon-preserving diffeomorphisms of a
generic black hole are enhanced to a larger BMS${}_3$ symmetry, which is
powerful enough to determine the Bekenstein-Hawking entropy. Here I provide
details and extensions of that argument, including a loosening of horizon
boundary conditions and a more thorough treatment of dimensional reduction and
meaning of a "near-horizon symmetry." | Pair creation in electric fields, anomalies, and renormalization of the
electric current: We investigate the Schwinger pair production phenomena in spatially
homogeneous strong electric fields. We first consider scalar QED in
four-dimensions and discuss the potential ambiguity in the adiabatic order
assignment for the electromagnetic potential required to fix the
renormalization subtractions. We argue that this ambiguity can be solved by
invoking the conformal anomaly when both electric and gravitational backgrounds
are present. We also extend the adiabatic regularization method for spinor QED
in two-dimensions and find consistency with the chiral anomaly. We focus on the
issue of the renormalization of the electric current $\langle j^\mu \rangle$
generated by the created pairs. We illustrate how to implement the
renormalization of the electric current for the Sauter pulse. |
Isospin precession in non-Abelian Aharonov-Bohm scattering: The concept of pseudoclassical isospin is illustrated by the non-Abelian
Aharonov-Bohm effect proposed by Wu and Yang in 1975. The spatial motion is
free however the isospin precesses when the enclosed magnetic flux and the
incoming particle's isosopin are not parallel. The non-Abelian phase factor
$\mathfrak{F}$ of Wu and Yang acts on the isospin as an S-matrix. The
scattering becomes side-independent when the enclosed flux is quantized,
${\Phi}_N=N\Phi_0$ with $N$ an integer. The gauge group $SU(2)$ is an internal
symmetry and generates conserved charges only when the flux is quantized, which
then splits into two series: for $N=2k$ $SU(2)$ acts trivially but for $N=1+2k$
the implementation is twisted. The orbital and the internal angular momenta are
separately conserved. The double rotational symmetry is broken to $SO(2)\times
SO(2)$ when $N$ odd. For unquantized flux there are no internal symmetries, the
charge is not conserved and protons can be turned into neutrons. | Quantum Transitions Between Classical Histories: Bouncing Cosmologies: In a quantum theory of gravity spacetime behaves classically when quantum
probabilities are high for histories of geometry and field that are correlated
in time by the Einstein equation. Probabilities follow from the quantum state.
This quantum perspective on classicality has important implications: (a)
Classical histories are generally available only in limited patches of the
configuration space on which the state lives. (b) In a given patch states
generally predict relative probabilities for an ensemble of possible classical
histories. (c) In between patches classical predictability breaks down and is
replaced by quantum evolution connecting classical histories in different
patches. (d) Classical predictability can break down on scales well below the
Planck scale, and with no breakdown in the classical equations of motion. We
support and illustrate (a)-(d) by calculating the quantum transition across the
de Sitter like throat connecting asymptotically classical, inflating histories
in the no-boundary quantum state. This supplies probabilities for how a
classical history on one side transitions and branches into a range of
classical histories on the opposite side. We also comment on the implications
of (a)-(d) for the dynamics of black holes and eternal inflation. |
Quantum Affine Lie Algebras, Casimir Invariants and Diagonalization of
the Braid Generator: Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie
algebra. A family of central elements or Casimir invariants are constructed and
their eigenvalues computed in any integrable irreducible highest weight
representation. These eigenvalue formulae are shown to absolutely convergent
when the deformation parameter $q$ is such that $|q|>1$. It is proven that the
universal R-matrix $R$ of $U_q(\hat{\cal G})$ satisfies the celebrated
conjugation relation $R^\dagger=TR$ with $T$ the usual twist map. As
applications, the braid generator is shown to be diagonalizable on arbitrary
tensor product modules of integrable irreducible highest weight $U_q(\hat{\cal
G})$-modules and a spectral decomposition formula for the braid generator is
obtained which is the generalization of Reshetikhin's and Gould's forms to the
present affine case. Casimir invariants acting on a specified module are also
constructed and their eigenvalues, again absolutely convergent for $|q|>1$,
computed by means of the spectral decomposition formula. | Time-dependent flow from an AdS Schwarzschild black hole: I discuss two examples of time-dependent flow which can be described in terms
of an AdS Schwarzschild black hole via holography. The first example involves
Bjorken hydrodynamics which should be applicable to the formation of the quark
gluon plasma in heavy ion collisions. The second example is the cosmological
evolution of our Universe. |
Electron stars for holographic metallic criticality: We refer to the ground state of a gravitating, charged ideal fluid of
fermions held at a finite chemical potential as an `electron star'. In a
holographic setting, electron stars are candidate gravity duals for strongly
interacting finite fermion density systems. We show how electron stars develop
an emergent Lifshitz scaling at low energies. This IR scaling region is a
consequence of the two way interaction between emergent quantum critical
bosonic modes and the finite density of fermions. By integrating from the IR
region to an asymptotically AdS_4 spacetime, we compute basic properties of the
electron stars, including their electrical conductivity. We emphasize the
challenge of connecting UV and IR physics in strongly interacting finite
density systems. | On the stability of field-theoretical regularizations of negative
tension branes: Any attempt to regularize a negative tension brane through a bulk scalar
requires that this field is a ghost. One can try to improve in this aspect in a
number of ways. For instance, it has been suggested to employ a field whose
kinetic term is not sign definite, in the hope that the background may be
overall stable. We show that this is not the case; the physical perturbations
(gravity included) of the system do not extend across the zeros of the kinetic
term; hence, all the modes are entirely localized either where the kinetic term
is positive, or where it is negative; this second type of modes are ghosts. We
show that this conclusion does not depend on the specific choice for the
kinetic and potential functions for the bulk scalar. |
Constructing the Supersymmetric anti-D3-brane action in KKLT: The derivation of the complete anti-D3-brane low energy effective action in
KKLT is reviewed. All worldvolume fields are included, together with the
background moduli. The result is recast into a manifest supersymmetric form in
terms of the three independent functions of $\mathcal{N}=1$ supergravity in
four dimensions: the Kaehler potential, the superpotential and the gauge
kinetic function. The latter differs from the expression one would expect by
analogy with the D3-brane case. | Dual dynamics of three dimensional asymptotically flat Einstein gravity
at null infinity: Starting from the Chern-Simons formulation, the two-dimensional dual theory
for three-dimensional asymptotically flat Einstein gravity at null infinity is
constructed. Solving the constraints together with suitable gauge fixing
conditions gives in a first stage a chiral Wess-Zumino-Witten like model based
on the Poincar\'e algebra in three dimensions. The next stage involves a
Hamiltonian reduction to a BMS3 invariant Liouville theory. These results are
connected to those originally derived in the anti-de Sitter case by rephrasing
the latter in a suitable gauge before taking their flat-space limit. |
How to Run Through Walls: Dynamics of Bubble and Soliton Collisions: It has recently been shown in high resolution numerical simulations that
relativistic collisions of bubbles in the context of a multi-vacua potential
may lead to the creation of bubbles in a new vacuum. In this paper, we show
that scalar fields with only potential interactions behave like free fields
during high-speed collisions; the kick received by them in a collision can be
deduced simply by a linear superposition of the bubble wall profiles. This
process is equivalent to the scattering of solitons in 1+1 dimensions. We
deduce an expression for the field excursion (shortly after a collision), which
is related simply to the field difference between the parent and bubble vacua,
i.e. contrary to expectations, the excursion cannot be made arbitrarily large
by raising the collision energy. There is however a minimum energy threshold
for this excursion to be realized. We verify these predictions using a number
of 3+1 and 1+1 numerical simulations. A rich phenomenology follows from these
collision induced excursions - they provide a new mechanism for scanning the
landscape, they might end/begin inflation, and they might constitute our very
own big bang, leaving behind a potentially observable anisotropy. | Superfluid Black Holes: We present what we believe is the first example of a "$\lambda$-line" phase
transition in black hole thermodynamics. This is a line of (continuous) second
order phase transitions which in the case of liquid $^4$He marks the onset of
superfluidity. The phase transition occurs for a class of asymptotically AdS
hairy black holes in Lovelock gravity where a real scalar field is conformally
coupled to gravity. We discuss the origin of this phase transition and outline
the circumstances under which it (or generalizations of it) could occur. |
Attractors, black objects, and holographic RG flows in 5d maximal gauged
supergravities: We perform a systematic search for static solutions in different sectors of
5d $N=8$ supergravities with compact and non-compact gauged R-symmetry groups,
finding new and listing already known backgrounds. Due to the variety of
possible gauge groups and resulting scalar potentials, the maximally symmetric
vacua we encounter in these theories can be Minkowski, de Sitter, or anti-de
Sitter. There exist BPS and non-BPS near-horizon geometries and full solutions
with all these three types of asymptotics, corresponding to black holes,
branes, strings, rings, and other black objects with more exotic horizon
topologies, supported by $U(1)$ and $SU(2)$ charges. The asymptotically AdS$_5$
solutions also have a clear holographic interpretation as RG flows of field
theories on D3 branes, wrapped on compact 2- and 3-manifolds. | Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5
superstrings: We consider bosonic subsectors of the q-deformed AdS_5 x S^5 superstring
action and study the classical integrable structure of anisotropic
Landau-Lifshitz sigma models (LLSMs) derived by taking fast-moving limits. The
subsectors are 1) deformed AdS_3 x S^1 and 2) R x deformed S^3. The cases 1)
and 2) lead to a time-like warped SL(2) LLSM and a squashed S^3 LLSM,
respectively. For each of them, we construct an infinite number of non-local
conserved charges and show a quantum affine algebra at the classical level.
Furthermore, a pp-wave like limit is applied for the case 1). The resulting
system is a null-like warped SL(2) LLSM and exhibits a couple of Yangians
through non-local gauge transformations associated with Jordanian twists. |
Entanglement entropy in higher derivative holography: We consider holographic entanglement entropy in higher derivative gravity
theories. Recently Lewkowycz and Maldacena arXiv:1304.4926 have provided a
method to derive the equations for the entangling surface from first
principles. We use this method to compute the entangling surface in four
derivative gravity. Certain interesting differences compared to the two
derivative case are pointed out. For Gauss-Bonnet gravity, we show that in the
regime where this method is applicable, the resulting equations coincide with
proposals in the literature as well as with what follows from considerations of
the stress tensor on the entangling surface. Finally we demonstrate that the
area functional in Gauss-Bonnet holography arises as a counterterm needed to
make the Euclidean action free of power law divergences. | Hawking radiation of Dirac particles from black strings: Hawking radiation has been studied as a phenomenon of quantum tunneling in
different black holes. In this paper we extend this semi-classical approach to
cylindrically symmetric black holes. Using the Hamilton-Jacobi method and WKB
approximation we calculate the tunneling probabilities of incoming and outgoing
Dirac particles from the event horizon and find the Hawking temperature of
these black holes. We obtain results both for uncharged as well as charged
particles. |
On the Construction of Correlation Functions for the Integrable
Supersymmetric Fermion Models: We review the recent progress on the construction of the determinant
representations of the correlation functions for the integrable supersymmetric
fermion models. The factorizing $F$-matrices (or the so-called $F$-basis) play
an important role in the construction. In the $F$-basis, the creation (and the
annihilation) operators and the Bethe states of the integrable models are given
in completely symmetric forms. This leads to the determinant representations of
the scalar products of the Bethe states for the models. Based on the scalar
products, the determinant representations of the correlation functions may be
obtained. As an example, in this review, we give the determinant
representations of the two-point correlation function for the $\gl$ (i.e.
q-deformed) supersymmetric t-J model. The determinant representations are
useful for analysing physical properties of the integrable models in the
thermodynamical limit. | Heterotic Calabi-Yau Compactifications with Flux: Compactifications of the heterotic string with NS flux normally require non
Calabi-Yau internal spaces which are complex but no longer K\"ahler. We point
out that this conclusion rests on the assumption of a maximally symmetric
four-dimensional space-time and can be avoided if this assumption is relaxed.
Specifically, it is shown that an internal Calabi-Yau manifold is consistent
with the presence of NS flux provided four-dimensional space-time is taken to
be a domain wall. These Calabi-Yau domain wall solutions can still be
associated with a covariant four-dimensional N=1 supergravity. In this
four-dimensional context, the domain wall arises as the "simplest" solution to
the effective supergravity due to the presence of a flux potential with a
runaway direction. Our main message is that NS flux is a legitimate ingredient
for moduli stabilization in heterotic Calabi-Yau models. Ultimately, the
success of such models depends on the ability to stabilize the runaway
direction and thereby "lift" the domain wall to a maximally supersymmetric
vacuum. |
Information Problem in Black Holes and Cosmology and Ghosts in Quadratic
Gravity: Black hole information problem is the question about unitarity of the
evolution operator during the collapse and evaporation of the black hole. One
can ask the same question about unitarity of quantum and inflationary
cosmology. In this paper we argue that in both cases, for black holes and for
cosmology, the answer is negative and we face non-unitarity.
Such a question can not be addressed by using the fixed classical
gravitational background since one has to take into account the backreaction.
To his end one uses the semi-classical gravity, which includes the expectation
value of the energy - momentum tensor operator of the matter fields. One has to
renormalize the energy-momentum tensor and one gets an effective action which
contains quadratic terms in scalar curvature and Ricci tensor. Such quadratic
gravity contains ghosts which in fact lead to violation of unitarity in black
holes and cosmology. We discuss the question whether black holes will emit
ghosts.
One can try to restrict ourselves to the $f(R)$ gravity that seems is a good
approximation to the semi-classical gravity and widely used in cosmology. The
black hole entropy in $f(R)$ gravity is different from the Bekenstein-Hawking
entropy and from entanglement island entropy. The black hole entropy in $R+R^2$
gravity goes to a constant during the evaporation process. This can be
interpreted as another indication to the possible non-unitarity in black holes
and cosmology | Exactly Solvable Quantum Mechanical Models with Infinite Renormalization
of the Wave Function: The main difficulty of quantum field theory is the problem of divergences and
renormalization. However, realistic models of quantum field theory are
renormalized within the perturbative framework only. It is important to
investigate renormalization beyond perturbation theory. However, known models
of constructive field theory do not contain such difficulties as infinite
renormalization of the wave function. In this paper an exactly solvable quantum
mechanical model with such a difficulty is constructed. This model is a
simplified analog of the large-N approximation to the $\Phi\phi^a\phi^a$-model
in 6-dimensional space-time. It is necessary to introduce an indefinite inner
product to renormalize the theory. The mathematical results of the theory of
Pontriagin spaces are essentially used. It is remarkable that not only the
field but also the canonically conjugated momentum become well-defined
operators after adding counterterms. |
Superconformal Tensor Calculus on an Orbifold in 5D: Superconformal tensor calculus on an orbifold S^1/Z_2 is given in
five-dimensional (5D) spacetime. The four-dimensional superconformal Weyl
multiplet and various matter multiplets are induced on the boundary planes from
the 5D supermultiplets in the bulk. We identify those induced 4D
supermultiplets and clarify a general method for coupling the bulk fields to
the matter fields on the boundaries in a superconformal invariant manner. | Explicit Bosonization of the Massive Thirring Model in 3+1 Dimensions: We bosonize the Massive Thirring Model in 3+1D for small coupling constant
and arbitrary mass. The bosonized action is explicitly obtained both in terms
of a Kalb-Ramond tensor field as well as in terms of a dual vector field. An
exact bosonization formula for the current is derived. The small and large mass
limits of the bosonized theory are examined in both the direct and dual forms.
We finally obtain the exact bosonization of the free fermion with an arbitrary
mass. |
Contextual viewpoint to quantum stochastics: We study the role of context, complex of physical conditions, in quantum as
well as classical experiments. It is shown that by taking into account
contextual dependence of experimental probabilities we can derive the quantum
rule for the addition of probabilities of alternatives. Thus we obtain quantum
interference without applying to wave or Hilbert space approach. The Hilbert
space representation of contextual probabilities is obtained as a consequence
of the elementary geometric fact: $\cos$-theorem. By using another fact from
elementary algebra we obtain complex-amplitude representation of probabilities.
Finally, we found contextual origin of noncommutativity of incompatible
observables. | Quantum Generation of the non-Abelian SU(N) Gauge Fields: In this paper we investigate a generation mechanism of the non-Abelian gauge
fields in the SU(N) gauge theory. It is shown that the SU(N) gauge fields
ensuring the local invariance of the theory are generated at the quantum level
only due to nonsmoothness of the scalar phases of the fundamental spinor
fields. The expression for the gauge fields are obtained in terms of the
nonsmooth scalar phases. |
Topological gauge theories from supersymmetric quantum mechanics on
spaces of connections: We rederive the recently introduced $N=2$ topological gauge theories,
representing the Euler characteristic of moduli spaces ${\cal M}$ of
connections, from supersymmetric quantum mechanics on the infinite dimensional
spaces ${\cal A}/{\cal G}$ of gauge orbits. To that end we discuss variants of
ordinary supersymmetric quantum mechanics which have meaningful extensions to
infinite-dimensional target spaces and introduce supersymmetric quantum
mechanics actions modelling the Riemannian geometry of submersions and
embeddings, relevant to the projections ${\cal A}\rightarrow {\cal A}/{\cal G}$
and inclusions ${\cal M}\subset{\cal A}/{\cal G}$ respectively. We explain the
relation between Donaldson theory and the gauge theory of flat connections in
$3d$ and illustrate the general construction by other $2d$ and $4d$ examples. | On gauge fields - strings duality as an integrable system: It was suggested in hep-th/0002106, that semiclassically, a partition
function of a string theory in the 5 dimensional constant negative curvature
space with a boundary condition at the absolute satisfy the loop equation with
respect to varying the boundary condition, and thus the partition function of
the string gives the expectation value of a Wilson loop in the 4 dimensional
QCD. In the paper, we present the geometrical framework, which reveals that the
equations of motion of such string theory are integrable, in the sense that
they can be written via a Lax pair with a spectral parameter. We also show,
that the issue of the loop equation rests solely on the properly posing the
boundary condition. |
The Holar Wind: String theory in AdS3 with purely NS-NS fluxes and vanishing RR moduli has a
continuum of winding string excitations in radial plane wave states. BTZ black
holes can emit such strings, which then flow out toward the AdS3 boundary as a
stream of massive quanta, and form a black hole analogue of the solar wind. The
winding string sector thus provides a decay channel for the black hole to
evaporate without having either to couple the system to an external reservoir
or to match the AdS3 throat onto an asymptotically flat region. We compute the
emission amplitude of this "holar wind" in the semi-classical approximation,
and consider the associated version of the black hole information paradox. | The quantization problem in Scherk-Schwarz compactifications: We re-examine the quantization of structure constants, or equivalently the
choice of lattice in the so-called flat group reductions, introduced originally
by Scherk and Schwarz. Depending on this choice, the vacuum either breaks
supersymmetry and lifts certain moduli, or preserves all supercharges and is
identical to the one obtained from the torus reduction. Nonetheless the
low-energy effective theory proposed originally by Scherk and Schwarz is a
gauged supergravity that describes supersymmetry breaking and moduli lifting
for all values of the structure constants. When the vacuum does not break
supersymmetry, such a description turns out to be an artifact of the consistent
truncation to left-invariant forms as illustrated for the example of ISO(2). We
furthermore discuss the construction of flat groups in d dimensions and find
that the Scherk--Schwarz algorithm is exhaustive. A classification of flat
groups up to six dimensions and a discussion of all possible lattices is
presented. |
QCD effective coupling constant and effective quark mass given in a
mass-dependent renormalization: The QCD one-loop renormalization is restudied in a mass-dependent subtraction
scheme in which the quark mass is not set to vanish and the renormalization
point is chosen to be an arbitrary timelike momentum. The correctness of the
subtraction is ensured by the Ward identities which are respected in all the
processes of subtraction. By considering the mass effect, the effective
coupling constant and the effective quark mass are given in improved
expressions which are different from the previous results. | Generalized Landau-Lifshitz models on the interval: We study the classical generalized gl(n) Landau-Lifshitz (L-L) model with
special boundary conditions that preserve integrability. We explicitly derive
the first non-trivial local integral of motion, which corresponds to the
boundary Hamiltonian for the sl(2) L-L model. Novel expressions of the modified
Lax pairs associated to the integrals of motion are also extracted. The
relevant equations of motion with the corresponding boundary conditions are
determined. Dynamical integrable boundary conditions are also examined within
this spirit. Then the generalized isotropic and anisotropic gl(n)
Landau-Lifshitz models are considered, and novel expressions of the boundary
Hamiltonians and the relevant equations of motion and boundary conditions are
derived. |
Potentials in N=4 superconformal mechanics: Proceeding from nonlinear realizations of (super)conformal symmetries, we
explicitly demonstrate that adding the harmonic oscillator potential to the
action of conformal mechanics does not break these symmetries but modifies the
transformation properties of the (super)fields. We also analyze the possibility
to introduce potentials in N=4 supersymmetric mechanics by coupling it with
auxiliary fermionic superfields. The new coupling we considered does not
introduce new fermionic degrees of freedom - all our additional fermions are
purely auxiliary ones. The new bosonic components have a first order kinetic
term and therefore they serve as spin degrees of freedom. The resulting system
contains, besides the potential term in the bosonic sector, a non-trivial
spin-like interaction in the fermionic sector. The superconformal mechanics we
constructed in this paper is invariant under the full $D(2,1;\alpha)$
superconformal group. This invariance is not evident and is achieved within
modified (super)conformal transformations of the superfields. | When Worlds Collide: We analyze the cosmological signatures visible to an observer in a Coleman-de
Luccia bubble when another such bubble collides with it. We use a gluing
procedure to generalize the results of Freivogel, Horowitz, and Shenker to the
case of a general cosmological constant in each bubble and study the resulting
spacetimes. The collision breaks the isotropy and homogeneity of the bubble
universe and provides a cosmological "axis of evil" which can affect the cosmic
microwave background in several unique and potentially detectable ways. Unlike
more conventional perturbations to the inflationary initial state, these
signatures can survive even relatively long periods of inflation. In addition,
we find that for a given collision the observers in the bubble with smaller
cosmological constant are safest from collisions with domain walls, possibly
providing another anthropic selection principle for small positive vacuum
energy. |
Quantization of the massive gravitino on FRW spacetimes: In this article we study the quantization and causal properties of a massive
spin 3/2 Rarita-Schwinger field on spatially flat Friedmann-Robertson-Walker
(FRW) spacetimes. We construct Zuckerman's universal conserved current and
prove that it leads to a positive definite inner product on solutions of the
field equation. Based on this inner product, we quantize the Rarita-Schwinger
field in terms of a CAR-algebra. The transversal and longitudinal parts
constituting the independent on-shell degrees of freedom decouple. We find a
Dirac-type equation for the transversal polarizations, ensuring a causal
propagation. The equation of motion for the longitudinal part is also of
Dirac-type, but with respect to an `effective metric'. We obtain that for all
four-dimensional FRW solutions with a matter equation of state p = w rho and w
in (-1,1] the light cones of the effective metric are more narrow than the
standard cones, which are recovered for the de Sitter case w=-1. In particular,
this shows that the propagation of the longitudinal part, although non-standard
for w different from -1, is completely causal in cosmological constant, dust
and radiation dominated universes. | Hessian eigenvalue distribution in a random Gaussian landscape: The energy landscape of multiverse cosmology is often modeled by a
multi-dimensional random Gaussian potential. The physical predictions of such
models crucially depend on the eigenvalue distribution of the Hessian matrix at
potential minima. In particular, the stability of vacua and the dynamics of
slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues.
The Hessian eigenvalue distribution has been studied earlier, using the saddle
point approximation, in the leading order of $1/N$ expansion, where $N$ is the
dimensionality of the landscape. This approximation, however, is insufficient
for the small eigenvalue end of the spectrum, where sub-leading terms play a
significant role. We extend the saddle point method to account for the
sub-leading contributions. We also develop a new approach, where the eigenvalue
distribution is found as an equilibrium distribution at the endpoint of a
stochastic process (Dyson Brownian motion). The results of the two approaches
are consistent in cases where both methods are applicable. We discuss the
implications of our results for vacuum stability and slow-roll inflation in the
landscape. |
RR charges of D2-branes in group manifold and Hanany-Witten effect: By exploiting the correspondence between the Cardy boundary state in SU(2)
group manifold and the BPS D3-brane configuration in the full asymptotically
flat geometry of NS5-branes, we show that the Hanany-Witten effect in 10D
background is encoded in the Cardy boundary states. The two RR Page D0 charges
of the $n$-th spherical D2-brane due to the contraction to $e$ or ($-e$) is
interpreted, and attributed to the Hanany-Witten effect. | N=2 Sigma Models for Ramond-Ramond Backgrounds: Using the U(4) hybrid formalism, manifestly N=(2,2) worldsheet supersymmetric
sigma models are constructed for the Type IIB superstring in Ramond-Ramond
backgrounds. The Kahler potential in these N=2 sigma models depends on four
chiral and antichiral bosonic superfields and two chiral and antichiral
fermionic superfields. When the Kahler potential is quadratic, the model is a
free conformal field theory which describes a flat ten-dimensional target space
with Ramond-Ramond flux and non-constant dilaton. For more general Kahler
potentials, the model describes curved target spaces with Ramond-Ramond flux
that are not plane-wave backgrounds. Ricci-flatness of the Kahler metric
implies the on-shell conditions for the background up to the usual four-loop
conformal anomaly. |
Casimir Effect in Problems with Spherical Symmetry: New Perspectives: Since the Maxwell theory of electromagnetic phenomena is a gauge theory, it
is quite important to evaluate the zero-point energy of the quantized
electromagnetic field by a careful assignment of boundary conditions on the
potential and on the ghost fields. Recent work by the authors has shown that,
for a perfectly conducting spherical shell, it is precisely the contribution of
longitudinal and normal modes of the potential which enables one to reproduce
the result first due to Boyer. This is obtained provided that one works with
the Lorenz gauge-averaging functional, and with the help of the Feynman choice
for a dimensionless gauge parameter. For arbitrary values of the gauge
parameter, however, covariant and non-covariant gauges lead to an entangled
system of three eigenvalue equations. Such a problem is crucial both for the
foundations and for the applications of quantum field theory. | Supersymmetric Nonlinear Sigma Models on Ricci-flat Kahler Manifolds
with O(N) Symmetry: We propose a class of N=2 supersymmetric nonlinear sigma models on the
Ricci-flat Kahler manifolds with O(n) symmetry. |
Topological Quantum Field Theory: A Progress Report: A brief introduction to Topological Quantum Field Theory as well as a
description of recent progress made in the field is presented. I concentrate
mainly on the connection between Chern-Simons gauge theory and Vassiliev
invariants, and Donaldson theory and its generalizations and Seiberg-Witten
invariants. Emphasis is made on the usefulness of these relations to obtain
explicit expressions for topological invariants, and on the universal structure
underlying both systems. | 5d Black Hole as Emergent Geometry of Weakly Interacting 4d Hot
Yang-Mills Gas: We demonstrate five-dimensional anti-de Sitter black hole emerges as dual
geometry holographic to weakly interacting N=4 superconformal Yang-Mills
theory. We first note that an ideal probe of the dual geometry is the
Yang-Mills instanton, probing point by point in spacetime. We then study
instanton moduli space at finite temperature by adopting Hitchin's proposal
that geometry of the moduli space is definable by Fisher-Rao "information
geometry". In Yang-Mills theory, the information metric is measured by a novel
class of gauge-invariant, nonlocal operators in the instanton sector. We show
that the moduli space metric exhibits (1) asymptotically anti-de Sitter, (2)
horizon at radial distance set by the Yang-Mills temperature, and (3) after
Wick rotation of the moduli space to the Lorentzian signature, a singularity at
the origin. We argue that the dual geometry emerges even for rank of gauge
groups of order unity and for weak `t Hooft coupling. |
Conformal Field Theories in Six-Dimensional Twistor Space: This article gives a study of the higher-dimensional Penrose transform
between conformally invariant massless fields on space-time and cohomology
classes on twistor space, where twistor space is defined to be the space of
projective pure spinors of the conformal group. We focus on the 6-dimensional
case in which twistor space is the six-quadric Q in CP^7 with a view to
applications to the self-dual (0,2)-theory. We show how spinor-helicity
momentum eigenstates have canonically defined distributional representatives on
twistor space (a story that we extend to arbitrary dimension). These give an
elementary proof of the surjectivity of the Penrose transform. We give a direct
construction of the twistor transform between the two different representations
of massless fields on twistor space (H^2 and H^3) in which the H^3s arise as
obstructions to extending the H^2s off Q into CP^7.
We also develop the theory of Sparling's `\Xi-transform', the analogous
totally real split signature story based now on real integral geometry where
cohomology no longer plays a role. We extend Sparling's \Xi-transform to all
helicities and homogeneities on twistor space and show that it maps kernels and
cokernels of conformally invariant powers of the ultrahyperbolic wave operator
on twistor space to conformally invariant massless fields on space-time. This
is proved by developing the 6-dimensional analogue of the half-Fourier
transform between functions on twistor space and momentum space. We give a
treatment of the elementary conformally invariant \Phi^3 amplitude on twistor
space and finish with a discussion of conformal field theories in twistor
space. | On Interpretation of Special Relativity: a complement to Covariant
Harmonic Oscillator Picture: In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant
differential equation capable to describe relativistic particle with mass and
internal space-time structure. By making use of new variables that
differentiate between space-time particle position and its space-time
separations, one finds this wave equation to become separable and providing the
two kinds of solutions endowed with different physical meanings. The first kind
constitutes the running waves that represent Klein-Gordon-like particle. The
second kind, widely discussed by Kim and Noz [4], constitutes standing waves
which are normalizable space-time wave functions. To fully appreciate how
valuable theses solutions are it seems necessarily, however, to verify a
general outlook on relativity issue that (still) is in force. It was explained
[5] that Lorentz symmetry should be perceived rather as the symmetry of
preferred frame quantum description (based on the freedom of choice of
comparison scale) than classical Galilean idea realized in a generalized form.
Currently we point to some basic consequences that relate to solutions of
Feynman equation framed in the new approach. In particular (i) Lorentz symmetry
group appears to describe energy-dependent geometry of extended quantum objects
instead of relativity of space and time measure, (ii) a new picture of
particle-wave duality involving running and standing waves emerges, (iii)
space-time localized quantum states are shown to provide a new way of
description of particle kinematics, and (iv) proposed by Witten [14]
generalized form of Heisenberg uncertainty relation is derived and shown be the
integral part of overall non-orthodox approach. |
Solving the Noether procedure for cubic interactions of higher spins in
(A)dS: The Noether procedure represents a perturbative scheme to construct all
possible consistent interactions starting from a given free theory. In this
note we describe how cubic interactions involving higher spins in any
constant-curvature background can be systematically derived within this
framework. | Casimir operator dependences of non-perturbative fermionic QCD
amplitudes: In eikonal and quenched approximation, it is argued that the strong coupling
fermionic QCD Green's functions and related amplitudes depart from a sole
dependence on the SUc(3) quadratic Casimir operator, C2f, evaluated over the
fundamental gauge group representation. Noticed in non-relativistic Quark
Models and in a non-perturbative generalization of the Schwinger mechanism, an
additional dependence on the cubic Casimir operator shows up, in
contradistinction with perturbation theory and other non-perturbative
approaches. However, it accounts for the full algebraic content of the rank-2
Lie algebra of SUc(3). Though numerically sub-leading effects, cubic Casimir
dependences, here and elsewhere, appear to be a signature of the
non-perturbative fermonic sector of QCD. |
1/J^2 corrections to BMN energies from the quantum long range
Landau-Lifshitz model: In a previous paper (hep-th/0509071), it was shown that quantum 1/J
corrections to the BMN spectrum in an effective Landau-Lifshitz (LL) model
match with the results from the one-loop gauge theory, provided one chooses an
appropriate regularization. In this paper we continue this study for the
conjectured Bethe ansatz for the long range spin chain representing
perturbative planar N=4 Super Yang-Mills in the SU(2) sector, and the ``quantum
string" Bethe ansatz for its string dual. The comparison is carried out for
corrections to BMN energies up to 3rd order in the effective expansion
parameter $\tl=\lambda/J^2$. After determining the ``gauge-theory'' LL action
to order $\tl^3$, which is accomplished indirectly by fixing the coefficients
in the LL action so that the energies of circular strings match with the
energies found using the Bethe ansatz, we find perfect agreement. We interpret
this as further support for an underlying integrability of the system. We then
consider the ``string-theory'' LL action which is a limit of the classical
string action representing fast string motion on an S^3 subspace of S^5 and
compare the resulting $\tl^3/J^2$ corrections to the prediction of the
``string'' Bethe ansatz. As in the gauge case, we find precise matching. This
indicates that the LL Hamiltonian supplemented with a normal ordering
prescription and zeta-function regularization reproduces the full superstring
result for the $1/J^2$ corrections, and also signifies that the string Bethe
ansatz does describe the quantum BMN string spectrum to order $1/J^2$. We also
comment on using the quantum LL approach to determine the non-analytic
contributions in $\lambda$ that are behind the strong to weak coupling
interpolation between the string and gauge results. | Functional Relations in Solvable Lattice Models I: Functional Relations
and Representation Theory: We study a system of functional relations among a commuting family of
row-to-row transfer matrices in solvable lattice models. The role of exact
sequences of the finite dimensional quantum group modules is clarified. We find
a curious phenomenon that the solutions of those functional relations also
solve the so-called thermodynamic Bethe ansatz equations in the high
temperature limit for $sl(r+1)$ models. Based on this observation, we propose
possible functional relations for models associated with all the simple Lie
algebras. We show that these functional relations certainly fulfill strong
constraints coming from the fusion procedure analysis. The application to the
calculations of physical quantities will be presented in the subsequent
publication. |
Non-perturbative Supersymmetry Breaking and Finite Temperature
Instabilities in N=4 Superstrings: We obtain the non-perturbative effective potential for the dual
five-dimensional N=4 strings in the context of finite-temperature regarded as a
breaking of supersymmetry into four space-time dimensions. Using the properties
of gauged N=4 supergravity we derive the universal thermal effective potential
describing all possible high-temperature instabilities of the known N=4
superstrings. These strings undergo a high-temperature transition to a new
phase in which five-branes condense. This phase is described in detail, using
both the effective supergravity and non-critical string theory in six
dimensions. In the new phase, supersymmetry is perturbatively restored but
broken at the non-perturbative level. | Generalised $G_2$-structures and type IIB superstrings: The recent mathematical literature introduces generalised geometries which
are defined by a reduction from the structure group $SO(d,d)$ of the vector
bundle $T^d\oplus T^{d*}$ to a special subgroup. In this article we show that
compactification of IIB superstring vacua on 7-manifolds with two covariantly
constant spinors leads to a generalised $G_2$-structure associated with a
reduction from SO(7,7) to $G_2\times G_2$. We also consider compactifications
on 6-manifolds where analogously we obtain a generalised SU(3)-structure
associated with $SU(3)\times SU(3)$, and show how these relate to generalised
$G_2$-structures. |
Conformal gravity with totally antisymmetric torsion: We present a gauge theory of the conformal group in four spacetime dimensions
with a non-vanishing torsion. In particular, we allow for a completely
antisymmetric torsion, equivalent by Hodge duality to an axial vector whose
presence does not spoil the conformal invariance of the theory, in contrast
with claims of antecedent literature. The requirement of conformal invariance
implies a differential condition (in particular, a Killing equation) on the
aforementioned axial vector which leads to a Maxwell-like equation in a
four-dimensional curved background. We also give some preliminary results in
the context of $\mathcal{N}=1$ four-dimensional conformal supergravity in the
geometric approach, showing that if we only allow for the constraint of
vanishing supertorsion all the other constraints imposed in the spacetime
approach are a consequence of the closure of the Bianchi identities in
superspace. This paves the way towards a future complete investigation of the
conformal supergravity using the Bianchi identities in the presence a
non-vanishing (super)torsion. | Stability Analysis of the Dilatonic Black Hole in Two Dimensions: We explicitly show that the net number of degrees of freedom in the
two-dimensional dilaton gravity is zero through the Hamiltonian constraint
analysis. This implies that the local space-time dependent physical excitations
do not exist. From the linear perturbation around the black hole background, we
explicitly prove that the exponentially growing mode with time is in fact
eliminated outside the horizon. Therefore, the two-dimensional dilation gravity
is essentially stable. |
QCD, Wick's Theorem for KdV $τ$-functions and the String Equation: Two consistency conditions for partition functions established by Akemann and
Dam-gaard in their studies of the fermionic mass dependence of the QCD
partition function at low energy ({\it a la} Leutwiller-Smilga-Verbaarschot)
are interpreted in terms of integrable hierarchies. Their algebraic relation is
shown to be a consequence of Wick's theorem for 2d fermionic correlators
(Hirota identities) in the special case of the 2-reductions of the KP hierarchy
(that is KdV/mKdV). The consistency condition involving derivatives is an
incarnation of the string equation associated with the particular matrix model
(the particular kind of the Kac-Schwarz operator). | New results for a two-loop massless propagator-type Feynman diagram: We consider the two-loop massless propagator-type Feynman diagram with an
arbitrary (non-integer) index on the central line. We analytically prove the
equality of the two well-known results existing in the literature which express
this diagram in terms of ${}_3F_2$-hypergeometric functions of argument $-1$
and $1$, respectively. We also derive new representations for this diagram
which may be of importance in practical calculations. |
Matrix Ernst Potentials and Orthogonal Symmetry for Heterotic String in
Three Dimensions: A new matrix representation for low-energy limit of heterotic string theory
reduced to three dimensions is considered. The pair of matrix Ernst Potentials
uniquely connected with the coset matrix is derived. The action of the symmetry
group on the Ernst potentials is established. | On the Emergence of Lorentz Invariance and Unitarity from the Scattering
Facet of Cosmological Polytopes: The concepts of Lorentz invariance of local (flat space) physics, and
unitarity of time evolution and the S-matrix, are famously rigid and robust,
admitting no obvious consistent theoretical deformations, and confirmed to
incredible accuracy by experiments. But neither of these notions seem to appear
directly in describing the spatial correlation functions at future infinity
characterizing the "boundary" observables in cosmology. How then can we see
them emerge as {\it exact} concepts from a possible ab-initio theory for the
late-time wavefunction of the universe? In this letter we examine this question
in a simple but concrete setting, for the perturbative wavefunction in a class
of scalar field models where an ab-initio description of the wavefunction has
been given by "cosmological polytopes". Singularities of the wavefunction are
associated with facets of the polytope. One of the singularities --
corresponding to the "total energy pole" -- is well known to be associated with
the flat-space scattering amplitude. We show how the combinatorics and geometry
of this {\it scattering facet} of the cosmological polytope straightforwardly
leads to the emergence of Lorentz invariance and unitarity for the S-matrix.
Unitarity follows from the way boundaries of the scattering facet factorize
into products of lower-dimensional polytopes, while Lorentz invariance follows
from a contour integral representation of the canonical form, which exists for
any polytope, specialized to cosmological polytopes. |
Rolling Closed String Tachyons and the Big Crunch: We study the low-energy effective field equations that couple gravity, the
dilaton, and the bulk closed string tachyon of bosonic closed string theory. We
establish that whenever the tachyon induces the rolling process, the string
metric remains fixed while the dilaton rolls to strong coupling. For negative
definite potentials we show that this results in an Einstein metric that
crunches the universe in finite time. This behavior is shown to be rather
generic even if the potentials are not negative definite. The solutions are
reminiscent of those in the collapse stage of a cyclic universe cosmology where
scalar field potentials with negative energies play a central role. | On the generalized Freedman-Townsend model: Consistent interactions that can be added to a free, Abelian gauge theory
comprising a finite collection of BF models and a finite set of two-form gauge
fields (with the Lagrangian action written in first-order form as a sum of
Abelian Freedman-Townsend models) are constructed from the deformation of the
solution to the master equation based on specific cohomological techniques.
Under the hypotheses of smoothness in the coupling constant, locality, Lorentz
covariance, and Poincare invariance of the interactions, supplemented with the
requirement on the preservation of the number of derivatives on each field with
respect to the free theory, we obtain that the deformation procedure modifies
the Lagrangian action, the gauge transformations as well as the accompanying
algebra. The interacting Lagrangian action contains a generalized version of
non-Abelian Freedman-Townsend model. The consistency of interactions to all
orders in the coupling constant unfolds certain equations, which are shown to
have solutions. |
QNMs of scalar fields on small Reissner-Nordström-AdS$\mathbf{_5}$
black holes: We study the quasinormal modes (QNMs) of a charged scalar field on a
Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS$_{5}$) black hole in the small
radius limit by using the isomonodromic method. We also derive the
low-temperature expansion of the fundamental QNM frequency. Finally, we provide
numerical evidence that instabilities appear in the small radius limit for
large values of the charge of the scalar field. | Modular application of an Integration by Fractional Expansion (IBFE)
method to multiloop Feynman diagrams: We present an alternative technique for evaluating multiloop Feynman
diagrams, using the integration by fractional expansion method. Here we
consider generic diagrams that contain propagators with radiative corrections
which topologically correspond to recursive constructions of bubble type
diagrams. The main idea is to reduce these subgraphs, replacing them by their
equivalent multiregion expansion. One of the main advantages of this
integration technique is that it allows to reduce massive cases with the same
degree of difficulty as in the massless case. |
BPS/CFT correspondence IV: sigma models and defects in gauge theory: Quantum field theory $L_1$ on spacetime $X_{1}$ can be coupled to another
quantum field theory $L_2$ on a spacetime $X_{2}$ via the third quantum field
theory $L_{12}$ living on $X_{12} = X_{1} \cap X_{2}$. We explore several such
constructions with two and four dimensional $X_{1}, X_{2}$'s and zero and two
dimensional $X_{12}$'s, in the context of $\mathcal{N}=2$ supersymmetry,
non-perturbative Dyson-Schwinger equations, and BPS/CFT correspondence. The
companion paper will show that the BPZ and KZ equations of two dimensional
conformal field theory are obeyed by the half-BPS surface defects in quiver
$\mathcal{N}=2$ gauge theories. | Overview and Warmup Example for Perturbation Theory with Instantons: The large $k$ asymptotics (perturbation series) for integrals of the form
$\int_{\cal F}\mu e^{i k S}$, where $\mu$ is a smooth top form and $S$ is a
smooth function on a manifold ${\cal F}$, both of which are invariant under the
action of a symmetry group ${\cal G}$, may be computed using the stationary
phase approximation. This perturbation series can be expressed as the integral
of a top form on the space $\cM$ of critical points of $S$ mod the action of
${\cal G}$. In this paper we overview a formulation of the ``Feynman rules''
computing this top form and a proof that the perturbation series one obtains is
independent of the choice of metric on ${\cal F}$ needed to define it. We also
overview how this definition can be adapted to the context of $3$-dimensional
Chern--Simons quantum field theory where ${\cal F}$ is infinite dimensional.
This results in a construction of new differential invariants depending on a
closed, oriented $3$-manifold $M$ together with a choice of smooth component of
the moduli space of flat connections on $M$ with compact structure group $G$.
To make this paper more accessible we warm up with a trivial example and only
give an outline of the proof that one obtains invariants in the Chern--Simons
case. Full details will appear elsewhere. |
N=1 superfield description of six-dimensional supergravity: We express the action of six-dimensional supergravity in terms of
four-dimensional N=1 superfields, focusing on the moduli dependence of the
action. The gauge invariance of the action in the tensor-vector sector is
realized in a quite nontrivial manner, and it determines the moduli dependence
of the action. The resultant moduli dependence is intricate, especially on the
shape modulus. Our result is reduced to the known superfield actions of
six-dimensional global SUSY theories and of five-dimensional supergravity by
replacing the moduli superfields with their background values and by performing
the dimensional reduction, respectively. | Friedel Oscillations in Holographic Metals: In this article we study the conditions under which holographic metallic
states display Friedel oscillations. We focus on systems where the bulk charge
density is not hidden behind a black hole horizon. Understanding holographic
Friedel oscillations gives a clean way to characterize the boundary system,
complementary to probe fermion calculations. We find that fermions in a "hard
wall" AdS geometry unambiguously display Friedel oscillations. However, similar
oscillations are washed out for electron stars, suggesting a smeared continuum
of Fermi surfaces. |
Solutions of coupled BPS equations for two-family Calogero and matrix
models: We consider a large N, two-family Calogero and matrix model in the
Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the
solutions to the coupled Bogomol'nyi-Prasad-Sommerfeld equations are given by
the static soliton configurations. We find all solutions close to constant and
construct exact one-parameter solutions in the strong-weak dual case. Full
classification of these solutions is presented. | Instabilities of microstate geometries with antibranes: One can obtain very large classes of horizonless microstate geometries
corresponding to near-extremal black holes by placing probe supertubes whose
action has metastable minima inside certain supersymmetric bubbling solutions.
We show that these minima can lower their energy when the bubbles move in
certain directions in the moduli space, which implies that these near-extremal
microstates are in fact unstable once one considers the dynamics of all their
degrees of freedom. The decay of these solutions corresponds to Hawking
radiation, and we compare the emission rate and frequency to those of the
corresponding black hole. Our analysis supports the expectation that generic
non-extremal black holes microstate geometries should be unstable. It also
establishes the existence of a new type of instabilities for antibranes in
highly-warped regions with charge dissolved in fluxes. |
Mesons from global Anti-de Sitter space: In the context of gauge/gravity duality, we study both probe D7-- and probe
D5--branes in global Anti-de Sitter space. The dual field theory is N=4 theory
on R x S^3 with added flavour. The branes undergo a geometrical phase
transition in this geometry as function of the bare quark mass m_q in units of
1/R with R the S^3 radius. The meson spectra are obtained from fluctuations of
the brane probes. First, we study them numerically for finite quark mass
through the phase transition. Moreover, at zero quark mass we calculate the
meson spectra analytically both in supergravity and in free field theory on R x
S^3 and find that the results match: For the chiral primaries, the lowest level
is given by the zero point energy or by the scaling dimension of the operator
corresponding to the fluctuations, respectively. The higher levels are
equidistant. Similar results apply to the descendents. Our results confirm the
physical interpretation that the mesons cannot pair-produce any further when
their zero-point energy exceeds their binding energy. | Vector Supersymmetry of 2D Yang-Mills Theory: The vector supersymmetry of the 2D topological BF model is extended to 2D
Yang-Mills. The consequences of the corresponding Ward identity on the
ultraviolet behavior of the theory are analyzed. |
Renormalization of the Non-Linear Sigma Model in Four Dimensions. A
two-loop example: The renormalization procedure of the non-linear SU(2) sigma model in D=4
proposed in hep-th/0504023 and hep-th/0506220 is here tested in a truly
non-trivial case where the non-linearity of the functional equation is crucial.
The simplest example, where the non-linear term contributes, is given by the
two-loop amplitude involving the insertion of two \phi_0 (the constraint of the
non-linear sigma model) and two flat connections. In this case we verify the
validity of the renormalization procedure: the recursive subtraction of the
pole parts at D=4 yields amplitudes that satisfy the defining functional
equation. As a by-product we give a formal proof that in D dimensions (without
counterterms) the Feynman rules provide a perturbative symmetric solution. | Central potential and examples of hidden algebra structure: We propose two generalisations of the Coulomb potential equation of quantum
mechanics and investigate the occurence of algebraic eigenfunctions for the
corresponding Scrh\"odinger equations. Some relativistic counterparts of these
problems are also discussed. |
The Hausdorff dimension of random walks and the correlation length
critical exponent in Euclidean field theory: We study the random walk representation of the two-point function in
statistical mechanics models near the critical point. Using standard scaling
arguments we show that the critical exponent $\nu$ describing the vanishing of
the physical mass at the critical point is equal to $\nu_\theta/ d_w$. $d_w$ is
the Hausdorff dimension of the walk. $\nu_\theta$ is the exponent describing
the vanishing of the energy per unit length of the walk at the critical point.
For the case of O(N) models, we show that $\nu_\theta=\varphi$, where $\varphi$
is the crossover exponent known in the context of field theory. This implies
that the Hausdorff dimension of the walk is $\varphi/\nu$ for O(N) models. | Moduli Stabilization in String Theory: We give an overview of moduli stabilization in compactifications of string
theory. We summarize current methods for construction and analysis of vacua
with stabilized moduli, and we describe applications to cosmology and particle
physics. This is a contribution to the Handbook of Quantum Gravity. |
Dynamics of Fundamental Matter in N=2* Yang-Mills Theory: We study the dynamics of quenched fundamental matter in $\mathcal{N}=2^\ast$
supersymmetric large $N$ SU(N) Yang-Mills theory at zero temperature. Our tools
for this study are probe D7-branes in the holographically dual
$\mathcal{N}=2^\ast$ Pilch-Warner gravitational background. Previous work using
D3-brane probes of this geometry has shown that it captures the physics of a
special slice of the Coulomb branch moduli space of the gauge theory, where the
$N$ constituent D3-branes form a dense one dimensional locus known as the
enhancon, located deep in the infrared. Our present work shows how this physics
is supplemented by the physics of dynamical flavours, revealed by the D7-branes
embeddings we find. The Pilch-Warner background introduces new divergences into
the D7-branes free energy, which we are able to remove with a single
counterterm. We find a family of D7-brane embeddings in the geometry and
discuss their properties. We study the physics of the quark condensate,
constituent quark mass, and part of the meson spectrum. Notably, there is a
special zero mass embedding that ends on the enhancon, which shows that while
the geometry acts repulsively on the D7-branes, it does not do so in a way that
produces spontaneous chiral symmetry breaking. | Self-adjointness and the Casimir effect with confined quantized spinor
matter: A generalization of the MIT bag boundary condition for spinor matter is
proposed basing on the requirement that the Dirac hamiltonian operator be
self-adjoint. An influence of a background magnetic field on the vacuum of
charged spinor matter confined between two parallel material plates is studied.
Employing the most general set of boundary conditions at the plates in the case
of the uniform magnetic field directed orthogonally to the plates, we find the
pressure from the vacuum onto the plates. In physically plausible situations,
the Casimir effect is shown to be repulsive, independently of a choice of
boundary conditions and of a distance between the plates. |
Noncommutative spacetime symmetries: Twist versus covariance: We prove that the Moyal product is covariant under linear affine spacetime
transformations. From the covariance law, by introducing an $(x,\Theta)$-space
where the spacetime coordinates and the noncommutativity matrix components are
on the same footing, we obtain a noncommutative representation of the affine
algebra, its generators being differential operators in $(x,\Theta)$-space. As
a particular case, the Weyl Lie algebra is studied and known results for Weyl
invariant noncommutative field theories are rederived in a nutshell. We also
show that this covariance cannot be extended to spacetime transformations
generated by differential operators whose coefficients are polynomials of order
larger than one. We compare our approach with the twist-deformed enveloping
algebra description of spacetime transformations. | Flips, dualities and symmetry enhancements: We present various 4d $\mathcal{N}=1$ theories enjoying IR global symmetry
enhancement. The models we consider have the $USp(2n)$ gauge group, 8
fundamental, one antisymmetric chirals and various numbers of gauge singlets.
By suitably turning on superpotential deformations involving the singlets which
break part of the UV symmetry we flow to SCFTs with $E_6$, $SO(10)$, $SO(9)$,
$SO(8)$ and $F_4$ IR global symmetry. We explain these patterns of symmetry
enhancement following two arguments due to Razamat, Sela and Zafrir. The first
one involves the study of the relations satisfied by marginal operators, while
the second one relies on the existence of self-duality frames. |
Second Order Langevin Equation and Definition of Quantum Gravity By
Stochastic Quantisation: Euclidean quantum gravity might be defined by stochastic quantisation that is
governed by a higher order Langevin equation rather than a first order
stochastic equation. In a transitory phase where the Lorentz time cannot be
defined, the parameter that orders the evolution of quantum gravity phenomena
is the stochastic time. This changes the definition of causality in the period
of primordial cosmology. The prediction of stochastically quantised gravity is
that there will a transition from an oscillating quantum phase to a
semi-classical one, when the Lorentz time emerges. The end of the transition,
as it can be observed from now and described by inflation models, is a diluted
Universe, following the inflation phenomenological evolution. It is filled at
the beginning with scattered classical primordial black holes. The smallest
ones will quickly decay in matter, with a standard quantum field theory
evolution till our period. The stable heavier black holes will remain, forming
a good fraction of the dark matter and the large black holes observed in the
galaxies. In a theoretically related way, this framework suggests the
possibility of a gravitational parton content for "point-like" particles, in
the same five dimensional quantum field theory context as in the primordial
cosmology, with a (+----) signature for the 5d metrics. The very precise and
explicit result expressed in this paper is actually far more modest than its
motivation. We compute explicitly the meaning of a second order Langevin
equation in zero dimensions and define precisely what is second order
stochastic quantisation in a soluble case. | $W_\infty$ Algebras, Hawking Radiation and Information Retention by
Stringy Black Holes: We have argued previously, based on the analysis of two-dimensional stringy
black holes, that information in stringy versions of four-dimensional
Schwarzschild black holes (whose singular regions are represented by
appropriate Wess-Zumino-Witten models) is retained by quantum $W$-symmetries
when the horizon area is not preserved due to Hawking radiation. It is key that
the exactly-marginal conformal world-sheet operator representing a massless
stringy particle interacting with the black hole requires a contribution from
$W_\infty$ generators in its vertex function. The latter correspond to
delocalised, non-propagating, string excitations that guarantee the transfer of
information between the string black hole and external particles. When
infalling matter crosses the horizon, these topological states are excited via
a process: (Stringy black hole) + infalling matter $\rightarrow $ (Stringy
black hole)$^\star$, where the black hole is viewed as a stringy state with a
specific configuration of $W_\infty$ charges that are conserved. Hawking
radiation is then the reverse process, with conservation of the $W_\infty$
charges retaining information. The Hawking radiation spectrum near the horizon
of a Schwarzschild or Kerr black hole is specified by matrix elements of
higher-order currents that form a phase-space $W_{1+\infty}$ algebra. We show
that an appropriate gauging of this algebra preserves the horizon
two-dimensional area classically, as expected because the latter is a conserved
Noether charge. |
N=1 Theories, T-duality, and AdS/CFT correspondence: We construct an N=1 superconformal field theory using branes of type IIA
string theory. The IIA construction is related via T-duality to a IIB
configuration with 3-branes in a background generated by two intersecting
O7-planes and 7-branes. The IIB background can be viewed as a local piece of an
F-theory compactification previously studied by Sen in connection with the
Gimon-Polchinski orientifold. We discuss the deformations of the IIA and IIB
constructions and describe a new supersymmetric configuration with curving
D6-branes. Starting from the IIB description we find the supergravity dual of
the large N field theory and discuss the matching of operators and KK states.
The matching of non-chiral primaries exhibits some interesting new features. We
also discuss a relevant deformation of the field theory under which it flows to
a line of strongly coupled N=1 fixed points in the infrared. For these fixed
points we find a partial supergravity description. | Results in susy field theory from 3-brane probe in F-theory: Employing Sen's picture of BPS states on a 3-brane probe world volume field
theory in a F-theory background. we determine some selection rules for the
allowed spectrum in massless $N_{f}\leq 4$ SU(2) Seiberg-Witten theory. The
spectrum for any $N_f \leq 4$ is consistent with previous conjectures and
analysis. |
Quadrupole Instabilities of Relativistic Rotating Membranes: We generalize recent study of the stability of isotropic (spherical) rotating
membranes to the anisotropic ellipsoidal membrane. We find that while the
stability persists for deformations of spin $l=1$, the quadrupole and higher
spin deformations ($l\geq 2$) lead to instabilities. We find the relevant
instability modes and the corresponding eigenvalues. These indicate that the
ellipsoidal rotating membranes generically decay into finger-like
configurations. | Why has spacetime torsion such negligible effect on our universe?: We attempt an answer to the question as to why the evolution of
four-dimensional universe is governed by spacetime curvature but not torsion.
An answer is found if there is an additional compact spacelike dimension with a
warped geometry, with torsion caused by a Kalb-Ramond (KR) antisymmetric tensor
field in the bulk. Starting from a Randall-Sundrum type of warped extra
dimension, and including the inevitable back reaction ensuing from the radius
stabilization mechanism, we show that there is always an extra exponential
suppression of the KR field on the four-dimensional projection that constitutes
our visible universe. The back reaction is found to facilitate the process of
such suppression. |
Ultraviolet divergences in maximal supergravity from a pure spinor point
of view: The ultraviolet divergences of amplitude diagrams in maximal supergravity are
investigated using the pure spinor superfield formalism in maximal
supergravity, with maximally supersymmetric Yang-Mills theory for reference. We
comment on the effects of the loop regularisation in relation to the actual
absence of high powers (within the degrees of freedom) of the non-minimal
variable r. The absence affects previous results of the field theory
description, which is examined more closely (with a new b-ghost) with respect
to the limit on the dimension for finiteness of the theory, dependent on the
number of loops present. The results imply a cut-off of the loop dependence at
six loops for the 4-point amplitude, and at seven loops otherwise. | Gauge-invariant operators of open bosonic string field theory in the
low-energy limit: In the AdS/CFT correspondence we consider correlation functions of
gauge-invariant operators on the gauge theory side, which we obtain in the
low-energy limit of the open string sector. To investigate this low-energy
limit we consider the action of open bosonic string field theory including
source terms for gauge-invariant operators and classically integrate out
massive fields to obtain the effective action for massless fields. While the
gauge-invariant operators depend linearly on the open string field and do not
resemble the corresponding operators such as the energy-momentum tensor in the
low-energy limit, we find that nonlinear dependence is generated in the process
of integrating out massive fields. We also find that the gauge transformation
is modified in such a way that the effective action and the modified gauge
transformation can be written in terms of the same set of multi-string products
which satisfy weak $A_\infty$ relations, and we present explicit expressions
for the multi-string products. |
Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories
in the $\varepsilon$ Expansion: The tensorial equations for non trivial fully interacting fixed points at
lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and
$3-\varepsilon$ dimensions are analysed for $N$-component fields and
corresponding multi-index couplings $\lambda$ which are symmetric tensors with
four or six indices. Both analytic and numerical methods are used. For
$N=5,6,7$ in the four-index case large numbers of irrational fixed points are
found numerically where $||\lambda ||^2$ is close to the bound found by Rychkov
and Stergiou in arXiv:1810.10541. No solutions, other than those already known,
are found which saturate the bound. These examples in general do not have
unique quadratic invariants in the fields. For $N \geqslant 6$ the stability
matrix in the full space of couplings always has negative eigenvalues. In the
six index case the numerical search generates a very large number of solutions
for $N=5$. | Inflationary field excursion in broad classes of scalar field models: In single field slow roll inflation models the height and slope of the
potential are to satisfy certain conditions, to match with observations. This
in turn translates into bounds on the number of e-foldings and the excursion of
the scalar field during inflation. In this work we consider broad classes of
inflationary models to study how much the field excursion starting from horizon
exit to the end of inflation, $\Delta \phi $, can vary for the set of
inflationary parameters given by Planck. We also derive an upper bound on the
number of e-foldings between the horizon exit of a cosmologically interesting
mode and the end of inflation. We comment on the possibility of having
super-Planckian and sub-Planckian field excursions within the framework of
single field slow roll inflation. |
A note on the hidden conformal structure of non-extremal black holes: We study, following Bertini et al. \cite{Bertini:2011ga}, the hidden
conformal symmetry of the massless Klein-Gordon equation in the background of
the general, charged, spherically symmetric, static black-hole solution of a
class of d-dimensional Lagrangians which includes the relevant parts of the
bosonic Lagrangian of any ungauged supergravity. We find that a hidden
SL(2,\mathbb{R}) symmetry appears at the near event and Cauchy-horizon limit. | The future evolution and finite-time singularities in $F(R)$-gravity
unifying the inflation and cosmic acceleration: We study the future evolution of quintessence/phantom dominated epoch in
modified $F(R)$-gravity which unifies the early-time inflation with late-time
acceleration and which is consistent with observational tests. Using the
reconstruction technique it is demonstrated that there are models where any
known (Big Rip, II, III or IV Type) singularity may classically occur. From
another side, in Einstein frame (scalar-tensor description) only IV Type
singularity occurs. Near the singularity the classical description breaks up,
it is demonstrated that quantum effects act against the singularity and may
prevent its appearance. The realistic $F(R)$-gravity which is future
singularity free is proposed. We point out that additional modification of any
$F(R)$-gravity by the terms relevant at the early universe is possible, in such
a way that future singularity does not occur even classically. |
Kink solutions in logarithmic scalar field theory: Excitation spectra,
scattering, and decay of bions: We consider the (1+1)-dimensional Lorentz-symmetric field-theoretic model
with logarithmic potential having a Mexican-hat form with two local minima
similar to that of the quartic Higgs potential in conventional electroweak
theory with spontaneous symmetry breaking and mass generation. We demonstrate
that this model allows topological solutions -- kinks. We analyze the kink
excitation spectrum, and show that it does not contain any vibrational modes.
We also study the scattering dynamics of kinks for a wide range of initial
velocities. The critical value of the initial velocity occurs in kink-antikink
collisions, which thus differentiates two regimes. Below this value, we observe
the capture of kinks and their fast annihilation; while above this value, the
kinks bounce off and escape to spatial infinities. Numerical studies show no
resonance phenomena in the kink-antikink scattering. | Holographic Description of Finite Size Effects in Strongly Coupled
Superconductors: Despite its fundamental and practical interest, the understanding of
mesoscopic effects in strongly coupled superconductors is still limited. Here
we address this problem by studying holographic superconductivity in a disk and
a strip of typical size $\ell$. For $\ell < \ell_c$, where $\ell_c$ depends on
the chemical potential and temperature, we have found that the order parameter
vanishes. The superconductor-metal transition at $\ell = \ell_c$ is controlled
by mean-field critical exponents which suggests that quantum and thermal
fluctuations induced by finite size effects are suppressed in holographic
superconductors. Intriguingly, the effective interactions that bind the order
parameter increases as $\ell$ decreases. Most of these results are consistent
with experimental observations in Pb nanograins at low temperature and
qualitatively different from the ones expected in a weakly coupled
superconductor. |
Comprehensive Solution to the Cosmological Constant, Zero-Point Energy,
and Quantum Gravity Problems: We present a solution to the cosmological constant, the zero-point energy,
and the quantum gravity problems within a single comprehensive framework. We
show that in quantum theories of gravity in which the zero-point energy density
of the gravitational field is well-defined, the cosmological constant and
zero-point energy problems solve each other by mutual cancellation between the
cosmological constant and the matter and gravitational field zero-point energy
densities. Because of this cancellation, regulation of the matter field
zero-point energy density is not needed, and thus does not cause any trace
anomaly to arise. We exhibit our results in two theories of gravity that are
well-defined quantum-mechanically. Both of these theories are locally conformal
invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based
quantum conformal gravity in four dimensions (a fourth-order derivative quantum
theory of the type that Bender and Mannheim have recently shown to be
ghost-free and unitary). Central to our approach is the requirement that any
and all departures of the geometry from Minkowski are to be brought about by
quantum mechanics alone. Consequently, there have to be no fundamental
classical fields, and all mass scales have to be generated by dynamical
condensates. In such a situation the trace of the matter field energy-momentum
tensor is zero, a constraint that obliges its cosmological constant and
zero-point contributions to cancel each other identically, no matter how large
they might be. Quantization of the gravitational field is caused by its
coupling to quantized matter fields, with the gravitational field not needing
any independent quantization of its own. With there being no a priori classical
curvature, one does not have to make it compatible with quantization. | Nested braneworlds and strong brane gravity: We find the gravitational field of a `nested' domain wall living entirely
within a brane-universe, or, a localised vortex within a wall. For a vortex
living on a critical Randall-Sundrum brane universe, we show that the induced
gravitational field on the brane is identical to that of an (n-1)-dimensional
vacuum domain wall. We also describe how to set-up a nested Randall-Sundrum
scenario using a flat critical vortex living on a subcritical (adS) brane
universe. |
Coulomb integrals and conformal blocks in the AdS3-WZNW model: We study spectral flow preserving four-point correlation functions in the
AdS3-WZNW model using the Coulomb gas method on the sphere. We present a
multiple integral realization of the conformal blocks and explicitly compute
amplitudes involving operators with quantized values of the sum of their spins,
i.e., requiring an integer number of screening charges of the first kind. The
result is given as a sum over the independent configurations of screening
contours yielding a monodromy invariant expansion in powers of the worldsheet
moduli. We then examine the factorization limit and show that the leading terms
in the sum can be identified, in the semiclassical limit, with products of
spectral flow conserving three-point functions. These terms can be rewritten as
the m-basis version of the integral expression obtained by J. Teschner from a
postulate for the operator product expansion of normalizable states in the
H3+-WZNW model. Finally, we determine the equivalence between the
factorizations of a particular set of four-point functions into products of two
three-point functions either preserving or violating spectral flow number
conservation. Based on this analysis we argue that the expression for the
amplitude as an integral over the spin of the intermediate operators holds
beyond the semiclassical regime, thus corroborating that spectral flow
conserving correlators in the AdS3-WZNW model are related by analytic
continuation to correlation functions in the H3+-WZNW model. | Entanglement of purification: from spin chains to holography: Purification is a powerful technique in quantum physics whereby a mixed
quantum state is extended to a pure state on a larger system. This process is
not unique, and in systems composed of many degrees of freedom, one natural
purification is the one with minimal entanglement. Here we study the entropy of
the minimally entangled purification, called the entanglement of purification,
in three model systems: an Ising spin chain, conformal field theories
holographically dual to Einstein gravity, and random stabilizer tensor
networks. We conjecture values for the entanglement of purification in all
these models, and we support our conjectures with a variety of numerical and
analytical results. We find that such minimally entangled purifications have a
number of applications, from enhancing entanglement-based tensor network
methods for describing mixed states to elucidating novel aspects of the
emergence of geometry from entanglement in the AdS/CFT correspondence. |
Plane-parallel waves as duals of the flat background: We give a classification of non-Abelian T-duals of the flat metric in D=4
dimensions with respect to the four-dimensional continuous subgroups of the
Poincare group. After dualizing the flat background, we identify majority of
dual models as conformal sigma models in plane-parallel wave backgrounds, most
of them having torsion. We give their form in Brinkmann coordinates. We find,
besides the plane-parallel waves, several diagonalizable curved metrics with
nontrivial scalar curvature and torsion. Using the non-Abelian T-duality, we
find general solution of the classical field equations for all the sigma models
in terms of d'Alembert solutions of the wave equation. | Particle Kinematics in Horava-Lifshitz Gravity: We study the deformed kinematics of point particles in the Horava theory of
gravity. This is achieved by considering particles as the optical limit of
fields with a generalized Klein-Gordon action. We derive the deformed geodesic
equation and study in detail the cases of flat and spherically symmetric
(Schwarzschild-like) spacetimes. As the theory is not invariant under local
Lorenz transformations, deviations from standard kinematics become evident even
for flat manifolds, supporting superluminal as well as massive luminal
particles. These deviations from standard behavior could be used for
experimental tests of this modified theory of gravity. |
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