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SL(2,Z) Multiplets in N=4 SYM Theory: We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in
the superconformal phase. The modular property of the operator's scaling
dimension determines whether the operator transforms as a singlet, or
covariantly, as part of a finite or infinite dimensional multiplet under the
SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet
transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the
non-perturbative local operators dual to the Konishi multiplet. | On the Scalar Manifold of Exceptional Supergravity: We construct two parametrizations of the non compact exceptional Lie group
G=E7(-25), based on a fibration which has the maximal compact subgroup K=(E6 x
U(1))/Z_3 as a fiber. It is well known that G plays an important role in the
N=2 d=4 magic exceptional supergravity, where it describes the U-duality of the
theory and where the symmetric space M=G/K gives the vector multiplets' scalar
manifold. First, by making use of the exponential map, we compute a realization
of G/K, that is based on the E6 invariant d-tensor, and hence exhibits the
maximal possible manifest [(E6 x U(1))/Z_3]-covariance. This provides a basis
for the corresponding supergravity theory, which is the analogue of the
Calabi-Vesentini coordinates. Then we study the Iwasawa decomposition. Its main
feature is that it is SO(8)-covariant and therefore it highlights the role of
triality. Along the way we analyze the relevant chain of maximal embeddings
which leads to SO(8). It is worth noticing that being based on the properties
of a "mixed" Freudenthal-Tits magic square, the whole procedure can be
generalized to a broader class of groups of type E7. |
Constraints on GUT 7-brane Topology in F-theory: We study the relation between phenomenological requirements and the topology
of the surfaces that GUT 7-branes wrap in F-theory compactifications. In
addition to the exotic matter free condition in the hypercharge flux scenario
of SU(5)_{GUT} breaking, we analyze a new condition that comes from a discrete
symmetry aligning the contributions to low-energy Yukawa matrices from a number
of codimension-three singularity points. We see that the exotic matter free
condition excludes Hirzebruch surfaces (except ${\mathbb F}_0$) as the GUT
surface, correcting an existing proof in the literature. We further find that
the discrete symmetry for the alignment of the Yukawa matrices excludes del
Pezzo surfaces and a rational elliptic surface as the GUT surface. Therefore,
some GUT 7-brane surfaces are good for some phenomenological requirements, but
sometimes not for others, and this aspect should be kept in mind in geometry
search in F-theory compactifications. | The anomaly in the central charge of the supersymmetric kink from
dimensional regularization and reduction: We show that the anomalous contribution to the central charge of the
1+1-dimensional N=1 supersymmetric kink that is required for BPS saturation at
the quantum level can be linked to an analogous term in the extra momentum
operator of a 2+1-dimensional kink domain wall with spontaneous parity
violation and chiral domain wall fermions. In the quantization of the domain
wall, BPS saturation is preserved by nonvanishing quantum corrections to the
momentum density in the extra space dimension. Dimensional reduction from 2+1
to 1+1 dimensions preserves the unbroken N=1/2 supersymmetry and turns these
parity-violating contributions into the anomaly of the central charge of the
supersymmetric kink. On the other hand, standard dimensional regularization by
dimensional reduction from 1 to (1-epsilon) spatial dimensions, which also
preserves supersymmetry, obtains the anomaly from an evanescent counterterm. |
Interacting Noncommutative Lumps: We consider interaction of two lumps corresponding to 0-branes in
noncommutative gauge theory | On the cigar CFT and Schwarzschild horizons: Aspects of shock waves and instantly-created folded strings operators in the
supersymmetric $SL(2)_k/U(1)$ CFT, and their relevance to the near-horizon
physics of Schwarzschild black holes in perurbative superstring theory, are
presented. |
On Type IIA String Theory on the PP-wave Background: We study type IIA superstring theory on a PP-wave background with 24
supercharges. This model can exactly be solved and then quantized. The open
string in this PP-wave background is also studied. We observe that the theory
has supersymmetric Dp-branes for p=2,4,6,8. | Regge Trajectories for Mesons in the Holographic Dual of Large-N_c QCD: We discuss Regge trajectories of dynamical mesons in large-N_c QCD, using the
supergravity background describing N_c D4-branes compactified on a thermal
circle. The flavor degrees of freedom arise from the addition of N_f<<N_c D6
probe branes. Our work provides a string theoretical derivation, via the
gauge/string correspondence, of a phenomenological model describing the meson
as rotating point-like massive particles connected by a flux string. The
massive endpoints induce nonlinearities for the Regge trajectory. For light
quarks the Regge trajectories of mesons are essentially linear. For massive
quarks our trajectories qualitatively capture the nonlinearity detected in
lattice calculations. |
Holographic Geometry and Noise in Matrix Theory: Using Matrix Theory as a concrete example of a fundamental holographic
theory, we show that the emergent macroscopic spacetime displays a new
macroscopic quantum structure, holographic geometry, and a new observable
phenomenon, holographic noise, with phenomenology similar to that previously
derived on the basis of a quasi-monochromatic wave theory. Traces of matrix
operators on a light sheet with a compact dimension of size $R$ are interpreted
as transverse position operators for macroscopic bodies. An effective quantum
wave equation for spacetime is derived from the Matrix Hamiltonian. Its
solutions display eigenmodes that connect longitudinal separation and
transverse position operators on macroscopic scales. Measurements of transverse
relative positions of macroscopically separated bodies, such as signals in
Michelson interferometers, are shown to display holographic nonlocality,
indeterminacy and noise, whose properties can be predicted with no parameters
except $R$. Similar results are derived using a detailed scattering calculation
of the matrix wavefunction. Current experimental technology will allow a
definitive and precise test or validation of this interpretation of holographic
fundamental theories. In the latter case, they will yield a direct measurement
of $R$ independent of the gravitational definition of the Planck length, and a
direct measurement of the total number of degrees of freedom. | The Kaluza-Klein Monopole in a Massive IIA Background: We construct the effective action of the KK-monopole in a massive Type IIA
background. We follow two approaches. First we construct a massive M-theory
KK-monopole from which the IIA monopole is obtained by double dimensional
reduction. This eleven dimensional monopole contains two isometries: one under
translations of the Taub-NUT coordinate and the other under massive
transformations of the embedding coordinates. Secondly, we construct the
massive T-duality rules that map the Type IIB NS-5-brane onto the massive Type
IIA KK-monopole. This provides a check of the action constructed from eleven
dimensions. |
Remarks on the Additional Symmetries and W-Constraints in the
Generalized KdV Hierarchy: Additional symmetries of the $p$-reduced KP hierarchy are generated by the
Lax operator $L$ and another operator $M$, satisfying $res (M^n L^{m+n/p})$ = 0
for $1 \leq n \leq p-1$ and $m \geq -1$ with the condition that ${\partial L
\over {\partial t_{kp}}}$ = 0, $k$ = 1, 2,..... We show explicitly that the
generators of these additional symmetries satisfy a closed and consistent
W-algebra only when we impose the extra condition that ${\partial M \over
{\partial t_{kp}}} = 0$. | The Geometric Construction of WZW Effective Action in Non-commutative
Manifold: By constructing close one cochain density ${\Omega^1}_{2n}$ in the gauge
group space we get WZW effective Lagrangian on high dimensional non-commutative
space.Especially consistent anomalies derived from this WZW effective action in
non-commutative four-dimensional space coincides with those by L.Bonora etc. |
Quantum Reflective Kinks: We scatter a meson off of a scalar kink in quantum field theory, at leading
order in perturbation theory. We calculate the full quantum state, at leading
order, at all times and also check that the reflection and transmission
coefficients agree with those which would be obtained in relativistic quantum
mechanics. | Light Front Formalism for Composite Systems and Some of Its Applications
in Particle and Relativistic Nuclear Physics: Light front formalism for composite systems is presented. Derivation of
equations for bound state and scattering problems are given. Methods of
constructing of elastic form factors and scattering amplitudes of composite
particles are reviewed. Elastic form factors in the impulse approximation are
calculated. Scattering amplitudes for relativistic bound states are
constructed. Some model cases for transition amplitudes are considered. Deep
inelastic form factors (structure functions) are expressed through light front
wave functions. It is shown that taking into account of transverse motion of
partons leads to the violation of Bjorken scaling and structure functions
become square of transverse momentum dependent. Possible explanation of the
EMC-effect is given. Problem of light front relativization of wave functions of
lightest nuclei is considered. Scaling properties of deuteron, ${}^3He$ and
${}^4He$ light front wave functions are checked in a rather wide energy range. |
Low-Energy Dynamics of Noncommutative CP^1 Solitons in 2+1 Dimensions: We investigate the low-energy dynamics of the BPS solitons of the
noncommutative CP^1 model in 2+1 dimensions using the moduli space metric of
the BPS solitons. We show that the dynamics of a single soliton coincides with
that in the commutative model. We find that the singularity in the two-soliton
moduli space, which exists in the commutative CP^1 model, disappears in the
noncommutative model.We also show that the two-soliton metric has the smooth
commutative limit. | Slinky evolution of domain wall brane cosmology: Invoking an initial symmetry between the time $ t $ and some extra spatial
dimension $ y $, we discuss a novel scenario where the dynamical formation of
the 4-dim brane and its cosmological evolution are induced simultaneously by a
common $ t<->y $ symmetry breaking mechanism. The local maximum of the
underlying scalar potential is mapped onto a 'watershed' curve in the $ (t,y) $
plane; the direction tangent to this curve is identified as the cosmic time,
whereas the perpendicular direction serves locally as the extra spatial
dimension. Special attention is devoted to the so-called slinky configurations,
whose brane cosmology is characterized by a decaying cosmological constant
along the watershed curve. Such a slinky solution is first constructed within a
simplified case where the watershed is constrained by $ y = 0 $. The physical
requirements for a slinky configuration to generate a realistic model of
cosmological evolution are then discussed in a more elaborated framework. |
One-Loop Free Energy of the Four-Dimensional Compact QED in the
Confining Phase: The one-loop free energy of the four-dimensional compact QED, which is known
to be equivalent to the vector Sine-Gordon model, is calculated in the strong
coupling regime. In the case, when the norm of the strength tensor of the
saddle-point value of the corresponding Sine-Gordon model is much larger than
the typical inverse area of a loop in the gas of the monopole rings, the
obtained free energy decays exponentially versus this norm. In the opposite
case, when the dominant configuration of the Sine-Gordon model is identically
zero, the resulting free energy decays with the growth of loops as an exponent
of the inverse square of their typical area. | The Large $N$ Limit of icMERA and Holography: In this work, we compute the entanglement entropy in continuous icMERA tensor
networks for large $N$ models at strong coupling. Our results show that the
$1/N$ quantum corrections to the Fisher information metric (interpreted as a
local bond dimension of the tensor network) in an icMERA circuit, are related
to quantum corrections to the minimal area surface in the Ryu-Takayanagi
formula. Upon picking two different non-Gaussian entanglers to build the icMERA
circuit, the results for the entanglement entropy only differ at subleading
orders in $1/G_N$, i.e, at the structure of the quantum corrections in the
bulk. The fact that the large $N$ part of the entropy can be always related to
the leading area term of the holographic calculation is very suggestive. These
results, constitute the first tensor network calculations at large $N$ and
strong coupling simultaneously, pushing the field of tensor network
descriptions of the emergence of dual spacetime geometries from the structure
of entanglement in quantum field theory. |
The Causal Phase in $QED_{3}$: The operator ${\bf S}$ in Fock space which describes the scattering and
particle production processes in an external time-dependent electromagnetic
potential $A$ can be constructed from the one-particle S-matrix up to a
physical phase $\lambda [A]$. In this work we determine this phase for $QED$ in
(2+1) dimensions, by means of causality, and show that no ultraviolet
divergences arise, in contrast to the usual formalism of $QED$. | Hartree-Fock approach to dynamical mass generation in the generalized
(2+1)-dimensional Thirring model: The (2+1)-dimensional generalized massless Thirring model with 4-component
Fermi-fields is investigated by the Hartree-Fock method. The Lagrangian of this
model is constructed from two different four-fermion structures. One of them
takes into account the vector$\times$vector channel of fermion interaction with
coupling constant $G_v$, the other - the scalar$\times$scalar channel with
coupling $G_s$. At some relation between bare couplings $G_s$ and $G_v$, the
Hartree-Fock equation for self-energy of fermions can be renormalized, and
dynamical generation of the Dirac and Haldane fermion masses is possible. As a
result, phase portrait of the model consists of two nontrivial phases. In the
first one the chiral symmetry is spontaneously broken due to dynamical
appearing of the Dirac mass term, while in the second phase a spontaneous
breaking of the spatial parity $\mathcal P$ is induced by Haldane mass term. It
is shown that in the particular case of pure Thirring model, i.e. at $G_s=0$,
the ground state of the system is indeed a mixture of these phases. Moreover,
it was found that dynamical generation of fermion masses is possible for any
finite number of Fermi-fields. |
Untwisting the symmetries of $β$-deformed Super-Yang--Mills: We demonstrate that the planar real-$\beta$-deformed Super-Yang--Mills theory
possesses an infinitely-dimensional Yangian symmetry algebra and thus is
classically integrable. This is achieved by the introduction of the twisted
coproduct which allows us to lift the apparent $\mathcal{N}=1$ supersymmetry
first to the full $\mathcal{N}=4$ symmetry of the parent $\mathcal{N} = 4$ SYM
theory, and subsequently to its Yangian. | Supersymmetrization of the Radiation Damping: We construct a supersymmetrized version of the model to the radiation damping
\cite{03} introduced by the present authors \cite{ACWF}. We dicuss its
symmetries and the corresponding conserved Noether charges. It is shown this
supersymmetric version provides a supersymmetric generalization of the Galilei
algebra obtained in \cite{ACWF}. We have shown that the supersymmetric action
can be splited into dynamically independent external and internal sectors. |
General Virasoro Construction on Orbifold Affine Algebra: We obtain the orbifold Virasoro master equation (OVME) at integer order
lambda, which summarizes the general Virasoro construction on orbifold affine
algebra. The OVME includes the Virasoro master equation when lambda=1 and
contains large classes of stress tensors of twisted sectors of conventional
orbifolds at higher lambda. The generic construction is like a twisted sector
of an orbifold (with non-zero ground state conformal weight) but new
constructions are obtained for which we have so far found no conventional
orbifold interpretation. | Vacuum polarization for compactified $QED_{4+1}$ in a magnetic flux
background: We evaluate one-loop effects for $QED_{4+1}$ compactified to ${\bf R}^4
\times S^1$, in a non-trivial vacuum for the gauge field, such that a
non-vanishing magnetic flux is encircled along the extra dimension. We obtain
the vacuum polarization tensor and evaluate the exact parity breaking term,
presenting the results from the point of view of the effective 3+1 dimensional
theory. |
Testing Effective String Models of Black Holes with Fixed Scalars: We solve the problem of mixing between the fixed scalar and metric
fluctuations. First, we derive the decoupled fixed scalar equation for the
four-dimensional black hole with two different charges. We proceed to the
five-dimensional black hole with different electric (1-brane) and magnetic
(5-brane) charges, and derive two decoupled equations satisfied by appropriate
mixtures of the original fixed scalar fields. The resulting greybody factors
are proportional to those that follow from coupling to dimension (2,2)
operators on the effective string. In general, however, the string action also
contains couplings to chiral operators of dimension (1,3) and (3,1), which
cause disagreements with the semiclassical absorption cross-sections.
Implications of this for the effective string models are discussed. | Thermodynamical First Laws of Black Holes in Quadratically-Extended
Gravities: Einstein gravities in general dimensions coupled to a cosmological constant
and extended with quadratic curvature invariants admit a variety of black holes
that may asymptote to Minkowski, anti-de Sitter or Lifshitz spacetimes. We
adopt the Wald formalism to derive an explicit formula for calculating the
thermodynamical first law for the static black holes with
spherical/toric/hyperbolic isometries in these theories. This allows us to
derive/rederive the first laws for a wide range of black holes in literature.
Furthermore, we construct many new exact solutions and obtain their first laws. |
Lattice polarized toric K3 surfaces: When studying mirror symmetry in the context of K3 surfaces, the hyperkaehler
structure of K3 makes the notion of exchanging Kaehler and complex moduli
ambiguous. On the other hand, the metric is not renormalized due to the higher
amount of supersymmetry of the underlying superconformal field theory. Thus one
can define a natural mapping from the classical K3 moduli space to the moduli
space of conformal field theories. Apart from the generalization of mirror
constructions for Calabi-Yau threefolds, there is a formulation of mirror
symmetry in terms of orthogonal lattices and global moduli space arguments. In
many cases both approaches agree perfectly - with a long outstanding exception:
Batyrev's mirror construction for K3 hypersurfaces in toric varieties does not
fit into the lattice picture whenever the Picard group of the K3 surface is not
generated by the pullbacks of the equivariant divisors of the ambient toric
variety. In this case, not even the ranks of the corresponding Picard lattices
add up as expected. In this paper the connection is clarified by refining the
lattice picture. We show (by explicit calculation with a computer) mirror
symmetry for all families of toric K3 hypersurfaces corresponding to dual
reflexive polyhedra, including the formerly problematic cases. | Kinematical Analogy for Marginal Dyon Decay: We describe a kinematical analogy for the marginal decay of 1/4-BPS dyons in
4-dimensional N=4 string compactifications. In this analogy, the electric and
magnetic charges play the role of spatial momenta, the BPS mass plays the role
of energy, and 1/2-BPS dyons correspond to massless particles. Using SO(12,1)
"Lorentz" invariance and standard kinematical formulae in particle physics, we
provide simple derivations of the curves of marginal stability. We also show
how these curves map into the momentum ellipsoid, and propose some applications
of this analogy. |
One Loop Renormalizability of Spontaneously Broken Gauge Theory with a
Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case: A generalization of the standard electroweak model to noncommutative
spacetime would involve a product gauge group which is spontaneously broken.
Gauge interactions in terms of physical gauge bosons are canonical with respect
to massless gauge bosons as required by the exact gauge symmetry, but not so
with respect to massive ones; and furthermore they are generally asymmetric in
the two sets of gauge bosons. On noncommutative spacetime this already occurs
for the simplest model of U(1) x U(1). We examine whether the above feature in
gauge interactions can be perturbatively maintained in this model. We show by a
complete one loop analysis that all ultraviolet divergences are removable with
a few renormalization constants in a way consistent with the above structure. | Soliton Equations Extracted from the Noncommutative Zero-Curvature
Equation: We investigate the equation where the commutation relation in 2-dimensional
zero-curvature equation composed of the algebra-valued potentials is replaced
by the Moyal bracket and the algebra-valued potentials are replaced by the
non-algebra-valued ones with two more new variables. We call the 4-dimensional
equation the noncommutative zero-curvature equation. We show that various
soliton equations are derived by the dimensional reduction of the equation. |
Mass Generation in the Supersymmetric Nambu--Jona--Lasinio Model in an
External Magnetic Field: The mass generation in the (3+1)-dimensional supersymmetric
Nambu-Jona-Lasinio model in a constant magnetic field is studied. It is shown
that the external magnetic field catalyzes chiral symmetry breaking. | Hypercharge flux in F-theory and the stable Sen limit: IIB compactifications enjoy the possibility to break GUT groups via fluxes
without giving mass to the hypercharge gauge field. Although this important
advantage has greatly motivated F-theory constructions, no such fluxes have
been constructed directly in terms of the M-theory $G_4$-form. In this note, we
give a general prescription for constructing hypercharge G-fluxes. By using a
stable version of Sen's weak coupling limit, we verify their connection with
IIB fluxes. We illustrate the lift of fluxes in a number of examples, including
a compact ${\rm SU}(5) \times {\rm U}(1)$ model with explicit realization of
doublet-triplet splitting. Finally, we prove an equivalence conjectured in an
earlier work as a by-product. |
The Collective Field Theory of a Singular Supersymmetric Matrix Model: The supersymmetric collective field theory with the potential $v'(x)=\omega
x-{\eta\over x}$ is studied, motivated by the matrix model proposed by Jevicki
and Yoneya to describe two dimensional string theory in a black hole
background. Consistency with supersymmetry enforces a two band solution. A
supersymmetric classical configuration is found, and interpreted in terms of
the density of zeros of certain Laguerre polynomials. The spectrum of the model
is then studied and is seen to correspond to a massless scalar and a majorana
fermion. The $x$ space eigenfunctions are constructed and expressed in terms of
Chebyshev polynomials. Higher order interactions are also discussed. | Lorentz-violating extension of the spin-one Duffin-Kemmer-Petiau
equation: We investigate the breaking of Lorentz symmetry caused by the inclusion of an
external four-vector via a Chern-Simons-like term in the Duffin-Kemmer-Petiau
Lagrangian for massless and massive spin-one fields. The resulting equations of
motion lead to the appearance of birefringence, where the corresponding photons
are split into two propagation modes. We discuss the gauge invariance of the
extended Lagrangian. Throughout the paper, we utilize projection operators to
reduce the wave-functions to their physical components, and we provide many new
properties of these projection operators. |
Two flavor massless Schwinger model on a torus at a finite chemical
potential: We study the thermodynamics of the two flavor massless Schwinger model on a
torus at a finite chemical potential. We show that thermodynamic quantities
only depend on the isospin chemical potential and there are marked deviations
from a free fermion theory. | Supersymmetry and Dual String Solitons: We present new classes of string-like soliton solutions in ($N=1$; $D=10$),
($N=2$; $D=6$) and ($N=4$; $D=4$) heterotic string theory. Connections are made
between the solution-generating subgroup of the $T$-duality group of the
compactification and the number of spacetime supersymmetries broken. Analogous
solutions are also noted in ($N=1,2$; $D=4$) compactifications, where a
different form of supersymmetry breaking arises. |
Spinning Dilaton Black Holes in 2 +1 Dimensions: Quasi-normal Modes and
the Area Spectrum: We have studied the perturbation of a spinning dilaton black hole in 2 +1
dimensions by a massless scalar field. The wave equations of a massless scalar
field is shown to be exactly solvable in terms of hypergeometric functions. The
quasinormal frequencies are computed for slowly spinning black holes. The
stability of the black hole is discussed. The asymptotic form of the
quasinormal frequencies are evaluated. The area spectrum of the quantum black
holes are evaluated by using the asymptotic quasi-normal frequencies and is
shown to be equally-spaced. | Non-perturbative to perturbative QCD via the FFBRST: Recently a new type of quadratic gauge was introduced in QCD in which the
degrees of freedom are suggestive of a phase of abelian dominance. In its
simplest form it is also free of Gribov ambiguity. However this gauge is not
suitable for usual perturbation theory. The finite field dependent BRST
(FFBRST) transformation is a method established to interrelate generating
functionals for different effective versions of gauge fixed field theories. In
this paper we propose a FFBRST transformation suitable for transforming the
theory in the new quadratic gauge into the standard Lorenz gauge Faddeev-Popov
version of the effective lagrangian. The task is made interesting by the fact
the BRST invariance obeyed by the two effective lagrangians are not the same,
however suitable extension of the previous procedures accomplishes the required
result. We are thus able to identify a field redefinition to go from a
non-perturbative phase of QCD to perturbative QCD. |
Dualisation of the Salam-Sezgin D=8 Supergravity: The first-order formulation of the Salam-Sezgin D=8 supergravity coupled to N
vector multiplets is discussed. The non-linear realization of the bosonic
sector of the D=8 matter coupled Salam-Sezgin supergravity is introduced by the
dualisation of the fields and by constructing the Lie superalgebra of the
symmetry group of the doubled field strength. | Radiation, entanglement and islands from a boundary local quench: We study the entanglement and the energy density of the radiation emitted
after a local quench in a boundary conformal field theory. We use the operator
product expansion (OPE) to predict the early- and late-time behavior of the
entanglement entropy and we find, under mild assumptions, a universal form for
the leading term, which we test on some treatable two-dimensional examples. We
also derive a general upper bound on the entanglement, valid along the full
time evolution. In two dimensions, the bound is computed analytically, while in
higher dimensions it is evaluated at early and late time via the OPE. These CFT
predictions are then compared with a doubly-holographic setup where the CFT is
interpreted as a reservoir for the radiation produced on an end-of-the-world
brane. After finding the gravitational dual of a boundary local quench, we
compute the time evolution of the holographic entanglement entropy, whose
late-time behavior is in perfect agreement with the CFT predictions. In the
brane+bath picture, unitarity of the time evolution is preserved thanks to the
formation of an island. The holographic results can be recovered explicitly
from the island formula, in the limit where the tension of the brane is close
to the maximal value. |
Towards brane-antibrane inflation in type $II_A$: The holographic MQCD
model: We describe type $II_A$ cosmological brane inflation scenarios based on the
holographic MQCD model of Aharony et al \cite{Aharony:2010mi}. The scenarios
can be related via T-duality to the type $II_B$ KKLMMT model
\cite{Kachru:2003sx}. They describe a probe brane configuration of $p$ D4
branes stretching between an $NS5$ and $NS5'$ branes in the holographic
background of large $N$ D4 branes. The resulting cosmological models have a
Wick-rotated D4-brane metric, with transverse dimensions compactified, and a
spiralling brane with flux $p$. In one model, the background has a small
nonextremality, and the inflaton is provided by the position of a "sliding"
D4-brane, and in the other, the background is supersymmetric, but with a
sliding anti-D4-brane. We obtain good and generic inflationary models, though
several unknowns remain, in particular about subleading corrections. The usual
caveat of volume stabilization generically spoiling slow-roll still applies. | Lecture Notes for Massless Spinor and Massive Spinor Triangle Diagrams: These notes present the details of the computation of massless and massive
spinor triangle loops for consistent anomalies in gauge theories. |
Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds: We construct heterotic standard models by compactifying on smooth Calabi-Yau
three-folds in the presence of purely Abelian internal gauge fields. A
systematic search over complete intersection Calabi-Yau manifolds with less
than six Kahler parameters leads to over 200 such models which we present. Each
of these models has precisely the matter spectrum of the MSSM, at least one
pair of Higgs doublets, the standard model gauge group and no exotics. For
about 100 of these models there are, naively, four additional U(1) symmetries,
however these are Green-Schwarz anomalous and, hence, massive. In the remaining
cases, three U(1) symmetries are anomalous while the fourth, massless one can
be spontaneously broken by singlet vacuum expectation values. The presence of
additional global U(1) symmetries, together with the possibility of switching
on singlet vacuum expectation values, leads to a rich phenomenology which is
illustrated for a particular example. Our database of standard models, which
can be further enlarged by simply extending the computer-based search, allows
for a detailed and systematic phenomenological analysis of string standard
models, covering issues such as the structure of Yukawa couplings, R-parity
violation, proton stability and neutrino masses. | Non-local partner to the cosmological constant: I show that quantum corrections due to a massive particle generates a
non-local term in the gravitational effective action which is of zeroth order
in the derivative expansion, much like the cosmological constant. It carries a
fixed coefficient which is very much larger than the cosmological constant, and
which cannot be fine-tuned. The interaction is active at scales above the
particle's mass. This is of the form $m^4 (\frac1{\Box}R)_x "<x|\log (\Box +m^2
)|y >" (\frac1{\Box}R)_y$, and I discuss the meaning of $ "<x|\log (\Box +m^2)
|y >" $ and other aspects of its interpretation. |
Gauge Invariant Treatment of $γ_{5}$ in the Scheme of 't Hooft and
Veltman: We propose moving all the $\gamma_{5}$ matrices to the rightmost position
before continuing the dimension, and show that this simple prescription will
enable the dimension regularization scheme proposed by 't Hooft and Veltman to
be consistent with gauge invariance. | One-loop effective action of the ${\mathbb C}P^{N-1}$ model at large
$μβ$: In this note we consider a non-linear, large-$N$ ${\mathbb C}P^{N-1}$ sigma
model on a finite size interval with periodic boundary conditions, at finite
temperature and chemical potential in the regime of $\beta \mu$ large. Our goal
is to extend previous calculations and obtain the coefficients of the
derivative expansion of the one-loop effective action in the region of $\beta
\mu$ large by carrying out the appropriate analytical continuation. This
calculation complements previous results and allows us to conclude that the
ground state remains homogeneous in this regime as long as it is assumed to be
a slowly varying function of the spatial coordinates. While this is reasonable
at the two extremes of small or large chemical potential, for intermediate
values of the chemical potential and small enough temperature, one might expect
(by analogy with other models) that lower energy crystalline solutions may
exist. In this case a simple derivative expansion, like the one discussed here,
would need to be modified in order to capture these features. |
p-Brane Black Holes as Stability Islands: In multidimensional gravity with an arbitrary number of internal Ricci-flat
factor spaces, interacting with electric and magnetic $p$-branes, spherically
symmetric configurations are considered. It is shown that all single-brane
black-hole solutions are stable under spherically symmetric perturbations,
whereas similar solutions possessing naked singularities turn out to be
catastrophically unstable. The black hole stability conclusion is extended to
some classes of configurations with intersecting branes. These results do not
depend on the particular composition of the $D$-dimensional space-time, on the
number of dilatonic scalar fields $\phi^a$ and on the values of their coupling
constants. Some examples from 11-dimensional supergravity are considered. | Winding out of the Swamp: Evading the Weak Gravity Conjecture with
F-term Winding Inflation?: We present a new model of large field inflation along a winding trajectory in
the field space of two axionic fields, where the 'axions' originate from the
complex structure moduli sector of a Calabi-Yau 3-fold at large complex
structure. The winding trajectory arises from fixing one combination of axions
by bulk fluxes and allows for a transplanckian effective field range. The
inflaton potential arises from small 'instantonic' corrections to the geometry
and realises natural inflation. By working in a regime of large complex
structure for two complex structure moduli the inflaton potential can be made
subdominant without severe tuning. We also discuss the impact of the recent
'no-go theorems' for transplanckian axion periodicities on our work.
Interestingly, our setup seems to realise a loophole pointed out in
arXiv:1503.00795 and arXiv:1503.04783: our construction is a candidate for a
string theory model of large field inflation which is consistent with the mild
form of the weak gravity conjecture for axions. |
The Standard Model and its Generalisations in Epstein-Glaser Approach to
Renormalisation Theory: We continue our study of non-Abelian gauge theories in the framework of
Epstein-Glaser approach to renormalisation theory. We consider the case when
massive spin-one Bosons are present into the theory and we modify appropriately
the analysis of the origin of gauge invariance performed in a preceding paper
in the case of null-mass spin-one Bosons. Then we are able to extend a result
of D\"utsch and Scharf concerning the uniqueness of the standard model
consistent with renormalisation theory. In fact we consider the most general
case i.e. the consistent interaction of $r$ spin-one Bosons and we do not
impose any restriction on the gauge group and the mass spectrum of the theory.
We show that, beside the natural emergence of a group structure (like in the
massless case) we obtain, new conditions of group-theoretical nature, namely
the existence of a certain representation of the gauge group associated to the
Higgs fields. Some other mass relations connecting the structure constants of
the gauge group and the masses of the Bosons emerge naturally. The proof is
done using Epstein-Glaser approach to renormalisation theory. | Scale Invariance plus Unitarity Implies Conformal Invariance in Four
Dimensions: We give a non-perturbative proof that any 4D unitary and Lorentz-invariant
quantum field theory with a conserved scale current is in fact conformally
invariant. We show that any scale invariant theory (unitary or not) must have
either a vanishing anomaly for global scale transformations or an operator of
spin 2 and dimension 2. Neither of these possibilities is allowed for unitary
theories, proving the result. This is also a strong constraint on non-unitary
Euclidean theories with scale but not conformal invariance, suggesting the
conjecture that all such theories are free field theories. |
Integrable asymmetric $λ$-deformations: We construct integrable deformations of the $\lambda$-type for asymmetrically
gauged WZW models. This is achieved by a modification of the Sfetsos gauging
procedure to account for a possible automorphism that is allowed in $G/G$
models. We verify classical integrability, derive the one-loop beta function
for the deformation parameter and give the construction of integrable D-brane
configurations in these models. As an application, we detail the case of the
$\lambda$-deformation of the cigar geometry corresponding to the axial gauged
$SL(2,R)/U(1)$ theory at large $k$. Here we also exhibit a range of both A-type
and B-type integrability preserving D-brane configurations. | Vortex Holography: We show that the Abelian Higgs field equations in the four dimensional anti
de Sitter spacetime have a vortex line solution. This solution, which has
cylindrical symmetry in AdS$_4$, is a generalization of the flat spacetime
Nielsen-Olesen string. We show that the vortex induces a deficit angle in the
AdS$_4$ spacetime that is proportional to its mass density. Using the AdS/CFT
correspondence, we show that the mass density of the string is uniform and dual
to the discontinuity of a logarithmic derivative of correlation function of the
boundary scalar operator. |
Observable effects of anisotropic bubble nucleation: Our universe may have formed via bubble nucleation in an eternally-inflating
background. Furthermore, the background may have a compact dimension--the
modulus of which tunnels out of a metastable minimum during bubble
nucleation--which subsequently grows to become one of our three large spatial
dimensions. Then the reduced symmetry of the background is equivalent to
anisotropic initial conditions in our bubble universe. We compute the
inflationary spectrum in such a scenario and, as a first step toward
understanding the effects of anisotropy, project it onto spherical harmonics.
The resulting spectrum exhibits anomalous multipole correlations, their
relative amplitude set by the present curvature parameter, which extend to
arbitrarily large multipole moments. This raises the possibility of future
detection, if slow-roll inflation does not last too long within our bubble. A
full understanding of the observational signal must account for the effects of
background anisotropy on photon free streaming, and is left to future work. | The many faces of OSp(1|32): We show that the complete superalgebra of symmetries, including central
charges, that underlies F-theories, M-theories and type II string theories in
dimensions 12, 11 and 10 of various signatures correspond to rewriting of the
same OSp(1|32) algebra in different covariant ways. One only has to distinguish
the complex and the unique real algebra. We develop a common framework to
discuss all signatures theories by starting from the complex form of OSp(1|32).
Theories are distinguished by the choice of basis for this algebra. We
formulate dimensional reductions and dualities as changes of basis of the
algebra. A second ingredient is the choice of a real form corresponding to a
specific signature. The existence of the real form of the algebra selects
preferred spacetime signatures. In particular, we show how the real d=10 IIA
and IIB superalgebras for various signatures are related by generalized
T-duality transformations that not only involve spacelike but also timelike
directions. A third essential ingredient is that the translation generator in
one theory plays the role of a central charge operator in the other theory. The
identification of the translation generator in these algebras leads to the star
algebras of Hull, which are characterized by the fact that the positive
definite energy operator is not part of the translation generators. We apply
our results to discuss different T-dual pictures of the D-instanton solution of
Euclidean IIB supergravity. |
Ingoing Eddington-Finkelstein Metric of an Evaporating Black Hole: We present an approximate time-dependent metric in ingoing
Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as
a first-order perturbation of the Schwarzschild metric, using the linearized
back reaction from a realistic approximation to the stress-energy tensor for
the Hawking radiation in the Unruh quantum state. | Superfield approach to a novel symmetry for non-Abelian gauge theory: In the framework of superfield formalism, we demonstrate the existence of a
new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the
BRST invariant Lagrangian density of a self-interacting two ($1 +
1$)-dimensional (2D) non-Abelian gauge theory (having no interaction with
matter fields). The local and nilpotent Noether conserved charges corresponding
to the above continuous symmetries find their geometrical interpretation as the
translation generators along the odd (Grassmannian) directions of the four ($2
+ 2)$-dimensional supermanifold. |
4D gravity on a brane from bulk higher-curvature terms: We study a gravity model where a tensionful codimension-one three-brane is
embedded on a bulk with infinite transverse length. We find that 4D gravity is
induced on the brane already at the classical level if we include
higher-curvature (Gauss-Bonnet) terms in the bulk. Consistency conditions
appear to require a negative brane tension as well as a negative coupling for
the higher-curvature terms. | Decoherence and entropy of primordial fluctuations II. The entropy
budget: We calculate the entropy of adiabatic perturbations associated with a
truncation of the hierarchy of Green functions at the first non trivial level,
i.e. in a self-consistent Gaussian approximation. We give the equation
governing the entropy growth and discuss its phenomenology. It is parameterized
by two model-dependent kernels. We then examine two particular inflationary
models, one with isocurvature perturbations, the other with corrections due to
loops of matter fields. In the first model the entropy grows rapidely, while in
the second the state remains pure (at one loop). |
N=2 supersymmetric AdS_4 solutions of M-theory: We analyse the most general N=2 supersymmetric solutions of D=11 supergravity
consisting of a warped product of four-dimensional anti-de-Sitter space with a
seven-dimensional Riemannian manifold Y_7. We show that the necessary and
sufficient conditions for supersymmetry can be phrased in terms of a local
SU(2)-structure on Y_7. Solutions with non-zero M2-brane charge also admit a
canonical contact structure, in terms of which many physical quantities can be
expressed, including the free energy and the scaling dimensions of operators
dual to supersymmetric wrapped M5-branes. We show that a special class of
solutions is singled out by imposing an additional symmetry, for which the
problem reduces to solving a second order non-linear ODE. As well as recovering
a known class of solutions, that includes the IR fixed point of a mass
deformation of the ABJM theory, we also find new solutions which are dual to
cubic deformations. In particular, we find a new supersymmetric warped AdS_4 x
S^7 solution with non-trivial four-form flux. | Fluctuation and dissipation within a deformed holographic model with
backreaction: In this work we study the fluctuation and dissipation of a string attached to
a brane in a deformed and backreated AdS-Schwarzschild spacetime. This space is
a solution of Einstein-dilaton equations and contains a conformal exponential
factor $\exp(k/r^2)$ in the metric. We consider the backreaction contributions
coming only from the exponential warp factor on the AdS-Schwarzschild black
hole, where the string and brane are in the probe approximation.
Within this Lorentz invariant holographic model we have computed the
admittance, the diffusion coefficient, the two-point functions and the
regularized mean square displacement $s^2_{reg}$. From this quantity we obtain
the diffuse and ballistic regimes characteristic of the Brownian motion. From
the two-point functions and the admittance, we also have checked the well know
fluctuation-dissipation theorem in this set up. |
Fermionic Coset Realization of the Critical Ising Model: We obtain an explicit realization of all the primary fields of the Ising
model in terms of a conformal field theory of constrained fermions. The
four-point correlators of the energy, order and disorder operators are
explicitly calculated. | One-loop Superstring Amplitude From Integrals on Pure Spinors Space: In the Type II superstring the 4-point function for massless NS-NS bosons at
one-loop is well known [1][14]. The overall constant factor in this amplitude
is very important because it needs to satisfy the unitarity and S-duality
conditions [14]. This coefficient has not been computed in the pure spinor
formalism due to the difficulty to solve the integrals on the pure spinors
space. In this paper we compute it by using the non-minimal pure spinor
formalism and we will show that the answer is in perfect agreement with the one
given in [14]. |
Unruh effect detection through chirality in curved graphene: We analyze a generalization of the analogue Unruh effect based on curved
graphene. To this end, we consider the fourth order in derivatives field
theoretic version of the Pais-Uhlenbeck oscillator, for which the Unruh effect
may be interpreted as the creation of two different particles with different
masses, corresponding to two Klein-Gordon subsystems. For our model, unlike the
standard case, electron chirality on the graphene sheet plays a main role as
chirality is essential to distinguish the couple of particles predicted by the
Unruh effect associated to the Pais-Uhlenbeck field model. | Representations of the Lie Superalgebra gl(1|n) in a Gel'fand-Zetlin
Basis and Wigner Quantum Oscillators: An explicit construction of all finite-dimensional irreducible
representations of the Lie superalgebra gl(1|n) in a Gel'fand-Zetlin basis is
given. Particular attention is paid to the so-called star type I
representations (``unitary representations''), and to a simple class of
representations V(p), with p any positive integer. Then, the notion of Wigner
Quantum Oscillators (WQOs) is recalled. In these quantum oscillator models, the
unitary representations of gl(1|DN) are physical state spaces of the N-particle
D-dimensional oscillator. So far, physical properties of gl(1|DN) WQOs were
described only in the so-called Fock spaces W(p), leading to interesting
concepts such as non-commutative coordinates and a discrete spatial structure.
Here, we describe physical properties of WQOs for other unitary
representations, including certain representations V(p) of gl(1|DN). These new
solutions again have remarkable properties following from the spectrum of the
Hamiltonian and of the position, momentum, and angular momentum operators.
Formulae are obtained that give the angular momentum content of all the
representations V(p) of gl(1|3N), associated with the N-particle 3-dimensional
WQO. For these representations V(p) we also consider in more detail the
spectrum of the position operators and their squares, leading to interesting
consequences. In particular, a classical limit of these solutions is obtained,
that is in agreement with the correspondence principle. |
Flow Equations for Non-BPS Extremal Black Holes: We exploit some common features of black hole and domain wall solutions of
(super)gravity theories coupled to scalar fields and construct a class of
stable extremal black holes that are non-BPS, but still can be described by
first-order differential equations. These are driven by a "superpotential'',
which replaces the central charge Z in the usual black hole potential. We
provide a general procedure for finding this class and deriving the associated
"superpotential''. We also identify some other cases which do not belong to
this class, but show a similar behaviour. | Lorentz Symmetry Breaking in $\mathcal{N} =2$ Superspace: In this paper, we will study the deformation of a three dimensional theory
with $\mathcal{N} =2$ supersymmetry. This theory will be deformed by the
presence of a constant vector field. This deformation will break the Lorentz
symmetry. So, we will analyse this theory using $\mathcal{N} =2$ aether
superspace. The $\mathcal{N} =2$ aether superspace will be obtained from a
deformation of the usual $\mathcal{N} =2$ superspace. This will be done by
deforming the generators of the three dimensional $\mathcal{N} =2$
supersymmetry. After analysing this deformed superalgebra, we will derive an
explicit expression for the superspace propagators in this deformed superspace.
Finally, we will use these propagators for performing perturbative
calculations. |
Inflation in Gauged 6D Supergravity: In this note we demonstrate that chaotic inflation can naturally be realized
in the context of an anomaly free minimal gauged supergravity in D=6 which has
recently been the focus of some attention. This particular model has a unique
maximally symmetric ground state solution, $R^{3,1} \times S^2$ which leaves
half of the six-dimensional supersymmetries unbroken. In this model, the
inflaton field $\phi$ originates from the complex scalar fields in the D=6
scalar hypermultiplet. The mass and the self couplings of the scalar field are
dictated by the D=6 Lagrangian. The scalar potential has an absolute munimum at
$\phi = 0$ with no undetermined moduli fields. Imposing a mild bound on the
radius of $S^2$ enables us to obtain chaotic inflation. The low eenrgy
equations of motion are shown to be consistent for the range of scalar field
values relevant for inflation. | Green-Schwarz Superstrings on AdS_3 and the Boundary N=4 Superconformal
Algebra: We study the hybrid formulation of Green-Schwarz superstrings on AdS_3 with
NS flux and the boundary N=4 superconformal algebra. We show the equivalence
between the NSR and GS superstrings by a field redefinition. The boundary N=4
superconformal algebra is realized by the free fields of the affine Lie
superalgebra A(1|1)^{(1)}. We also consider the light-cone gauge and obtain the
N=4 super-Liouville theory which describes the effective theory of the single
long string near the singularities of the D1-D5 system. |
Expansions for semiclassical conformal blocks: We propose a relation the expansions of regular and irregular semiclassical
conformal blocks at different branch points making use of the connection
between the accessory parameters of the BPZ decoupling equations to the
logarithm derivative of isomonodromic tau functions. We give support for these
relations by considering two eigenvalue problems for the confluent Heun
equations obtained from the linearized perturbation theory of black holes. We
first derive the large frequency expansion of the spheroidal equations, and
then compare numerically the excited quasi-normal mode spectrum for the
Schwarzschild case obtained from the large frequency expansion to the one
obtained from the low frequency expansion and with the literature, indicating
that the relations hold generically in the complex modulus plane. | Classification of Finite Spectral Triples: It is known that the spin structure on a Riemannian manifold can be extended
to noncommutative geometry using the notion of a spectral triple. For finite
geometries, the corresponding finite spectral triples are completely described
in terms of matrices and classified using diagrams. When tensorized with the
ordinary space-time geometry, finite spectral triples give rise to Yang-Mills
theories with spontaneous symmetry breaking, whose characteristic features are
given within the diagrammatic approach: vertices of the diagram correspond to
gauge multiplets of chiral fermions and links to Yukawa couplings. |
Unitary theory of massive non-Abelian vector bosons: This paper is being revised to make it intelligible, and to incorporate some
corrections. | Probabilities and Path-Integral Realization of Exclusion Statistics: A microscopic formulation of Haldane's exclusions statistics is given in
terms of a priori occupation probabilities of states. It is shown that negative
probabilities are always necessary to reproduce fractional statistics. Based on
this formulation, a path-integral realization for systems with exclusion
statistics is derived. This has the advantage of being generalizable to
interacting systems, and can be used as the starting point for further
generalizations of statistics. As a byproduct, the vanishing of the heat
capacity at zero temperature for exclusion statistics systems is proved. |
Notes on time entanglement and pseudo-entropy: Following arXiv:2210.12963 [hep-th], we investigate aspects of the time
evolution operator regarded as a density operator and associated
entanglement-like structures in various quantum systems. These involve timelike
separations and generically lead to complex-valued entropy, although there are
interesting real subfamilies. There are many parallels and close relations with
reduced transition matrices and pseudo-entropy, which we discuss and clarify.
For instance, a related quantity involves the time evolution operator along
with a projection onto some initial state, which amounts to analysing
pseudo-entropy for the initial state and its time-evolved final state. | Explicit Non-Abelian Gerbes with Connections: We define the notion of adjustment for strict Lie 2-groups and provide the
complete cocycle description for non-Abelian gerbes with connections whose
structure 2-group is an adjusted 2-group. Most importantly, we depart from the
common fake-flat connections and employ adjusted connections. This is an
important generalisation that is needed for physical applications especially in
the context of supergravity. We give a number of explicit examples; in
particular, we lift the spin structure on $S^4$, corresponding to an
instanton-anti-instanton pair, to a string structure, a 2-group bundle with
connection. We also outline how categorified forms of Bogomolny monopoles known
as self-dual strings can be obtained via a Penrose-Ward transform of string
bundles over twistor space. |
From BFV to BV and spacetime covariance: The BFV formulation of a given gauge theory is usually significantly easier
to obtain than its BV formulation. Grigoriev and Damgaard introduced simple
formulas for obtaining the latter from the former. Since BFV relies on the
Hamiltonian version of the gauge theory, however, it does not come as a
surprise that in general the resulting BV theory does not exhibit space-time
covariance. We provide an explicit example of this phenomenon in two spacetime
dimensions and show how to restore covariance of the BV data by improving the
Grigoriev--Damgaard procedure with appropriate adaptations of its original
formulas. | Static, non-SUSY $p$-branes in diverse dimensions: We give explicit constructions of static, non-supersymmetric $p$-brane (for
$p \leq d-4$, where $d$ is the space-time dimensionality and including $p=-1$
or D-instanton) solutions of type II supergravities in diverse dimensions. A
subclass of these are the static counterpart of the time dependent solutions
obtained in [hep-th/0309202]. Depending on the forms of the non-extremality
function $G(r)$ defined in the text, we discuss various possible solutions and
their region of validity. We show how one class of these solutions interpolate
between the $p$-brane--anti $p$-brane solutions and the usual BPS $p$-brane
solutions in $d=10$, while the other class, although have BPS limits, do not
have such an interpretation. We point out how the time dependent solutions
mentioned above can be obtained by a Wick rotation of one class of these static
solutions. We also discuss another type of solutions which might seem
non-supersymmetric, but we show by a coordinate transformation that they are
nothing but the near horizon limits of the various BPS $p$-branes already
known. |
Phase structure and phase transitions of the SU(2) x O(N) symmetric
scalar field theory: Radiatively induced SU(2) symmetry breaking is shown to be a genuine feature
of SU(2) x O(N) globally symmetric renormalisable field theories in the large N
limit, describing interaction of a complex SU(2) doublet, O(N)-singlet field
with an SU(2) singlet, O(N) vector. Symmetry breaking solutions are found even
when all fields have positive renormalised squared mass. The emerging novel
mechanism of symmetry breaking can reproduce with a choice of N~300 the
standard range of the electroweak condensate and the Higgs mass occurring in
the extended Higgs dynamics of an SU(2) symmetric Gauge+Higgs model. | Characters of the BMS Group in Three Dimensions: Using the Frobenius formula, we evaluate characters associated with certain
induced representations of the centrally extended BMS$_3$ group. This
computation involves a functional integral over a coadjoint orbit of the
Virasoro group; a delta function localizes the integral to a single point,
allowing us to obtain an exact result. The latter is independent of the
specific form of the functional measure, and holds for all values of the
BMS$_3$ central charges and all values of the chosen mass and spin. It can also
be recovered as a flat limit of Virasoro characters. |
The eleven-dimensional supermembrane revisited: It is argued that the type IIA 10-dimensional superstring theory is actually
a compactified 11-dimensional supermembrane theory in which the fundamental
supermembrane is identified with the the solitonic membrane of 11-dimensional
supergravity. The charged extreme black holes of the 10-dimensional type IIA
string theory are interpreted as the Kaluza-Klein modes of 11-dimensional
supergravity and the dual sixbranes as the analogue of Kaluza-Klein monopoles.
All other p-brane solutions of the type IIA superstring theory are derived from
the 11-dimensional membrane and its magnetic dual fivebrane soliton. | The slow expansion with nonminimal derivative coupling and its conformal
dual: We show that the primordial gravitational wave with scale-invariant spectrum
might emerge from a nearly Minkowski space, in which the gravity is
asymptotic-past free. We illustrate it with a model, in which the derivative of
background scalar field nonminimally couples to gravity. We also show that
since here the tensor perturbation is dominated by its growing mode,
mathematically our slowly expanding background is conformally dual to the
matter contraction, but there is no the anisotropy problem. |
Basis Optimization Renormalization Group for Quantum Hamiltonian: We find an algorithm of numerical renormalization group for spin chain
models. The essence of this algorithm is orthogonal transformation of basis
states, which is useful for reducing the number of relevant basis states to
create effective Hamiltonian. We define two types of rotations and combine them
to create appropriate orthogonal transformation. | Interactions in the SL(2,R)/U(1) Black Hole Background: We calculate two- and three-point tachyon amplitudes of the SL(2,R)/U(1)
two-dimensional Euclidean black hole for spherical topologies in the continuum
approach proposed by Bershadsky and Kutasov. We find an interesting relation to
the tachyon scattering amplitudes of standard non-critical string theory. |
Global Structure of Deffayet (Dvali-Gabadadze-Porrati) Cosmologies: We detail the global structure of the five-dimensional bulk for the
cosmological evolution of Dvali-Gabadadze-Porrati braneworlds. The picture
articulated here provides a framework and intuition for understanding how
metric perturbations leave (and possibly reenter) the brane universe. A bulk
observer sees the braneworld as a relativistically expanding bubble, viewed
either from the interior (in the case of the
Friedmann-Lemaitre-Robertson-Walker phase) or the exterior (the
self-accelerating phase). Shortcuts through the bulk in the first phase can
lead to an apparent brane causality violation and provide an opportunity for
the evasion of the horizon problem found in conventional four-dimensional
cosmologies. Features of the global geometry in the latter phase anticipate a
depletion of power for linear metric perturbations on large scales. | Quantum quenches of holographic plasmas: We employ holographic techniques to study quantum quenches at finite
temperature, where the quenches involve varying the coupling of the boundary
theory to a relevant operator with an arbitrary conformal dimension
$2\leq\D\leq4$. The evolution of the system is studied by evaluating the
expectation value of the quenched operator and the stress tensor throughout the
process. The time dependence of the new coupling is characterized by a fixed
timescale and the response of the observables depends on the ratio of the this
timescale to the initial temperature. The observables exhibit universal scaling
behaviours when the transitions are either fast or slow, i.e. when this ratio
is very small or very large. The scaling exponents are smooth functions of the
operator dimension. We find that in fast quenches, the relaxation time is set
by the thermal timescale regardless of the operator dimension or the precise
quenching rate. |
Bounds on Tensor wave and Twisted Inflation: We study the bounds on tensor wave in a class of twisted inflation models
where $D(4+2k)$-branes are wrapped on cycles in the compact manifold and wrap
the KK-direction in the corresponding effective field theory. While the lower
bound is found to be analogous to that in Type IIB models of brane inflation,
the upper bound turns out to be significantly different. This is argued for a
range of values for the parameter $g_s M$ satisfying the self-consistency
relation and the WMAP data. Further, we observe that the wrapped $D8$-brane
appears to be the most attractive from a cosmological perspective. | Bulk photons in Asymmetrically Warped Space-times and Non-trivial Vacuum
Refractive Index: We consider asymmetrically warped brane models, or equivalently brane models
where the background metric is characterized by different time and space warp
factors. The main feature of these models is that 4D Lorentz symmetry is
violated for fields which propagate in the bulk, such as gravitons. In this
paper we examine the case of bulk photons in asymmetrically warped brane
models. Although our results are general, we examine here two specific but
characteristic solutions: 1) AdS-Schwarzschild 5D Black Hole solution and 2)
AdS-Reissner Nordstrom 5D Black Hole solution. We show that the standard
Lorentz invariant dispersion relation for 4D photons is corrected by nonlinear
terms which lead to an Energy-dependent speed of light. Specifically, we obtain
a sub-luminous Energy-dependent refractive index of the form
n_{eff}(\omega)=1+c_{G} \omega^2, where \omega is the energy of the photon, and
the factor c_G is always positive and depends on the free parameters of the
model. Finally, comparing the results with recent data from the MAGIC
Telescope, claiming a delayed arrival of photons from the Active Galactic
Nucleus of Mk501, we impose concrete restrictions to the two sets of models
examined in this work. We shall also discuss briefly other possible
astrophysical constraints on our models. |
40 Bilinear Relations of q-Painleve VI from N=4 Super Chern-Simons
Theory: We investigate partition functions of the circular-quiver supersymmetric
Chern-Simons theory which corresponds to the q-deformed Painleve VI equation.
From the partition functions with the lowest rank vanishing, where the circular
quiver reduces to a linear one, we find 40 bilinear relations. The bilinear
relations extend naturally to higher ranks if we regard these partition
functions as those in the lowest order of the grand canonical partition
functions in the fugacity. Furthermore, we show that these bilinear relations
are a powerful tool to determine some unknown partition functions. We also
elaborate the relation with some previous works on q-Painleve equations. | Lightfront holography and area density of entropy associated with
localization on wedge-horizons: It is shown that a suitably formulated algebraic lightfront holography, in
which the lightfront is viewed as the linear extension of the upper causal
horizon of a wedge region, is capable of overcoming the shortcomings of the old
lightfront quantization. The absence of transverse vacuum fluctuations which
this formalism reveals, is responsible for an area (edge of the wedge)
-rearrangement of degrees of freedom which in turn leads to the notion of area
density of entropy for a ``split localization''. This area proportionality of
horizon associated entropy has to be compared to the volume dependence of
ordinary heat bath entropy. The desired limit, in which the split distance
vanishes and the localization on the horizon becomes sharp, can at most yield a
relative area density which measures the ratio of area densities for different
quantum matter. In order to obtain a normalized area density one needs the
unknown analog of a second fundamental law of thermodynamics for thermalization
caused by vacuum fluctuation through localization on causal horizons. This is
similar to the role of the classical Gibbs form of that law which relates
Bekenstein's classical area formula with the Hawking quantum mechanism for
thermalization from black holes. PACS: 11.10.-z, 11.30.-j, 11.55.-m |
A new continuum limit of matrix models: We define a new scaling limit of matrix models which can be related to the
method of causal dynamical triangulations (CDT) used when investigating
two-dimensional quantum gravity. Surprisingly, the new scaling limit of the
matrix models is also a matrix model, thus explaining why the recently
developed CDT continuum string field theory (arXiv:0802.0719) has a
matrix-model representation (arXiv:0804.0252). | A Brief Introduction to Poisson Sigma-Models: The theory of Poisson-$\sigma$-models employs the mathematical notion of
Poisson manifolds to formulate and analyze a large class of topological and
almost topological two dimensional field theories. As special examples this
class of field theories includes pure Yang-Mills and gravity theories, and, to
some extent, the G/G gauged WZW-model. The aim of this contribution is to give
a pedagogical introduction, explaining many aspects of the general theory by
illustrative examples. |
Possible origin of CMB temperature fluctuations: Vacuum fluctuations of
Kaluza-Klein and string states during inflationary era: We point out that the temperature fluctuations of cosmic microwave background
(CMB) can be generated in a way that is different from the one usually assumed
in slow-roll inflation. Our mechanism is based on vacuum fluctuations of fields
which are at rest at the bottom of the potential, such as Kaluza-Klein modes or
string excited states. When there are a large number (typically of order $N\sim
10^{14}$) of fields with small mass in unit of Hubble parameter during the
inflationary era, this effect can give significant contributions to the CMB
temperature fluctuations. This number $N$ makes it possible to enhance scalar
perturbation relative to tensor perturbation. Comparison with the observed
amplitudes suggests that models with string scale of order $10^{-5}$ of 4D
Planck scale are favorable. | A black lens in bubble of nothing: Applying the inverse scattering method to static and bi-axisymmetric Einstein
equations, we construct a non-rotating black lens inside bubble of nothing
whose horizon is topologically lens space L(n,1)=S^3/Z_n. Using this solution,
we discuss whether a static black lens can be in equilibrium by the force
balance between the expansion and gravitational attraction. |
Spectrum of rotating black holes and its implications for Hawking
radiation: The reduced phase space formalism for quantising black holes has recently
been extended to find the area and angular momentum spectra of four dimensional
Kerr black holes. We extend this further to rotating black holes in all
spacetime dimensions and show that although as in four dimensions the spectrum
is discrete, it is not equispaced in general. As a result, Hawking radiation
spectra from these black holes are continuous, as opposed to the discrete
spectrum predicted for four dimensional black holes. | Spacetime Brout-Englert-Higgs effect in General Relativity interacting
with p-brane matter: We review the manifestation of the Brout-Englert-Higgs effect in general
relativity interacting with point-like and extended objects (p-branes including
string for p=1 and membrane for p=2), which manifests itself in the appearance
of the brane source in the Einstein equation while the graviton remains
massless (hep-th/0112207, hep-th/0507197 and refs therein), and discuss briefly
its relation and differences with the model for massive spin 2 field proposed
recently by G. t'Hooft in [arXiv:0708.3184 [hep-th]]. |
Wormholes in 2d Horava-Lifshitz quantum gravity: We quantize the two-dimensional projectable Horava-Lifshitz gravity with a
bi-local as well as space-like wormhole interaction. The resulting quantum
Hamiltonian coincides with the one obtained through summing over all genus in
the string field theory for two-dimensional causal dynamical triangulations.
This implies that our wormhole interaction can be interpreted as a splitting or
joining interaction of one-dimensional strings. | Hermitian-Einstein metrics from noncommutative $U\left(1 \right)$
instantons: We show that Hermitian-Einstein metrics can be locally constructed by a map
from (anti-)self-dual two-forms on Euclidean ${\mathbb R}^4$ to symmetric
two-tensors introduced in "Gravitational instantons from gauge theory," H. S.
Yang and M. Salizzoni, Phys. Rev. Lett. (2006) 201602, [hep-th/0512215]. This
correspondence is valid not only for a commutative space but also for a
noncommutative space. We choose $U(1)$ instantons on a noncommutative ${\mathbb
C}^2$ as the self-dual two-form, from which we derive a family of
Hermitian-Einstein metrics. We also discuss the condition when the metric
becomes K\"ahler. |
Loop corrections and graceful exit in string cosmology: We examine the effect of perturbative string loops on the cosmological
pre-big-bang evolution. We study loop corrections derived from heterotic string
theory compactified on a $Z_N$ orbifold and we consider the effect of the
all-order loop corrections to the Kahler potential and of the corrections to
gravitational couplings, including both threshold corrections and corrections
due to the mixed Kahler-gravitational anomaly. We find that string loops can
drive the evolution into the region of the parameter space where a graceful
exit is in principle possible, and we find solutions that, in the string frame,
connect smoothly the superinflationary pre-big-bang evolution to a phase where
the curvature and the derivative of the dilaton are decreasing. We also find
that at a critical coupling the loop corrections to the Kahler potential induce
a ghost-like instability, i.e. the kinetic term of the dilaton vanishes. This
is similar to what happens in Seiberg-Witten theory and signals the transition
to a new regime where the light modes in the effective action are different and
are related to the original ones by S-duality. In a string context, this means
that we enter a D-brane dominated phase. | Homological Algebra and Yang-Mills Theory: The antifield-BRST formalism and the various cohomologies associated with it
are surveyed and illustrated in the context of Yang-Mills gauge theory. In
particular, the central role played by the Koszul-Tate resolution and its
relation to the characteristic cohomology are stressed. |
Yang-Baxter Equation on Two-Dimensional Lattice and Some Infinite
Dimensional Algebras: We show that the Yang-Baxter equation is equivalent to the associativity of
the algebra generated by non-commuting link operators. Starting from these link
operators we build out the (FFZ) algebras, the $s\ell_q (2)$ is derived by
considering a special combination of the generators of (FFZ) algebra. | Meromorphic CFTs have central charges c = 8$\mathbb{N}$: a proof by the
MLDE approach: In this short note, we present a simple and elementary proof that meromorphic
conformal field theories (CFTs) have central charges of the form: $c=8N$ with
$N\in\mathbb{N}$ (the set of natural numbers) using the modular linear
differential equations (MLDEs) approach. We first set up the 1-character MLDE
for arbitrary value of the Wronskian index: $\ell$. From this we get the
general form of the meromorphic CFT's character. We then study its modular
transformations and the asymptotic value of it's Fourier coefficients to
conclude that odd values of $\ell$ make the character in-admissible implying
that the central charge for admissible character has to be a multiple of 8. |
Power-law cosmologies in minimal and maximal gauged supergravity: In this paper we search for accelerating power-law solutions and ekpyrotic
solutions within minimal and maximal four dimensional supergravity theories. We
focus on the STU model for N=1 and on the new CSO(p,q,r) theories, which were
recently obtained exploiting electromagnetic duality, for N=8. In the minimal
case we find some new ekpyrotic solutions, while in the maximal case we find
some new generic power-law solutions. We do not find any new accelerating
solutions for these models. | Quantization of the Type II Superstring in a Curved Six-Dimensional
Background: A sigma model action with N=2 D=6 superspace variables is constructed for the
Type II superstring compactified to six curved dimensions with Ramond-Ramond
flux. The action can be quantized since the sigma model is linear when the
six-dimensional spacetime is flat. When the six-dimensional spacetime is
$AdS_3\times S^3$, the action reduces to one found earlier with Vafa and
Witten. |
Gauge fixing and BRST formalism in non-Abelian gauge theories: In this Thesis we present a comprehensive study of perturbative and
non-perturbative non-Abelian gauge theories in the light of gauge-fixing
procedures, focusing our attention on the BRST formalism in Yang-Mills theory.
We propose first a model to re-write the Faddeev-Popov quantisation method in
terms of group-theoretical techniques and then we give a possible way to solve
the no-go theorem of Neuberger for lattice Yang-Mills theory with double BRST
symmetry. In the final part we present a study of the Batalin-Vilkovisky
quantisation method for non-linear gauges in non-Abelian gauge theories. | N=2 Supersymmetric U(1) Gauge Theory in Noncommutative Harmonic
Superspace: We study N=2 supersymmetric U(1) gauge theory in the noncommutative harmonic
superspace with nonanticommutative fermionic coordinates. We examine the gauge
transformation which preserves the Wess-Zumino gauge by harmonic expansions of
component fields. The gauge transformation is shown to depend on the
deformation parameters and the anti-holomorphic scalar field. We compute the
action explicitly up to the third order in component fields and discuss the
field redefinitions so that the component fields transform canonically. |
Three Dimensional Chern-Simons Theory as a Theory of Knots and Links: Three dimensional SU(2) Chern-Simons theory has been studied as a topological
field theory to provide a field theoretic description of knots and links in
three dimensions. A systematic method has been developed to obtain the
link-invariants within this field theoretic framework. The monodromy properties
of the correlators of the associated Wess-Zumino SU(2)$_k$ conformal field
theory on a two-dimensional sphere prove to be useful tools. The method is
simple enough to yield a whole variety of new knot invariants of which the
Jones polynomials are the simplest example. | Anomalous Thresholds for the S-matrix of Unstable Particles: In this work, we study the analytic properties of S-matrix for unstable
particles, which is defined as the residues on the unphysical sheets where
unstable poles reside. We demonstrate that anomalous threshold associated with
UV physics is unavoidable for unstable particles. This is in contrast to stable
particles, where the anomalous thresholds are due to IR physics, set by the
scale of the external kinematics. As a result any dispersive representation for
the amplitude will involve contributions from these thresholds that are not
computable from the IR theory, and thus invalidates general positivity bound.
Indeed using toy models, we explicitly demonstrate that the four-derivative
couplings for unstable particles can become negative, violating positivity
bounds even for non-gravitational theories. Along the way we show that
contributions from anomalous thresholds in a given channel can be captured by
the double discontinuity of that channel. |
A mini-course on topological strings: These are the lecture notes for a short course in topological string theory
that I gave at Uppsala University in the fall of 2004. The notes are aimed at
PhD students who have studied quantum field theory and general relativity, and
who have some general knowledge of ordinary string theory. The main purpose of
the course is to cover the basics: after a review of the necessary mathematical
tools, a thorough discussion of the construction of the A- and B-model
topological strings from twisted N=(2,2) supersymmetric field theories is
given. The notes end with a brief discussion on some selected applications. | Light-Front Quantization and Spontaneous Symmetry Breaking: The spontaneous symmetry breaking (and Higgs) mechanism in the theory
quantized on the light-front ({\it l.f.}), in the {\it discretized
formulation}, is discussed. The infinite volume limit is taken to obtain the
{\it continuum version}. The hamiltonian formulation is shown to contain a new
ingredient in the form of nonlocal {\it constraint eqs.} which lead to a {\it
nonlocal l.f. Hamiltonian}. The description of the broken symmetry here has the
same physical content as in the conventional formulation though arrived at
through a different mechanism. |
Adding flavour to the S-matrix bootstrap: We explore the S-matrices of gapped, unitary, Lorentz invariant quantum field
theories with a global O($N$) symmetry in 1+1 dimensions. We extremize various
cubic and quartic couplings in the two-to-two scattering amplitudes of vector
particles. Saturating these bounds, we encounter known integrable models with
O($N$) symmetry such as the O($N$) Gross-Neveu and non-linear sigma models and
the scattering of kinks in the sine-Gordon model. We also considered more
general mass spectra for which we move away from the integrable realm. In this
regime we find (numerically, through a large N analysis and sometimes even
analytically) that the S-matrices saturating the various coupling bounds have
an extremely rich structure exhibiting infinite resonances and virtual states
in the various kinematical sheets. They are rather exotic in that they admit no
particle production yet they do not obey Yang-Baxter equations. We discuss
their physical (ir)relevance and speculate, based on some preliminary numerics,
that they might be close to more realistic realistic theories with particle
production. | Chiral Symmetry restoration in the massive Thirring model at finite T
and $μ$: Dimensional reduction and the Coulomb gas: We show that in certain limits the (1+1)-dimensional massive Thirring model
at finite temperature $T$ is equivalent to a one-dimensional Coulomb gas of
charged particles at the same $T$. This equivalence is then used to explore the
phase structure of the massive Thirring model. For strong coupling and $T>>m$
(the fermion mass) the system is shown to behave as a free gas of "molecules"
(charge pairs in the Coulomb gas terminology) made of pairs of chiral
condensates. This binding of chiral condensates is responsible for the
restoration of chiral symmetry as $T\to\infty$. In addition, when a fermion
chemical potential $\mu\neq 0$ is included, the analogy with a Coulomb gas
still holds with $\mu$ playing the role of a purely imaginary external electric
field. For small $T$ and $\mu$ we find a typical massive Fermi gas behaviour
for the fermion density, whereas for large $\mu$ it shows chiral restoration by
means of a vanishing effective fermion mass. Some similarities with the chiral
properties of low-energy QCD at finite $T$ and baryon chemical potential are
discussed. |
Helical Phase Inflation: We show that the quadratic inflation can be realized by the phase of a
complex field with helicoid potential. Remarkably, this helicoid potential can
be simply realized in minimal supergravity. The global $U(1)$ symmetry of the
K\"ahler potential introduces a flat direction and evades the $\eta$ problem
automatically. So such inflation is technically natural. The phase excursion is
super-Planckian as required by the Lyth bound, while the norm of the complex
field can be suppressed in the sub-Planckian region. This model resolves the
ultraviolet sensitive problem of the large field inflation, besides, it also
provides a new type of monodromy inflation in supersymmetric field theory with
consistent field stabilization. | Stochastic Processes and the Dirac Equation with External Fields: The equation describing the stochastic motion of a classical particle in
1+1-dimensional space-time is connected to the Dirac equation with external
gauge fields. The effects of assigning different turning probabilities to the
forward and the backward moving particles in time are discussed. |
Production of Dirac Particles in External Electromagnetic Fields: Pair creation of spin- 1/2 particles in Minkowski spacetime is investigated
by obtaining exact solu- tions of the Dirac equation in the presence of
electromagnetic fields and using them for determining the Bogoliubov
coefficients. The resulting particle creation number density depends on the
strength of the electric and magnetic fields. | N=2 Superstrings with (1,2m) Spacetime Signature: We show that the $N=2$ superstring in $d=2D\ge6$ real dimensions, with
criticality achieved by including background charges in the two real time
directions, exhibits a ``coordinate-freezing'' phenomenon, whereby the momentum
in one of the two time directions is constrained to take a specific value for
each physical state. This effectively removes this time direction as a physical
coordinate, leaving the theory with $(1,d-2)$ real spacetime signature. Norm
calculations for low-lying physical states suggest that the theory is ghost
free. |
Linear Response Theory for Symmetry Improved Two Particle Irreducible
Effective Actions: We investigate the linear response of an O(N) scalar quantum field theory
subject to external perturbations using the symmetry improved two particle
irreducible effective action formalism [A. Pilaftsis and D. Teresi, Nucl. Phys.
B874, 594 (2013)]. Despite satisfactory equilibrium behavior, we find a number
of unphysical effects at the linear response level. Goldstone boson field
fluctuations are over-determined, with the only consistent solution being to
set the fluctuations and their driving sources to zero, except for momentum
modes where the Higgs and Goldstone self-energies obey a particular
relationship. Also Higgs field fluctuations propagate masslessly, despite the
Higgs propagator having the correct mass. These pathologies are independent of
any truncation of the effective action and still exist even if we relax the
over-determining Ward identities, so long as the constraint is formulated
O(N)-covariantly. We discuss possible reasons for the apparent incompatibility
of the constraints and linear response approximation and possible ways forward. | Conformal dynamics of quantum gravity with torsion: The trace anomaly induced dynamics of the conformal factor is investigated in
four-dimensional quantum gravity with torsion. The constraints for the coupling
constants of torsion matter interaction are obtained in the infrared stable
fixed point of the effective scalar theory. |
Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes: Finite-dimensional nonrelativistic conformal Lie algebras spanned by
polynomial vector fields of Galilei spacetime arise if the dynamical exponent
is z=2/N with N=1,2,.... Their underlying group structure and matrix
representation are constructed (up to a covering) by means of the Veronese map
of degree N. Suitable quotients of the conformal Galilei groups provide us with
Newton-Hooke nonrelativistic spacetimes with a quantized reduced negative
cosmological constant \lambda=-N. | ER = EPR revisited: On the Entropy of an Einstein-Rosen Bridge: We propose a new link between entropy and area: an eternal black hole with an
ER bridge with cross-section $A$ can carry a macroscopic amount of quantum
information, or be in a mixed state, with entropy bounded by $S \leq A/4G_N$.
We substantiate our proposal in the context of AdS3 and JT gravity, by using
the Island prescription and replica wormhole method for computing the black
hole entropy. We argue that the typical mixed state of a two sided black hole
takes the form of an entangled `thermo-mixed double' state with only classical
correlations between the two sides. Our result for the von Neumann entropy of a
post-Page time two-sided black hole is smaller by a factor of two from previous
answers. Our reasoning implies that black hole quantum information is
topologically protected, similar to the information stored inside a topological
quantum memory. |
Comments on N=4 Superconformal Algebras: We present a new and asymmetric N=4 superconformal algebra for arbitrary
central charge, thus completing our recent work on its classical analogue with
vanishing central charge. Besides the Virasoro generator and 4 supercurrents,
the algebra consists of an internal SL(2) \otimes U(1) Kac-Moody algebra in
addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to
be invariant under a linear twist of the generators, except for a unique value
of the continuous twist parameter. At this value, the invariance is broken and
the algebra collapses to the small N=4 superconformal algebra. In the context
of string theory, the asymmetric N=4 superconformal algebra is provided with an
explicit construction on the boundary of AdS_3, and is induced by an affine
SL(2|2) current superalgebra residing on the world sheet. Substituting the
world sheet SL(2|2) by the coset SL(2|2)/U(1) results in the small N=4
superconformal algebra on the boundary of AdS_3. | Cosmological Rescaling through Warped Space: We discuss a scenario where at least part of the homogeneity on a brane world
can be directly related to the hierarchy problem through warped space. We study
the dynamics of an anti-D3-brane moving toward the infrared cut-off of a warped
background. After a region described by the DBI action, the self-energy of the
anti-D3-brane will dominate over the background. Then the world-volume scale of
the anti-D3-brane is no longer comoving with the background geometry. After it
settles down in the infrared end, the world-volume inhomogeneity will appear,
to a Poincare observer, to be stretched by an exponentially large ratio. This
ratio is close to that of the hierarchy problem between the gravitational and
electroweak scales. |
Electric-magnetic Duality and Deformations of Three-Dimensional CFT's: SL(2,Z) duality transformations in asymptotically AdS4 x S^7 act
non-trivially on the three-dimensional SCFT of coincident M2-branes on the
boundary. We show how S-duality acts away from the IR fixed point. We develop a
systematic method to holographically obtain the deformations of the boundary
CFT and show how electric-magnetic duality relates different deformations. We
analyze in detail marginal deformations and deformations by dimension 4
operators. In the case of massive deformations, the RG flow relates S-dual
CFT's. Correlation functions in the CFT are computed by varying magnetic bulk
sources, whereas correlation functions in the dual CFT are computed by electric
bulk sources. Under massive deformations, the boundary effective action is
generically minimized by massive self-dual configurations of the U(1) gauge
field. We show that a self-dual choice of boundary conditions exists, and it
corresponds to the self-dual topologically massive gauge theory in 2+1
dimensions. Thus, self-duality in three dimensions can be understood as a
consequence of electric-magnetic invariance in the bulk of AdS4. | $W$-Infinity Ward Identities and Correlation Functions in the $C=1$
Matrix Model: We explore consequences of $W$-infinity symmetry in the fermionic field
theory of the $c=1$ matrix model. We derive exact Ward identities relating
correlation functions of the bilocal operator. These identities can be
expressed as equations satisfied by the effective action of a {\it three}
dimensional theory and contain non-perturbative information about the model. We
use these identities to calculate the two point function of the bilocal
operator in the double scaling limit. We extract the operator whose two point
correlator has a {\it single} pole at an (imaginary) integer value of the
energy. We then rewrite the \winf~ charges in terms of operators in the matrix
model and use this derive constraints satisfied by the partition function of
the matrix model with a general time dependent potential. |
Axionic Membranes: A metal ring removed from a soap-water solution encloses a film of soap which
can be mathematically described as a minimal surface having the ring as its
only boundary. This is known to everybody. In this letter we suggest a
relativistic extension of the above fluidodynamic system where the soap film is
replaced by a Kalb-Ramond gauge potential $\b(x)$ and the ring by a closed
string. The interaction between the $\b$-field and the string current excites a
new configuration of the system consisting of a relativistic membrane bounded
by the string. We call such a classical solution of the equation of motion an
axionic membrane. As a dynamical system, the axionic membrane admits a
Hamilton-Jacobi formulation which is an extension of the H-J theory of
electromagnetic strings. | Multi-Instanton Check of the Relation Between the Prepotential F and the
Modulus u in N=2 SUSY Yang-Mills Theory: By examining multi-instantons in N=2 supersymmetric SU(2) gauge theory, we
derive, on very general grounds, and to all orders in the instanton number, a
relationship between the prepotential F(Phi), and the coordinate on the quantum
moduli space u=<Tr Phi^2>. This relation was previously obtained by Matone in
the context of the explicit Seiberg-Witten low-energy solution of the model.
Our findings can be viewed as a multi-instanton check of the proposed exact
results in supersymmetric gauge theory. |
Amplification of the scattering cross section due to non-trivial
topology of the spacetime: In previous articles it was demonstrated that the total cross section of the
scattering of two light particles (zero modes of the Kaluza-Klein tower) in the
six-dimensional $\lambda \phi^{4}$ model differs significantly from the cross
section of the same process in the conventional $\lambda \phi^{4}$ theory in
four space-time dimensions even for the energies below the threshold of the
first heavy particle. Here the analytical structure of the cross section in the
same model with torus compactification for arbitrary radii of the
two-dimensional torus is studied. Further amplification of the total cross
section due to interaction of the scalar field with constant background Abelian
gauge potential in the space of extra dimensions is shown. | Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories: Non-BPS non-Abelian vortices with CP^1 internal moduli space are studied in
an N=2 supersymmetric U(1) x SU(2) gauge theory with softly breaking adjoint
mass terms. For generic internal orientations the classical force between two
vortices can be attractive or repulsive. On the other hand, the mass of the
scalars in the theory is always less than that of the vector bosons; also, the
force between two vortices with the same CP^1 orientation is always attractive:
for these reasons we interpret our model as a non-Abelian generalization of
type I superconductors. We compute the effective potential in the limit of two
well separated vortices. It is a function of the distance and of the relative
colour-flavour orientation of the two vortices; in this limit we find an
effective description in terms of two interacting CP^1 sigma models. In the
limit of two coincident vortices we find two different solutions with the same
topological winding and, for generic values of the parameters, different
tensions. One of the two solutions is described by a CP^1 effective sigma
model, while the other is just an Abelian vortex without internal degrees of
freedom. For generic values of the parameters, one of the two solutions is
metastable, while there are evidences that the other one is truly stable. |
Models for (super)conformal higher-spin fields on curved backgrounds: This thesis is devoted to the construction of theories describing the
consistent propagation of (super)conformal higher-spin fields on curved three-
and four-dimensional (super)spaces. In the first half of this thesis we
systematically derive models for conformal fields of arbitrary rank on various
types of curved spacetimes. On generic conformally-flat backgrounds in three
$(3d)$ and four $(4d)$ dimensions, we obtain closed-form expressions for the
actions which are manifestly gauge and Weyl invariant. Similar results are
provided for generalised conformal fields, which have higher-depth gauge
transformations. In three dimensions, conformally-flat spacetimes are the most
general backgrounds allowing consistent propagation. In four dimensions, it is
widely expected that gauge invariance can be extended to Bach-flat backgrounds,
although no complete models for spin greater than two exist. We confirm these
expectations for the first time by constructing a number of complete
gauge-invariant models for conformal fields with higher spin. In the second
half of this thesis we employ superspace techniques to extend the above results
to conformal higher-spin theories possessing off-shell supersymmetry.
Several novel applications of our results are also provided. In particular,
transverse projection operators are constructed in $4d$ anti-de Sitter
(AdS$_4$) space, and their poles are shown to be associated with
partially-massless fields. This allows us to demonstrate that on such
backgrounds, the (super)conformal higher-spin kinetic operator factorises into
products of second order operators. Similar conclusions are drawn in AdS$_3$
(super)space. Finally, we make use of the (super)conformal higher-spin models
in $3d$ Minkowski and AdS (super)space to build topologically massive gauge
theories. | Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal N=4$
non-Abelian quiver gauge theories: We study Vertex Operator Algebras (VOAs) obtained from the H-twist of 3d
$\mathcal{N}=4$ linear quiver gauge theories. We find that H-twisted VOAs can
be regarded as the ''chiralization'' of the extended Higgs branch: many of the
ingredients of the Higgs branch are naturally ''uplifted'' into the VOAs, while
conversely the Higgs branch can be recovered as the associated variety of the
VOA. We also discuss the connection of our VOA with affine
$\mathcal{W}$-algebras. For example, we construct an explicit homomorphism from
an affine $\mathcal{W}$-algebra
$\mathcal{W}^{-n+1}(\mathfrak{gl}_n,f_{\mathrm{min}})$ into the H-twisted VOA
for $T^{[2,1^{n-2}]}_{[1^n]}[\mathrm{SU}(n)]$ theories. Motivated by the
relation with affine $\mathcal{W}$-algebras, we introduce a reduction procedure
for the quiver diagram, and use this to give an algorithm to systematically
construct novel free-field realizations for VOAs associated with general linear
quivers. |
Quantum Mechanics and Black Holes in Four-Dimensional String Theory: In previous papers we have shown how strings in a two-dimensional target
space reconcile quantum mechanics with general relativity, thanks to an
infinite set of conserved quantum numbers, ``W-hair'', associated with
topological soliton-like states. In this paper we extend these arguments to
four dimensions, by considering explicitly the case of string black holes with
radial symmetry. The key infinite-dimensional W-symmetry is associated with the
$\frac{SU(1,1)}{U(1)}$ coset structure of the dilaton-graviton sector that is a
model-independent feature of spherically symmetric four-dimensional strings.
Arguments are also given that the enormous number of string {\it discrete
(topological)} states account for the maintenance of quantum coherence during
the (non-thermal) stringy evaporation process, as well as quenching the large
Hawking-Bekenstein entropy associated with the black hole. Defining the latter
as the measure of the loss of information for an observer at infinity, who -
ignoring the higher string quantum numbers - keeps track only of the classical
mass,angular momentum and charge of the black hole, one recovers the familiar a
quadratic dependence on the black-hole mass by simple counting arguments on the
asymptotic density of string states in a linear-dilaton background. | Phase Transitions in Charged Topological-AdS Black Holes: We study the perturbative behaviour of charged topological-AdS black holes.
We calculate both analytically and numerically the quasi-normal modes of the
electromagnetic and gravitational perturbations. Keeping the charge-to-mass
ratio constant, we show that there is a second-order phase transition at a
critical temperature at which the mass of the black hole vanishes. We pay
special attention to the purely dissipative modes appearing in the spectrum as
they behave singularly at the critical point. |
A matrix S for all simple current extensions: A formula is presented for the modular transformation matrix S for any simple
current extension of the chiral algebra of a conformal field theory. This
provides in particular an algorithm for resolving arbitrary simple current
fixed points, in such a way that the matrix S we obtain is unitary and
symmetric and furnishes a modular group representation. The formalism works in
principle for any conformal field theory. A crucial ingredient is a set of
matrices S^J_{ab}, where J is a simple current and a and b are fixed points of
J. We expect that these input matrices realize the modular group for the torus
one-point functions of the simple currents. In the case of WZW-models these
matrices can be identified with the S-matrices of the orbit Lie algebras that
we introduced in a previous paper. As a special case of our conjecture we
obtain the modular matrix S for WZW-theories based on group manifolds that are
not simply connected, as well as for most coset models. | A Modern Fareytail: We revisit the "fareytail expansions" of elliptic genera which have been used
in discussions of the AdS_3/CFT_2 correspondence and the OSV conjecture. We
show how to write such expansions without the use of the problematic "fareytail
transform." In particular, we show how to write a general vector-valued modular
form of non-positive weight as a convergent sum over cosets of SL(2,Z). This
sum suggests a new regularization of the gravity path integral in AdS_3,
resolves the puzzles associated with the "fareytail transform," and leads to
several new insights. We discuss constraints on the polar coefficients of
negative weight modular forms arising from modular invariance, showing how
these are related to Fourier coefficients of positive weight cusp forms. In
addition, we discuss the appearance of holomorphic anomalies in the context of
the fareytail. |
A holographic bound on the scaling contribution to black hole entropy: We discuss the existence of scaling solutions for multicenter black hole
configurations. One of the central results is the equivalence between the
existence of two centered scaling solutions and the holographic entropy bound.
This equivalence (and another one) are proved rigorously at the end of the
paper, and allow to simplify the process counting of certain (fuzzball-like)
contributions to black hole entropy. | Soluble field theory with a massless gauge invariant limit: It is shown that there exists a soluble four parameter model in (1+1)
dimensions all of whose propagators can be determined in terms of the
corresponding known propagators of the vector coupling theory. Unlike the
latter case, however, the limit of zero bare mass is nonsingular and yields a
nontrivial theory with a rigorously unbroken gauge invariance. |
Loop operators and S-duality from curves on Riemann surfaces: We study Wilson-'t Hooft loop operators in a class of N=2 superconformal
field theories recently introduced by Gaiotto. In the case that the gauge group
is a product of SU(2) groups, we classify all possible loop operators in terms
of their electric and magnetic charges subject to the Dirac quantization
condition. We then show that this precisely matches Dehn's classification of
homotopy classes of non-self-intersecting curves on an associated Riemann
surface--the same surface which characterizes the gauge theory. Our analysis
provides an explicit prediction for the action of S-duality on loop operators
in these theories which we check against the known duality transformation in
several examples. | $α'$ corrections to KPV: An uplifting story: In earlier work, the effect of $\alpha'^2$ curvature corrections on the
NS5-brane responsible for the decay of anti-D3-branes in the set-up of Kachru,
Pearson, and Verlinde (KPV) was considered. We extend this analysis to include
all known $\alpha'^2$ corrections to the action of an abelian fivebrane which
involve not just curvature but also gauge fields and flux. We compute the value
of these terms at the tip of the Klebanov-Strassler throat to obtain the
$\alpha'^2$ corrected potential for the NS5-brane of KPV. The resulting
potential provides a novel uplifting mechanism where one can obtain metastable
vacua with an arbitrarily small positive uplifting potential by fine-tuning
$\alpha'$ corrections against the tree-level potential. This mechanism works
for small warped throats, both in terms of size and contribution to the
D3-tadpole, thereby sidestepping the issues associated with a standard deep
warped throat uplift which are deadly in KKLT and, as we explicitly check,
severely constraining in the Large Volume Scenario. |
Graded parafermions: standard and quasi-particle bases: Two bases of states are presented for modules of the graded parafermionic
conformal field theory associated to the coset $\osp(1,2)_k/\uh(1)$. The first
one is formulated in terms of the two fundamental (i.e., lowest dimensional)
parafermionic modes. In that basis, one can identify the completely reducible
representations, i.e., those whose modules contain an infinite number of
singular vectors; the explicit form of these vectors is also given.
The second basis is a quasi-particle basis, determined in terms of a modified
version of the $\ZZ_{2k}$ exclusion principle. A novel feature of this model is
that none of its bases are fully ordered and this reflects a hidden structural
$\Z_3$ exclusion principle. | All superalgebras for warped AdS$_2$ and black hole near horizon
geometries: We identify all symmetry superalgebras $\mathfrak{g}$ of near horizon
geometries of black holes with a Killing horizon, assuming the solution is
smooth and that the spatial cross section of the event horizon is compact
without boundary. This includes all warped AdS$_2$ backgrounds with the most
general allowed fluxes in 10- and 11-dimensional supergravities. If the index
of a particular Dirac operator vanishes, we find that the even symmetry
subalgebra decomposes as $\mathfrak{g}_0=\mathfrak{sl}(2,\mathbb{R})\oplus
\mathfrak{t}_0$, where $\mathfrak{t}_0/\mathfrak{c}$ is the Lie algebra of a
group that acts transitively and effectively on spheres, and $\mathfrak{c}$ is
the center of $\mathfrak{g}$. If the Dirac operator index does not vanish, then
the symmetry superalgebra is nilpotent with one even generator. We also
demonstrate that there are no near horizon geometries, and also therefore no
warped AdS$_2$ backgrounds, in 10- and 11-dimensions that preserve more than 16
supersymmetries. |
Large N Expansion From Fuzzy AdS_2: We study the quantum analogue of primary fields and their descendants on
fuzzy AdS_2, proposed in hep-th/0004072. Three-point vertices are calculated
and shown to exhibit the conventional 1/N expansion as well as nonperturtive
effects in large N, thus providing a strong consistency check of the fuzzy
AdS_2 model. A few new physical motivations for this model are also presented. | Supersymmetric localization in two dimensions: This is an introductory review to localization techniques in supersymmetric
two-dimensional gauge theories. In particular we describe how to construct
Lagrangians of N=(2,2) theories on curved spaces, and how to compute their
partition functions and certain correlators on the sphere, the hemisphere and
other curved backgrounds. We also describe how to evaluate the partition
function of N=(0,2) theories on the torus, known as the elliptic genus. Finally
we summarize some of the applications, in particular to probe mirror symmetry
and other non-perturbative dualities. |
Projective quantum spaces: Associated to the standard $SU_{q}(n)$ R-matrices, we introduce quantum
spheres $S_{q}^{2n-1}$, projective quantum spaces $CP_{q}^{n-1}$, and quantum
Grassmann manifolds $G_{k}(C_{q}^{n})$. These algebras are shown to be
homogeneous quantum spaces of standard quantum groups and are also quantum
principle bundles in the sense of T Brzezinski and S. Majid (Comm. Math. Phys.
157,591 (1993)). | Global Properties of Exact Solutions in Integrable Dilaton-Gravity
Models: Global canonical transformations to free chiral fields are constructed for DG
models minimally coupled to scalar fields. The boundary terms for such
canonical transformations are shown to vanish in asymptotically static
coordinates if there is no scalar field. |
Thermodynamics of Rotating Charged Black Branes in Third Order Lovelock
Gravity and the Counterterm Method: We generalize the quasilocal definition of the stress energy tensor of
Einstein gravity to the case of third order Lovelock gravity, by introducing
the surface terms that make the action well-defined. We also introduce the
boundary counterterm that removes the divergences of the action and the
conserved quantities of the solutions of third order Lovelock gravity with zero
curvature boundary at constant $t$ and $r$. Then, we compute the charged
rotating solutions of this theory in $n+1$ dimensions with a complete set of
allowed rotation parameters. These charged rotating solutions present black
hole solutions with two inner and outer event horizons, extreme black holes or
naked singularities provided the parameters of the solutions are chosen
suitable. We compute temperature, entropy, charge, electric potential, mass and
angular momenta of the black hole solutions, and find that these quantities
satisfy the first law of thermodynamics. We find a Smarr-type formula and
perform a stability analysis by computing the heat capacity and the determinant
of Hessian matrix of mass with respect to its thermodynamic variables in both
the canonical and the grand-canonical ensembles, and show that the system is
thermally stable. This is commensurate with the fact that there is no
Hawking-Page phase transition for black objects with zero curvature horizon. | Covariant calculation of the partition function of the two-dimensional
sigma model on compact two-surfaces: Motivated by string theory connection, a covariant procedure for perturbative
calculation of the partition function of the two-dimensional generalized
$\sigma$-model is considered. The importance of a consistent regularization of
the measure in the path integral is emphasized. The partition function is
computed for a number of specific 2-manifolds: sphere, disk and torus. |
On the Bound States of Matrix Strings: We investigate excitations in Matrix Theory on T^2 corresponding to bound
states of strings. We demonstrate the Dirichlet aspect of R-R charged vacua
through a non-trivial connection between the U(1) and SU(n) sectors of the
matrix SYM. | On-shell Correlators and Color-Kinematics Duality in Curved Symmetric
Spacetimes: We define a perturbatively calculable quantity--the on-shell
correlator--which furnishes a unified description of particle dynamics in
curved spacetime. Specializing to the case of flat and anti-de Sitter space,
on-shell correlators coincide precisely with on-shell scattering amplitudes and
boundary correlators, respectively. Remarkably, we find that symmetric
manifolds admit a generalization of on-shell kinematics in which the
corresponding momenta are literally the isometry generators of the spacetime
acting on the external kinematic data. These isometric momenta are
intrinsically non-commutative but exhibit on-shell conditions that are
identical to those of flat space, thus providing a common language for
computing and representing on-shell correlators which is agnostic about the
underlying geometry. Afterwards, we compute tree-level on-shell correlators for
biadjoint scalar (BAS) theory and the nonlinear sigma model (NLSM) and learn
that color-kinematics duality is manifested at the level of fields under a
mapping of the color algebra to the algebra of gauged isometries on the
spacetime manifold. Last but not least, we present a field theoretic derivation
of the fundamental BCJ relations for on-shell correlators following from the
existence of certain conserved currents in BAS theory and the NLSM. |
Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for
gauge groups in four-dimensional F-theory: In a previous study, we constructed a family of elliptic Calabi-Yau 4-folds
possessing a geometric structure that allowed them to be split into a pair of
rational elliptic 4-folds. In the present study, we introduce a method of
classifying the singularity types of this class of elliptic Calabi-Yau 4-folds.
In brief, we propose a method to classify the non-Abelian gauge groups formed
in four-dimensional (4D) $N=1$ F-theory for this class of elliptic Calabi-Yau
4-folds. To demonstrate our method, we explicitly construct several elliptic
Calabi-Yau 4-folds belonging to this class and study the 4D F-theory thereupon.
These constructions include a 4D model with two U(1) factors. | One loop corrections to coupling constants in String Effective Field
Theory: In the framework of a recently proposed method for computing exactly string
amplitudes regularized in the infra-red, I determine the one-loop correlators
for auxiliary fields in the symmetric $Z_2\times Z_2$ orbifold model. The
$D$-field correlation function turns out to give the one-loop corrections for
the gauge couplings, which amounts to a string-theory supersymmetry Ward
identity. The two-point function for uncharged $F$ fields leads to the one-loop
renormalization of the moduli K\"ahler metric, and eventually to the
corrections for the Yukawa couplings. |
Quantum anomaly and geometric phase; their basic differences: It is sometimes stated in the literature that the quantum anomaly is regarded
as an example of the geometric phase. Though there is some superficial
similarity between these two notions, we here show that the differences bewteen
these two notions are more profound and fundamental. As an explicit example, we
analyze in detail a quantum mechanical model proposed by M. Stone, which is
supposed to show the above connection. We show that the geometric term in the
model, which is topologically trivial for any finite time interval $T$,
corresponds to the so-called ``normal naive term'' in field theory and has
nothing to do with the anomaly-induced Wess-Zumino term. In the fundamental
level, the difference between the two notions is stated as follows: The
topology of gauge fields leads to level crossing in the fermionic sector in the
case of chiral anomaly and the {\em failure} of the adiabatic approximation is
essential in the analysis, whereas the (potential) level crossing in the matter
sector leads to the topology of the Berry phase only when the precise adiabatic
approximation holds. | Nature's Book Keeping System: Establishing how one should describe and study natures fundamental degrees of
freedom is a notoriously difficult problem. It is tempting to assume that the
number of bits (or qubits) needed in a given Planckian 3-volume, or perhaps
2-volume, is a fixed finite number, but this ansatz does not make the problem
much easier. We come not even close to solving this problem, but we propose
various ingredients in phrasing the questions, possibilities and limitations
that may serve as starting points. |
Effective Lagrangian of Domain Wall Networks: Domain wall networks are studied in N=2 supersymmetric U(N_C) gauge theory
with N_F (>N_C) flavors. We find a systematic method to construct domain wall
networks in terms of moduli matrices. Normalizable moduli parameters of the
network are found to be sizes and phases of the loop. We obtain moduli space
metric which specifies the effective Lagrangian on the domain wall networks. It
is used to study dynamics of domain wall networks with the moduli
approximation. | On the absence of BPS preonic solutions in IIA and IIB supergravities: We consider the present absence of 31 out of 32 supersymmetric solutions in
supergravity i.e., of solutions describing BPS preons. A recent result
indicates that (bosonic) BPS preonic solutions do not exist in type IIB
supergravity. We reconsider this analysis by using the G-frame method, extend
it to the IIA supergravity case, and show that there are no (bosonic) preonic
solutions for type IIA either. For the classical D=11 supergravity no
conclusion can be drawn yet, although the negative IIA results permit
establishing the conditions that preonic solutions would have to satisfy. For
supergravities with `stringy' corrections, the existence of BPS preonic
solutions remains fully open. |
On the space of solutions of the Horava theory at the kinetic-conformal
point: The nonprojectable Horava theory at the kinetic-conformal point is defined by
setting a specific value of the coupling constant of the kinetic term of the
Lagrangian. This formulation has two additional second class-constraints that
eliminate the extra mode. We show that the space of solutions of this theory in
the Hamiltonian formalism is bigger than the space of solutions in the original
Lagrangian formalism. In the Hamiltonian formalism there are certain
configurations for the Lagrange multupliers that lead to solutions that cannot
be found in the original Lagrangian formulation. We show specific examples in
vacuum and with a source. The solution with the source has homogeneous and
isotropic spatial hypersurfaces. The enhancement of the space of solutions
leaves the possibility that new solutions applicable to cosmology, or to other
physical systems, can be found in the Hamiltonian formalism. | Anomalous U(1) Vortices and The Dilaton: The role of the (dynamical) dilaton in the vortices associated with the
spontaneous breaking of an anomalous U(1) from heterotic string theory is
examined. We demonstrate how the anomaly (and the coupling to the
dilaton/axion) can appear in the Lagrangian and associated field equations as a
controlled perturbation about the standard Nielsen-Olesen equations. In such a
picture, the additional field equation for the dilaton becomes a series of
corrections to a constant dilaton vev as the anomaly is turned on. In
particular we find that even the first nontrivial correction to a constant
dilaton generically leads to a (positive) logarithmic divergence of the
heterotic dilaton near the vortex core. Since the dilaton field governs the
strength of quantum fluctuations in string theory, this runaway behaviour
implies that anomalous U(1) vortices in string theory are intrinsically quantum
mechanical objects. |
Algebraic structures in exceptional geometry: Exceptional field theory (EFT) gives a geometric underpinning of the
U-duality symmetries of M-theory. In this talk I give an overview of the
surprisingly rich algebraic structures which naturally appear in the context of
EFT. This includes Borcherds superalgebras, Cartan type superalgebras (tensor
hierarchy algebras) and $L_\infty$ algebras. This is the written version of a
talk based mainly on refs. [1-6], presented at ISQS25, Prague, June 2017, at
QTS-10/LT-12, Varna, June 2017, at SQS 2017, Dubna, Aug. 2017, and at the 9th
Mathematical Physics Meeting, Belgrade, Sept. 2017. | Monopoles and Modifications of Bundles over Elliptic Curves: Modifications of bundles over complex curves is an operation that allows one
to construct a new bundle from a given one. Modifications can change a
topological type of bundle. We describe the topological type in terms of the
characteristic classes of the bundle. Being applied to the Higgs bundles
modifications establish an equivalence between different classical integrable
systems. Following Kapustin and Witten we define the modifications in terms of
monopole solutions of the Bogomolny equation. We find the Dirac monopole
solution in the case $R $\times$ (elliptic curve). This solution is a
three-dimensional generalization of the Kronecker series. We give two
representations for this solution and derive a functional equation for it
generalizing the Kronecker results. We use it to define Abelian modifications
for bundles of arbitrary rank. We also describe non-Abelian modifications in
terms of theta-functions with characteristic. |
Scale Invariance in the Causal Approach to Renormalization Theory: The dilation invariance is studied in the framework of Epstein-Glaser
approach to renormalization theory. Some analogues of the Callan-Symanzik
equations are found and they are applied to the scalar field theory and to
Yang-Mills models. We find the interesting result that, if all the fields of
the theory have zero masses, then from purely cohomological consideration, one
can obtain the anomalous terms of logarithmic type. | Instantons, Topological Strings and Enumerative Geometry: We review and elaborate on certain aspects of the connections between
instanton counting in maximally supersymmetric gauge theories and the
computation of enumerative invariants of smooth varieties. We study in detail
three instances of gauge theories in six, four and two dimensions which
naturally arise in the context of topological string theory on certain
non-compact threefolds. We describe how the instanton counting in these gauge
theories are related to the computation of the entropy of supersymmetric black
holes, and how these results are related to wall-crossing properties of
enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants.
Some features of moduli spaces of torsion-free sheaves and the computation of
their Euler characteristics are also elucidated. |
Spectral Bundles and the DRY-Conjecture: Supersymmetric heterotic string models, built from a Calabi-Yau threefold $X$
endowed with a stable vector bundle $V$, usually start from a
phenomenologically motivated choice of a bundle $V_v$ in the visible sector,
the spectral cover construction on an elliptically fibered $X$ being a
prominent example. The ensuing anomaly mismatch between $c_2(V_v)$ and
$c_2(X)$, or rather the corresponding differential forms, is often 'solved', on
the cohomological level, by including a fivebrane. This leads to the question
whether the difference can be alternatively realized by a further stable
bundle. The 'DRY'-conjecture of Douglas, Reinbacher and Yau in math.AG/0604597
gives a sufficient condition on cohomology classes on $X$ to be realized as the
Chern classes of a stable sheaf. In arXiv:1010.1644 we showed that infinitely
many classes on $X$ exist for which the conjecture ist true. In this note we
give the sufficient condition for the mentioned fivebrane classes to be
realized by a further stable bundle in the hidden sector. Using a result
obtained in arXiv:1011.6246 we show that corresponding bundles exist, thereby
confirming this version of the DRY-Conjecture. | Higher dimensional Reissner-Nordström black holes supporting static
scalar shells: We analytically study scalarization of higher-dimensional charged
Reissner-Nordstr\"{o}m (RN) black hole. It is shown that static massive scalar
field which is non-minimally coupled to Gauss-Bonnet invariant can be supported
by higher-dimensional black hole in super-critical charge regime $Q/M\ge
\bar{C}_d$ with $Q, M$ charge and mass of the black hole and $\bar{C}_d$ some
unitless spacetime dimension-dependent quantity. Moreover, we show that the
static massive scalar shell can be quite thin in the large mass regime $\mu
M^{\frac{1}{d-3}}\gg 1$ with $\mu$ mass of the scalar field. |
Uncertainty relation in Schwarzschild spacetime: We explore the entropic uncertainty relation in the curved background outside
a Schwarzschild black hole, and find that Hawking radiation introduces a
nontrivial modification on the uncertainty bound for particular observer,
therefore it could be witnessed by proper uncertainty game experimentally. We
first investigate an uncertainty game between a free falling observer and his
static partner holding a quantum memory initially entangled with the quantum
system to be measured. Due to the information loss from Hawking decoherence, we
find an inevitable increase of the uncertainty on the outcome of measurements
in the view of static observer, which is dependent on the mass of the black
hole, the distance of observer from event horizon, and the mode frequency of
quantum memory. To illustrate the generality of this paradigm, we relate the
entropic uncertainty bound with other uncertainty probe, e.g., time-energy
uncertainty. In an alternative game between two static players, we show that
quantum information of qubit can be transferred to quantum memory through a
bath of fluctuating quantum fields outside the black hole. For a particular
choice of initial state, we show that the Hawking decoherence cannot counteract
entanglement generation after the dynamical evolution of system, which triggers
an effectively reduced uncertainty bound that violates the intrinsic limit
$-\log_2c$. Numerically estimation for a proper choice of initial state shows
that our result is comparable with possible real experiments. Finally, a
discussion on the black hole firewall paradox in the context of entropic
uncertainty relation is given. | Quantum field theory with an interaction on the boundary: We consider quantum theory of fields \phi defined on a D dimensional manifold
(bulk) with an interaction V(\phi) concentrated on a d<D dimensional surface
(brane). Such a quantum field theory can be less singular than the one in d
dimensions with the interaction $V(\phi)$. It is shown that scaling properties
of fields on the brane are different from the ones in the bulk. |
Qubit Transport Model for Unitary Black Hole Evaporation without
Firewalls: We give an explicit toy qubit transport model for transferring information
from the gravitational field of a black hole to the Hawking radiation by a
continuous unitary transformation of the outgoing radiation and the black hole
gravitational field. The model has no firewalls or other drama at the event
horizon, and it avoids a counterargument that has been raised for subsystem
transfer models as resolutions of the firewall paradox. Furthermore, it fits
the set of six physical constraints that Giddings has proposed for models of
black hole evaporation. It does utilize nonlocal qubits for the gravitational
field but assumes that the radiation interacts locally with these nonlocal
qubits, so in some sense the nonlocality is confined to the gravitational
sector. Although the qubit model is too crude to be quantitively correct for
the detailed spectrum of Hawking radiation, it fits qualitatively with what is
expected. | No isomorphism between the affine $\hat sl(2)$ algebra and the N=2
superconformal algebras: Since 1999 it became obvious that the would be `isomorphism' between the
affine $\hat sl(2)$ algebra and the N=2 superconformal algebras, proposed by
some authors, simply does not work. However, this issue was never properly
discussed in the literature and, as a result, some confusion still remains. In
this article we finally settle down, clearly and unambiguously, the true facts:
there is no isomorphism between the affine $\hat sl(2)$ algebra and the N=2
superconformal algebras. |
Time-dependent backgrounds of 2D string theory: Non-perturbative effects: We study the non-perturbative corrections (NPC) to the partition function of
a compactified 2D string theory in a time-dependent background generated by a
tachyon source. The sine-Liouville deformation of the theory is a particular
case of such a background. We calculate the leading as well as the subleading
NPC using the dual description of the string theory as matrix quantum
mechanics. As in the minimal string theories, the NPC are classified by the
double points of a complex curve. We calculate them by two different methods:
by solving Toda equation and by evaluating the quasiclassical fermion wave
functions. We show that the result can be expressed in terms of correlation
functions of the bosonic field associated with the tachyon source and identify
the leading and the subleading corrections as the contributions from the
one-point (disk) and two-point (annulus) correlation functions. | D-branes in the diagonal SU(2) coset: The symmetry preserving D-branes in coset theories have previously been
described as being centered around projections of products of conjugacy classes
in the underlying Lie groups. Here, we investigate the coset where a diagonal
action of SU(2) is divided out from SU(2)\times SU(2). The corresponding target
space is described as a (3-dimensional) pillow with four distinguished corners.
It is shown that the (fractional) brane which corresponds to the fixed point
that arises in the CFT description, is spacefilling. Moreover, the spacefilling
brane is the only one that reaches all of the corners. The other branes are 3,
1 and 0 - dimensional. |
Boundaries in the Moyal plane: We study the oscillations of a scalar field on a noncommutative disc
implementing the boundary as the limit case of an interaction with an
appropriately chosen confining background. The space of quantum fluctuations of
the field is finite dimensional and displays the rotational and parity symmetry
of the disc. We perform a numerical evaluation of the (finite) Casimir energy
and obtain similar results as for the fuzzy sphere and torus. | Gauge anomalies of finite groups: We show how the theory of characters can be used to analyse an anomaly
corresponding to chiral fermions carrying an arbitrary representation of a
gauge group that is finite, but otherwise arbitrary. By way of example, we do
this for some groups of relevance for the study of quark and lepton masses and
mixings. |
Fermion excitations of a tense brane black hole: By finding the spinor eigenvalues for a single deficit angle (d-2)-sphere, we
derive the radial potential for fermions on a d-dimensional black hole
background that is embedded on a codimension two brane with conical
singularity, where the deficit angle is related to the brane tension. From this
we obtain the quasi-normal mode spectrum for bulk fermions on such a
background. As a byproduct of our method, this also gives a rigorous proof for
integer spin fields on the deficit 2-sphere. | Conformal symmetry limit of QED and QCD and identities between
perturbative contributions to deep-inelastic scattering sum rules: Conformal symmetry-based relations between concrete perturbative QED and QCD
approximations for the Bjorken, the Ellis-Jaffe sum rules of polarized lepton-
nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of
neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector
channels are derived. They result from the application of the operator product
expansion to three triangle Green functions, constructed from the non-singlet
axial-vector, and two vector currents, the singlet axial-vector and two
non-singlet vector currents and the non-singlet axial-vector, vector and
singlet vector currents in the limit, when the conformal symmetry of the gauge
models with fermions is considered unbroken. We specify the perturbative
conditions for this symmetry to be valid in the case of the $U(1)$ and
$SU(N_c)$ models. The all-order perturbative identity following from the
conformal invariant limit between the concrete contributions to the Bjorken,
the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The
analytical and numerical $O(\alpha^4)$ and $O(\alpha_s^2)$ conformal symmetry
based approximations for these sum rules and for the Adler function of the
non-singlet vector currents are summarized. Possible theoretical applications
of the results presented are discussed. |
Reduction of General One-loop Integrals Using Auxiliary Vector: As a key method to deal with loop integrals, Integration-By-Parts (IBP)
method can be used to do reduction as well as establish the differential
equations for master integrals. However, when talking about tensor reduction,
the Passarino-Veltman (PV) reduction method is also widely used for one-loop
integrals. Recently, we have proposed an improved PV reduction method, i.e.,
the PV reduction method with auxiliary vector $R$, which can easily give
analytical reduction results for any tensor rank. However, our results are only
for integrals with propagators with power one. In this paper, we generalize our
method to one-loop integrals with general tensor structures and propagators
with general powers. Our ideas are simple. We solve the generalised reduction
problem by combining differentiation over masses and proper limit of reduction
with power-one propagators. Finally, we demonstrate our method with several
examples. With the result in this paper, we have shown that our improved
PV-reduction method with auxiliary vector is a self-completed reduction method
for one-loop integrals. | Entanglement entropy at CFT junctions: We consider entanglement through permeable junctions of $N$
$(1+1)$-dimensional free boson and free fermion conformal field theories. In
the folded picture we constrain the form of the general boundary state. We
calculate replicated partition functions with interface operators inserted in
the partially-folded picture, from which the entanglement entropy is
calculated. The functional form of the universal and constant terms are the
same as the $N=2$ case, depending only of the total transmission of the
junction and the unit volume of the zero mode lattice. For $N>2$ we see a
sub-leading divergent term which does not depend on the parameters of the
junction. For $N=3$ we consider some specific geometries and discuss various
limits. |
Non-Abelian Magnetic Monopoles in a Background of Gravitation with
Fermions: The purpose of this paper is to study static solution configuration which
describes the magnetic monopoles in a scenary where the gravitation is coupled
with Higgs, Yang-Mills and fermions. We are looking for analysis of the energy
functional and Bogomol'nyi equations. The Einstein equations now take into
consideration the fermions' contribution for energy-momentum tensor. The
interesting aspect here is to verify that the fermion field gives a
contribution for non abelian magnetic field and for potential which minimise
the energy functional. | The SU(2) sector in AdS/CFT: In the large N limit of N=4 Super Yang-Mills, the mixing under dilatations of
the SU(2) sector, single trace operators composed of L complex scalar fields of
two types, is closed to all orders in perturbation theory. By relying on the
AdS/CFT correspondence, and by examining the currents for semiclassical
strings, we present evidence which implies that there are small mixings that
contradict the closure of the SU(2) sector in the strong coupling limit. These
mixings first appear to second order in the \lambda/L^2 expansion. |
Equivalence Postulate and the Quantum Potential of Two Free Particles: Commutativity of the diagram of the maps connecting three one--particle
state, implied by the Equivalence Postulate (EP), gives a cocycle condition
which unequivocally leads to the quantum Hamilton--Jacobi equation. Energy
quantization is a direct consequences of the local homeomorphicity of the
trivializing map. We review the EP and show that the quantum potential for two
free particles, which depends on constants which may have a geometrical
interpretation, plays the role of interaction term that admits solutions which
do not vanish in the classical limit. | 3d N=4 Bootstrap and Mirror Symmetry: We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field
theory by uniting the non-perturbative methods of the conformal bootstrap and
supersymmetric localization, and utilizing special features of 3d ${\cal N} =
4$ theories such as mirror symmetry and a protected sector described by
topological quantum mechanics (TQM). Supersymmetric localization allows for the
exact determination of the conformal and flavor central charges, and the latter
can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE
data. We examine the implications of the $\mathbb{Z}_2$ mirror action for the
SCFT single- and mixed-branch crossing equations for the moment map operators,
and apply numerical bootstrap to obtain universal constraints on OPE data for
given flavor symmetry groups. A key ingredient in applying the bootstrap
analysis is the determination of the mixed-branch superconformal blocks. Among
other results, we show that the simplest known self-mirror theory with $SU(2)
\times SU(2)$ flavor symmetry saturates our bootstrap bounds, which allows us
to extract the non-BPS data and examine the self-mirror $\mathbb{Z}_2$ symmetry
thereof. |
Renormalization In Coupled-Abelian Self-Dual Chern-Simons Models: An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs
systems leads to coupled-abelian self-dual models with intricate mass spectra.
The vacua are characterized by embeddings of SU(2) into the gauge algebra; and
in the broken phases, the gauge and real scalar masses are related to the
exponents of the gauge algebra. In this paper we compute the gauge-gauge-Higgs
couplings in the broken phases and use this to compute the finite
renormalizations of the Chern-Simons coefficient in the various vacua. | Remarks on cosmological issues in some string theoretic brane worlds: We examine, in the context of certain string compactifications resulting in
five dimensional brane worlds the mechanisms of (self) tuning of the
cosmological constant and the recovery of standard cosmological evolution. We
show that self tuning can occur only as long as supersymmetry is unbroken
(unless additional assumptions are made) and that the adjustment of the
cosmological constant to zero after supersymmetry breaking and the recovery of
standard evolution are the same problem verifying previously made statements in
the context of general i.e. not necessarily string theoretic brane worlds. We
emphasize, however, that contrary to general brane worlds where the above
adjustment requires a fine tuning, stringy brane worlds contain an additional
integration constant due to the presence of the compact space thus allowing the
adjustment to be done only with integration constants. |
Renormalized non-perturbative scalar and fermions models in Covariant
Light Front Dynamics: Within the framework of the Covariant formulation of Light-Front Dynamics, we
develop a general non-perturbative renormalization scheme, based on the Fock
decomposition of the state vector and its truncation. The explicit dependence
of our formalism on the orientation of the light front, defined by a light-like
four vector $\omega$, is essential in order to analyze the structure of the
counterterms needed to renormalize the theory. We illustrate our framework for
scalar and fermion models | Revisiting light stringy states in view of the 750 GeV diphoton excess: We investigate light massive string states that appear at brane
intersections. They replicate the massless spectrum in a richer fashion and may
be parametrically lighter than standard Regge excitations. We identify the
first few physical states and determine their BRST invariant vertex operators.
In the supersymmetric case we reconstruct the super-multiplet structure. We
then compute some simple interactions, such as the decay rate of a massive
scalar or vector into two massless fermions. Finally we suggest an alternative
interpretation of the 750 GeV diphoton excess at LHC in terms of a light
massive string state, a replica of the Standard Model Higgs. |
Nonlocality in Quantum Gravity and the Breakdown of Effective Field
Theory: We argue that quantum gravity is nonlocal, first by recalling well-known
arguments that support this idea and then by focusing on a point not usually
emphasized: that making a conventional effective field theory (EFT) for quantum
gravity is particularly difficult, and perhaps impossible in principle. This
inability to realize an EFT comes down to the fact that gravity itself sets
length scales for a problem: when integrating out degrees of freedom above some
cutoff, the effective metric one uses will be different, which will itself
re-define the cutoff. We also point out that even if the previous problem is
fixed, naively applying EFT in gravity can lead to problems - we give a
particular example in the case of black holes. | Generalised diffeomorphisms for E$_9$: We construct generalised diffeomorphisms for E$_9$ exceptional field theory.
The transformations, which like in the E$_8$ case contain constrained local
transformations, close when acting on fields. This is the first example of a
generalised diffeomorphism algebra based on an infinite-dimensional Lie algebra
and an infinite-dimensional coordinate module. As a byproduct, we give a simple
generic expression for the invariant tensors used in any extended geometry. We
perform a generalised Scherk--Schwarz reduction and verify that our
transformations reproduce the structure of gauged supergravity in two
dimensions. The results are valid also for other affine algebras. |
Holographically smeared Fermi surface: Quantum oscillations and
Luttinger count in electron stars: We apply a small magnetic field to strongly interacting matter with a gravity
dual description as an electron star. These systems are both metallic and
quantum critical at low energies. The resulting quantum oscillations are shown
to be of the Kosevich-Lifshitz form characteristic of Fermi liquid theory. It
is seen that only fermions at a single radius in the electron star contribute
to the oscillations. We proceed to show that the Fermi surface area extracted
from the quantum oscillations does not obey the simplest statement of the
Luttinger theorem, that is, it is not universally proportional to the total
charge density. It follows that our system is a non-Fermi liquid that
nonetheless exhibits Kosevich-Lifshitz quantum oscillations. We explain how the
Luttinger count is recovered via a field theoretic description involving a
continuum of `smeared' fermionic excitations. | Translation map in quantum principal bundles: The notion of a translation map in a quantum principal bundle is introduced.
A translation map is then used to prove that the cross sections of a quantum
fibre bundle $E(B,V,A)$ associated to a quantum principal bundle $P(B,A)$ are
in bijective correspondence with equivariant maps $V\to P$, and that a quantum
principal bundle is trivial if it admits a cross section which is an algebra
map. The vertical automorphisms and gauge transformations of a quantum
principal bundle are discussed. In particular it is shown that vertical
automorphisms are in bijective correspondence with $\ad$-covariant maps $A\to
P$. |
Toward Thermalization in Heavy Ion Collisions at Strong Coupling: We find the trapped surface for a collision of two sourceless shock waves in
AdS$_5$ and conclude that such collisions always lead to a creation of a black
hole in the bulk. Due to holographic correspondence, in the boundary gauge
theory this result proves that a thermalized medium (quark-gluon plasma) is
produced in heavy ion collisions at strong coupling (albeit in ${\cal N} =4$
super-Yang-Mills theory). We present new evidence supporting the analytic
estimate for the time of thermalization that exists in the literature and find
that thermalization time is parametrically much shorter than the time of shock
wave stopping, indicating that our result may be relevant for description of
heavy ion collision experiments. | Symmetries and String Field Theory in D=2: (This talk was presented at the Third International Wigner Symposium on Group
Theory, Oxford, September, 1993.) Matrix models provides us with the most
powerful framework in which to analyze D=2 string theory, yet some of its
miraculous features, such as discrete states and $w(\infty)$, remain rather
obscure, because the string degrees of freedom have been removed. Liouville
theory, on the other hand, has all its string degrees of freedom intact, yet is
notoriously difficult to solve. In this paper, we present the second quantized
formulation of Liouville theory in D=2, where discrete states and $w(\infty)$
have a natural, field theoretic interpretation. We generalize the
non-polynomial closed string field theory, first developed by the author and
the Kyoto and MIT groups, to the D=2 case. We find that, in second quantized
field theory language, the rather mysterious features of matrix models have an
intuitively transparent interpretation, similar to standard gauge theory. Latex
file. |
Supersymmetric Janus solutions of dyonic $ISO(7)$-gauged
$\mathcal{N}\,=\,8$ supergravity: We study supersymmetric Janus solutions of dyonic $ISO(7)$-gauged
$\mathcal{N}$ = 8 supergravity. We mostly find Janus solutions flowing to 3d
$\mathcal{N}$ = 8 SYM phase which is the worldvolume theory on D2-branes and
non-conformal. There are also solutions flowing from the critical points which
are dual to 3d SCFTs from deformations of the D2-brane theory. | Contraints on Matter from Asymptotic Safety: Recent studies of the ultraviolet behaviour of pure gravity suggest that it
admits a non-Gaussian attractive fixed point, and therefore that the theory is
asymptotically safe. We consider the effect on this fixed point of massless
minimally coupled matter fields. The existence of a UV attractive fixed point
puts bounds on the type and number of such fields. |
How are the degrees of freedom responsible for entropy in BTZ spacetime?: The entanglement entropy approach to study the dependence of entropy upon the
location of degrees of freedom (dof) (near/far) from the horizon is discussed
in this article. We try to understand the physical deviation of the area law
for the excited states by incorporating the logarithmic and power law
corrections. We show that the dof near the horizon gives contribution to the
total entropy of the system in the ground state and away from the event horizon
gives contribution to the excited state. | The infinitesimal moduli space of heterotic $G_2$ systems: Heterotic string compactifications on integrable $G_2$ structure manifolds
$Y$ with instanton bundles $(V,A), (TY,\tilde{\theta})$ yield supersymmetric
three-dimensional vacua that are of interest in physics. In this paper, we
define a covariant exterior derivative $\cal D$ and show that it is equivalent
to a heterotic $G_2$ system encoding the geometry of the heterotic string
compactifications. This operator $\cal D$ acts on a bundle ${\cal
Q}=T^*Y\oplus{\rm End}(V)\oplus{\rm End}(TY)$ and satisfies a nilpotency
condition $\check{\cal D}^2=0$, for an appropriate projection of $\cal D$.
Furthermore, we determine the infinitesimal moduli space of these systems and
show that it corresponds to the finite-dimensional cohomology group $\check
H^1_{\check{\cal D}}(\cal Q)$. We comment on the similarities and differences
of our result with Atiyah's well-known analysis of deformations of holomorphic
vector bundles over complex manifolds. Our analysis leads to results that are
of relevance to all orders in the $\alpha'$ expansion. |
Asymptotic Solutions to the Quantized Knizhnik-Zamolodchikov Equation
and Bethe Vectors: Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation
associated with $\frak{gl}_{N+1}$ are constructed. The leading term of an
asymptotic solution is the Bethe vector -- an eigenvector of the
transfer-matrix of a quantum spin chain model. We show that the norm of the
Bethe vector is equal to the product of the Hessian of a suitable function and
an explicitly written rational function. This formula is an analogue of the
Gaudin-Korepin formula for the norm of the Bethe vector. It is shown that,
generically, the Bethe vectors form a base for the $\frak{gl}_2$ case. | Winding strings and AdS_3 black holes: We start a systematic study of string theory in AdS_3 black hole backgrounds.
Firstly, we analyse in detail the geodesic structure of the BTZ black hole,
including spacelike geodesics. Secondly, we study the spectrum for massive and
massless scalar fields, paying particular attention to the connection between
Sl(2,R) subgroups, the theory of special functions and global properties of the
BTZ black holes. We construct classical strings that wind the black holes.
Finally, we apply the general formalism to the vacuum black hole background,
and formulate the boundary spacetime Virasoro algebra in terms of worldsheet
operators. We moreover establish the link between a proposal for a ghost free
spectrum for Sl(2,R) string propagation and the massless black hole background,
thereby claryfing aspects of the AdS3/CFT correspondence. |
On Ward Identities in Lifshitz-like Field Theories: In this work, we develop a normal product algorithm suitable to the study of
anisotropic field theories in flat space, apply it to construct the symmetries
generators and describe how their possible anomalies may be found. In
particular, we discuss the dilatation anomaly in a scalar model with critical
exponent z=2 in six spatial dimensions. | Violation of the phase space general covariance as a diffeomorphism
anomaly in quantum mechanics: We consider a topological quantum mechanics described by a phase space path
integral and study the 1-dimensional analog for the path integral
representation of the Kontsevich formula. We see that the naive bosonic
integral possesses divergences, that it is even naively non-invariant and thus
is ill-defined. We then consider a super-extension of the theory which
eliminates the divergences and makes the theory naively invariant. This
super-extension is equivalent to the correct choice of measure and was
discussed in the literature. We then investigate the behavior of this extended
theory under diffeomorphisms of the extended phase space and despite of its
naive invariance find out that the theory possesses anomaly under nonlinear
diffeomorphisms. We localize the origin of the anomaly and calculate the lowest
nontrivial anomalous contribution. |
R-current six-point correlators in AdS_5 Supergravity: Within the conjectured duality between N=4 super Yang-Mills and Anti-deSitter
string theory, the BFKL Pomeron of the gauge theory corresponds to the graviton
mode of the dual string. As a first step towards analyzing multigraviton
exchange, we investigate R-current six-point functions within the supergravity
approximation. We compute the analogue of diffractive scattering, and we
analyze the triple Regge limit. In the supergravity approximation the triple
graviton vertex is found to vanish. | Scrambling time from local perturbations of the rotating BTZ black hole: In this paper, we investigate the entanglement entropy of the rotating BTZ
black hole perturbed by a massive back-reacting free falling particle. Then,
mutual information between two finite intervals in two asymptotic regions of
rotating BTZ is derived. It allows us to find the scrambling time, the time
scale in which mutual information vanishes. We give a dual large $c$ CFT
description in terms of a thermofield double state with different temperatures
for left and right moving modes that is perturbed by a local operator. Exact
matching between gravity and CFT results is obtained. |
Quiver Yangian and Supersymmetric Quantum Mechanics: The statistical model of crystal melting represents BPS configurations of
D-branes on a toric Calabi-Yau three-fold. Recently it has been noticed that an
infinite-dimensional algebra, the quiver Yangian, acts consistently on the
crystal-melting configurations. We physically derive the algebra and its action
on the BPS states, starting with the effective supersymmetric quiver quantum
mechanics on the D-brane worldvolume. This leads to remarkable combinatorial
identities involving equivariant integrations on the moduli space of the
quantum mechanics, which can be checked by numerical computations. | A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge
Fields: In gauge theories, physical histories are represented by space-time
connections modulo gauge transformations. The space of histories is thus
intrinsically non-linear. The standard framework of constructive quantum field
theory has to be extended to face these {\it kinematical} non-linearities
squarely. We first present a pedagogical account of this problem and then
suggest an avenue for its resolution. |
Chiral splitting and world-sheet gravitinos in higher-derivative string
amplitudes: We report on progress made in the construction of higher-derivative
superinvariants for type-II theories in ten dimensions. The string amplitude
calculations required for this analysis exhibit interesting features which have
received little attention in the literature so far. We discuss two examples
from a forthcoming publication: the construction of the (H_{NS})^2 R^3 terms
and the fermionic completion of the \epsilon\epsilon R^4 terms. We show that a
correct answer requires very careful treatment of the chiral splitting theorem,
implies unexpected new relations between fermionic correlators, and most
interestingly, necessitates the use of worldsheet gravitino zero modes in the
string vertex operators. In addition, we discuss the relation of our results to
the predictions of the linear scalar superfield of the type-IIB theory and find
(and explain) an interesting discrepancy. | MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial
Sphere: The Cachazo-Strominger subleading soft graviton theorem for a positive
helicity soft graviton is equivalent to the Ward identities for
$\overline{SL(2,\mathbb C)}$ currents. This naturally gives rise to a
$\overline{SL(2,\mathbb C)}$ current algebra living on the celestial sphere.
The generators of the $\overline{SL(2,\mathbb C)}$ current algebra and the
supertranslations, coming from a positive helicity leading soft graviton, form
a closed algebra. We find that the OPE of two graviton primaries in the
Celestial CFT, extracted from MHV amplitudes, is completely determined in terms
of this algebra. To be more precise, 1) The subleading terms in the OPE are
determined in terms of the leading OPE coefficient if we demand that both sides
of the OPE transform in the same way under this local symmetry algebra. 2)
Positive helicity gravitons have null states under this local algebra whose
decoupling leads to differential equations for MHV amplitudes. An $n$ point MHV
amplitude satisfies two systems of $(n-2)$ linear first order PDEs
corresponding to $(n-2)$ positive helicity gravitons. We have checked, using
Hodges' formula, that one system of differential equations is satisfied by any
MHV amplitude, whereas the other system has been checked up to six graviton MHV
amplitude. 3) One can determine the leading OPE coefficients from these
differential equations.
This points to the existence of an autonomous sector of the Celestial CFT
which holographically computes the MHV graviton scattering amplitudes and is
completely defined by this local symmetry algebra. The MHV-sector of the
Celestial CFT is like a minimal model of $2$-D CFT. |
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