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Minimal Stability in Maximal Supergravity: Recently, it has been shown that maximal supergravity allows for
non-supersymmetric AdS critical points that are perturbatively stable. We
investigate this phenomenon of stability without supersymmetry from the
sGoldstino point of view. In particular, we calculate the projection of the
mass matrix onto the sGoldstino directions, and derive the necessary conditions
for stability. Indeed we find a narrow window allowing for stable SUSY breaking
points. As a by-product of our analysis, we find that it seems impossible to
perturb supersymmetric critical points into non-supersymmetric ones: there is a
minimal amount of SUSY breaking in maximal supergravity.
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The Amplitude for Classical Gravitational Scattering at Third
Post-Minkowskian Order: We compute the scattering amplitude for classical black-hole scattering to
third order in the Post-Minkowskian expansion, keeping all terms needed to
derive the scattering angle to that order from the eikonal formalism. Our
results confirm a conjectured relation between the real and imaginary parts of
the amplitude by Di Vecchia, Heissenberg, Russo, and Veneziano, and are in
agreement with a recent computation by Damour based on radiation reaction in
general relativity.
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Why the Universe Started from a Low Entropy State: We show that the inclusion of backreaction of massive long wavelengths
imposes dynamical constraints on the allowed phase space of initial conditions
for inflation, which results in a superselection rule for the initial
conditions. Only high energy inflation is stable against collapse due to the
gravitational instability of massive perturbations. We present arguments to the
effect that the initial conditions problem {\it cannot} be meaningfully
addressed by thermostatistics as far as the gravitational degrees of freedom
are concerned. Rather, the choice of the initial conditions for the universe in
the phase space and the emergence of an arrow of time have to be treated as a
dynamic selection.
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Canonical supermultiplets and their Koszul duals: The pure spinor superfield formalism reveals that, in any dimension and with
any amount of supersymmetry, one particular supermultiplet is distinguished
from all others. This "canonical supermultiplet" is equipped with an additional
structure that is not apparent in any component-field formalism: a (homotopy)
commutative algebra structure on the space of fields. The structure is
physically relevant in several ways; it is responsible for the interactions in
ten-dimensional super Yang-Mills theory, as well as crucial to any
first-quantised interpretation. We study the $L_\infty$ algebra structure that
is Koszul dual to this commutative algebra, both in general and in numerous
examples, and prove that it is equivalent to the subalgebra of the Koszul dual
to functions on the space of generalised pure spinors in internal degree
greater than or equal to three. In many examples, the latter is the positive
part of a Borcherds-Kac-Moody superalgebra. Using this result, we can interpret
the canonical multiplet as the homotopy fiber of the map from generalised pure
spinor space to its derived replacement. This generalises and extends work of
Movshev-Schwarz and G\'alvez-Gorbounov-Shaikh-Tonks in the same spirit. We also
comment on some issues with physical interpretations of the canonical
multiplet, which are illustrated by an example related to the complex Cayley
plane, and on possible extensions of our construction, which appear relevant in
an example with symmetry type $G_2 \times A_1$.
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A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological
Strings: We demonstate the existence of a large $N$ phase transition with respect to
the 't Hooft coupling in q-deformed Yang-Mills theory on $S^2$. The strong
coupling phase is characterized by the formation of a clump of eigenvalues in
the associated matrix model of Douglas-Kazakov (DK) type (hep-th/9305047). By
understanding this in terms of instanton contributions to the q-deformed
Yang-Mills theory, we gain some insight into the strong coupling phase as well
as probe the phase diagram at nonzero values of the $\theta$ angle. The
Ooguri-Strominger-Vafa relation (hep-th/0405146) of this theory to topological
strings on the local Calabi-Yau $\mathcal{O}(-p) \oplus \mathcal{O}(p-2) \to
\mathbb{P}^1$ via a chiral decompostion at large $N$ hep-th/0411280, motivates
us to investigate the phase structure of the trivial chiral block, which
corresponds to the topological string partition function, for $p>2$. We find a
phase transition at a different value of the coupling than in the full theory,
indicating the likely presence of a rich phase structure in the sum over chiral
blocks.
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Topological terms and anomaly matching in effective field theories on
$\mathbb{R}^3\times S^1$: I. Abelian symmetries and intermediate scales: We explicitly calculate the topological terms that arise in IR effective
field theories for $SU(N)$ gauge theories on $\mathbb{R}^3 \times S^1$ by
integrating out all but the lightest modes. We then show how these terms match
all global-symmetry 't Hooft anomalies of the UV description. We limit our
discussion to theories with abelian 0-form symmetries, namely those with one
flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions.
While anomaly matching holds as required, it takes a different form than
previously thought. For example, cubic- and mixed-$U(1)$ anomalies are matched
by local background-field-dependent topological terms (background TQFTs)
instead of chiral-lagrangian Wess-Zumino terms. We also describe the coupling
of 0-form and 1-form symmetry backgrounds in the magnetic dual of
super-Yang-Mills theory in a novel way, valid throughout the RG flow and
consistent with the monopole-instanton 't Hooft vertices. We use it to discuss
the matching of the mixed chiral-center anomaly in the magnetic dual.
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Gauge Theory and a Dirac Operator on a Noncommutative Space: As a tool to carry out the quantization of gauge theory on a noncommutative
space, we present a Dirac operator that behaves as a line element of the
canonical noncommutative space. Utilizing this operator, we construct the
Dixmier trace, which is the regularized trace for infinite-dimensional
matrices. We propose the possibility of solving the cosmological constant
problem by applying our gauge theory on the noncommutative space.
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An Analytic Description of Semi-Classical Black-Hole Geometry: We study analytically the spacetime geometry of the black-hole formation and
evaporation. As a simplest model of the collapse, we consider a spherical thin
shell, and take the back-reaction from the negative energy of the quantum
vacuum state. For definiteness, we will focus on quantum effects of s-waves. We
obtain an analytic solution of the semi-classical Einstein equation for this
model, that provides an overall description of the black hole geometry form the
formation to evaporation. As an application of this result, we find its
interesting implication that, after the collapsing shell enters the apparent
horizon, the proper distance between the shell and the horizon remains as small
as the Planck length even when the difference in their areal radii is of the
same order as the Schwarzschild radius. The position of the shell would be
regarded as the same place to the apparent horizon in the semi-classical regime
of gravity.
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Statistics on the Heterotic Landscape: Gauge Groups and Cosmological
Constants of Four-Dimensional Heterotic Strings: Recent developments in string theory have reinforced the notion that the
space of stable supersymmetric and non-supersymmetric string vacua fills out a
``landscape'' whose features are largely unknown. It is then hoped that
progress in extracting phenomenological predictions from string theory -- such
as correlations between gauge groups, matter representations, potential values
of the cosmological constant, and so forth -- can be achieved through
statistical studies of these vacua. To date, most of the efforts in these
directions have focused on Type I vacua. In this note, we present the first
results of a statistical study of the heterotic landscape, focusing on more
than 10^5 explicit non-supersymmetric tachyon-free heterotic string vacua and
their associated gauge groups and one-loop cosmological constants. Although
this study has several important limitations, we find a number of intriguing
features which may be relevant for the heterotic landscape as a whole. These
features include different probabilities and correlations for different
possible gauge groups as functions of the number of orbifold twists. We also
find a vast degeneracy amongst non-supersymmetric string models, leading to a
severe reduction in the number of realizable values of the cosmological
constant as compared with naive expectations. Finally, we also find strong
correlations between cosmological constants and gauge groups which suggest that
heterotic string models with extremely small cosmological constants are
overwhelmingly more likely to exhibit the Standard-Model gauge group at the
string scale than any of its grand-unified extensions. In all cases, heterotic
worldsheet symmetries such as modular invariance provide important constraints
that do not appear in corresponding studies of Type I vacua.
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Elongation of Moving Noncommutative Solitons: We discuss the characteristic properties of noncommutative solitons moving
with constant velocity. As noncommutativity breaks the Lorentz symmetry, the
shape of moving solitons is affected not just by the Lorentz contraction along
the velocity direction, but also sometimes by additional `elongation'
transverse to the velocity direction. We explore this in two examples:
noncommutative solitons in a scalar field theory on two spatial dimension and
`long stick' shaped noncommutative U(2) magnetic monopoles. However the
elongation factors of these two cases are different, and so not universal.
|
A note on instanton counting for N=2 gauge theories with classical gauge
groups: We study the prepotential of N=2 gauge theories using the instanton counting
techniques introduced by Nekrasov. For the SO theories without matter we find a
closed expression for the full prepotential and its string theory gravitational
corrections. For the more subtle case of Sp theories without matter we discuss
general features and compute the prepotential up to instanton number three. We
also briefly discuss SU theories with matter in the symmetric and antisymmetric
representations. We check all our results against the predictions of the
corresponding Seiberg-Witten geometries.
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Seiberg-Witten and "Polyakov-like" magnetic bion confinements are
continuously connected: We study four-dimensional N=2 supersymmetric pure-gauge (Seiberg-Witten)
theory and its N=1 mass perturbation by using compactification S**1 x R**3. It
is well known that on R**4 (or at large S**1) the perturbed theory realizes
confinement through monopole or dyon condensation. At small S**1, we
demonstrate that confinement is induced by a generalization of Polyakov's
three-dimensional instanton mechanism to a locally four-dimensional theory -
the magnetic bion mechanism - which also applies to a large class of
nonsupersymmetric theories. Using a large- vs. small-L Poisson duality, we show
that the two mechanisms of confinement, previously thought to be distinct, are
in fact continuously connected.
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Effective superpotentials for compact D5-brane Calabi-Yau geometries: For compact Calabi-Yau geometries with D5-branes we study N=1 effective
superpotentials depending on both open- and closed-string fields. We develop
methods to derive the open/closed Picard-Fuchs differential equations, which
control D5-brane deformations as well as complex structure deformations of the
compact Calabi-Yau space. Their solutions encode the flat open/closed
coordinates and the effective superpotential. For two explicit examples of
compact D5-brane Calabi-Yau hypersurface geometries we apply our techniques and
express the calculated superpotentials in terms of flat open/closed
coordinates. By evaluating these superpotentials at their critical points we
reproduce the domain wall tensions that have recently appeared in the
literature. Finally we extract orbifold disk invariants from the
superpotentials, which, up to overall numerical normalizations, correspond to
orbifold disk Gromov-Witten invariants in the mirror geometry.
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E$_{7(7)}$ Exceptional Field Theory in Superspace: We formulate the locally supersymmetric E$_{7(7)}$ exceptional field theory
in a $(4+56|32)$ dimensional superspace, corresponding to a 4D $N\!=\!8$
"external" superspace augmented with an "internal" 56-dimensional space. This
entails the unification of external diffeomorphisms and local supersymmetry
transformations into superdiffeomorphisms. The solutions to the superspace
Bianchi identities lead to on-shell duality equations for the $p$-form field
strengths for $p\leq 4$. The reduction to component fields provides a complete
description of the on-shell supersymmetric theory. As an application of our
results, we perform a generalized Scherk-Schwarz reduction and obtain the
superspace formulation of maximal gauged supergravity in four dimensions
parametrized by an embedding tensor.
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Hyperboloid, instanton, oscillator: We suggest the exactly solvable model of the oscillator on a four-dimensional
hyperboloid which interacts with a SU(2) instanton. We calculate its
wavefunctions and spectrum.
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Supersymmetric KP Systems Embedded in Supersymmetric Self-Dual
Yang-Mills Theory: We show that $~N=1$~ {\it supersymmetric} Kadomtsev-Petviashvili (SKP)
equations can be embedded into recently formulated $~N=1$~ self-dual {\it
supersymmetric} Yang-Mills theories after appropriate dimensional reduction and
truncation, which yield three-dimensional supersymmetric Chern-Simons theories.
Based on this result, we also give conjectural \hbox{$N=2~$} SKP equations.
Subsequently some exact solutions of these systems including fermionic fields
are given.
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Classifying Galileon $p$-form theories: We provide a complete classification of all abelian gauge invariant $p$-form
theories with equations of motion depending only on the second derivative of
the field---the $p$-form analogues of the Galileon scalar field theory. We
construct explicitly the nontrivial actions that exist for spacetime dimension
$D\leq11$, but our methods are general enough and can be extended to arbitrary
$D$. We uncover in particular a new $4$-form Galileon cubic theory in $D\geq8$
dimensions. As a by-product we give a simple proof of the fact that the
equations of motion depend on the $p$-form gauge fields only through their
field strengths, and show this explicitly for the recently discovered $3$-form
Galileon quartic theory.
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A Supersymmetric Solution in N=2 Gauged Supergravity with the Universal
Hypermultiplet: We present supersymmetric solutions for the theory of gauged supergravity in
five dimensions obtained by gauging the shift symmetry of the axion of the
universal hypermultiplet. This gauged theory can also be obtained by
dimensionally reducing M-theory on a Calabi-Yau threefold with background flux.
The solution found preserves half of the N=2 supersymmetry, carries electric
fields and has nontrivial scalar field representing the CY-volume. We comment
on the possible solutions of more general hypermultiplet gauging.
|
S-brane solutions with acceleration in models with forms and multiple
exponential potentials: A family of generalized S-brane solutions with orthogonal intersection rules
and n Ricci-flat factor spaces in the theory with several scalar fields,
antisymmetric forms and multiple scalar potential is considered. Two subclasses
of solutions with power-law and exponential behaviour of scale factors are
singled out. These subclasses contain sub-families of solutions with
accelerated expansion of certain factor spaces. Some examples of solutions with
exponential dependence of one scale factor and constant scale factors of
"internal" spaces (e.g. Freund-Rubin type solutions) are also considered.
|
Linear and Chiral Superfields are Usefully Inequivalent: Chiral superfields have been used, and extensively, almost ever since
supersymmetry has been discovered. Complex linear superfields afford an
alternate representation of matter, but are widely misbelieved to be
'physically equivalent' to chiral ones. We prove the opposite is true.
Curiously, this re-enables a previously thwarted interpretation of the
low-energy (super)field limit of superstrings.
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Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group: We analyze the hamiltonian quantization of Chern-Simons theory associated to
the universal covering of the Lorentz group SO(3,1). The algebra of observables
is generated by finite dimensional spin networks drawn on a punctured
topological surface. Our main result is a construction of a unitary
representation of this algebra. For this purpose, we use the formalism of
combinatorial quantization of Chern-Simons theory, i.e we quantize the algebra
of polynomial functions on the space of flat SL(2,C)-connections on a
topological surface with punctures. This algebra admits a unitary
representation acting on an Hilbert space which consists in wave packets of
spin-networks associated to principal unitary representations of the quantum
Lorentz group. This representation is constructed using only Clebsch-Gordan
decomposition of a tensor product of a finite dimensional representation with a
principal unitary representation. The proof of unitarity of this representation
is non trivial and is a consequence of properties of intertwiners which are
studied in depth. We analyze the relationship between the insertion of a
puncture colored with a principal representation and the presence of a
world-line of a massive spinning particle in de Sitter space.
|
Consistency of supersymmetric 't Hooft anomalies: We consider recent claims that supersymmetry is anomalous in the presence of
a R-symmetry anomaly. We revisit arguments that such an anomaly in
supersymmetry can be removed and write down an explicit counterterm that
accomplishes it. Removal of the supersymmetry anomaly requires enlarging the
corresponding current multiplet. As a consequence the Ward identities for other
symmetries that are already anomalous acquire extra terms. This procedure can
only be impeded when the choice of current multiplet is forced. We show how
Wess-Zumino consistency conditions are modified when the anomaly is removed.
Finally we check that the modified Wess-Zumino consistency conditions are
satisfied, and supersymmetry unbroken, in an explicit one loop computation
using Pauli-Villars regulators. To this end we comment on how to use
Pauli-Villars to regulate correlators of components of (super)current
multiplets in a manifestly supersymmetric way.
|
Quantum groups and quantum field theory: I. The free scalar field: The quantum field algebra of real scalar fields is shown to be an example of
infinite dimensional quantum group. The underlying Hopf algebra is the
symmetric algebra S(V) and the product is Wick's normal product. Two
coquasitriangular structures can be built from the two-point function and the
Feynman propagator of scalar fields to reproduce the operator product and the
time-ordered product as twist deformations of the normal product. A
correspondence is established between the quantum group and the quantum field
concepts. On the mathematical side the underlying structures come out of Hopf
algebra cohomology.
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Matrix Model for membrane and dynamics of D-Particles in a curved
space-time geometry and presence of form fields: We study dynamics of a membrane and its matrix regularisation. We present the
matrix regularisation for a membrane propagating in a curved space-time
geometry in the presence of an arbitrary 3-form field. In the matrix
regularisation, we then study the dynamics of D-particles. We show how the
Riemann curvature of the target space-time geometry, or any other form fields
can polarise the D-Particles, cause entanglement among them and create fuzzy
solutions. We review the fuzzy sphere and we present fuzzy hyperbolic and
ellipsoid solutions.
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Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories: Anomalies arising from nonplanar triangle diagrams of noncommutative gauge
theory are studied. Local chiral gauge anomalies for both noncommutative U(1)
and U(N) gauge theories with adjoint matter fields are shown to vanish. For
noncommutative QED with fundamental matters, due to UV/IR mixing a finite
anomaly emerges from the nonplanar contributions. It involves a generalized
$\star$-product of gauge fields.
|
Three Lectures on Complexity and Black Holes: Given at PiTP 2018 summer program entitled "From Qubits to Spacetime." The
first lecture describes the meaning of quantum complexity, the analogy between
entropy and complexity, and the second law of complexity.
Lecture two reviews the connection between the second law of complexity and
the interior of black holes. I discuss how firewalls are related to periods of
non-increasing complexity which typically only occur after an exponentially
long time.
The final lecture is about the thermodynamics of complexity, and
"uncomplexity" as a resource for doing computational work. I explain the
remarkable power of "one clean qubit," in both computational terms and in
space-time terms.
The lectures can also be found online at
\url{https://static.ias.edu/pitp/2018/node/1796.html} .
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Accretion of Ghost Condensate by Black Holes: The intent of this letter is to point out that the accretion of a ghost
condensate by black holes could be extremely efficient. We analyze steady-state
spherically symmetric flows of the ghost fluid in the gravitational field of a
Schwarzschild black hole and calculate the accretion rate. Unlike minimally
coupled scalar field or quintessence, the accretion rate is set not by the
cosmological energy density of the field, but by the energy scale of the ghost
condensate theory. If hydrodynamical flow is established, it could be as high
as tenth of a solar mass per second for 10MeV-scale ghost condensate accreting
onto a stellar-sized black hole, which puts serious constraints on the
parameters of the ghost condensate model.
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An Orientifold of Type-IIB Theory on $K3$: A new orientifold of Type-IIB theory on $K3$ is constructed that has $N=1$
supersymmetry in six dimensions. The orientifold symmetry consists of a $Z_2$
involution of $K3$ combined with orientation-reversal on the worldsheet. The
closed-string sector in the resulting theory contains nine tensor multiplets
and twelve neutral hypermultiplets in addition to the gravity multiplet, and is
anomaly-free by itself. The open-string sector contains only 5-branes and gives
rise to maximal gauge groups $SO(16)$ or $U(8)\times U(8)$ at different points
in the moduli space. Anomalies are canceled by a generalization of the
Green-Schwarz mechanism that involves more than one tensor multiplets.
|
Derivation of Index Theorems by Localization of Path Integrals: We review the derivation of the Atiyah-Singer and Callias index theorems
using the recently developed localization method to calculate exactly the
relevant supersymmetric path integrals. (Talk given at the III International
Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta,
Ukraine, June 13-24, 1993)
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Towards an Explicit Model of D-brane Inflation: We present a detailed analysis of an explicit model of warped D-brane
inflation, incorporating the effects of moduli stabilization. We consider the
potential for D3-brane motion in a warped conifold background that includes
fluxes and holomorphically-embedded D7-branes involved in moduli stabilization.
Although the D7-branes significantly modify the inflaton potential, they do not
correct the quadratic term in the potential, and hence do not cause a uniform
change in the slow-roll parameter eta. Nevertheless, we present a simple
example based on the Kuperstein embedding of D7-branes, z_1=constant, in which
the potential can be fine-tuned to be sufficiently flat for inflation. To
derive this result, it is essential to incorporate the fact that the
compactification volume changes slightly as the D3-brane moves. We stress that
the compactification geometry dictates certain relationships among the
parameters in the inflaton Lagrangian, and these microscopic constraints impose
severe restrictions on the space of possible models. We note that the shape of
the final inflaton potential differs from projections given in earlier studies:
in configurations where inflation occurs, it does so near an inflection point.
Finally, we comment on the difficulty of making precise cosmological
predictions in this scenario. This is the companion paper to arXiv:0705.3837.
|
Formulae for Line Bundle Cohomology on Calabi-Yau Threefolds: We present closed form expressions for the ranks of all cohomology groups of
holomorphic line bundles on several Calabi-Yau threefolds realised as complete
intersections in products of projective spaces. The formulae have been obtained
by systematising and extrapolating concrete calculations and they have been
checked computationally. Although the intermediate calculations often involve
laborious computations of ranks of Leray maps in the Koszul spectral sequence,
the final results for cohomology follow a simple pattern. The space of line
bundles can be divided into several different regions, and in each such region
the ranks of all cohomology groups can be expressed as polynomials in the line
bundle integers of degree at most three. The number of regions increases and
case distinctions become more complicated for manifolds with a larger Picard
number. We also find explicit cohomology formulae for several non-simply
connected Calabi-Yau threefolds realised as quotients by freely acting discrete
symmetries. More cases may be systematically handled by machine learning
algorithms.
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Holographic Entanglement Entropy from 2d CFT: Heavy States and Local
Quenches: We consider the entanglement entropy in 2d conformal field theory in a class
of excited states produced by the insertion of a heavy local operator. These
include both high-energy eigenstates of the Hamiltonian and time-dependent
local quenches. We compute the universal contribution from the stress tensor to
the single interval Renyi entropies and entanglement entropy, and conjecture
that this dominates the answer in theories with a large central charge and a
sparse spectrum of low-dimension operators. The resulting entanglement
entropies agree precisely with holographic calculations in three-dimensional
gravity. High-energy eigenstates are dual to microstates of the BTZ black hole,
so the corresponding holographic calculation is a geodesic length in the black
hole geometry; agreement between these two answers demonstrates that
entanglement entropy thermalizes in individual microstates of holographic CFTs.
For local quenches, the dual geometry is a highly boosted black hole or conical
defect. On the CFT side, the rise in entanglement entropy after a quench is
directly related to the monodromy of a Virasoro conformal block.
|
Solving String Field Equations: New Uses for Old Tools: It is argued that the (NS-sector) superstring field equations are integrable,
i.e. their solutions are obtainable from linear equations. We adapt the
25-year-old solution-generating "dressing" method and reduce the construction
of nonperturbative superstring configurations to a specific cohomology problem.
The application to vacuum superstring field theory is outlined.
|
Generalized Squeezed States from Generalized Coherent States: Both the coherent states and also the squeezed states of the harmonic
oscillator have long been understood from the three classical points of view:
the 1) displacement operator, 2) annihilation- (or ladder-) operator, and
minimum-uncertainty methods. For general systems, there is the same
understanding except for ladder-operator and displacement-operator squeezed
states. After reviewing the known concepts, I propose a method for obtaining
generalized minimum-uncertainty squeezed states, give examples, and relate it
to known concepts. I comment on the remaining concept, that of general
displacement-operator squeezed states.
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Light-cone M5 and multiple M2-branes: We present the light-cone gauge fixed Lagrangian for the M5-brane; it has a
residual `exotic' gauge invariance with the group of 5-volume preserving
diffeomorphisms, SDiff(5), as gauge group. For an M5-brane of topology R2 x M3,
for closed 3-manifold M3, we find an infinite tension limit that yields an
SO(8)-invariant (1+2)-dimensional field theory with `exotic' SDiff(3) gauge
invariance. We show that this field theory is the Carrollian limit of the Nambu
bracket realization of the `BLG' model for multiple M2-branes.
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Correlators of supersymmetric Wilson loops at weak and strong coupling: We continue our study of the correlators of a recently discovered family of
BPS Wilson loops in N=4 supersymmetric U(N) Yang-Mills theory. We perform
explicit computations at weak coupling by means of analytical and numerical
methods finding agreement with the exact formula derived from localization. In
particular we check the localization prediction at order g^6 for different BPS
"latitude" configurations, the N=4 perturbative expansion reproducing the
expected results within a relative error of 10^(-4). On the strong coupling
side we present a supergravity evaluation of the 1/8 BPS correlator in the
limit of large separation, taking into account the exchange of all relevant
modes between the string world-sheets. While reproducing the correct
geometrical dependence, we find that the associated coefficient does not match
the localization result.
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Vector Braids: In this paper we define a new family of groups which generalize the {\it
classical braid groups on} $\C $. We denote this family by $\{B_n^m\}_{n \ge
m+1}$ where $n,m \in \N$. The family $\{ B_n^1 \}_{n \in \N}$ is the set of
classical braid groups on $n$ strings. The group $B_n^m$ is the set of motions
of $n$ unordered points in $\C^m$, so that at any time during the motion, each
$m+1$ of the points span the whole of $\C^m$ as an affine space. There is a map
from $B_n^m$ to the symmetric group on $n$ letters. We let $P_n^m$ denote the
kernel of this map. In this paper we are mainly interested in understanding
$P_n^2$. We give a presentation of a group $PL_n$ which maps surjectively onto
$P_n^2$. We also show the surjection $PL_n \to P_n^2$ induces an isomorphism on
first and second integral homology and conjecture that it is an isomorphism. We
then find an infinitesimal presentation of the group $P_n^2$. Finally, we also
consider the analagous groups where points lie in $\P^m$ instead of $\C^m$.
These groups generalize of the classical braid groups on the sphere.
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Topological Terms and Diffeomorphism Anomalies in Fluid Dynamics and
Sigma Models: The requirement of diffeomorphism symmetry for the target space can lead to
anomalous commutators for the energy-momentum tensor for sigma models and for
fluid dynamics, if certain topological terms are added to the action. We
analyze several examples . A particular topological term is shown to lead to
the known effective hydrodynamics of a dense collection of vortices, i.e. the
vortex fluid theory in 2+1 dimensions. The possibility of a similar vortex
fluid in 3+1 dimensions, as well as a fluid of knots and links, with possible
extended diffeomorphism algebras is also discussed.
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Zero-brane approach to study of particle-like solitons in classical and
quantum Liouville field theory: The effective p-brane action approach is generalized for arbitrary scalar
field and applied for the Liouville theory near a particle-like solution. It
was established that this theory has the remarkable features discriminating it
from the theories studied earlier. Removing zero modes we obtain the effective
action describing the solution as a point particle with curvature, quantize it
as the theory with higher derivatives and calculate the quantum corrections to
mass.
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Cosmology with orthogonal nilpotent superfields: We study the application of a supersymmetric model with two constrained
supermultiplets to inflationary cosmology. The first superfield S is a
stabilizer chiral superfield satisfying a nilpotency condition of degree 2,
S^2=0. The second superfield Phi is the inflaton chiral superfield, which can
be combined into a real superfield B=(Phi-Phi*)/2i. The real superfield B is
orthogonal to S, S B=0, and satisfies a nilpotency condition of degree 3,
B^3=0. We show that these constraints remove from the spectrum the complex
scalar sgoldstino, the real scalar inflaton partner (i.e. the "sinflaton"), and
the fermionic inflatino. The corresponding supergravity model with de Sitter
vacua describes a graviton, a massive gravitino, and one real scalar inflaton,
with both the goldstino and inflatino being absent in unitary gauge. We also
discuss relaxed superfield constraints where S^2=0 and S Phi* is chiral, which
removes the sgoldstino and inflatino, but leaves the sinflaton in the spectrum.
The cosmological model building in both of these inflatino-less models offers
some advantages over existing constructions.
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Solutions of the bosonic master-field equation from a supersymmetric
matrix model: It has been argued that the bosonic large-$N$ master field of the IIB matrix
model can give rise to an emergent classical spacetime. In a recent paper, we
have obtained solutions of a simplified bosonic master-field equation from a
related matrix model. In this simplified equation, the effects of dynamic
fermions were removed. We now consider the full bosonic master-field equation
from a related supersymmetric matrix model for dimensionality $D=3$ and matrix
size $N=3$. In this last equation, the effects of dynamic fermions are
included. With an explicit realization of the random constants entering this
algebraic equation, we establish the existence of nontrivial solutions. The
small matrix size, however, does not allow us to make a definitive statement as
to the appearance of a diagonal/band-diagonal structure in the obtained
matrices.
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Ground state energy of twisted $AdS_{3}\times S^{3}\times T^{4}$
superstring and the TBA: We use the lightcone $AdS_{3}\times S^{3}\times T^{4}$ superstring sigma
model with fermions and bosons subject to twisted boundary conditions to find
the ground state energy in the semi-classical approximation where effective
string tension $h$ and the light-cone momentum $L$ are sent to infinity in such
a way that ${\cal J}\equiv L/h$ is kept fixed. We then analyse the ground state
energy of the model by means of the mirror TBA equations for the $AdS_{3}\times
S^{3}\times T^{4}$ superstring in the pure RR background. The calculation is
performed for small twist $\mu$ with $L$ and $h$ fixed, for large $L$ with
$\mu$ and $h$ fixed, and for small $h$ with $\mu$ and $L$ fixed. In these
limits the contribution of the gapless worldsheet modes coming from the $T^4$
bosons and fermions can be computed exactly, and is shown to be proportional to
$hL/(4L^2-1)$. Comparison with the semi-classical result shows that the TBA
equations involve only one $Y_0$-function for massless excitations but not two
as was conjectured before. Some of the results obtained are generalised to the
mixed-flux $AdS_{3}\times S^{3}\times T^{4}$ superstring.
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Wilson Renormalization Group and Continuum Effective Field Theories: This is an elementary introduction to Wilson renormalization group and
continuum effective field theories. We first review the idea of Wilsonian
effective theory and derive the flow equation in a form that allows multiple
insertion of operators in Green functions. Then, based on this formalism, we
prove decoupling and heavy-mass factorization theorems, and discuss how the
continuum effective field theory is formulated in this approach.
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Ghost-Free Superconformal Action for Multiple M2-Branes: The Bagger--Lambert construction of N = 8 superconformal field theories
(SCFT) in three dimensions is based on 3-algebras. Three groups of researchers
recently realized that an arbitrary semisimple Lie algebra can be incorporated
by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a
candidate for the SCFT describing coincident M2-branes. However, these theories
contain ghost degrees of freedom, which is unsatisfactory. We modify them by
gauging certain global symmetries. This eliminates the ghosts from these
theories while preserving all of their desirable properties. The resulting
theories turn out to be precisely equivalent to N = 8 super Yang--Mills
theories.
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Extremal Kerr black hole/CFT correspondence in the five dimensional
Gödel universe: We extend the method of Kerr/CFT correspondence recently proposed in
arXiv:0809.4266 [hep-th] to the extremal (charged) Kerr black hole embedded in
the five-dimensional G\"{o}del universe. With the aid of the central charges in
the Virasoro algebra and the Frolov-Thorne temperatures, together with the use
of the Cardy formula, we have obtained the microscopic entropies that precisely
agree with the ones macroscopically calculated by Bekenstein-Hawking area law.
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One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes
in N=4 Super Yang-Mills: Recently it has been argued that tree-level scattering amplitudes in N=4
Yang-Mills theory are uniquely determined by a careful study of their
superconformal and Yangian symmetries. However, at one-loop order these
symmetries are known to become anomalous due to infrared divergences. We
compute these one-loop anomalies for amplitudes defined through dimensional
regularisation by studying the tree-level symmetry transformations of the
unitarity branch cuts, keeping track of the crucial collinear terms arising
from the holomorphic anomaly. We extract the superconformal anomalies and show
that they may be cancelled through a universal one-loop deformation of the
tree-level symmetry generators which involves only tree-level data.
Specialising to the planar theory we also obtain the analogous deformation for
the level-one Yangian generator of momentum. Explicit checks of our one-loop
deformation are performed for MHV and the 6-point NMHV amplitudes.
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Chern-Simons dualities with multiple flavors at large $N$: We study $U(N)_k$ Chern-Simons theory coupled to fundamental fermions and
scalars in a large $N$ `t Hooft limit. We compute the thermal free energy at
high temperature, as well as two- and three-point functions of simple
gauge-invariant operators. Our findings support various dualities between
Chern-Simons-matter theories with $\mathcal{N}=0,1,$ and $2$ supersymmetry.
|
Hamiltonian lattice gauge models and the Heisenberg double: Hamiltonian lattice gauge models based on the assignment of the Heisenberg
double of a Lie group to each link of the lattice are constructed in arbitrary
space-time dimensions. It is shown that the corresponding generalization of the
gauge-invariant Wilson line observables requires to attach to each vertex of
the line a vertex operator which goes to the unity in the continuum limit.
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Kerr-NUT-de Sitter as an Inhomogeneous Non-Singular Bouncing Cosmology: We present exact non-singular bounce solutions of general relativity in the
presence of a positive cosmological constant and an electromagnetic field,
without any exotic matter. The solutions are distinguished by being spatially
inhomogeneous in one direction, while they can also contain non-trivial
electromagnetic field lines. The inhomogeneity may be substantial, for
instance, there can be one bounce in one region of the universe and two bounces
elsewhere. Since the bounces are followed by a phase of accelerated expansion,
the metrics described here also permit the study of (geodesically complete)
models of inflation with inhomogeneous initial conditions. Our solutions admit
two Killing vectors and may be re-interpreted as the pathology-free interior
regions of Kerr-de Sitter black holes with non-trivial NUT charge. Remarkably
enough, within this cosmological context, the NUT parameter does not introduce
any string singularity nor closed timelike curves but renders the geometry
everywhere regular, eliminating the big bang singularity by means of a bounce.
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Refined large N duality for knots: We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory
with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we
provide the explicit form of low-energy effective actions of Type IIA string
theory with D4-branes on the $\Omega$-background. This form enables us to
relate refined Chern-Simons invariants of a torus knot/link in $S^3$ to refined
BPS invariants in the resolved conifold. Assuming that the extra
$\mathrm{U}(1)$ global symmetry acts on BPS states trivially, the duality
predicts graded dimensions of cohomology groups of moduli spaces of M2-M5 bound
states associated to a torus knot/link in the resolved conifold. Thus, this
formulation can be interpreted as a positivity conjecture of refined
Chern-Simons invariants of torus knots/links. We also discuss about an
extension to non-torus knots.
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Scattering of zero branes off elementary strings in Matrix Theory: We consider the scattering of zero branes off an elementary string in Matrix
theory or equivalently gravitons off a longitudinally wrapped membrane. The
leading supergravity result is recovered by a one-loop calculation in zero
brane quantum mechanics.
Simple scaling arguments are used to show that there are no further
corrections at higher loops, to the leading term in the large impact parameter,
low velocity expansion. The mechanism for this agreement is identified in terms
of properties of a recently discovered boundary conformal field theory.
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Super Black Hole from Cosmological Supergravity with a Massive
Superparticle: We describe in superspace a classical theory of two dimensional $(1,1)$
cosmological dilaton supergravity coupled to a massive superparticle. We give
an exact non-trivial superspace solution for the compensator superfield that
describes the supergravity, and then use this solution to construct a model of
a two-dimensional supersymmetric black hole.
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An AAD Model of Point Particle and the Pauli Equation: The classical relativistic linear AAD interaction, introduced by the author,
leads in the case of weak coupling to a pointlike particle capable to be sub-
mitted to quantization via Feynman's path integrals along the line adequate to
the requirements of the Pauli equation. In the discussed nonrelativistic case
of the model the concept of spin is considered within early Feynman's ideas.
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Submerging islands through thermalization: We illustrate scenarios in which Hawking radiation collected in finite
regions of a reservoir provides temporary access to the interior of black holes
through transient entanglement "islands". Whether these islands appear and the
amount of time for which they dominate - sometimes giving way to a
thermalization transition - is controlled by the amount of radiation we probe.
In the first scenario, two reservoirs are coupled to an eternal black hole. The
second scenario involves two holographic quantum gravitating systems at
different temperatures interacting through a Rindler-like reservoir, which acts
as a heat engine maintaining thermal equilibrium. The latter situation, which
has an intricate phase structure, describes two eternal black holes radiating
into each other through a shared reservoir.
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On broken zero modes of a string world sheet, and a correlation function
of a 1/4 BPS Wilson loop and a 1/2 BPS local operator: We reconsider a gravity dual of a 1/4 BPS Wilson loop. In the case of an
expectation value of the Wilson loop, it is known that broken zero modes of a
string world sheet in the gravity side play important roles in the limit
$\lambda \to \infty$ with keeping the combination $\lambda \cos^2 \theta_0$
finite. Here, $\lambda$ is the 't Hooft coupling constant and $\theta_0$ is a
parameter of the Wilson loop. In this paper, we reconsider a gravity dual of a
correlation function between the Wilson loop and a 1/2 BPS local operator with
R charge $J$. We take account of contributions coming from the same
configurations of the above-mentioned broken zero modes. We find an agreement
with the gauge theory side in the limit $J \ll \sqrt{\lambda \cos^2 \theta_0}
$.
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Mass protection via translational invariance: We propose a way of protecting a Dirac fermion interacting with a scalar
field from acquiring a mass from the vacuum. It is obtained through an
implementation of translational symmetry when the theory is formulated with a
momentum cutoff, which forbids the usual Yukawa term. We consider that this
mechanism can help to understand the smallness of neutrino masses without a
tuning of the Yukawa coupling. The prohibition of the Yukawa term for the
neutrino forbids at the same time a gauge coupling between the right-handed
electron and neutrino. We prove that this mechanism can be implemented on the
lattice.
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Local BRST cohomology of the gauged principal non-linear sigma model: The local BRST cohomology of the gauged non-linear sigma model on a group
manifold is worked out for any Lie group G. We consider both, the case where
the gauge field is dynamical and the case where it has no kinetic term (G/G
topological theory). Our results shed a novel light on the problem of gauging
the WZW term as well as on the nature of the topological terms introduced a few
years ago by De Wit, Hull and Rocek. We also consider the BRST cohomology of
the rigid symmetries of the ungauged model and recover the results of D'Hoker
and Weinberg on the most general effective actions compatible with the
symmetries.
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Scattering ripples from branes: A novel probe of D-brane dynamics is via scattering of a high energy ripple
traveling along an attached string. The inelastic processes in which the
D-brane is excited through emission of an additional attached string is
considered. Corresponding amplitudes can be found by factorizing a one-loop
amplitude derived in this paper. This one-loop amplitude is shown to have the
correct structure, but extraction of explicit expressions for the scattering
amplitudes is difficult. It is conjectured that the exponential growth of
available string states with energy leads to an inclusive scattering rate that
becomes large at the string scale, due to excitation of the ``string halo,''
and meaning that such probes do not easily see structure at shorter scales.
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Correspondence between Noncommutative Soliton and Open String/D-brane
System via Gaussian Damping Factor: The gaussian damping factor (g.d.f.) and the new interaction vertex with the
symplectic tensor are the characteristic properties of the N-point
scalar-vector scattering amplitudes of the p-p' (p < p') open string system
which realizes noncommutative geometry. The g.d.f. is here interpreted as a
form factor of the Dp-brane by noncommutative U(1) current. Observing that the
g.d.f. is in fact equal to the Fourier transform of the noncommutative
projector soliton introduced by Gopakumar, Minwalla and Strominger, we further
identify the Dp-brane in the zero slope limit with the noncommutative soliton
state. It is shown that the g.d.f. depends only on the total momentum of N-2
incoming/outgoing photons in the zero slope limit. In the description of the
low-energy effective action (LEEA) proposed before, this is shown to follow
from the delta function propagator and the form of the initial/final wave
functions in the soliton sector which resides in x^{m} m= p+1, ...p' dependent
part of the scalar field \Phi(x^\mu, x^m). The three and four point amplitudes
computed from LEEA agree with string calculation. We discuss related issues
which are resummation/lifting of infinite degeneracy and conservation of
momentum transverse to the Dp-brane.
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On a Derivation of the Dirac Hamiltonian From a Construction of Quantum
Gravity: The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge
in a semi-classical approximation from a abstract spectral triple construction.
The spectral triple is constructed over an algebra of holonomy loops,
corresponding to a configuration space of connections, and encodes information
of the kinematics of General Relativity. The emergence of the Dirac Hamiltonian
follows from the observation that the algebra of loops comes with a dependency
on a choice of base-point. The elimination of this dependency entails spinor
fields and, in the semi-classical approximation, the structure of the Dirac
Hamiltonian.
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Superrotation Charge and Supertranslation Hair on Black Holes: It is shown that black hole spacetimes in classical Einstein gravity are
characterized by, in addition to their ADM mass $M$, momentum $\vec P$, angular
momentum $\vec J$ and boost charge $\vec K$, an infinite head of
supertranslation hair. The distinct black holes are distinguished by classical
superrotation charges measured at infinity. Solutions with supertranslation
hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms
are part of the BMS subgroup and act nontrivially on the physical phase space.
It is shown that a black hole can be supertranslated by throwing in an
asymmetric shock wave. A leading-order Bondi-gauge expression is derived for
the linearized horizon supertranslation charge and shown to generate, via the
Dirac bracket, supertranslations on the linearized phase space of gravitational
excitations of the horizon. The considerations of this paper are largely
classical augmented by comments on their implications for the quantum theory.
|
Yangian Bootstrap for Conformal Feynman Integrals: We explore the idea to bootstrap Feynman integrals using integrability. In
particular, we put the recently discovered Yangian symmetry of conformal
Feynman integrals to work. As a prototypical example we demonstrate that the
D-dimensional box integral with generic propagator powers is completely fixed
by its symmetries to be a particular linear combination of Appell
hypergeometric functions. In this context the Bloch-Wigner function arises as a
special Yangian invariant in 4D. The bootstrap procedure for the box integral
is naturally structured in algorithmic form. We then discuss the Yangian
constraints for the six-point double box integral as well as for the related
hexagon. For the latter we argue that the constraints are solved by a set of
generalized Lauricella functions and we comment on complications in identifying
the integral as a certain linear combination of these. Finally, we elaborate on
the close relation to the Mellin-Barnes technique and argue that it generates
Yangian invariants as sums of residues.
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Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams: We show how Feynman amplitudes of standard QFT on flat and homogeneous space
can naturally be recast as the evaluation of observables for a specific spin
foam model, which provides dynamics for the background geometry. We identify
the symmetries of this Feynman graph spin foam model and give the gauge-fixing
prescriptions. We also show that the gauge-fixed partition function is
invariant under Pachner moves of the triangulation, and thus defines an
invariant of four-dimensional manifolds. Finally, we investigate the algebraic
structure of the model, and discuss its relation with a quantization of 4d
gravity in the limit where the Newton constant goes to zero.
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On Three-point Functions in the AdS_4/CFT_3 Correspondence: We calculate planar, tree-level, non-extremal three-point functions of
operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we
generalize the determinant representation, found by Foda for the three-point
functions of the SU(2) sector of N=4 SYM, to the present case and find that the
ABJM result up to normalization factors factorizes into a product of two N=4
SYM correlation functions. Secondly, we treat the case where two operators are
heavy and one is light and BPS, using a coherent state description of the heavy
ones. We show that when normalized by the three-point function of three BPS
operators the heavy-heavy-light correlation function agrees, in the
Frolov-Tseytlin limit, with its string theory counterpart which we calculate
holographically.
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Improving the five-point bootstrap: We present a new algorithm for the numerical evaluation of five-point
conformal blocks in $d$-dimensions, greatly improving the efficiency of their
computation. To do this we use an appropriate ansatz for the blocks as a series
expansion in radial coordinates, derive a set of recursion relations for the
unknown coefficients in the ansatz, and evaluate the series using a Pad\'e
approximant to accelerate its convergence. We then study the
$\langle\sigma\sigma\epsilon\sigma\sigma\rangle$ correlator in the 3d critical
Ising model by truncating the operator product expansion (OPE) and only
including operators with conformal dimension below a cutoff $\Delta\leqslant
\Delta_{\rm cutoff}$. We approximate the contributions of the operators above
the cutoff by the corresponding contributions in a suitable disconnected
five-point correlator. Using this approach, we compute a number of OPE
coefficients with greater accuracy than previous methods.
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Manton's five vortex equations from self-duality: We demonstrate that the five vortex equations recently introduced by Manton
ariseas symmetry reductions of the anti-self-dual Yang--Mills equations in four
dimensions. In particular the Jackiw--Pi vortex and the Ambj\o rn--Olesen
vortex correspond to the gauge group $SU(1, 1)$, and respectively the Euclidean
or the $SU(2)$ symmetry groups acting with two-dimensional orbits. We show how
to obtain vortices with higher vortex numbers, by superposing vortex equations
of different types. Finally we use the kinetic energy of the Yang--Mills theory
in 4+1 dimensions to construct a metric on vortex moduli spaces. This metric is
not positive-definite in cases of non-compact gauge groups.
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Open string instantons and superpotentials: We study the F-terms in N=1 supersymmetric, d=4 gauge theories arising from
D(p+3)-branes wrapping supersymmetric p-cycles in a Calabi-Yau threefold. If p
is even the spectrum and superpotential for a single brane are determined by
purely classical ($\alpha^\prime \to 0$) considerations. If p=3,
superpotentials for massless modes are forbidden to all orders in
$\alpha^\prime$ and may only be generated by open string instantons. For this
latter case we find that such instanton effects are generically present. Mirror
symmetry relates even and odd p and thus perturbative and nonperturbative
superpotentials; we provide a preliminary discussion of a class of examples of
such mirror pairs.
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Effects of dark energy on $P-V$ criticality and efficiency of charged
Rotational black hole: In this paper, we study $P-V$ criticality of Kerr-Newman $AdS$ black hole
with a quintessence field. We calculate critical quantities and show that for
the equation state parameter $\omega= -\frac{1}{3}$, the obtained universal
ratio ($\frac{P_{c}\upsilon_{c}}{T_{c}}$) is quite same as Kerr-Newman $AdS$
black hole without dark energy parameter. We investigate the influence of
quintessence field $\alpha$, equation state parameter $\omega$ and angular
momentum $J$ on the efficiency $\eta$. We find that $\eta$ is increased by
increasing $J$ and $\alpha$ and decreasing charge $Q$ of black hole. We show
when $\omega$ increases from $-1$ to $-\frac{1}{3}$ the efficiency decreases.
Also we study ratio $\frac{\eta}{\eta_{C}}$ (which $\eta_{C}$ is the Carnot
efficiency) and see that the second law of the thermodynamics is satisfied by
special values of $J$ and $\alpha$ and holds for any value of $Q$. We notice
that in this case by increasing $\omega$ from $-1$ to $-\frac{1}{3}$ the range
of $J$ and $\alpha$ increases.
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Toda-like (0,2) mirrors to products of projective spaces: One of the open problems in understanding (0,2) mirror symmetry concerns the
construction of Toda-like Landau-Ginzburg mirrors to (0,2) theories on Fano
spaces. In this paper, we begin to fill this gap by making an ansatz for (0,2)
Toda-like theories mirror to (0,2) supersymmetric nonlinear sigma models on
products of projective spaces, with deformations of the tangent bundle,
generalizing a special case previously worked out for P1xP1. We check this
ansatz by matching correlation functions of the B/2-twisted Toda-like theories
to correlation functions of corresponding A/2-twisted nonlinear sigma models,
computed primarily using localization techniques. These (0,2) Landau-Ginzburg
models admit redundancies, which can lend themselves to multiple
distinct-looking representatives of the same physics, which we discuss.
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Minimal Length Uncertainty Relation and gravitational quantum well: The dynamics of a particle in a gravitational quantum well is studied in the
context of nonrelativistic quantum mechanics with a particular deformation of a
two-dimensional Heisenberg algebra. This deformation yields a new
short-distance structure characterized by a finite minimal uncertainty in
position measurements, a feature it shares with noncommutative theories. We
show that an analytical solution can be found in perturbation and we compare
our results to those published recently, where noncommutative geometry at the
quantum mechanical level was considered. We find that the perturbations of the
gravitational quantum well spectrum in these two approaches have different
signatures. We also compare our modified energy spectrum to the results
obtained with the GRANIT experiment, where the effects of the Earth's
gravitational field on quantum states of ultra cold neutrons moving above a
mirror are studied. This comparison leads to an upper bound on the minimal
length scale induced by the deformed algebra we use. This upper bound is weaker
than the one obtained in the context of the hydrogen atom but could still be
useful if the deformation parameter of the Heisenberg algebra is not a
universal constant but a quantity that depends on the energetic content of the
system.
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N=2 supersymmetry in the twistor description of higher-spin holography: We study the holographic duality between higher-spin (HS) gravity in 4d and
free vector models in 3d, with special attention to the role of N=2
supersymmetry (SUSY). For the type-A bosonic bulk theory, dual to spin-0 fields
on the boundary, there exists a twistor-space description; this maps both
single-trace boundary operators and linearized bulk fields to
spacetime-independent twistor functions, whose HS-algebra products compute all
boundary correlators. Here, we extend this description to the type-B bosonic
theory (dual to spin-1/2 fields on the boundary), and to the supersymmetric
theory containing both. A key role is played by boundary bilocals, which in
type-A are dual to the Didenko-Vasiliev 1/2-BPS "black hole". We extend this to
an infinite family of linearized 1/2-BPS "black hole" solutions. Remarkably,
the full supersymmetric theory (along with the SUSY generators) fits in the
same space of twistor functions as the type-A theory. Instead of two sets of
bosonic bulk fields, the formalism sees one set of linearized fields, but with
both types of boundary data allowed.
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On α' corrections in N=1 F-theory compactifications: We consider N=1 F-theory and Type IIB orientifold compactifications and
derive new \alpha' corrections to the four-dimensional effective action. They
originate from higher derivative corrections to eleven-dimensional supergravity
and survive the M-theory to F-theory limit. We find a correction to the Kahler
moduli depending on a non-trivial intersection curve of seven-branes. We also
analyze a four-dimensional higher curvature correction.
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Instantons versus Monopoles: We review results of the last two years concerning caloron solutions of unit
charge with non-trivial holonomy, revealing the constituent monopole nature of
these instantons. For SU(n) there are n such BPS constituents. New is the
presentation of the exact values for the Polyakov loop at the three constituent
locations for the SU(3) caloron with arbitrary holonomy. At these points two
eigenvalues coincide, extending earlier results for SU(2) to a situation more
generic for general SU(n).
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Integrable Systems for Particles with Internal Degrees of Freedom: We show that a class of models for particles with internal degrees of freedom
are integrable. These systems are basically generalizations of the models of
Calogero and Sutherland. The proofs of integrability are based on a recently
developed exchange operator formalism. We calculate the wave-functions for the
Calogero-like models and find the ground-state wave-function for a
Calogero-like model in a position dependent magnetic field. This last model
might have some relevance for matrix models of open strings.
|
More on counterterms in the gravitational action and anomalies: The addition of boundary counterterms to the gravitational action of
asymptotically anti-de Sitter spacetimes permits us to define the partition
function unambiguously without background subtraction. We show that the
inclusion of p-form fields in the gravitational action requires the addition of
further counterterms which we explicitly identify. We also relate logarithmic
divergences in the action dependent on the matter fields to anomalies in the
dual conformal field theories. In particular we find that the anomaly predicted
for the correlator of the stress energy tensor and two vector currents in four
dimensions agrees with that of the ${\cal{N}} = 4$ superconformal SU(N) gauge
theory.
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Conformal invariant interaction of a scalar field with the higher spin
field in AdS_{D}: The explicit form of linearized gauge invariant interactions of scalar and
general higher even spin fields in the $AdS_{D}$ space is obtained. In the case
of general spin $\ell$ a generalized 'Weyl' transformation is proposed and the
corresponding 'Weyl' invariant action is constructed. In both cases the
invariant actions of the interacting higher even spin gauge field and the
scalar field include the whole tower of invariant actions for couplings of the
same scalar with all gauge fields of smaller even spin. For the particular
value of $\ell=4$ all results are in exact agreement with hep-th/0403241
|
Ghost-free higher-derivative theory: We present an example of the quantum system with higher derivatives in the
Lagrangian, which is ghost-free: the spectrum of the Hamiltonian is bounded
from below and unitarity is preserved.
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Is a truly marginal perturbation of the $G_k\times G_k$ WZNW model at
$k=-2c_V(G)$ an exception to the rule?: It is shown that there exists a truly marginal deformation of the direct sum
of two $G_k$ WZNW models at $k=-2c_V(G)$ (where $c_V(G)$ is the eigenvalue of
the quadratic Casimir operator in the adjoint representation of the group $G$)
which does not seem to fit the Chaudhuri-Schwartz criterion for truly marginal
perturbations. In addition, a continuous family of WZNW models is constructed.
|
Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrodinger
Equation: We show that the supersymmetric nonlinear Schr\"odinger equation is a
bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of
the theory from the ones of the supersymmetric two boson hierarchy through a
field redefinition. We also show how the two Hamiltonian structures of the
supersymmetric KdV equation can be derived from a Hamiltonian reduction of the
supersymmetric two boson hierarchy as well.
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The Nuts and Bolts of Brane Resolution: We construct various non-singular p-branes on higher-dimensional
generalizations of Taub-NUT and Taub-BOLT instantons. Among other solutions,
these include S^1-wrapped D3-branes and M5-branes, as well as deformed
M2-branes. The resulting geometries smoothly interpolate between product spaces
which include Minkowski elements of different dimensionality. The new solutions
do not preserve any supersymmetry.
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Supertwistor description of the $AdS$ pure spinor string: We describe the pure spinor string in the $AdS_5\times S^5$ using
unconstrained matrices first used by Roiban and Siegel for the Green-Schwarz
superstring.
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Two loop mass renormalisation in heterotic string theory: NS states: In this work computation of the renormalised mass at two loop order for the
NS sector of heterotic string theory is attempted. We first implement the
vertical integration prescription for choosing a section avoiding the spurious
poles due to the presence of a required number of picture changing operators.
As a result the relevant amplitude on genus 2 Riemann surface can be written as
a boundary term. We then identify the 1PI region of the moduli space having
chosen a gluing compatible local coordinates around the external punctures. We
also identify the relevant integrands and the relevant region of integration
for the modular parameters at the boundary.
|
Symmetries, Microcausality and Physics on Canonical Noncommutative
Spacetime: In this paper we describe how to implement symmetries on a canonical
noncommutative spacetime. We focus on noncommutative Lorentz transformations.
We then discuss the structure of the light cone on a canonical noncommutative
spacetime and show that field theories formulated on these spaces do not
violate mircocausality.
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Gauged supergravities and their symmetry-breaking vacua in F-theory: We first derive a class of six-dimensional (1,0) gauged supergravities
arising from threefold compactifications of F-theory with background fluxes.
The derivation proceeds via the M-theory dual reduction on an SU(3)-structure
manifold with four-form G_4-flux. We then show that vacuum solutions of these
six-dimensional theories describes four-dimensional flat space times a compact
two-dimensional internal space with additional localized sources. This induces
a spontaneous compactification to four space-time dimensions and breaks the
supersymmetry from N=2 to N=1, which allows the reduced theory to have a
four-dimensional chiral spectrum. We perform the reduction explicitly and
derive the N=1 characteristic data of the four-dimensional effective theory.
The match with fourfold reductions of F-theory is discussed and many of the
characteristic features are compared. We comment, in particular, on warping
effects and one-loop Chern-Simons terms generically present in four-dimensional
F-theory reductions.
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Remarks about Dyson's instability in the large-N limit: There are known examples of perturbative expansions in the 't Hooft coupling
lt with a finite radius of convergence. This seems to contradict Dyson's
argument suggesting that the instability at negative coupling implies a zero
radius of convergence. Using the example of the linear sigma model in three
dimensions, we discuss to which extent the two points of view are compatible.
We show that a saddle point persists for negative values of lt until a critical
value -|lt_c| is reached. A numerical study of the perturbative series for the
renormalized mass confirms an expected singularity of the form (lt
+|lt_c|)^1/2. However, for -|lt_c|< lt <0, the effective potential does not
exist if phi^2 >phi^2_{max}(lt) and not at all if lt<-|lt_c|. We show that
phi^2_{max}(lt) propto 1/|lt | for small negative lt. The finite radius of
convergence can be justified if the effective theory is defined with a large
field cutoff phi^2_{max}(lt) which provides a quantitative measure of the
departure from the original model considered.
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Time Dependent Couplings as Observables in de Sitter Space: We summarize and expand our investigations concerning the soft graviton
effects on microscopic matter dynamics in de Sitter space. The physical
couplings receive IR logarithmic corrections which are sensitive to the IR
cut-off at the one-loop level. The scale invariant spectrum in the
gravitational propagator at the super-horizon scale is the source of the de
Sitter symmetry breaking. The quartic scalar, Yukawa and gauge couplings become
time dependent and diminish with time. In contrast, the Newton's constant
increases with time. We clarify the physical mechanism behind these effects in
terms of the conformal mode dynamics in analogy with 2d quantum gravity. We
show that they are the inevitable consequence of the general covariance and
lead to gauge invariant predictions. We construct a simple model in which the
cosmological constant is self-tuned to vanish due to UV-IR mixing effect. We
also discuss phenomenological implications such as decaying Dark Energy and
SUSY breaking at the Inflation era. The quantum effect alters the classical
slow roll picture in general if the tensor-to-scalar ratio $r$ is as small as
$0.01$.
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From Fixed Points to the Fifth Dimension: 4D Lorentzian conformal field theory (CFT) is mapped into 5D anti-de Sitter
spacetime (AdS), from the viewpoint of "geometrizing" conformal current
algebra. A large-N expansion of the CFT is shown to lead to (infinitely many)
weakly coupled AdS particles, in one-to-one correspondence with
minimal-color-singlet CFT primary operators. If all but a finite number of
"protected" primary operators have very large scaling dimensions, it is shown
that there exists a low-AdS-curvature effective field theory regime for the
corresponding finite set of AdS particles. Effective 5D gauge theory and
General Relativity on AdS are derived in this way from the most robust examples
of protected CFT primaries, Noether currents of global symmetries and the
energy-momentum tensor. Witten's prescription for computing CFT local operator
correlators within the AdS dual is derived. The main new contribution is the
derivation of 5D locality of AdS couplings. This is accomplished by studying a
confining IR-deformation of the CFT in the large-N "planar" approximation,
where the discrete spectrum and existence of an S-matrix allow the constraints
of unitarity and crossing symmetry to be solved (in standard fashion) by a
tree-level expansion in terms of 4D local "glueball" couplings. When the
deformation is carefully removed, this 4D locality (with plausible technical
assumptions specifying its precise nature) combines with the restored conformal
symmetry to yield 5D AdS locality. The sense in which AdS/CFT duality
illustrates the possibility of emergent relativity, and the special role of
strong coupling, are briefly discussed. Care is taken to conclude each step
with well-defined mathematical expressions and convergent integrals.
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Gaudin Models and Multipoint Conformal Blocks III: Comb channel
coordinates and OPE factorisation: We continue the exploration of multipoint scalar comb channel blocks for
conformal field theories in 3D and 4D. The central goal here is to construct
novel comb channel cross ratios that are well adapted to perform projections
onto all intermediate primary fields. More concretely, our new set of cross
ratios includes three for each intermediate mixed symmetry tensor exchange.
These variables are designed such that the associated power series expansion
coincides with the sum over descendants. The leading term of this expansion is
argued to factorise into a product of lower point blocks. We establish this
remarkable factorisation property by studying the limiting behaviour of the
Gaudin Hamiltonians that are used to characterise multipoint conformal blocks.
For six points we can map the eigenvalue equations for the limiting Gaudin
differential operators to Casimir equations of spinning four-point blocks.
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Hamilton-Jacobi Renormalization for Lifshitz Spacetime: Just like AdS spacetimes, Lifshitz spacetimes require counterterms in order
to make the on-shell value of the bulk action finite. We study these
counterterms using the Hamilton-Jacobi method. Rather than imposing boundary
conditions from the start, we will derive suitable boundary conditions by
requiring that divergences can be canceled using only local counterterms. We
will demonstrate in examples that this procedure indeed leads to a finite bulk
action while at the same time it determines the asymptotic behavior of the
fields. This puts more substance to the belief that Lifshitz spacetimes are
dual to well-behaved field theories. As a byproduct, we will find the analogue
of the conformal anomaly for Lifshitz spacetimes.
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Consistent quantization of massless fields of any spin and the
generalized Maxwell's equations: A simplified formalism of first quantized massless fields of any spin is
presented. The angular momentum basis for particles of zero mass and finite
spin s of the D^(s-1/2,1/2) representation of the Lorentz group is used to
describe the wavefunctions. The advantage of the formalism is that by equating
to zero the s-1 components of the wave functions, the 2s-1 subsidiary
conditions (needed to eliminate the non-forward and non-backward helicities)
are automatically satisfied. Probability currents and Lagrangians are derived
allowing a first quantized formalism. A simple procedure is derived for
connecting the wave functions with potentials and gauge conditions. The spin 1
case is of particular interest and is described with the D^(1/2,1/2) vector
representation of the well known self-dual representation of the Maxwell's
equations. This representation allows us to generalize Maxwell's equations by
adding the E_0 and B_0 components to the electric and magnetic four-vectors.
Restrictions on their existence are discussed.
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Cosmological Particle Production at Strong Coupling: We study the dynamics of a strongly-coupled quantum field theory in a
cosmological spacetime using the holographic AdS/CFT correspondence.
Specifically we consider a confining gauge theory in an expanding FRW universe
and track the evolution of the stress-energy tensor during a period of
expansion, varying the initial temperature as well as the rate and amplitude of
the expansion. At strong coupling, particle production is inseparable from
entropy production. As a result, we find significant qualitative differences
from the weak coupling results: at strong coupling the system rapidly loses
memory of its initial state as the amplitude is increased. Furthermore, in the
regime where the Hubble parameter is parametrically smaller than the initial
temperature, the dynamics is well modelled as a plasma evolving
hydrodynamically towards equilibrium.
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Cluster Convergence Theorem: A power-counting theorem is presented, that is designed to play an analogous
role, in the proof of a BPHZ convergence theorem, in Euclidean position space,
to the role played by Weinberg's power-counting theorem, in Zimmermann's proof
of the BPHZ convergence theorem, in momentum space. If $x$ denotes a position
space configuration, of the vertices, of a Feynman diagram, and $\sigma$ is a
real number, such that $0 < \sigma < 1$, a $\sigma$-cluster, of $x$, is a
nonempty subset, $J$, of the vertices of the diagram, such that the maximum
distance, between any two vertices, in $J$, is less than $\sigma$, times the
minimum distance, from any vertex, in $J$, to any vertex, not in $J$. The set
of all the $\sigma$-clusters, of $x$, has similar combinatoric properties to a
forest, and the configuration space, of the vertices, is cut up into a finite
number of sectors, classified by the set of all their $\sigma$-clusters. It is
proved that if, for each such sector, the integrand can be bounded by an
expression, that satisfies a certain power-counting requirement, for each
$\sigma$-cluster, then the integral, over the position, of any one vertex, is
absolutely convergent, and the result can be bounded by the sum of a finite
number of expressions, of the same type, each of which satisfies the
corresponding power-counting requirements.
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The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability: The dilatation generator measures the scaling dimensions of local operators
in a conformal field theory. In this thesis we consider the example of
maximally supersymmetric gauge theory in four dimensions and develop and extend
techniques to derive, investigate and apply the dilatation operator.
We construct the dilatation operator by purely algebraic means: Relying on
the symmetry algebra and structural properties of Feynman diagrams we are able
to bypass involved, higher-loop field theory computations. In this way we
obtain the complete one-loop dilatation operator and the planar, three-loop
deformation in an interesting subsector. These results allow us to address the
issue of integrability within a planar four-dimensional gauge theory: We prove
that the complete dilatation generator is integrable at one-loop and present
the corresponding Bethe ansatz. We furthermore argue that integrability extends
to three-loops and beyond. Assuming that it holds indeed, we finally construct
a novel spin chain model at five-loops and propose a Bethe ansatz which might
be valid at arbitrary loop-order!
We illustrate the use of our technology in several examples and also present
two key applications for the AdS/CFT correspondence.
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Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic
Geometry: Rational coefficients of special functions in scattering amplitudes are known
to simplify on singular surfaces, often diverging less strongly than the
na\"ive expectation. To systematically study these surfaces and rational
functions on them, we employ tools from algebraic geometry. We show how the
divergences of a rational function constrain its numerator to belong to
symbolic powers of ideals associated to the singular surfaces. To study the
divergences of the coefficients, we make use of $p$-adic numbers, closely
related to finite fields. These allow us to perform numerical evaluations close
to the singular surfaces in a stable manner and thereby characterize the
divergences of the coefficients. We then use this information to construct
low-dimensional Ans\"atze for the rational coefficients. As a proof-of-concept
application of our algorithm, we reconstruct the two-loop $0 \rightarrow q\bar
q\gamma\gamma\gamma$ pentagon-function coefficients with fewer than 1000
numerical evaluations.
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Orbifolds of M-Theory and Type II String Theories in Two Dimensions: We consider several orbifold compactifications of M-theory and their
corresponding type II duals in two space-time dimensions. In particular, we
show that while the orbifold compactification of M-theory on $T^9/J_9$ is dual
to the orbifold compactification of type IIB string theory on $T^8/I_8$, the
same orbifold $T^8/I_8$ of type IIA string theory is dual to M-theory
compactified on a smooth product manifold $K3 \times T^5$. Similarly, while the
orbifold compactification of M-theory on $(K3 \times T^5)/\sigma ... J_5$ is
dual to the orbifold compactification of type IIB string theory on $(K3 \times
T^4)/\sigma ... I_4$, the same orbifold of type IIA string theory is dual to
the orbifold $T^4 \times (K3 \times S^1)/\sigma ... J_1$ of M-theory. The
spectrum of various orbifold compactifications of M-theory and type II string
theories on both sides are compared giving evidence in favor of these duality
conjectures. We also comment on a connection between Dasgupta-Mukhi-Witten
conjecture and Dabholkar-Park-Sen conjecture for the six-dimensional orbifold
models of type IIB string theory and M-theory.
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First Reduce or First Quantize? A Lagrangian Approach and Application to
Coset Spaces: A Lagrangian treatment of the quantization of first class Hamiltonian systems
with constraints and Hamiltonian linear and quadratic in the momenta
respectively is performed. The ``first reduce and then quantize'' and the
``first quantize and then reduce'' (Dirac's) methods are compared. A new source
of ambiguities in this latter approach is revealed and its relevance on issues
concerning self-consistency and equivalence with the ``first reduce'' method is
emphasized. One of our main results is the relation between the propagator
obtained {\it \`a la Dirac} and the propagator in the full space, eq. (5.25).As
an application of the formalism developed, quantization on coset spaces of
compact Lie groups is presented. In this case it is shown that a natural
selection of a Dirac quantization allows for full self-consistency and
equivalence. Finally, the specific case of the propagator on a two-dimensional
sphere $S^2$ viewed as the coset space $SU(2)/U(1)$ is worked out.
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4-string Junction and Its Network: We study a BPS configuration in which four strings (of different type) meet
at a point in $N = 2, D = 8$ supergravity, i.e., the low energy effective
theory of $T^2$-compactified type II string theory. We demonstrate that the
charge conservation of the four strings implies the vanishing of the net force
(due to the tensions of various strings) at the junction and vice versa, using
the tension formula for $SL(3, Z)$ strings obtained recently by the present
authors. We then show that a general 4-string junction preserves 1/8 of the
spacetime supersymmetries. Using 4-string junctions as building blocks, we
construct a string network which also preserves 1/8 of the spacetime
supersymmetries.
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Tree and $1$-loop fundamental BCJ relations from soft theorems: We provide a new derivation of the fundamental BCJ relation among double
color ordered tree amplitudes of bi-adjoint scalar theory, based on the leading
soft theorem for external scalars. Then, we generalize the fundamental BCJ
relation to $1$-loop Feynman integrands. We also use the fundamental BCJ
relation to understand the Adler's zero for tree amplitudes of non-linear Sigma
model and Born-Infeld theories.
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Seiberg dualities and the 3d/4d connection: We discuss the degeneration limits of d=4 superconformal indices that relate
Seiberg duality for the d=4 N=1 SQCD theory to Aharony and Giveon-Kutasov
dualities for d=3 N=2 SQCD theories. On a mathematical level we argue that this
3d/4d connection entails a new set of non-standard degeneration identities
between hyperbolic hypergeometric integrals. On a physical level we propose
that such degeneration formulae provide a new route to the still illusive
Seiberg dualities for d=3 N=2 SQCD theories with SU(N) gauge group.
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Integrable hierarchy underlying topological Landau-Ginzburg models of
D-type: A universal integrable hierarchy underlying topological Landau-Ginzburg
models of D-tye is presented. Like the dispersionless Toda hierarchy, the new
hierarchy has two distinct (``positive" and ``negative") set of flows. Special
solutions corresponding to topological Landau-Ginzburg models of D-type are
characterized by a Riemann-Hilbert problem, which can be converted into a
generalized hodograph transformation. This construction gives an embedding of
the finite dimensional small phase space of these models into the full space of
flows of this hierarchy. One of flat coordinates in the small phase space turns
out to be identical to the first ``negative" time variable of the hierarchy,
whereas the others belong to the ``positive" flows.
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Baryonic symmetries in AdS_4/CFT_3: an overview: Global symmetries play an important role in classifying the spectrum of a
gauge theory. In the context of the AdS/CFT duality, global baryon-like
symmetries are specially interesting. In the gravity side, they correspond to
vector fields in AdS arising from KK reduction of the SUGRA p-form potentials.
We concentrate on the AdS_4/CFT_3 case, which presents very interesting
characteristic features. Following arXiv:1004.2045, we review aspects of such
symmetries, clarifying along the way some arguments in that reference. As a
byproduct, and in a slightly unrelated context, we also study Z-minimization,
focusing in the HVZ theory.
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${\cal N}=2$ supersymmetric higher spin gauge theories and current
multiplets in three dimensions: We describe several families of primary linear supermultiplets coupled to
three-dimensional ${\cal N}=2$ conformal supergravity and use them to construct
topological $BF$-type terms. We introduce conformal higher-spin gauge
superfields and associate with them Chern-Simons-type actions that are
constructed as an extension of the linearised action for ${\cal N}=2$ conformal
supergravity. These actions possess gauge and super-Weyl invariance in any
conformally flat superspace and involve a higher-spin generalisation of the
linearised ${\cal N}=2$ super-Cotton tensor. For massless higher-spin
supermultiplets in (1,1) anti-de Sitter (AdS) superspace, we propose two
off-shell Lagrangian gauge formulations, which are related to each other by a
dually transformation. Making use of these massless theories allows us to
formulate consistent higher-spin supercurrent multiplets in (1,1) AdS
superspace. Explicit examples of such supercurrent multiplets are provided for
models of massive chiral supermultiplets. Off-shell formulations for massive
higher-spin supermultiplets in (1,1) AdS superspace are proposed.
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Entanglement between two disjoint universes: We use the replica method to compute the entanglement entropy of a universe
without gravity entangled in a thermofield-double-like state with a disjoint
gravitating universe. Including wormholes between replicas of the latter gives
an entropy functional which includes an "island" on the gravitating universe.
We solve the back-reaction equations when the cosmological constant is negative
to show that this island coincides with a causal shadow region that is created
by the entanglement in the gravitating geometry. At high entanglement
temperatures, the island contribution to the entropy functional leads to a
bound on entanglement entropy, analogous to the Page behavior of evaporating
black holes. We demonstrate that the entanglement wedge of the non-gravitating
universe grows with the entanglement temperature until, eventually, the
gravitating universe can be entirely reconstructed from the non-gravitating
one.
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On Gauge Equivalence of Tachyon Solutions in Cubic Neveu-Schwarz String
Field Theory: Simple analytic solution to cubic Neveu-Schwarz String Field Theory including
the $GSO(-)$ sector is presented. This solution is an analog of the
Erler-Schnabl solution for bosonic case and one of the authors solution for the
pure $GSO(+)$ case. Gauge transformations of the new solution to others known
solutions for the $NS$ string tachyon condensation are constructed explicitly.
This gauge equivalence manifestly supports the early observed fact that these
solutions have the same value of the action density.
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Exact solutions to quantum spectral curves by topological string theory: We generalize the conjectured connection between quantum spectral problems
and topological strings to many local almost del Pezzo surfaces with arbitrary
mass parameters. The conjecture uses perturbative information of the
topological string in the unrefined and the Nekrasov-Shatashvili limit to solve
non-perturbatively the quantum spectral problem. We consider the quantum
spectral curves for the local almost del Pezzo surfaces of $\mathbb{F}_2$,
$\mathbb{F}_1$, the blowup of $\mathbb{P}^2$ in two points and a mass
deformation of the $E_8$ del Pezzo corresponding to different deformations of
the three-term operators $\mathsf{O}_{1,1}$, $\mathsf{O}_{1,2}$ and
$\mathsf{O}_{2,3}$. To check the conjecture, we compare the predictions for the
spectrum of these operators with numerical results for the eigenvalues. We also
compute the first few fermionic spectral traces from the conjectural spectral
determinant, and we compare them to analytic and numerical results in spectral
theory. In all these comparisons, we find that the conjecture is fully
validated with high numerical precision. For local $\mathbb{F}_2$ we expand the
spectral determinant around the orbifold point and find intriguing relations
for Jacobi theta functions. We also give an explicit map between the geometries
of $\mathbb{F}_0$ and $\mathbb{F}_2$ as well as a systematic way to derive the
operators $\mathsf{O}_{m,n}$ from toric geometries.
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Viscous Asymptotically Flat Reissner-Nordström Black Branes: We study electrically charged asymptotically flat black brane solutions whose
world-volume fields are slowly varying with the coordinates. Using familiar
techniques, we compute the transport coefficients of the fluid dynamic
derivative expansion to first order. We show how the shear and bulk viscosities
are modified in the presence of electric charge and we compute the charge
diffusion constant which is not present for the neutral black p-brane. We
compute the first order dispersion relations of the effective fluid. For small
values of the charge the speed of sound is found to be imaginary and the brane
is thus Gregory-Laflamme unstable as expected. For sufficiently large values of
the charge, the sound mode becomes stable, however, in this regime the
hydrodynamic mode associated with charge diffusion is found to be unstable. The
electrically charged brane is thus found to be (classically) unstable for all
values of the charge density in agreement with general thermodynamic arguments.
Finally, we show that the shear viscosity to entropy bound is saturated, as
expected, while the proposed bounds for the bulk viscosity to entropy can be
violated in certain regimes of the charge of the brane.
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Zero Mode Effect Generalization for the Electromagnetic Current in the
Light Front: We consider in this work the electromagnetic current for a system composed by
two charged bosons and show that it has a structure of many bodies even in the
impulse approximation, when described in the light front time $x^+$. In terms
of the two-body component for the bound state, the current contains two-body
operators. We discuss the process of pair creation from the interacting photon
and interpret it as a zero mode contribution to the current and its
consequences for the components of currents in the light-front.
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Scalar-Tensor theories and current Cosmology: Scalar-tensor theories are studied in the context of cosmological evolution,
where the expansion history of the Universe is reconstructed. It is considered
quintessence/phantom models, where inflation and cosmic acceleration are
reproduced. Also, the non-minimally coupling regime between the scalar field
and the Ricci scalar is studied and cosmological solutions are obtained. The
Chamaleon mechanism is shown as a solution of the local gravity tests problems
presented in this kind of theories.
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Maintaining Gauge Symmetry in Renormalizing Chiral Gauge Theories: It is known that the $\gamma_{5}$ scheme of Breitenlohner and Maison (BM) in
dimensional regularization requires finite counter-term renormalization to
restore gauge symmetry and implementing this finite renormalization in
practical calculation is a daunting task even at 1-loop order. In this paper,
we show that there is a simple and straightforward method to obtain these
finite counter terms by using the rightmost $\gamma_{5}$ scheme in which we
move all the $\gamma_{5}$ matrices to the rightmost position before
analytically continuing the dimension. For any 1-loop Feynman diagram, the
difference between the amplitude regularized in the rightmost $\gamma_{5}$
scheme and the amplitude regularized in the BM scheme can be easily calculated.
The differences for all 1-loop diagrams in the chiral Abelian-Higgs gauge
theory and in the chiral non-Abelian gauge theory are shown to be the same as
the amplitudes due to the finite counter terms that are required to restore
gauge symmetry.
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Statefinder Diagnostic for Born-Infeld Type Dark Energy Model: Using a new method--statefinder diagnostic which can differ one dark energy
model from the others, we investigate in this letter the dynamics of
Born-Infeld(B-I) type dark energy model. The evolutive trajectory of B-I type
dark energy with Mexican hat potential model with respect to $e-folding$ time
$N$ is shown in the $r(s)$ diagram. When the parameter of noncanonical kinetic
energy term $\eta\to0$ or kinetic energy $\dot{\phi}^2\to0$, B-I type dark
energy(K-essence) model reduces to Quintessence model or $\Lambda$CDM model
corresponding to the statefinder pair $\{r, s\}$=$\{1, 0\}$ respectively. As a
result, the the evolutive trajectory of our model in the $r(s)$ diagram in
Mexican hat potential is quite different from those of other dark energy
models.
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A Note on a Standard Embedding on Half-Flat Manifolds: It is argued that the ten dimensional solution that corresponds to the
compactification of $E_8 \times E_8$ heterotic string theory on a half-flat
manifold is the product space-time $R^{1,2} \times Z_7$ where $Z_7$ is a
generalized cylinder with $G_2$ riemannian holonomy. Standard embedding on
$Z_7$ then implies an embedding on the half-flat manifold which involves the
torsionful connection rather than the Levi-Civita connection. This leads to the
breakdown of $E_8 \times E_8$ to $E_6 \times E_8$, as in the case of the
standard embedding on Calabi-Yau manifolds, which agrees with the result
derived recently by Gurrieri, Lukas and Micu (arXiv:0709.1932) using a
different approach. Green-Schwarz anomaly cancellation is then implemented via
the torsionful connection on half-flat manifolds.
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Supersymmetry in 5d Gravity: We study a 5d gravity theory with a warped metric and show that two N = 2
supersymmetric quantum-mechanical systems are hidden in the 4d spectrum. The
supersymmetry can be regarded as a remnant of higher-dimensional general
coordinate invariance and turns out to become a powerful tool to determine the
physical 4d spectrum and the allowed boundary conditions. Possible extensions
of the N = 2 supersymmetry are briefly discussed.
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Finite-gap systems, tri-supersymmetry and self-isospectrality: We show that an n-gap periodic quantum system with parity-even smooth
potential admits $2^n-1$ isospectral super-extensions. Each is described by a
tri-supersymmetry that originates from a higher-order differential operator of
the Lax pair and two-term nonsingular decompositions of it; its local part
corresponds to a spontaneously partially broken centrally extended nonlinear
N=4 supersymmetry. We conjecture that any finite-gap system having antiperiodic
singlet states admits a self-isospectral tri-supersymmetric extension with the
partner potential to be the original one translated for a half-period. Applying
the theory to a broad class of finite-gap elliptic systems described by a
two-parametric associated Lame equation, our conjecture is supported by the
explicit construction of the self-isospectral tri-supersymmetric pairs. We find
that the spontaneously broken tri-supersymmetry of the self-isospectral
periodic system is recovered in the infinite period limit.
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The Physics of Negative Energy Densities: I review some recent results showing that the physics of negative energy
densities, as predicted by relativistic quantum field theories, is more
complicated than has generally been appreciated. On the one hand, in external
potentials where there is a time--dependence, however slight, the Hamiltonians
are unbounded below. On the other, there are limitations of quantum measurement
in detecting or utilizing these negative energies.
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Three Dimensional Quantum Chromodynamics: The subject of this talk was the review of our study of three ($2+1$)
dimensional Quantum Chromodynamics. In our previous works, we showed the
existence of a phase where parity is unbroken and the flavor group $U(2n)$ is
broken to a subgroup $U(n)\times U(n)$. We derived the low energy effective
action for the theory and showed that it has solitonic excitations with Fermi
statistic, to be identified with the three dimensional ``baryon''. Finally, we
studied the current algebra for this effective action and we found a
co-homologically non trivial generalization of Kac-Moody algebras to three
dimensions.
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Spectral Form Factor in Non-Gaussian Random Matrix Theories: We consider Random Matrix Theories with non-Gaussian potentials that have a
rich phase structure in the large $N$ limit. We calculate the Spectral Form
Factor (SFF) in such models and present them as interesting examples of
dynamical models that display multi-criticality at short time-scales and
universality at large time scales. The models with quartic and sextic
potentials are explicitly worked out. The disconnected part of the Spectral
Form Factor (SFF) shows a change in its decay behavior exactly at the critical
points of each model. The dip-time of the SFF is estimated in each of these
models. The late time behavior of all polynomial potential matrix models is
shown to display a certain universality. This is related to the universality in
the short distance correlations of the mean-level densities. We speculate on
the implications of such universality for chaotic quantum systems including the
SYK model.
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Joint Statistics of Cosmological Constant and SUSY Breaking in Flux
Vacua with Nilpotent Goldstino: We obtain the joint distribution of the gravitino mass and the cosmological
constant in KKLT and LVS models with anti-D3 brane uplifting described via the
nilpotent goldstino formalism. Moduli stabilisation (of both complex structure
and Kaehler moduli) is incorporated so that we sample only over points
corresponding to vacua. Our key inputs are the distributions of the flux
superpotential, the string coupling and the hierarchies of warped throats. In
the limit of zero cosmological constant, we find that both in KKLT and LVS the
distributions are tilted favourably towards lower scales of supersymmetry
breaking.
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Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two-
and Three Dimensional Euclidean Space: Path integral formulations for the Smorodinsky-Winternitz potentials in two-
and three-dimen\-sional Euclidean space are presented. We mention all
coordinate systems which separate the Smorodinsky-Winternitz potentials and
state the corresponding path integral formulations. Whereas in many coordinate
systems an explicit path integral formulation is not possible, we list in all
soluble cases the path integral evaluations explicitly in terms of the
propagators and the spectral expansions into the wave-functions.
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Symplectic realizations and Lie groupoids in Poisson Electrodynamics: We define the gauge potentials of Poisson electrodynamics as sections of a
symplectic realization of the spacetime manifold and infinitesimal gauge
transformations as a representation of the associated Lie algebroid acting on
the symplectic realization. Finite gauge transformations are obtained by
integrating the sections of the Lie algebroid to bisections of a symplectic
groupoid, which form a one-parameter group of transformations, whose action on
the fields of the theory is realized in terms of an action groupoid. A
covariant electromagnetic two-form is obtained, together with a dual two-form,
invariant under gauge transformations. The duality appearing in the picture
originates from the existence of a pair of orthogonal foliations of the
symplectic realization, which produce dual quotient manifolds, one related with
space-time, the other with momenta.
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Measuring finite Quantum Geometries via Quasi-Coherent States: We develop a systematic approach to determine and measure numerically the
geometry of generic quantum or "fuzzy" geometries realized by a set of
finite-dimensional hermitian matrices. The method is designed to recover the
semi-classical limit of quantized symplectic spaces embedded in $\mathbb{R}^d$
including the well-known examples of fuzzy spaces, but it applies much more
generally. The central tool is provided by quasi-coherent states, which are
defined as ground states of Laplace- or Dirac operators corresponding to
localized point branes in target space. The displacement energy of these
quasi-coherent states is used to extract the local dimension and tangent space
of the semi-classical geometry, and provides a measure for the quality and
self-consistency of the semi-classical approximation. The method is discussed
and tested with various examples, and implemented in an open-source Mathematica
package.
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Study of Gribov Copies in the Yang-Mills ensemble: Recently, based on a new procedure to quantize the theory in the continuum,
it was argued that Singer's theorem points towards the existence of a
Yang-Mills ensemble. In the new approach, the gauge fields are mapped into an
auxiliary field space used to separately fix the gauge on different sectors
labeled by center vortices. In this work, we study this procedure in more
detail. We provide examples of configurations belonging to sectors labeled by
center vortices and discuss the existence of nonabelian degrees of freedom.
Then, we discuss the importance of the mapping injectivity, and show that this
property holds infinitesimally for typical configurations of the vortex-free
sector and for the simplest example in the one-vortex sector. Finally, we show
that these configurations are free from Gribov copies.
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Thermodynamics of Near BPS Black Holes in AdS$_4$ and AdS$_7$: We develop the thermodynamics of black holes in AdS$_4$ and AdS$_7$ near
their BPS limit. In each setting we study the two distinct deformations
orthogonal to the BPS surface as well as their nontrivial interplay with each
other and with BPS properties. Our results illuminate recent microscopic
calculations of the BPS entropy. We show that these microscopic computations
can be leveraged to also describe the near BPS regime, by generalizing the
boundary conditions imposed on states.
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Low energy effective theory on a regularized brane in six-dimensional
flux compactifications: Conical brane singularities in six-dimensional flux compactification models
can be resolved by introducing cylindrical codimension-one branes with regular
caps instead of 3-branes (a la Kaluza-Klein braneworlds with fluxes). In this
paper, we consider such a regularized braneworld with axial symmetry in
six-dimensional Einstein-Maxwell theory. We derive a low energy effective
theory on the regularized brane by employing the gradient expansion approach,
and show that standard four-dimensional Einstein gravity is recovered at low
energies. Our effective equations extend to the nonlinear gravity regime,
implying that conventional cosmology can be reproduced in the regularized
braneworld.
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Strings on AdS Wormholes and Nonsingular Black Holes: Certain AdS black holes in the STU model can be conformally scaled to
wormhole and black hole solutions of an f(R) type theory which have two
asymptotically AdS regions and are completely free of curvature singularities.
While there is a delta-function source for the dilaton, classical string probes
are not sensitive to this singularity. If the AdS/CFT correspondence can be
applied in this context, then the wormhole background describes a phase in
which two copies of a conformal field theory interact with each other, whereas
the nonsingular black hole describes entangled states. By studying the behavior
of open strings on these backgrounds, we extract a number of features of the
quarks and anti-quarks that live in the field theories. In the interacting
phase, we find that there is a maximum speed with which the quarks can move
without losing energy, beyond which energy is transferred from a quark in one
field theory to a quark in the other. We also compute the rate at which moving
quarks within entangled states lose energy to the two surrounding plasmas.
While a quark-antiquark pair within a single field theory exhibits Coulomb
interaction for small separation, a quark in one field theory exhibits
spring-like confinement with an anti-quark in the other field theory. For the
entangled states, we study how the quark-antiquark screening length depends on
temperature and chemical potential. In the interacting phase of the two field
theories, a quadruplet made up of one quark-antiquark pair in each field theory
can undergo transitions involving how the quarks and antiquarks are paired in
terms of the screening.
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Doubly Supersymmetric Null Strings and String Tension Generation: We propose a twistor--like formulation of N=1, D=3,4,6 and 10 null
superstrings. The model possesses N=1 target space supersymmetry and n=D-2
local worldsheet supersymmetry, the latter replaces the kappa-symmetry of the
conventional approach to the strings. Adding a Wess--Zumino term to a null
superstring action we observe a string tension generation mechanism: the
induced worldsheet metric becomes non-degenerate and the resulting model turns
out to be classically equivalent to the heterotic string.
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On the Deformation of Time Harmonic Flows: It is shown that time-harmonic motions of spherical and toroidal surfaces can
be deformed non-locally without loosing the existence of infinitely many
constants of the motion.
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Gauge Zero-Modes on ALE Manifolds: In this paper we find the general (i.e. valid for arbitrary values of the
winding number) form of the gauge zero-modes, in the adjoint representation,
for theories living on manifolds of the ALE type.
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Lectures on non-equilibrium effective field theories and fluctuating
hydrodynamics: We review recent progress in developing effective field theories (EFTs) for
non-equilibrium processes at finite temperature, including a new formulation of
fluctuating hydrodynamics, and a new proof of the second law of thermodynamics.
There are a number of new elements in formulating EFTs for such systems.
Firstly, the nature of IR variables is very different from those of a system in
equilibrium or near the vacuum. Secondly, while all static properties of an
equilibrium system can in principle be extracted from the partition function,
there appears no such quantity which can capture all non-equilibrium
properties. Thirdly, non-equilibrium processes often involve dissipation, which
is notoriously difficult to deal with using an action principle. The purpose of
the review is to explain how to address these issues in a pedagogic manner,
with fluctuating hydrodynamics as a main example.
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Transverse spin in the light-ray OPE: We study a product of null-integrated local operators $\mathcal{O}_1$ and
$\mathcal{O}_2$ on the same null plane in a CFT. Such null-integrated operators
transform like primaries in a fictitious $d-2$ dimensional CFT in the
directions transverse to the null integrals. We give a complete description of
the OPE in these transverse directions. The terms with low transverse spin are
light-ray operators with spin $J_1+J_2-1$. The terms with higher transverse
spin are primary descendants of light-ray operators with higher spins
$J_1+J_2-1+n$, constructed using special conformally-invariant differential
operators that appear precisely in the kinematics of the light-ray OPE. As an
example, the OPE between average null energy operators contains light-ray
operators with spin $3$ (as described by Hofman and Maldacena), but also novel
terms with spin $5,7,9,$ etc.. These new terms are important for describing
energy two-point correlators in non-rotationally-symmetric states, and for
computing multi-point energy correlators. We check our formulas in a
non-rotationally-symmetric energy correlator in $\mathcal{N}=4$ SYM, finding
perfect agreement.
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Helical Phase Inflation and Monodromy in Supergravity Theory: We study helical phase inflation in supergravity theory in details. The
inflation is driven by the phase component of a complex field along helical
trajectory. The helicoid structure originates from the monodromy of
superpotential with an singularity at origin.
We show that such monodromy can be formed by integrating out heavy fields in
supersymmetric field theory. The supergravity corrections to the potential
provide strong field stabilizations for the scalars except inflaton, therefore
the helical phase inflation accomplishes the "monodromy inflation" within
supersymmetric field theory.
The phase monodromy can be easily generalized for natural inflation, in which
the super-Planckian phase decay constant is realized with consistent field
stabilization. The phase-axion alignment is fulfilled indirectly in the process
of integrating out the heavy fields.
Besides, we show that the helical phase inflation can be naturally realized
in no-scale supergravity with $SU(2,1)/SU(2)\times U(1)$ symmetry since the
no-scale K\"ahler potential provides symmetry factors of phase monodromy
directly. We also demonstrate that the helical phase inflation can reduce to
the shift symmetry realization of supergravity inflation. The super-Planckian
field excursion is accomplished by the phase component, which admits no
dangerous polynomial higher order corrections. The helical phase inflation
process is free from the UV-sensitivity problem, and it suggests that inflation
can be effectively studied in supersymmetric field theory close to the
unification scale in Grand Unified Theory and a UV-completed frame is not
prerequisite.
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Noninvariant renormalization in the background-field method: We investigate the consistency of the background-field formalism when
applying various regularizations and renormalization schemes. By an example of
a two-dimensional $\sigma$ model it is demonstrated that the background-field
method gives incorrect results when the regularization (and/or renormalization)
is noninvariant. In particular, it is found that the cut-off regularization and
the differential renormalization belong to this class and are incompatible with
the background-field method in theories with nonlinear symmetries.
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Quantum $φ^4$ Theory in AdS${}_4$ and its CFT Dual: We compute the two- and four-point holographic correlation functions up to
the second order in the coupling constant for a scalar $\phi^4$ theory in
four-dimensional Euclidean anti-de Sitter space. Analytic expressions for the
anomalous dimensions of the leading twist operators are found at one loop, both
for Neumann and Dirichlet boundary conditions.
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Dirac Spectra and Real QCD at Nonzero Chemical Potential: We show that QCD Dirac spectra well below Lambda_{QCD}, both at zero and at
nonzero chemical potential, can be obtained from a chiral Lagrangian. At
nonzero chemical potential Goldstone bosons with nonzero baryon number condense
beyond a critical value. Such superfluid phase transition is likely to occur in
any system with a chemical potential with the quantum numbers of the Goldstone
bosons. We discuss the phase diagram for one such system, QCD with two colors,
and show the existence of a tricritical point in an effective potential
approach.
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Topological partition function and string-string duality: The evidence for string/string-duality can be extended from the matching of
the vector couplings to gravitational couplings. In this note this is shown in
the rank three example, the closest stringy analog of the Seiberg/Witten-setup,
which is related to the Calabi-Yau $WP^4_{1,1,2,2,6}(12)$. I provide an exact
analytical verification of a relation checked by coefficient comparison to
fourth order by Kaplunovsky, Louis and Theisen.
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Quantum Gravity and Phenomenology: Dark Matter, Dark Energy, Vacuum
Selection, Emergent Spacetime, and Wormholes: We discuss the relevance of quantum gravity to the frontier questions in high
energy phenomenology: the problems of dark matter, dark energy, and vacuum
selection as well as the problems of emergent spacetime and wormholes. Dark
matter and dark energy phenomenology, and the problem of vacuum selection are
discussed within the context of string theory as a model of quantum gravity.
Emergent spacetime and wormholes are discussed in a more general context of
effective theories of quantum gravity.
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A note on quantum groups and integrable systems: Free-field formalism for quantum groups provides a special choice of
coordinates on a quantum group. In these coordinates the construction of
associated integrable system is especially simple. This choice also fits into
general framework of cluster varieties -- natural changes of coordinates are
cluster mutations.
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Five-Dimensional Eguchi-Hanson Solitons in Einstein-Gauss-Bonnet Gravity: Eguchi-Hanson solitons are odd-dimensional generalizations of the
four-dimensional Eguchi-Hanson metric and are asymptotic to
AdS$_5$\mathbb{Z}_p$ when the cosmological constant is either positive or
negative. We find soliton solutions to Lovelock gravity in 5 dimensions that
are generalizations of these objects.
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One-loop Yukawa Couplings in Local Models: We calculate the one-loop Yukawa couplings and threshold corrections for
supersymmetric local models of branes at singularities in type IIB string
theory. We compute the corrections coming both from wavefunction and vertex
renormalisation. The former comes in the IR from conventional field theory
running and in the UV from threshold corrections that cause it to run from the
winding scale associated to the full Calabi-Yau volume. The vertex correction
is naively absent as it appears to correspond to superpotential
renormalisation. However, we find that while the Wilsonian superpotential is
not renormalised there is a physical vertex correction in the 1PI action
associated to light particle loops.
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Heterotic Modular Invariants and Level--Rank Duality: New heterotic modular invariants are found using the level-rank duality of
affine Kac-Moody algebras. They provide strong evidence for the consistency of
an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field
theories. We call the basic construction the dual-flip, since it flips
chirality (exchanges left and right movers) and takes the level-rank dual. We
compare the dual-flip to the method of conformal subalgebras, another way of
constructing heterotic invariants. To do so, new level-one heterotic invariants
are first found; the complete list of a specified subclass of these is
obtained. We also prove (under a mild hypothesis) an old conjecture concerning
exceptional $A_{r,k}$ invariants and level-rank duality.
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Duality and modular symmetry in the quantum Hall effect from Lifshitz
holography: The temperature dependence of quantum Hall conductivities is studied in the
context of the AdS/CMT paradigm using a model with a bulk theory consisting of
(3+1)-dimensional Einstein-Maxwell action coupled to a dilaton and an axion,
with a negative cosmological constant. We consider a solution which has a
Lifshitz like geometry with a dyonic black-brane in the bulk. There is an
$Sl(2,R)$ action in the bulk corresponding to electromagnetic duality, which
maps between classical solutions, and is broken to $Sl(2,Z)$ by Dirac
quantisation of dyons. This bulk $Sl(2,Z)$ action translates to an action of
the modular group on the 2-dimensional transverse conductivities. The
temperature dependence of the infra-red conductivities is then linked to
modular forms via gradient flow and the resulting flow diagrams show remarkable
agreement with existing experimental data on the temperature flow of both
integral and fractional quantum Hall conductivities.
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Notes on reductions of superstring theory to bosonic string theory: It is in general very subtle to integrate over the odd moduli of super
Riemann surfaces in perturbative superstring computations. We study how these
subtleties go away in favorable cases, including the embedding of N=0 string to
N=1 string by Berkovits and Vafa, and the relation of the graviphoton amplitude
and the topological string amplitude by Antoniadis, Gava, Narain and Taylor and
Bershadsky, Cecotti, Ooguri and Vafa. The Poincar\'e dual of the moduli space
of Riemann surfaces in the moduli space of super Riemann surfaces plays an
important role.
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On the General Structure of the Non-Abelian Born-Infeld Action: We discuss the general structure of the non-abelian Born-Infeld action,
together with all of the alpha-prime derivative corrections, in flat
D-dimensional space-time. More specifically, we show how the connection between
open strings propagating in background magnetic fields and gauge theories on
non-commutative spaces can be used to constrain the form of the effective
action for the massless modes of open strings at week coupling. In particular,
we exploit the invariance in form of the effective action under a change of
non-commutativity scale of space-time to derive algebraic equations relating
the various terms in the alpha- prime expansion. Moreover, we explicitly solve
these equations in the simple case D=2, and we show, in particular, how to
construct the minimal invariant derivative extension of the NBI action.
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Two more solutions for the parafermionic chiral algebra Z_{3} with the
dimension of the principal parafermionic fields, psi(z), psi^{+}(z),
Delta_{psi}=8/3: In this paper, which is the second one in a series of two papers, we shall
present two more solutions, non-minimal ones, for the Z_{3} parafermionic
chiral algebra with Delta_{psi}=Delta_{psi^{+}}=8/3, psi(z), psi^{+}(z) being
the principal parafermionic fields.
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A quantum group version of quantum gauge theories in two dimensions: For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi
i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in
two dimensions. We exhibit the similarities to Witten's combinatorial approach
which is based on ideas of Migdal. The main ingredient is the Turaev-Viro
combinatorial construction of topological invariants of closed, compact
3-manifolds and its extension to arbitrary compact 3-manifolds as given by the
authors in collaboration with W. Mueller.
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The Tachyon at the End of the Universe: We show that a tachyon condensate phase replaces the spacelike singularity in
certain cosmological and black hole spacetimes in string theory. We analyze
explicitly a set of examples with flat spatial slices in various dimensions
which have a winding tachyon condensate, using worldsheet path integral methods
from Liouville theory. In a vacuum with no excitations above the tachyon
background in the would-be singular region, we analyze the production of closed
strings in the resulting state in the bulk of spacetime. We find a thermal
result reminiscent of the Hartle-Hawking state, with tunably small energy
density. The amplitudes exhibit a self-consistent truncation of support to the
weakly-coupled small-tachyon region of spacetime. We argue that the background
is accordingly robust against back reaction, and that the resulting string
theory amplitudes are perturbatively finite, indicating a resolution of the
singularity and a mechanism to start or end time in string theory. Finally, we
discuss the generalization of these methods to examples with positively curved
spatial slices.
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Gauge Coupling Instability and Dynamical Mass Generation in N=1
Supersymmetric QED(3): Using superfield Dyson-Schwinger equations, we compute the infrared dynamics
of the semi-amputated full vertex, corresponding to the effective running gauge
coupling, in N-flavour {\mathcal N}=1 supersymmetric QED(3). It is shown that
the presence of a supersymmetry-preserving mass for the matter multiplet
stabilizes the infrared gauge coupling against oscillations present in the
massless case, and we therefore infer that the massive vacuum is thus selected
at the level of the (quantum) effective action. We further demonstrate that
such a mass can indeed be generated dynamically in a self-consistent way by
appealing to the superfield Dyson-Schwinger gap equation for the full matter
propagator.
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Aspects of U-duality in BLG models with Lorentzian metric 3-algebras: In our previous paper, it was shown that BLG model based on a Lorentzian
metric 3-algebra gives Dp-brane action whose worldvolume is compactified on
torus T^d (d=p-2). Here the 3-algebra was a generalized one with d+1 pairs of
Lorentzian metric generators and expressed in terms of a loop algebra with
central extensions. In this paper, we derive the precise relation between the
coupling constant of the super Yang-Mills, the moduli of T^d and some R-R flux
with VEV's of ghost fields associated with Lorentzian metric generators. In
particular, for d=1, we derive the Yang-Mills action with theta term and show
that SL(2,Z) Montonen-Olive duality is realized as the rotation of two VEV's.
Furthermore, some moduli parameters such as NS-NS 2-form flux are identified as
the deformation parameters of the 3-algebras. By combining them, we recover
most of the moduli parameters which are required by U-duality symmetry.
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Nearby CFT's in the operator formalism: The role of a connection: There are two methods to study families of conformal theories in the operator
formalism. In the first method we begin with a theory and a family of deformed
theories is defined in the state space of the original theory. In the other
there is a distinct state space for each theory in the family, with the
collection of spaces forming a vector bundle. This paper establishes the
equivalence of a deformed theory with that in a nearby state space in the
bundle via a connection that defines maps between nearby state spaces. We find
that an appropriate connection for establishing equivalence is one that arose
in a recent paper by Kugo and Zwiebach. We discuss the affine geometry induced
on the space of backgrounds by this connection. This geometry is the same as
the one obtained from the Zamolodchikov metric.
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The Peculiarity of a Negative Coordinate Axis in Dyonic Solutions of
Noncommutative N=4 Super Yang-Mills: We show that in a certain region of a negative coordinate axis, the
U(1amaharia) sector of the static dyonic solutions to the noncommutative U(4)
N=4 Super Yang-Mills (SYM) can be consistently decoupled from the SU(4) to {\it
all orders in the noncommutativity parameter}. We show the above decoupling in
two ways. First, we show the noncommutative dyon being the same as the
commutative dyon, is a consistent solution to noncommutative equations of
motion in that region of noncommutative space. Second, as an example of
decoupling of a non-null U(1) sector, we also obtain a family of solutions with
nontrivial U(1) components for {\it all} components of the gauge field in the
same region of noncommutative space. In both cases, the SU(4) and U(1)
components separately satisfy the equations of motion.
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Nonreductive WZW models and their CFTs: We study two-dimensional WZW models with target space a nonreductive Lie
group. Such models exist whenever the Lie group possesses a bi-invariant
metric. We show that such WZW models provide a lagrangian description of the
nonreductive (affine) Sugawara construction. We investigate the gauged WZW
models and we prove that gauging a diagonal subgroup results in a conformal
field theory which can be identified with a coset construction. A large class
of exact four-dimensional string backgrounds arise in this fashion. We then
study the topological conformal field theory resulting from the $G/G$ coset. We
identify the Kazama algebra extending the BRST algebra, and the BV algebra
structure in BRST cohomology which it induces.
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Cosmic optical activity from an inhomogeneous Kalb-Ramond field: The effects of introducing a harmonic spatial inhomogeneity into the
Kalb-Ramond field, interacting with the Maxwell field according to a
`string-inspired' proposal made in earlier work are investigated. We examine in
particular the effects on the polarization of synchrotron radiation from
cosmologically distant (i.e. of redshift greater than 2) galaxies, as well as
the relation between the electric and magnetic components of the radiation
field. The rotation of the polarization plane of linearly polarized radiation
is seen to acquire an additional contribution proportional to the square of the
frequency of the dual Kalb-Ramond axion wave, assuming that it is far smaller
compared to the frequency of the radiation field.
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Multiplicative renormalization and Hopf algebras: We derive the existence of Hopf subalgebras generated by Green's functions in
the Hopf algebra of Feynman graphs of a quantum field theory. This means that
the coproduct closes on these Green's functions. It allows us for example to
derive Dyson's formulas in quantum electrodynamics relating the renormalized
and bare proper functions via the renormalization constants and the analogous
formulas for non-abelian gauge theories. In the latter case, we observe the
crucial role played by Slavnov--Taylor identities.
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New insights in particle dynamics from group cohomology: The dynamics of a particle moving in background electromagnetic and
gravitational fields is revisited from a Lie group cohomological perspective.
Physical constants characterising the particle appear as central extension
parameters of a group which is obtained from a centrally extended kinematical
group (Poincare or Galilei) by making local some subgroup. The corresponding
dynamics is generated by a vector field inside the kernel of a presymplectic
form which is derived from the canonical left-invariant one-form on the
extended group. A non-relativistic limit is derived from the geodesic motion
via an Inonu-Wigner contraction. A deeper analysis of the cohomological
structure reveals the possibility of a new force associated with a non-trivial
mixing of gravity and electromagnetism leading to in principle testable
predictions.
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Deliberations on 11D Superspace for the M-Theory Effective Action: In relation to the superspace modifications of 11D supergeometry required to
describe the M-theory low-energy effective action, we present an analysis of
infinitesimal supergravity fluctuations about the flat superspace limit. Our
investigation confirms Howe's interpretation of our previous Bianchi identity
analysis. However, the analysis also shows that should 11D supergravity obey
the rules of other off-shell supergravity theories, the complete M-theory
corrections will necessarily excite our previously anticipated spin-1/2
engineering dimension-1/2 spinor auxiliary multiplet superfield. The analysis
of fluctuations yields more evidence that Howe's 1997 theorem is specious when
applied to Poincar\' e supergravity or 11D supergravity/M-theory. We end by
commenting upon recent advances in this area.
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Real and virtual photons in an external constant electromagnetic field
of most general form: The photon behavior in an arbitrary superposition of constant magnetic and
electric fields is considered on most general grounds basing on the first
principles like Lorentz- gauge- charge- and parity-invariance. We make model-
and approximation-independent, but still rather informative, statements about
the behavior that the requirement of causal propagation prescribes to massive
and massless branches of dispersion curves, and describe the way the eigenmodes
are polarized. We find, as a consequence of Hermiticity in the transparency
domain, that adding a smaller electric field to a strong magnetic field in
parallel to the latter causes enhancement of birefringence. We find the
magnetic field produced by a point electric charge far from it (a manifestation
of magneto-electric phenomenon). We establish degeneracies of the polarization
tensor that (under special kinematic conditions) occur due to space-time
symmetries of the vacuum left after the external field is imposed.
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Wess-Zumino term in the N=4 SYM effective action revisited: The low-energy effective action for the N=4 super Yang-Mills on the Coulomb
branch is known to include an SO(6)-invariant Wess-Zumino (WZ) term for the six
scalar fields. For each maximal, non-anomalous subgroup of the SU(4)
R-symmetry, we find a four-dimensional form of the WZ term with this subgroup
being manifest. We then show that a recently proposed expression for the
four-derivative part of the effective action in N=4 USp(4) harmonic superspace
yields the WZ term with manifest SO(5) R-symmetry subgroup. The N=2 SU(2)
harmonic superspace form of the effective action produces the WZ term with
manifest SO(4) x SO(2). We argue that there is no four-dimensional form of the
WZ term with manifest SU(3) R-symmetry, which is relevant for N=1 and N=3
superspace formulations of the effective action.
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An extension of Birkhoff's theorem to a class of 2-d gravity theories
containing black holes: A class of 2-dimensional models including 2-d dilaton gravity, spherically
symmetric reduction of d-dimensional Einstein gravity and other related
theories are classically analyzed. The general analytic solutions in the
absence of matter fields other than a U(1) gauge field are obtained under a new
gauge choice and recast in the conventional conformal gauge. These solutions
imply that Birkhoff's theorem, originally applied to spherically symmetric 4-d
Einstein gravity, can be applied to all models we consider. Some issues related
to the coupling of massless scalar fields and the quantization are briefly
discussed.
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Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras: Darboux coordinates are constructed on rational coadjoint orbits of the
positive frequency part $\wt{\frak{g}}^+$ of loop algebras. These are given by
the values of the spectral parameters at the divisors corresponding to
eigenvector line bundles over the associated spectral curves, defined within a
given matrix representation. A Liouville generating function is obtained in
completely separated form and shown, through the Liouville-Arnold integration
method, to lead to the Abel map linearization of all Hamiltonian flows induced
by the spectral invariants. Serre duality is used to define a natural
symplectic structure on the space of line bundles of suitable degree over a
permissible class of spectral curves, and this is shown to be equivalent to the
Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general
construction is given for $\frak{g}=\frak{gl}(r)$ or $\frak{sl}(r)$, with
reductions to orbits of subalgebras determined as invariant fixed point sets
under involutive automorphisms. The case $\frak{g=sl}(2)$ is shown to reproduce
the classical integration methods for finite dimensional systems defined on
quadrics, as well as the quasi-periodic solutions of the cubically nonlinear
Schr\"odinger equation. For $\frak{g=sl}(3)$, the method is applied to the
computation of quasi-periodic solutions of the two component coupled nonlinear
Schr\"odinger equation.
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Perturbative Relations between Gravity and Gauge Theory: We review the relations that have been found between multi-loop scattering
amplitudes in gauge theory and gravity, and their implications for ultraviolet
divergences in supergravity.
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Induced Lorentz-Violating Chern-Simons Term in QED: Uncovering Short
Distance Interaction Terms in the Effective Lagrangian without the Shadow of
Regularization: We show that the correctly evaluated effective Lagrangian should include
short-distance interaction terms which have been avoided under the protection
of usual regularization and must be properly identified and reinstated if
regularization is to be removed. They have special physical and mathematical
significance as well as restoring gauge invariance and suppressing divergence
in the effective Lagrangian. The rich structure of the short-distance
interaction terms can open up challenging opportunities where the conventional
regularization with rigid structure is unavailable and inappropriate. It
becomes clear that gauge invariance is preserved with or without regularization
and therefore there is no Lorentz-Violating Chern-Simons term in QED.
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The Role of Solvable Groups in Quantization of Lie Algebras: The elements of the wide class of quantum universal enveloping algebras are
prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups.
Such quantum algebras are quantum groups for simply connected solvable Lie
groups $P(H)$. This provides utilities for a new algorithm of constructing
quantum algebras especially useful for nonsemisimple ones. The quantization
procedure can be carried out over an arbitrary field. The properties of the
algorithm are demonstrated on examples.
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Loop Variables and Gauge Invariant Interactions of Massive Modes in
String Theory: The loop variable approach used earlier to obtain free equations of motion
for the massive modes of the open string, is generalized to include interaction
terms. These terms, which are polynomial, involve only modes of strictly lower
mass. Considerations based on operator product expansions suggest that these
equations are particular truncations of the full string equations. The method
involves broadening the loop to a band of finite thickness that describes all
the different interacting strings. Interestingly, in terms of these variables,
the theory appears non-interacting.
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On the anatomy of multi-spin magnon and single spike string solutions: We study rigid string solutions rotating in $AdS_5\times S^5$ background. For
particular values of the parameters of the solutions we find multispin
solutions corresponding to giant magnons and single spike strings. We present
an analysis of the dispersion relations in the case of three spin solutions
distributed only in $S^5$ and the case of one spin in $AdS_5$ and two spins in
$S^5$. The possible relation of these string solutions to gauge theory
operators and spin chains are briefly discussed.
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Non Pauli-Fierz Massive Gravitons: We study general Lorentz invariant theories of massive gravitons. We show
that, contrary to the standard lore, there exist consistent theories where the
graviton mass term violates Pauli-Fierz structure. For theories where the
graviton is a resonance this does not imply the existence of a scalar ghost if
the deviation from Pauli-Fierz becomes sufficiently small at high energies.
These types of mass terms are required by any consistent realization of the DGP
model in higher dimension.
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AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model: We study dual geometries to a deformed ABJM model with spatially dependent
source functions at finite temperature. These source functions are proportional
to the mass function $m(x)= m_0 \sin k x$ and its derivative $m'(x)$. As dual
geometries, we find hairy black branes and AdS solitons corresponding to
deconfinement phase and confining phase of the dual field theory, respectively.
It turns out that the hairy AdS solitons have lower free energy than the black
branes when the Hawking temperature is smaller than the confining scale.
Therefore the dual system undergoes the first order phase transition. Even
though our study is limited to the so-called Q-lattice ansatz, the solution
space contains a set of solutions dual to a supersymmetric mass deformation. As
a physical quantity to probe the confining phase, we investigate the
holographic entanglement entropy and discuss its behavior in terms of
modulation effect.
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On the nonclassicality in quantum JT gravity: In this note, we consider the question of classicality for the theory which
is known to be the effective description of two-dimensional black holes - the
Morse quantum mechanics. We calculate the Wigner function and the Fisher
information characterizing classicality/quantumness of single-particle systems
and briefly discuss further directions to study.
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The Weyl Double Copy for Gravitational Waves: We establish the status of the Weyl double copy relation for radiative
solutions of the vacuum Einstein equations. We show that all type N vacuum
solutions, which describe the radiation region of isolated gravitational
systems with appropriate fall-off for the matter fields, admit a degenerate
Maxwell field that squares to give the Weyl tensor. The converse statement also
holds, i.e. if there exists a degenerate Maxwell field on a curved background,
then the background is type N. This relation defines a scalar that satisfies
the wave equation on the background. We show that for non-twisting radiative
solutions, the Maxwell field and the scalar also satisfy the Maxwell equation
and the wave equation on Minkowski spacetime. Hence, non-twisting solutions
have a straightforward double copy interpretation.
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Unwinding the Amplituhedron in Binary: We present new, fundamentally combinatorial and topological characterizations
of the amplituhedron. Upon projecting external data through the amplituhedron,
the resulting configuration of points has a specified (and maximal) generalized
'winding number'. Equivalently, the amplituhedron can be fully described in
binary: canonical projections of the geometry down to one dimension have a
specified (and maximal) number of 'sign flips' of the projected data. The
locality and unitarity of scattering amplitudes are easily derived as
elementary consequences of this binary code. Minimal winding defines a natural
'dual' of the amplituhedron. This picture gives us an avatar of the
amplituhedron purely in the configuration space of points in vector space
(momentum-twistor space in the physics), a new interpretation of the canonical
amplituhedron form, and a direct bosonic understanding of the scattering
super-amplitude in planar N = 4 SYM as a differential form on the space of
physical kinematical data.
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Kinetic and Magnetic Mixing with Antisymmetric Gauge Fields: A general procedure to describe the coupling $U_A (1) \times U_B (1)$ between
antisymmetric gauge fields is proposed. For vector gauge theories the inclusion
of magnetic mixing in the hidden sector induces millicharges -- in principle --
observable. We extend the analysis to antisymmetric fields and the extension to
higher order monopoles is discussed. A modification of the model discussed in
\cite{Ibarra} with massless antisymmetric fields as dark matter is also
considered and the total cross section ratio are found and discussed.
|
Infrared-safe scattering without photon vacuum transitions and
time-dependent decoherence: Scattering in 3+1-dimensional QED is believed to give rise to transitions
between different photon vacua. We show that these transitions can be removed
by taking into account off-shell modes which correspond to Li\'enard-Wiechert
fields of asymptotic states. This makes it possible to formulate scattering in
3+1-dimensional QED on a Hilbert space which furnishes a single representation
of the canonical commutation relations (CCR). Different QED selection sectors
correspond to inequivalent representations of the photon CCR and are stable
under the action of an IR finite, unitary S-matrix. Infrared divergences are
cancelled by IR radiation. Using this formalism, we discuss the time-dependence
of decoherence and phases of out-going density matrix elements in the presence
of classical currents. The results demonstrate that although no information
about a scattering process is stored in strictly zero-energy modes of the
photon field, entanglement between charged matter and low energy modes
increases over time.
|
G-structures and Domain Walls in Heterotic Theories: We consider heterotic string solutions based on a warped product of a
four-dimensional domain wall and a six-dimensional internal manifold,
preserving two supercharges. The constraints on the internal manifolds with
SU(3) structure are derived. They are found to be generalized half-flat
manifolds with a particular pattern of torsion classes and they include
half-flat manifolds and Strominger's complex non-Kahler manifolds as special
cases. We also verify that previous heterotic compactifications on half-flat
mirror manifolds are based on this class of solutions.
|
Fermionic R-Operator for the Fermion Chain Model: The integrability of the one-dimensional (1D) fermion chain model is
investigated in the framework of the Quantum Inverse Scattering Method (QISM).
We introduce a new R-operator for the fermion chain model, which is expressed
in terms of the fermion operators. The R-operator satisfies a new type of the
Yang-Baxter relation with fermionic L-operator. We derive the fermionic
Sutherland equation from the relation, which is equivalent to the fermionic Lax
equation. It also provides a mathematical foundation of the boost operator
approach for the fermion model. In fact, we obtain some higher conserved
quantities of the fermion model using the boost operator.
|
ODE/IM correspondence and modified affine Toda field equations: We study the two-dimensional affine Toda field equations for affine Lie
algebra $\hat{\mathfrak{g}}$ modified by a conformal transformation and the
associated linear equations. In the conformal limit, the associated linear
problem reduces to a (pseudo-)differential equation. For classical affine Lie
algebra $\hat{\mathfrak{g}}$, we obtain a (pseudo-)differential equation
corresponding to the Bethe equations for the Langlands dual of the Lie algebra
$\mathfrak{g}$, which were found by Dorey et al. in study of the ODE/IM
correspondence.
|
The emergence of noncommutative target space in noncritical string
theory: We show how a noncommutative phase space appears in a natural way in
noncritical string theory, the noncommutative deformation parameter being the
string coupling.
|
Some Issues in Non-commutative Tachyon Condensation: Techniques of non-commutative field theories have proven to be useful in
describing D-branes as tachyonic solitons in open string theory. However, this
procedure also leads to unwanted degeneracy of solutions not present in the
spectrum of D-branes in string theories. In this paper we explore the
possibility that this apparent multiplicity of solutions is due to the wrong
choice of variables in describing the solutions, and that with the correct
choice of variables the unwanted degeneracy disappears.
|
Hidden Conformal Symmetry of Rotating Black Hole with four Charges: Kerr/CFT correspondence exhibits many remarkable connections between the near
horizon Kerr black hole and a CFT. Recently, a hidden conformal symmetry in the
solution space of Kerr black hole is shown by Castro, Maloney and Strominger.
Applying the formula on a rotating black hole with four independent U(1)
charges derived in string theory which is known as the 4D Cvetic-Youm solution,
we show that the same hidden conformal symmetry is also held. The temperatures
we derived match the Cardy formula correctly and we give a clarification about
old explains on them. The calculation on entropy and absorption cross section
is also given, which totally agrees with the previous results. This work
together with previous ones in this series, robustly support the validity of
the way in which the hidden conformal symmetry is derived, and reflect the
evidence of Kerr/CFT correspondence.
|
Chen's Iterated Integral represents the Operator Product Expansion: The recently discovered formalism underlying renormalization theory, the Hopf
algebra of rooted trees, allows to generalize Chen's lemma. In its generalized
form it describes the change of a scale in Green functions, and hence relates
to the operator product expansion. Hand in hand with this generalization goes
the generalization of the ordinary factorial $n!$ to the tree factorial $t^!$.
Various identities on tree-factorials are derived which clarify the relation
between Connes-Moscovici weights and Quantum Field Theory.
|
The complete Kaluza-Klein spectra of $\mathcal{N} = 1$ and $\mathcal{N}
= 0$ M-theory on $AdS_4 \times (\text{squashed } S^7)$: The squashed seven-sphere operator spectrum is completed by deriving the
spectrum of the spin-3/2 operator. The implications of the results for the
$AdS_4$ $\mathcal{N} = 1$ supermultiplets obtained from compactification of
eleven-dimensional supergravity are analysed. The weak $G_2$ holonomy plays an
important role when solving the eigenvalue equations on the squashed sphere.
Here, a novel and more universal algebraic approach to the whole eigenvalue
problem on coset manifolds is provided. Having obtained full control of all the
operator spectra, we can finally determine the irreps $D(E_0, s)$ for all
supermultiplets in the left-squashed vacuum. This includes an analysis of
possible boundary conditions. By performing an orientation flip on the
seven-sphere, we also obtain the full spectrum for the non-supersymmetric
right-squashed compactification which is of interest in the swampland context
and in particular for the $AdS$ swampland conjecture. Here, a number of
boundary condition ambiguities arise making the analysis of dual marginal
operators somewhat involved. This work is a direct continuation of [1] and [2].
|
Supercharge Operator of Hidden Symmetry in the Dirac Equation: As is known, the so-called Dirac $K$-operator commutes with the Dirac
Hamiltonian for arbitrary central potential $V(r)$. Therefore the spectrum is
degenerate with respect to two signs of its eigenvalues. This degeneracy may be
described by some operator, which anticommutes with $K$. If this operator
commutes with the Dirac Hamiltonian at the same time, then it establishes new
symmetry, which is Witten's supersymmetry. We construct the general
anticommuting with $K$ operator, which under the requirement of this symmetry
unambiguously select the Coulomb potential. In this particular case our
operator coincides with that, introduced by Johnson and Lippmann many years
ago.
|
Charged scalar quasi-normal modes for higher-dimensional Born-Infeld
dilatonic black holes with Lifshitz scaling: We study quasi-normal modes for a higher dimensional black hole with Lifshitz
scaling, as these quasi-normal modes can be used to test Lifshitz models with
large extra dimensions. Furthermore, as the effective Planck scale is brought
down in many models with large extra dimensions, we study these quasi-normal
modes for a UV completion action. Thus, we analyze quasi-normal modes for
higher dimensional dilaton-Lifshitz black hole solutions coupled to a
non-linear Born-Infeld action. We will analyze the charged perturbations for
such a black hole solution. We will first analyze the general conditions for
stability analytically, for a positive potential. Then, we analyze this system
for a charged perturbation as well as negative potential, using the asymptotic
iteration method for quasi-normal modes. Thus, we analyze the behavior of these
modes numerically.
|
On the Berezin Description of Kahler Quotients: We survey geometric quantization of finite dimensional affine Kahler
manifolds. Its corresponding prequantization and the Berezin's deformation
quantization formulation, as proposed by Cahen et al., is used to quantize
their corresponding Kahler quotients. Equivariant formalism greatly facilitates
the description.
|
The renormalized Hamiltonian truncation method in the large $E_T$
expansion: Hamiltonian Truncation Methods are a useful numerical tool to study strongly
coupled QFTs. In this work we present a new method to compute the exact
corrections, at any order, in the Hamiltonian Truncation approach presented by
Rychkov et al. in Refs. [1-3]. The method is general but as an example we
calculate the exact $g^2$ and some of the $g^3$ contributions for the $\phi^4$
theory in two dimensions. The coefficients of the local expansion calculated in
Ref. [1] are shown to be given by phase space integrals. In addition we find
new approximations to speed up the numerical calculations and implement them to
compute the lowest energy levels at strong coupling. A simple diagrammatic
representation of the corrections and various tests are also introduced.
|
A minimal b ghost: The $b$ ghost, or $b$ operator, used for fixing Siegel gauge in the pure
spinor superfield formalism, is a composite operator of negative ghost number,
satisfying $\{q,b\}=\square$, where $q$ is the pure spinor differential (BRST
operator). It is traditionally constructed using non-minimal variables.
However, since all cohomology has minimal representatives, it seems likely that
there should be versions of physically meaningful operators, also with negative
ghost number, using only minimal variables. The purpose of this letter is to
demonstrate that this statement holds by providing a concrete construction in
$D=10$ super-Yang-Mills theory, and to argue that it is a general feature in
the pure spinor superfield formalism.
|
Democratic Lagrangians for Nonlinear Electrodynamics: We construct a Lagrangian for general nonlinear electrodynamics that features
electric and magnetic potentials on equal footing. In the language of this
Lagrangian, discrete and continuous electric-magnetic duality symmetries can be
straightforwardly imposed, leading to a simple formulation for theories with
the $SO(2)$ duality invariance. When specialized to the conformally invariant
case, our construction provides a manifestly duality-symmetric formulation of
the recently discovered ModMax theory. We briefly comment on a natural
generalization of this approach to $p$-forms in $2p+2$ dimensions.
|
Alice and Bob in an anisotropic expanding spacetime: We investigate a quantum teleportation process between two comoving observers
Alice and Bob in an anisotropic expanding spacetime. In this model, we
calculate the fidelity of teleportation and we noted an oscillation of its
spectrum as a function of the azimuthal angle. We found that for the polar
angle $\phi = \frac{\pi}{2}$ and the azimuthal angle $\theta \neq
\frac{3\pi}{4} + n\pi$ with $n = 0, 1, 2, ...$ the efficiency of the process
decreases, i.e., the fidelity is less than one. In addition, it is shown that
the anisotropic effects on the fidelity becomes more significative in the
regime of smooth expansion and the limit of massless particles. On the other
hand, the influence of curvature coupling becomes noticeable in the regime of
fast expansion (values of $\frac{\rho}{\omega} \gg 1$).
|
p-adic CFT is a holographic tensor network: The p-adic AdS/CFT correspondence relates a CFT living on the p-adic numbers
to a system living on the Bruhat-Tits tree. Modifying our earlier proposal for
a tensor network realization of p-adic AdS/CFT, we prove that the path integral
of a p-adic CFT is equivalent to a tensor network on the Bruhat-Tits tree, in
the sense that the tensor network reproduces all correlation functions of the
p-adic CFT. Our rules give an explicit tensor network for any p-adic CFT (as
axiomatized by Melzer), and can be applied not only to the p-adic plane, but
also to compute any correlation functions on higher genus p-adic curves.
Finally, we apply them to define and study RG flows in p-adic CFTs,
establishing in particular that any IR fixed point is itself a p-adic CFT.
|
A new regularization of loop integral, no divergence, no hierarchy
problem: We find a new regularization scheme which is motivated by the Bose-Einstein
condensation. The energy of the virtual particle is considered as discrete.
Summing them and regulating the summation by the Riemann $\zeta$ function can
give the result of loop integral. All the divergences vanish, we can get almost
the same results as Dimensional Regularization. The prediction beyond
Dimensional Regularization is also shown in the QED. The hierarchy problem of
the radiative correction of scalar mass completely vanish.
|
Conductivity bounds in probe brane models: We discuss upper and lower bounds on the electrical conductivity of finite
temperature strongly coupled quantum field theories, holographically dual to
probe brane models, within linear response. In a probe limit where disorder is
introduced entirely through an inhomogeneous background charge density, we find
simple lower and upper bounds on the electrical conductivity in arbitrary
dimensions. In field theories in two spatial dimensions, we show that both
bounds persist even when disorder is included in the bulk metric. We discuss
the challenges with finding sharp lower bounds on conductivity in three or more
spatial dimensions when the metric is inhomogeneous.
|
Exact bounds on the free energy in QCD: We consider the free energy $W[J] = W_k(H)$ of QCD coupled to an external
source $J_\mu^b(x) = H_\mu^b \cos(k \cdot x)$, where $H_\mu^b$ is, by analogy
with spin models, an external "magnetic" field with a color index that is
modulated by a plane wave. We report an optimal bound on $W_k(H)$ and an exact
asymptotic expression for $W_k(H)$ at large $H$. They imply confinement of
color in the sense that the free energy per unit volume $W_k(H)/V$ and the
average magnetization $m(k, H) ={1 \over V} {\p W_k(H) \over \p H}$ vanish in
the limit of constant external field $k \to 0$. Recent lattice data indicate a
gluon propagator $D(k)$ which is non-zero, $D(0) \neq 0$, at $k = 0$. This
would imply a non-analyticity in $W_k(H)$ at $k = 0$. We also give some general
properties of the free energy $W(J)$ for arbitrary $J(x)$. Finally we present a
model that is consistent with the new results and exhibits (non)-analytic
behavior. Direct numerical tests of the bounds are proposed.
|
Building an explicit de Sitter: We construct an explicit example of a de Sitter vacuum in type IIB string
theory that realizes the proposal of K\"ahler uplifting. As the large volume
limit in this method depends on the rank of the largest condensing gauge group
we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric
Calabi-Yau threefolds. We find large numbers of models with the largest gauge
group factor easily exceeding a rank of one hundred. We construct a global
model with K\"ahler uplifting on a two-parameter model on
$\mathbb{CP}^4_{11169}$, by an explicit analysis from both the type IIB and
F-theory point of view. The explicitness of the construction lies in the
realization of a D7 brane configuration, gauge flux and RR and NS flux choices,
such that all known consistency conditions are met and the geometric moduli are
stabilized in a metastable de Sitter vacuum with spontaneous GUT scale
supersymmetry breaking driven by an F-term of the K\"ahler moduli.
|
What is Special Kähler Geometry ?: The scalars in vector multiplets of N=2 supersymmetric theories in 4
dimensions exhibit `special Kaehler geometry', related to duality symmetries,
due to their coupling to the vectors. In the literature there is some confusion
on the definition of special geometry. We show equivalences of some definitions
and give examples which show that earlier definitions are not equivalent, and
are not sufficient to restrict the Kaehler metric to one that occurs in N=2
supersymmetry. We treat the rigid as well as the local supersymmetry case. The
connection is made to moduli spaces of Riemann surfaces and Calabi-Yau 3-folds.
The conditions for the existence of a prepotential translate to a condition on
the choice of canonical basis of cycles.
|
Asymptotic safety in $O(N)$ scalar models coupled to gravity: We extend recent results on scalar-tensor theories to the case of an
O(N)-invariant multiplet. Some exact fixed point solutions of the RG flow
equations are discussed. We find that also in the functional context, on
employing a standard "type-I" cutoff, too many scalars destroy the
gravitational fixed point. For d=3 we show the existence of the gravitationally
dressed Wilson-Fisher fixed point also for N>1. We discuss also the results of
the analysis for a different, scalar-free, coarse-graining scheme.
|
Helicity Decomposition of Ghost-free Massive Gravity: We perform a helicity decomposition in the full Lagrangian of the class of
Massive Gravity theories previously proven to be free of the sixth (ghost)
degree of freedom via a Hamiltonian analysis. We demonstrate, both with and
without the use of nonlinear field redefinitions, that the scale at which the
first interactions of the helicity-zero mode come in is $\Lambda_3=(M_Pl
m^2)^{1/3}$, and that this is the same scale at which helicity-zero
perturbation theory breaks down. We show that the number of propagating
helicity modes remains five in the full nonlinear theory with sources. We
clarify recent misconceptions in the literature advocating the existence of
either a ghost or a breakdown of perturbation theory at the significantly lower
energy scales, $\Lambda_5=(M_Pl m^4)^{1/5}$ or $\Lambda_4=(M_Pl m^3)^{1/4}$,
which arose because relevant terms in those calculations were overlooked. As an
interesting byproduct of our analysis, we show that it is possible to derive
the Stueckelberg formalism from the helicity decomposition, without ever
invoking diffeomorphism invariance, just from a simple requirement that the
kinetic terms of the helicity-two, -one and -zero modes are diagonalized.
|
The Geometry of 6D, N = (1,0) Superspace and its Matter Couplings: This thesis is dedicated to the study of the geometry of six-dimensional
superspace, endowed with the minimal amount of supersymmetry. In the first part
of it, we unfold the main geometrical features of such superspace by solving
completely the Bianchi identities for the constrained superspace torsion, which
allow us to determine the full six-dimensional derivate superalgebra. Next, the
conformal structure of the supergeometry is considered. Specifically, it is
shown that the conventional torsion constraints remain invariant under
super-Weyl transformations generated by a real scalar superfield parameter. In
the second part of this work, the field content and superconformal matter
couplings of the supergeometry are explored. The component field content of the
Weyl multiplet is presented and the question of how this multiplet emerges in
superspace is addressed. Finally, the constraints that conformal invariance
imposes on some matter representations are analyzed.
|
Non-orientable surfaces and electric-magnetic duality: We consider the reduction along two compact directions of a twisted N=4 gauge
theory on a 4-dimensional orientable manifold which is not a global product of
two surfaces but contains a non-orientable surface. The low energy theory is a
sigma-model on a 2-dimensional worldsheet with a boundary which lives on branes
constructed from the Hitchin moduli space of the non-orientable surface. We
modify 't Hooft's notion of discrete electric and magnetic fluxes in gauge
theory due to the breaking of discrete symmetry and we match these fluxes with
the homotopy classes of maps in sigma-model. We verify the mirror symmetry of
branes as predicted by S-duality in gauge theory.
|
Superstring vertex operators in type IIB matrix model: We clarify the relation between the vertex operators in type IIB matrix model
and superstring. Green-Schwarz light-cone closed superstring theory is obtained
from IIB matrix model on two dimensional noncommutative backgrounds.
Superstring vertex operators should be reproduced from those of IIB matrix
model through this connection. Indeed, we confirm that supergravity vertex
operators in IIB matrix model on the two dimensional backgrounds reduce to
those in superstring theory. Noncommutativity plays an important role in our
identification. Through this correspondence, we can reproduce superstring
scattering amplitudes from IIB matrix model.
|
Hypermoduli Stabilization, Flux Attractors, and Generating Functions: We study stabilization of hypermoduli with emphasis on the effects of
generalized fluxes. We find a class of no-scale vacua described by ISD
conditions even in the presence of geometric flux. The associated flux
attractor equations can be integrated by a generating function with the
property that the hypermoduli are determined by a simple extremization
principle. We work out several orbifold examples where all vector moduli and
many hypermoduli are stabilized, with VEVs given explicitly in terms of fluxes.
|
Paragrassmann Analysis and Quantum Groups: Paragrassmann algebras with one and many paragrassmann variables are
considered from the algebraic point of view without using the Green ansatz.
Operators of differentiation with respect to paragrassmann variables and a
covariant para-super-derivative are introduced giving a natural generalization
of the Grassmann calculus to a paragrassmann one. Deep relations between
paragrassmann algebras and quantum groups with deformation parameters being
roots of unity are established.
|
Lovelock theories, holography and the fate of the viscosity bound: We consider Lovelock theories of gravity in the context of AdS/CFT. We show
that, for these theories, causality violation on a black hole background can
occur well in the interior of the geometry, thus posing more stringent
constraints than were previously found in the literature. Also, we find that
instabilities of the geometry can appear for certain parameter values at any
point in the geometry, as well in the bulk as close to the horizon. These new
sources of causality violation and instability should be related to CFT
features that do not depend on the UV behavior. They solve a puzzle found
previously concerning unphysical negative values for the shear viscosity that
are not ruled out solely by causality restrictions. We find that, contrary to
previous expectations, causality violation is not always related to positivity
of energy. Furthermore, we compute the bound for the shear viscosity to entropy
density ratio of supersymmetric conformal field theories from d=4 till d=10 -
i.e., up to quartic Lovelock theory -, and find that it behaves smoothly as a
function of d. We propose an approximate formula that nicely fits these values
and has a nice asymptotic behavior when d goes to infinity for any Lovelock
gravity. We discuss in some detail the latter limit. We finally argue that it
is possible to obtain increasingly lower values for the shear viscosity to
entropy density ratio by the inclusion of more Lovelock terms.
|
Regularization by $\varepsilon$-metric. II. Limit $\varepsilon = + 0$: In a wide class of propagators regularized by the $\varepsilon$-metric [1],
the $R$-operation is formulated. It is proved that the limit of renormalized
Feynman integrals exists and is covariant. Possible applications in gravity are
discussed. (The paper is an English translation of the second of two articles
in Russian published by the author in 1987-88: V.D. Ivashchuk, Regularization
by $\varepsilon$-metric. II. Limit $\varepsilon = +0$, Izvestiya Akademii Nauk
Moldavskoy SSR, Ser. fiziko-tekhnicheskih i matematicheskih nauk, No. 1, p.
10-20 (1988) [in Russian] .)
|
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