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Quantum gravitational corrections to the propagator in spacetimes with
constant curvature: The existence of a minimal and fundamental length scale, say, the Planck
length, is a characteristic feature of almost all the models of quantum
gravity. The presence of the fundamental length is expected to lead to an
improved ultra-violet behavior of the semi-classical propagators. The
hypothesis of path integral duality provides a prescription to evaluate the
modified propagator of a free, quantum scalar field in a given spacetime,
taking into account the existence of the fundamental length in a locally
Lorentz invariant manner. We use this prescription to compute the quantum
gravitational modifications to the propagators in spacetimes with constant
curvature, and show that: (i) the modified propagators are ultra-violet finite,
and (ii) the modifications are non-perturbative in the Planck length. We
discuss the implications of our results. | Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear
Sigma Model: It is well-known that the standard BCFW construction cannot be used for
on-shell amplitudes in effective field theories due to bad behavior for large
shifts. We show how to solve this problem in the case of the SU(N) non-linear
sigma model, i.e. non-renormalizable model with infinite number of interaction
vertices, using scaling properties of the semi-on-shell currents, and we
present new on-shell recursion relations for all on-shell tree-level amplitudes
in this theory. |
A Feynman integral via higher normal functions: We study the Feynman integral for the three-banana graph defined as the
scalar two-point self-energy at three-loop order. The Feynman integral is
evaluated for all identical internal masses in two space-time dimensions. Two
calculations are given for the Feynman integral; one based on an interpretation
of the integral as an inhomogeneous solution of a classical Picard-Fuchs
differential equation, and the other using arithmetic algebraic geometry,
motivic cohomology, and Eisenstein series. Both methods use the rather special
fact that the Feynman integral is a family of regulator periods associated to a
family of K3 surfaces. We show that the integral is given by a sum of elliptic
trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm
value is related to the regulator of a class in the motivic cohomology of the
K3 family. We prove a conjecture by David Broadhurst that at a special
kinematical point the Feynman integral is given by a critical value of the
Hasse-Weil L-function of the K3 surface. This result is shown to be a
particular case of Deligne's conjectures relating values of L-functions inside
the critical strip to periods. | Single Extra Dimension from $κ$-Poincaré and Gauge Invariance: We show that $\kappa$-Poincar\'e invariant gauge theories on
$\kappa$-Minkowski space with physically acceptable commutative (low energy)
limit must be 5-d. The gauge invariance requirement of the action fixes the
dimension of the $\kappa$-Minkowski space to $d=5$ and selects the unique
twisted differential calculus with which the construction can be achieved. We
characterize a BRST symmetry related to the 5-d noncommutative gauge invariance
though the definition of a nilpotent operation, which is used to construct a
gauge-fixed action. We also consider standard scenarios assuming
(compactification of) flat extra dimension, for which the 5-d deformation
parameter $\kappa$ can be viewed as the bulk 5-d Planck mass. We study physical
properties of the resulting 4-d effective theories. Recent data from collider
experiments require $\kappa\gtrsim\mathcal{O}(10^{13})\ \text{GeV}$. The use of
standard test of in-vacuo dispersion relations of Gamma Ray Burst photons
increases this lower bound by 4 orders of magnitude. The robustness of this
bound is discussed in the light of possible new features of noncommutative
causal structures. |
Symmetries of Holographic Minimal Models: It was recently proposed that a large N limit of a family of minimal model
CFTs is dual to a certain higher spin gravity theory in AdS_3, where the 't
Hooft coupling constant of the CFT is related to a deformation parameter of the
higher spin algebra. We identify the asymptotic symmetry algebra of the higher
spin theory for generic 't Hooft parameter, and show that it coincides with a
family of W-algebras previously discovered in the context of the KP hierarchy.
We furthermore demonstrate that this family of W-algebras controls the
representation theory of the minimal model CFTs in the 't Hooft limit. This
provides a non-trivial consistency check of the proposal and explains part of
the underlying mechanism. | Inflation and Large Internal Dimensions: We consider some aspects of inflation in models with large internal
dimensions. If inflation occurs on a 3D wall after the stabilization of
internal dimensions in the models with low unification scale (M ~ 1 TeV), the
inflaton field must be extremely light. This problem may disappear In models
with intermediate (M ~10^{11} GeV) to high (M ~ 10^{16} GeV) unification scale.
However, in all of these cases the wall inflation does not provide a complete
solution to the horizon and flatness problems. To solve them, there must be a
stage of inflation in the bulk before the compactification of internal
dimensions. |
Universal properties of cold holographic matter: We study the collective excitations of holographic quantum liquids formed in
the low energy theory living at the intersection of two sets of D-branes. The
corresponding field theory dual is a supersymmetric Yang-Mills theory with
massless matter hypermultiplets in the fundamental representation of the gauge
group which generically live on a defect of the unflavored theory. Working in
the quenched (probe) approximation, we focus on determining the universal
properties of these systems. We analyze their thermodynamics, the speed of
first sound, the diffusion constant, and the speed of zero sound. We study the
influence of temperature, chemical potential, and magnetic field on these
quantities, as well as on the corresponding collisionless/hydrodynamic
crossover. We also generalize the alternative quantization for all conformally
$AdS_4$ cases and study the anyonic correlators. | $SU(n)$ symmetry breaking by rank three and rank two antisymmetric
tensor scalars: We study $SU(n)$ symmetry breaking by rank three and rank two antisymmetric
tensor fields. Using tensor analysis, we derive branching rules for the adjoint
and antisymmetric tensor representations, and explain why for general $SU(n)$
one finds the same $U(1)$ generator mismatch that we noted earlier in special
cases. We then compute the masses of the various scalar fields in the branching
expansion, in terms of parameters of the general renormalizable potential for
the antisymmetric tensor fields. |
Dynamical Breakdown of Symmetry in a (2+1) Dimensional Model Containing
the Chern-Simons Field: We study the vacuum stability of a model of massless scalar and fermionic
fields minimally coupled to a Chern-Simons field. The classical Lagrangian only
involves dimensionless parameters, and the model can be thought as a (2+1)
dimensional analog of the Coleman-Weinberg model. By calculating the effective
potential, we show that dynamical symmetry breakdown occurs in the two-loop
approximation. The vacuum becomes asymmetric and mass generation, for the boson
and fermion fields takes place. Renormalization group arguments are used to
clarify some aspects of the solution. | D-instanton induced interactions on a D3-brane: Non-perturbative features of the derivative expansion of the effective action
of a single D3-brane are obtained by considering scattering amplitudes of open
and closed strings. This motivates expressions for the coupling constant
dependence of world-volume interactions of the form $(\partial F)^4$ (where F
is the Born-Infeld field strength), $(\partial^2\phi)^4$ (where $\phi$ are the
normal coordinates of the D3-brane) and other interactions related by $\calN=4$
supersymmetry. These include terms that transform with non-trivial modular
weight under Montonen-Olive duality. The leading D-instanton contributions that
enter into these effective interactions are also shown to follow from an
explicit stringy construction of the moduli space action for the
D-instanton/D3-brane system in the presence of D3-brane open-string sources
(but in the absence of a background antisymmetric tensor potential). Extending
this action to include closed-string sources leads to a unified description of
non-perturbative terms in the effective action of the form (embedding
curvature)$^2$ together with open-string interactions that describe
contributions of the second fundamental form. |
Global Flows of Foliated Gravity-Matter Systems: Asymptotic safety is a promising mechanism for obtaining a consistent and
predictive quantum theory for gravity. The ADM formalism allows to introduce a
(Euclidean) time-direction in this framework. It equips spacetime with a
foliation structure by encoding the gravitational degrees of freedom in a lapse
function, shift vector, and a metric measuring distances on the spatial slices.
We use the Wetterich equation to study the renormalization group flow of the
graviton 2-point function extracted from the spatial metric. The flow is driven
by the 3- and 4-point vertices generated by the foliated Einstein-Hilbert
action supplemented by minimally coupled scalar and vector fields. We derive
bounds on the number of matter fields cast by asymptotic safety. Moreover, we
show that the phase diagram obtained in the pure gravity case is qualitatively
stable within these bounds. An intriguing feature is the presence of an
IR-fixed point for the graviton mass which prevents the squared mass taking
negative values. This feature persists for any number of matter fields and, in
particular, also in situations where there is no suitable interacting fixed
point rendering the theory asymptotically safe. Our work complements earlier
studies of the subject by taking contributions from the matter fields into
account. | Entanglement Entropy in Lifshitz Theories: We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free
Lifshitz scalar field theories with arbitrary dynamical exponents. We consider
both the subinterval and periodic sublattices in the discretized theory as
subsystems. In both cases, we are able to analytically demonstrate that the EE
grows linearly as a function of the dynamical exponent. Furthermore, for the
subinterval case, we determine that as the dynamical exponent increases, there
is a crossover from an area law to a volume law. Lastly, we deform Lifshitz
field theories with certain relevant operators and show that the EE decreases
from the ultraviolet to the infrared fixed point, giving evidence for a
possible c-theorem for deformed Lifshitz theories. |
Cauchy formula and the character ring: Cauchy summation formula plays a central role in application of character
calculus to many problems, from AGT-implied Nekrasov decomposition of conformal
blocks to topological-vertex decompositions of link invariants. We briefly
review the equivalence between Cauchy formula and expressibility of skew
characters through the Littlewood-Richardson coefficients. As
not-quite-a-trivial illustration we consider how this equivalence works in the
case of plane partitions -- at the simplest truly interesting level of just
four boxes. | Solution of quantum Dirac constraints via path integral: The semiclassical solution of quantum Dirac constraints in generic
constrained system is obtained by directly calculating in the one-loop
approximation the gauge field path integral with relativistic gauge fixing
procedure. The gauge independence property of this path integral is analyzed by
the method of Ward identities with a special emphasis on boundary conditions
for gauge fields. The calculations are based on the known reduction algorithms
for functional determinants extended to gauge theories. The mechanism of
transition from relativistic gauge conditions to unitary gauges, participating
in the construction of this solution, is explicitly revealed. Implications of
this result in problems with spacetime boundaries, quantum gravity and
cosmology are briefly discussed. |
Translation-Invariant Noncommutative Gauge Theories, Matrix Modeling and
Noncommutative Geometry: A matrix modeling formulation for translation-invariant noncommutative gauge
theories is given in the setting of differential graded algebras and quantum
groups. Translation-invariant products are discussed in the setting of
{\alpha}-cohomology and it is shown that loop calculations are entirely
determined by {\alpha}-cohomology class of star product in all orders.
Noncommutative version of geometric quantization and (anti-) BRST
transformations is worked out which leads to a noncommutative description of
consistent anomalies and Schwinger terms. | The Dark Dimension, the Swampland, and the Dark Matter Fraction Composed
of Primordial Black Holes: Very recently, it was suggested that combining the Swampland program with the
smallness of the dark energy and confronting these ideas to experiment lead to
the prediction of the existence of a single extra-dimension (dubbed the dark
dimension) with characteristic length-scale in the micron range. We show that
the rate of Hawking radiation slows down for black holes perceiving the dark
dimension and discuss the impact of our findings in assessing the dark matter
fraction that could be composed of primordial black holes. We demonstrate that
for a species scale of ${\cal O}(10^{10}~{\rm GeV})$, an all-dark-matter
interpretation in terms of primordial black holes should be feasible for masses
in the range $10^{14} \leq M_{BH}/{\rm g}\leq 10^{21}$. This range is extended
compared to that in the 4D theory by 3 orders of magnitude in the low mass
region. We also show that PBHs with $M_{\rm BH} \sim 10^{12}~{\rm g}$ could
potentially explain the well-known Galactic 511 keV gamma-ray line if they make
up a tiny fraction of the total dark matter density. |
Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function: We study Ihara zeta function for graphs in the context of quivers arising
from gauge theories, especially under Seiberg duality transformations. The
distribution of poles is studied as we proceed along the duality tree, in light
of the weak and strong graph versions of the Riemann Hypothesis. As a
by-product, we find a refined version of Ihara zeta function to be the
generating function for the generic superpotential of the gauge theory. | BRST symmetry and fictitious parameters: Our goal in this work is to present the variational method of fictitious
parameters and its connection with the BRST symmetry. Firstly we implement the
method in QED at zero temperature and then we extend the analysis to GQED at
finite temperature. As we will see the core of the study is the general
statement in gauge theories at finite temperature, assigned by Tyutin work,
that the physics does not depend on the gauge choices, covariant or not, due to
BRST symmetry. |
Note on massless and partially massless spin-2 particles in a curved
background via a nonsymmetric tensor: In the last few years we have seen an increase interest on gravitational
waves due to recent and striking experimental results confirming Einstein's
general relativity once more. From the field theory point of view, gravity
describes the propagation of self-interacting massless spin-2 particles. They
can be identified with metric perturbations about a given background metric.
Since the metric is a symmetric tensor, the massless spin-2 particles present
in the Einstein-Hilbert (massless Fierz-Pauli) theory are naturally described
by a symmetric rank-2 tensor. However, this is not the only possible consistent
massless spin-2 theory at linearized level. In particular, if we add a mass
term, a new one parameter $(a_1)$ family of models ${\cal L}(a_1)$ shows up.
They consistently describe massive spin-2 particles about Einstein spaces in
terms of a non-symmetric rank-2 tensor. Here we investigate the massless
version of ${\cal L}(a_1)$ in a curved background. In the case $a_1=-1/12$ we
show that the massless spin-2 particles consistently propagate, at linearized
level, in maximally symmetric spaces. A similar result is obtained otherwise
$(a_1 \ne -1/12)$ where we have a non-symmetric scalar-tensor massless model.
The case of partially massless non-symmetric models is also investigated. | Monodromy Relations in Higher-Loop String Amplitudes: New monodromy relations of loop amplitudes are derived in open string theory.
We particularly study N-point one-loop amplitudes described by a world-sheet
cylinder (planar and non-planar) and derive a set of relations between
subamplitudes of different color orderings. Various consistency checks are
performed by matching alpha'-expansions of planar and non-planar amplitudes
involving elliptic iterated integrals with the resulting periods giving rise to
two sets of multiple elliptic zeta values. The latter refer to the two homology
cycles on the once-punctured complex elliptic curve and the monodromy equations
provide relations between these two sets of multiple elliptic zeta values.
Furthermore, our monodromy relations involve new objects for which we present a
tentative interpretation in terms of open string scattering amplitudes in the
presence of a non-trivial gauge field flux. Finally, we provide an outlook on
how to generalize the new monodromy relations to the non-oriented case and
beyond the one-loop level. Comparing a subset of our results with recent
findings in the literature we find therein several serious issues related to
the structure and significance of monodromy phases and the relevance of missed
contributions from contour integrations. |
Supersymmetric gauge theory, (2,0) theory and twisted 5d
Super-Yang-Mills: Twisted compactification of the 6d N=(2,0) theories on a punctured Riemann
surface give a large class of 4d N=1 and N=2 gauge theories, called class S. We
argue that nonperturbative dynamics of class S theories are described by 5d
maximal Super-Yang-Mills (SYM) twisted on the Riemann surface. In a sense,
twisted 5d SYM might be regarded as a "Lagrangian" for class S theories on
R^{1,2} times S^1. First, we show that twisted 5d SYM gives generalized
Hitchin's equations which was proposed recently. Then, we discuss how to
identify chiral operators with quantities in twisted 5d SYM. Mesons, or
holomorphic moment maps, are identified with operators at punctures which are
realized as 3d superconformal theories T_rho[G] coupled to twisted 5d SYM.
"Baryons" are identified qualitatively through a study of 4d N=2 Higgs
branches. We also derive a simple formula for dynamical superpotential vev
which is relevant for BPS domain wall tensions. With these tools, we examine
many examples of 4d N=1 theories with several phases such as confining, Higgs,
and Coulomb phases, and show perfect agreements between field theories and
twisted 5d SYM. Spectral curve is an essential tool to solve generalized
Hitchin's equations, and our results clarify the physical information encoded
in the curve. | On the Various Types of D-Branes in the Boundary H3+ Model: We comment on the D-brane solutions for the boundary H3+ model that have been
proposed so far and point out that many more types of D-branes should be
considered possible. We start a systematic derivation of the 1/2- and
b^{-2}/2-shift equations corresponding to each type. These equations serve as
consistency conditions and we discuss their possible solutions. On this basis,
we show for the known AdS_2^(d) branes, that only strings transforming in
finite dimensional SL(2) representations can couple to them. Moreover, we also
demonstrate that strings in the infinite dimensional continuous SL(2)
representations do not couple consistently to the known AdS_2 branes. For some
other types, we show that no consistent solutions seem to exist at all. |
Four dimensional cubic supersymmetry: A four dimensional non-trivial extension of the Poincar\'e algebra different
from supersymmetry is explicitly studied. Representation theory is investigated
and an invariant Lagrangian is exhibited. Some discussion on the Noether
theorem is also given. | Curvatures and potential of M-theory in D=4 with fluxes and twist: We give the curvatures of the free differential algebra (FDA) of M--theory
compactified to D=4 on a twisted seven--torus with the 4--form flux switched
on. Two formulations are given, depending on whether the 1--form field
strengths of the scalar fields (originating from the 3--form gauge field
$\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonic
equations of motion and discuss at length the scalar potential which emerges in
this type of compactifications. For flat groups we show the equivalence of this
potential with a dual formulation of the theory which has the full $\rE_{7(7)}$
symmetry. |
Heat kernel for higher-order differential operators and generalized
exponential functions: We consider the heat kernel for higher-derivative and nonlocal operators in
$d$-dimensional Euclidean space-time and its asymptotic behavior. As a building
block for operators of such type, we consider the heat kernel of the minimal
operator - generic power of the Laplacian - and show that it is given by the
expression essentially different from the conventional exponential
Wentzel-Kramers-Brillouin (WKB) ansatz. Rather it is represented by the
generalized exponential function (GEF) directly related to what is known in
mathematics as the Fox-Wright $\varPsi$-functions and Fox $H$-functions. The
structure of its essential singularity in the proper time parameter is
different from that of the usual exponential ansatz, which invalidated previous
attempts to directly generalize the Schwinger-DeWitt heat kernel technique to
higher-derivative operators. In particular, contrary to the conventional
exponential decay of the heat kernel in space, we show the oscillatory behavior
of GEF for higher-derivative operators. We give several integral
representations for the generalized exponential function, find its asymptotics
and semiclassical expansion, which turns out to be essentially different for
local operators and nonlocal operators of noninteger order. Finally, we briefly
discuss further applications of the GEF technique to generic higher-derivative
and pseudodifferential operators in curved space-time, which might be
critically important for applications of Horava-Lifshitz and other UV
renormalizable quantum gravity models. | Pure Spinor Formalism for Conformal Fermion and Conserved Currents: Pure spinor formalism and non-integrable exponential factors are used for
constructing the conformal-invariant wave equation and Lagrangian density for
massive fermion. It is proved that canonical Dirac Lagrangian for massive
fermion is invariant under induced projective conformal transformations. |
Black holes from large N singlet models: The emergent nature of spacetime geometry and black holes can be directly
probed in simple holographic duals of higher spin gravity and tensionless
string theory. To this end, we study time dependent thermal correlation
functions of gauge invariant observables in suitably chosen free large N gauge
theories. At low temperature and on short time scales the correlation functions
encode propagation through an approximate AdS spacetime while interesting
departures emerge at high temperature and on longer time scales. This includes
the existence of evanescent modes and the exponential decay of time dependent
boundary correlations, both of which are well known indicators of bulk black
holes in AdS/CFT. In addition, a new time scale emerges after which the
correlation functions return to a bulk thermal AdS form up to an overall
temperature dependent normalization. A corresponding length scale was seen in
equal time correlation functions in the same models in our earlier work. | Burgers' equation in non-commutative space-time: The Moyal *-deformed noncommutative version of Burgers' equation is
considered. Using the *-analog of the Cole-Hopf transformation, the
linearization of the model in terms of the linear heat equation is found.
Noncommutative q-deformations of shock soliton solutions and their interaction
are described |
Effective Field Theory of Quantum Black Holes: We review and extend recent progress on the quantum description of
near-extremal black holes in the language of effective quantum field theory.
With black holes in Einstein-Maxwell theory as the main example, we derive the
Schwarzian low energy description of the AdS$_2$ region from a spacetime point
of view. We also give a concise formula for the symmetry breaking scale, we
relate rotation to supersymmetry, and we discuss quantum corrections to black
hole entropy. | Supersymmetric Heterotic Action out of M5 Brane: Generalizing the work by Cherkis and Schwarz [1], we carry out the double
dimensional reduction of supersymmetric M5 brane on K3 to obtain the
supersymmetric action of heterotic string in 7-dimensional flat space-time.
Motivated by this result, we propose the supersymmetric heterotic action in
10-dimensional flat space-time where the current algebra is realized in a novel
way. We explicitly verify the kappa-symmetry of the proposed action. |
The connected wedge theorem and its consequences: In the AdS/CFT correspondence, bulk causal structure has consequences for
boundary entanglement. In quantum information science, causal structures can be
replaced by distributed entanglement for the purposes of information
processing. In this work, we deepen the understanding of both of these
statements, and their relationship, with a number of new results. Centrally, we
present and prove a new theorem, the $n$-to-$n$ connected wedge theorem, which
considers $n$ input and $n$ output locations at the boundary of an
asymptotically AdS$_{2+1}$ spacetime described by AdS/CFT. When a sufficiently
strong set of causal connections exists among these points in the bulk, a set
of $n$ associated regions in the boundary will have extensive-in-N mutual
information across any bipartition of the regions. The proof holds in three
bulk dimensions for classical spacetimes satisfying the null curvature
condition and for semiclassical spacetimes satisfying standard conjectures. The
$n$-to-$n$ connected wedge theorem gives a precise example of how causal
connections in a bulk state can emerge from large-N entanglement features of
its boundary dual. It also has consequences for quantum information theory: it
reveals one pattern of entanglement which is sufficient for information
processing in a particular class of causal networks. We argue this pattern is
also necessary, and give an AdS/CFT inspired protocol for information
processing in this setting.
Our theorem generalizes the $2$-to-$2$ connected wedge theorem proven in
arXiv:1912.05649. We also correct some errors in the proof presented there, in
particular a false claim that existing proof techniques work above three bulk
dimensions. | Resonances and PT symmetry in quantum curves: In the correspondence between spectral problems and topological strings, it
is natural to consider complex values for the string theory moduli. In the
spectral theory side, this corresponds to non-Hermitian quantum curves with
complex spectra and resonances, and in some cases, to PT-symmetric spectral
problems. The correspondence leads to precise predictions about the spectral
properties of these non-Hermitian operators. In this paper we develop
techniques to compute the complex spectra of these quantum curves, providing in
this way precision tests of these predictions. In addition, we analyze quantum
Seiberg-Witten curves with PT symmetry, which provide interesting and exactly
solvable examples of spontaneous PT-symmetry breaking. |
Instanton Calculus, Topological Field Theories and N=2 Super Yang-Mills
Theories: The results obtained by Seiberg and Witten for the low-energy Wilsonian
effective actions of N=2 supersymmetric theories with gauge group SU(2) are in
agreement with instanton computations carried out for winding numbers one and
two. This suggests that the instanton saddle point saturates the
non-perturbative contribution to the functional integral. A natural framework
in which corrections to this approximation are absent is given by the
topological field theory built out of the N=2 Super Yang-Mills theory. After
extending the standard construction of the Topological Yang-Mills theory to
encompass the case of a non-vanishing vacuum expectation value for the scalar
field, a BRST transformation is defined (as a supersymmetry plus a gauge
variation), which on the instanton moduli space is the exterior derivative. The
topological field theory approach makes the so-called "constrained instanton"
configurations and the instanton measure arise in a natural way. As a
consequence, instanton-dominated Green's functions in N=2 Super Yang-Mills can
be equivalently computed either using the constrained instanton method or
making reference to the topological twisted version of the theory. We
explicitly compute the instanton measure and the contribution to $u=<\Tr
\phi^2>$ for winding numbers one and two. We then show that each
non-perturbative contribution to the N=2 low-energy effective action can be
written as the integral of a total derivative of a function of the instanton
moduli. Only instanton configurations of zero conformal size contribute to this
result. Finally, the 8k-dimensional instanton moduli space is built using the
hyperkahler quotient procedure, which clarifies the geometrical meaning of our
approach. | Thermodynamical properties of a noncommutative anti-de
Sitter-Einstein-Born-Infeld spacetime from gauge theory of gravity: We construct a deformed adS-Einstein-Born-Infeld black hole from
noncommutative gauge theory of gravity and determine the metric coefficients up
to second order on the noncommutative parameter. We analyse the modifications
on the thermodynamical properties of the black hole due to the noncommutative
contributions, and we show that noncommutativity has as a direct consequence,
the removal of critical points. |
Covariant Quantum Fields on Noncommutative Spacetimes: A spinless covariant field $\phi$ on Minkowski spacetime $\M^{d+1}$ obeys the
relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where
$(a,\Lambda)$ is an element of the Poincar\'e group $\Pg$ and $U:(a,\Lambda)\to
U(a,\Lambda)$ is its unitary representation on quantum vector states. It
expresses the fact that Poincar\'e transformations are being unitary
implemented. It has a classical analogy where field covariance shows that
Poincar\'e transformations are canonically implemented. Covariance is
self-reproducing: products of covariant fields are covariant. We recall these
properties and use them to formulate the notion of covariant quantum fields on
noncommutative spacetimes. In this way all our earlier results on dressing,
statistics, etc. for Moyal spacetimes are derived transparently. For the Voros
algebra, covariance and the *-operation are in conflict so that there are no
covariant Voros fields compatible with *, a result we found earlier. The notion
of Drinfel'd twist underlying much of the preceding discussion is extended to
discrete abelian and nonabelian groups such as the mapping class groups of
topological geons. For twists involving nonabelian groups the emergent
spacetimes are nonassociative. | On Covariant Actions for Chiral $p-$Forms: We construct a Lorentz and generally covariant, polynomial action for free
chiral $p-$forms, classically equivalent to the Pasti-Sorokin-Tonin (PST)
formulation. The minimal set up requires introducing an auxiliary $p-$form on
top of the physical gauge $p-$form and the PST scalar. The action enjoys
multiple duality symmetries, including those that exchange the roles of
physical and auxiliary $p-$form fields. Actions of the same type are available
for duality-symmetric formulations, which is demonstrated on the example of the
electromagnetic field in four dimensions. There, the degrees of freedom of a
single Maxwell field are described employing four distinct vector gauge fields
and a scalar field. |
Small Amplitude Forced Fluid Dynamics from Gravity at T = 0: The usual derivative expansion of gravity duals of charged fluid dynamics is
known to break down in the zero temperature limit. In this case, the
fluid-gravity duality is not understood precisely. We explore this problem for
a zero temperature charged fluid driven by a low frequency, small amplitude and
spatially homogeneous external force. In the gravity dual, this corresponds to
time dependent boundary value of the dilaton. We calculate the bulk solution
for the dilaton and the leading backreaction to the metric and the gauge fields
using the modified low frequency expansion of [11]. The resulting solutions are
regular everywhere, establishing fluid-gravity duality to this order. | Effective field theory of slowly-moving "extreme black holes": We consider the non-relativistic effective field theory of ``extreme black
holes'' in the Einstein-Maxwell-dilaton theory with an arbitrary dilaton
coupling. We investigate finite-temperature behavior of gas of ``extreme black
holes'' using the effective theory. The total energy of the classical many-body
system is also derived. |
On the supersymmetric limit of Kerr-NUT-AdS metrics: Generalizing the scaling limit of Martelli and Sparks [hep-th/0505027] into
an arbitrary number of spacetime dimensions we re-obtain the (most general
explicitly known) Einstein-Sasaki spaces constructed by Chen, Lu, and Pope
[hep-th/0604125]. We demonstrate that this limit has a well-defined geometrical
meaning which links together the principal conformal Killing-Yano tensor of the
original Kerr-NUT-(A)dS spacetime, the Kahler 2-form of the resulting
Einstein-Kahler base, and the Sasakian 1-form of the final Einstein-Sasaki
space. The obtained Einstein-Sasaki space possesses the tower of Killing-Yano
tensors of increasing rank, underlined by the existence of Killing spinors. A
similar tower of hidden symmetries is observed in the original
(odd-dimensional) Kerr-NUT-(A)dS spacetime. This rises an interesting question
whether also these symmetries can be related to the existence of some
"generalized" Killing spinor. | The Casimir Energy in a Separable Potential: The Casimir energy is the first-order-in-\hbar correction to the energy of a
time-independent field configuration in a quantum field theory. We study the
Casimir energy in a toy model, where the classical field is replaced by a
separable potential. In this model the exact answer is trivial to compute,
making it a good place to examine subtleties of the problem. We construct two
traditional representations of the Casimir energy, one from the Greens
function, the other from the phase shifts, and apply them to this case. We show
that the two representations are correct and equivalent in this model. We study
the convergence of the Born approximation to the Casimir energy and relate our
findings to computational issues that arise in more realistic models. |
Casimir energy through transfer operators for weak curved backgrounds: The quantum vacuum interaction energy between a pair of semitransparent
two-dimensional plates represented by Dirac delta potentials and its first
derivative, embedded in the topological background of a sine-Gordon kink is
studied through an extension of the TGTG-formula (firstly discovered by O.
Kenneth and I. Klich) to weak curved backgrounds. Quantum vacuum oscillations
around the sine-Gordon kink solutions are interpreted as a quantum scalar field
theory in the spacetime of a domain wall. Moreover, the relation between the
phase shift and the density of states (the well-known Dashen-Hasslacher-Neveu
formula) is also exploited to characterize the quantum vacuum energy. | Branes at Quantum Criticality: In this paper we propose new non-relativistic p+1 dimensional theory. This
theory is defined in such a way that the potential term obeys the principle of
detailed balance where the generating action corresponds to p-brane action.
This condition ensures that the norm of the vacuum wave functional of p+1
dimensional theory is equal to the partition function of p-brane theory. |
Partial Supergravity Breaking and the Effective Action of Consistent
Truncations: We study vacua of N = 4 half-maximal gauged supergravity in five dimensions
and determine crucial properties of the effective theory around the vacuum. The
main focus is on configurations with exactly two broken supersymmetries, since
they frequently appear in consistent truncations of string theory and
supergravity. Evaluating one-loop corrections to the Chern-Simons terms we find
necessary conditions to ensure that a consistent truncation also gives rise to
a proper effective action of an underlying more fundamental theory. To obtain
concrete examples, we determine the N=4 action of M-theory on six-dimensional
SU(2)-structure manifolds with background fluxes. Calabi-Yau threefolds with
vanishing Euler number are examples of SU(2)-structure manifolds that yield N=2
Minkowski vacua. We find that that one-loop corrections to the Chern-Simons
terms vanish trivially and thus do not impose constraints on identifying
effective theories. This result is traced back to the absence of isometries on
these geometries. Examples with isometries arise from type IIB supergravity on
squashed Sasaki-Einstein manifolds. In this case the one-loop gauge
Chern-Simons terms vanish due to non-trivial cancellations, while the one-loop
gravitational Chern-Simons terms are non-zero. | Maximal D=2 supergravities from higher dimensions: We develop in detail the general framework of consistent Kaluza-Klein
truncations from D=11 and type II supergravities to gauged maximal
supergravities in two dimensions. In particular, we unveil the complete bosonic
dynamics of all gauged maximal supergravities that admit a geometric uplift.
Our construction relies on generalised Scherk-Schwarz reductions of E$_9$
exceptional field theory. The application to the reduction of D=11 supergravity
on $S^8\times S^1$ to SO(9) gauged supergravity is presented in a companion
paper. |
Model Building with F-Theory: Despite much recent progress in model building with D-branes, it has been
problematic to find a completely convincing explanation of gauge coupling
unification. We extend the class of models by considering F-theory
compactifications, which may incorporate unification more naturally. We explain
how to derive the charged chiral spectrum and Yukawa couplings in N=1
compactifications of F-theory with G-flux. In a class of models which admit
perturbative heterotic duals, we show that the F-theory and heterotic
computations match. | Quantum mirror curve of periodic chain geometry: The mirror curves enable us to study B-model topological strings on
non-compact toric Calabi--Yau threefolds. One of the method to obtain the
mirror curves is to calculate the partition function of the topological string
with single brane. In this paper, we discuss two types of geometries; one is
the chain of $N$ $\mathbb{P}^1$'s which we call `$N$-chain geometry,' the other
is the chain of $N$ $\mathbb{P}^1$'s with a compactification which we call
`periodic $N$-chain geometry.' We calculate the partition functions of the open
topological strings on these geometries, and obtain the mirror curves and their
quantization. Through the computation, we find some difference equations of
(elliptic) hypergeometric functions. We also find a relation between the
periodic chain and $\infty$-chain geometries, which implies a possible
connection between 5d and 6d gauge theories in the large $N$ limit. |
Projected Proca Field Theory: a One-Loop Study: The recent discovery of two-dimensional Dirac materials, such as graphene and
transition-metaldichalcogenides, has raised questions about the treatment of
hybrid systems, in which electrons moving in a two-dimensional plane interact
via virtual photons from the three-dimensional space. In this case, a projected
non-local theory, known as Pseudo-QED, or reduced QED, has shown to provide a
correct framework for describing the interactions displayed by these systems.
In a related situation, in planar materials exhibiting a superconducting phase,
the electromagnetic field has a typical exponential decay that is interpreted
as the photons having an effective mass, as a consequence of the Anderson-Higgs
mechanism. Here, we use an analogous projection to that used to obtain the
pseudo-QED to derive a Pseudo-Proca equivalent model. In terms of this model,
we unveil the main effects of attributing a mass to the photons and to the
quasi-relativistic electrons. The one-loop radiative corrections to the
electron mass, to the photon and to the electron-photon vertex are computed. We
calculate the quantum corrections to the electron g-factor and show that it
smoothly goes to zero in the limit when the photon mass is much larger than the
electron mass. In addition, we correct the results obtained for graphene within
Pseudo-QED in the limit when the photon mass vanishes. | Extended superconformal symmetry and Calogero-Marchioro model: We show that the two dimensional Calogero-Marchioro Model (CMM) without the
harmonic confinement can naturally be embedded into an extended SU(1,1|2)
superconformal Hamiltonian. We study the quantum evolution of the
superconformal Hamiltonian in terms of suitable compact operators of the N=2
extended de Sitter superalgebra with central charge and discuss the pattern of
supersymmetry breaking. We also study the arbitrary D dimensional CMM having
dynamical OSp(2|2) supersymmetry and point out the relevance of this model in
the context of the low energy effective action of the dimensionally reduced
Yang-Mills theory. |
Explicit Modular Invariant Two-Loop Superstring Amplitude Relevant for
R^4: In this note we derive an explicit modular invariant formula for the two loop
4-point amplitude in superstring theory in terms of a multiple integral (7
complex integration variables) over the complex plane which is shown to be
convergent. We consider in particular the case of the leading term for
vanishing momenta of the four graviton amplitude, which would correspond to the
two-loop correction of the R^4 term in the effective Action. The resulting
expression is not positive definite and could be zero, although we cannot see
that it vanishes. | Brane Induced Gravity: Codimension-2: We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG)
in 6D. Among a large diversity of regulated codimension-2 branes, we find that
for near-critical tensions branes live inside very deep throats which
efficiently compactify the angular dimension. In there, 4D gravity first
changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent
of the tension, but the crossover from 5D to 6D is not. This shows how the
vacuum energy problem manifests in BIG: instead of tuning vacuum energy to
adjust the 4D curvature, generically one must tune it to get the desired
crossover scales and the hierarchy between the scales governing the 4D \to 5D
\to 6D transitions. In the near-critical limit, linearized perturbation theory
remains under control below the crossover scale, and we find that linearized
gravity around the vacuum looks like a scalar-tensor theory. |
Quantum Deformation of BRST Algebra: We investigate the $q$-deformation of the BRST algebra, the algebra of the
ghost, matter and gauge fields on one spacetime point using the result of the
bicovariant differential calculus. There are two nilpotent operations in the
algebra, the BRST transformation $\brs$ and the derivative $d$. We show that
one can define the covariant commutation relations among the fields and their
derivatives consistently with these two operation as well as the $*$-operation,
the antimultiplicative inner involution. | Observables and Microscopic Entropy of Higher Spin Black Holes: In the context of recently proposed holographic dualities between higher spin
theories in AdS3 and 1+1-dimensional CFTs with W-symmetry algebras, we revisit
the definition of higher spin black hole thermodynamics and the dictionary
between bulk fields and dual CFT operators. We build a canonical formalism
based on three ingredients: a gauge-invariant definition of conserved charges
and chemical potentials in the presence of higher spin black holes, a canonical
definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned
with the asymptotic symmetry algebra. We show that our canonical formalism
shares the same formal structure as the so-called holomorphic formalism, but
differs in the definition of charges and chemical potentials and in the
bulk-to-boundary dictionary. Most importantly, we show that it admits a
consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail
and generalize our construction to theories based on the hs[\lambda] algebra,
and on the sl(N,R) algebra for any choice of sl(2,R) embedding. |
Modular Constructions of Quantum Field Theories with Interactions: We extend the previously introduced constructive modular method to
nonperturbative QFT. In particular the relevance of the concept of ``quantum
localization'' (via intersection of algebras) versus classical locality (via
support properties of test functions) is explained in detail, the wedge
algebras are constructed rigorously and the formal aspects of double cone
algebras for d=1+1 factorizing theories are determined. The well-known on-shell
crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in
such theories is intimately related to the KMS properties of new quantum-local
PFG (one-particle polarization-free generators) of these wedge algebras. These
generators are ``on-shell'' and their Fourier transforms turn out to fulfill
the Zamolodchikov-Faddeev algebra. As the wedge algebras contain the crossing
symmetry informations, the double cone algebras reveal the particle content of
fields. Modular theory associates with this double cone algebra two very useful
chiral conformal quantum field theories which are the algebraic versions of the
light ray algebras. | Ideals generated by traces in the symplectic reflection algebra
$H_{1,ν_1, ν_2}(I_2(2m))$. II: The associative algebra of symplectic reflections $\mathcal H:= H_{1,\nu_1,
\nu_2}(I_2(2m))$ based on the group generated by the root system $I_2(2m)$ has
two parameters, $\nu_1$ and $\nu_2$. For every value of these parameters, the
algebra $\mathcal H$ has an $m$-dimensional space of traces. A given trace
${\rm tr}$ is called degenerate if the associated bilinear form $B_{\rm
tr}(x,y)={\rm tr}(xy)$ is degenerate. Previously, there were found all values
of $\nu_1$ and $\nu_2$ for which there are degenerate traces in the space of
traces, and consequently the algebra $\mathcal H$ has a two-sided ideal. We
proved earlier that any linear combination of degenerate traces is a degenerate
trace. It turns out that for certain values of parameters $\nu_1$ and $\nu_2$,
degenerate traces span a 2-dimensional space. We prove that non-zero traces in
this $2d$ space generate three proper ideals of $\mathcal H$. |
Quantum Complexity and Negative Curvature: As time passes, once simple quantum states tend to become more complex. For
strongly coupled k-local Hamiltonians, this growth of computational complexity
has been conjectured to follow a distinctive and universal pattern. In this
paper we show that the same pattern is exhibited by a much simpler system:
classical geodesics on a compact two-dimensional geometry of uniform negative
curvature. This striking parallel persists whether the system is allowed to
evolve naturally or is perturbed from the outside. | Higher-Order Theories of Gravitation: We study higher-order theories of gravitation; in particular, we will focus
our attention on the second-order theory, in which conformal symmetry can be
implemented. |
New Supersymmetric String Theories from Discrete Theta Angles: We describe three previously unnoticed components of the moduli space of
minimally supersymmetric string theories in $d\geq 7$, describing in some
detail their spectrum and duality properties. We find a new component in nine
and eight dimensions, and two additional ones in seven dimensions. These
theories were originally discovered in a bottom-up classification of possible
F/M-theory singularity freezing patterns in the K3 lattice, described in a
companion paper. The 9d/8d component can be understood as F/M-theory on a
twisted fibration of the Klein bottle over a circle, while the new
seven-dimensional components are described as IIB on Bieberbach manifolds with
a duality bundle and RR-NSNS backgrounds turned on. All the new components can
be obtained from previously known theories by turning on certain discrete theta
angles; however, the spectrum of massive objects is very different, and most
strikingly, they feature an incomplete lattice of BPS strings, showing that
string BPS completeness is not true in general even with sixteen supercharges.
In all cases we find non-BPS representatives for each value of the charge, so
the Completeness Principle is satisfied. We also analyze analogous theta angles
in nonsupersymmetric string theories, and provide a detailed explanation of why
the Type I discrete $\theta$ angle proposed in 1304.1551 is unphysical, using
this to clarify certain non-perturbative phenomena in $O8$ planes. | Thermodynamics of the quantum $su(1,1)$ Landau-Lifshitz model: We present thermodynamics of the quantum su(1,1) Landau-Lifshitz model,
following our earlier exposition [J. Math. Phys. 50, 103518 (2009)] of the
quantum integrability of the theory, which is based on construction of
self-adjoint extensions, leading to a regularized quantum Hamiltonian for an
arbitrary n-particle sector. Starting from general discontinuity properties of
the functions used to construct the self-adjoint extensions, we derive the
thermodynamic Bethe Ansatz equations. We show that due to non-symmetric and
singular kernel, the self-consistency implies that only negative chemical
potential values are allowed, which leads to the conclusion that, unlike its
su(2) counterpart, the su(1,1) LL theory at T=0 has no instabilities. |
A Construction of Killing Spinors on S^n: We derive simple general expressions for the explicit Killing spinors on the
n-sphere, for arbitrary n. Using these results we also construct the Killing
spinors on various AdS x Sphere supergravity backgrounds, including AdS_5 x
S^5$, AdS_4 x S^7 and AdS_7 x S^4. In addition, we extend previous results to
obtain the Killing spinors on the hyperbolic spaces H^n. | Elevating the Free-Fermion $Z_2\times Z_2$ Orbifold Model to a
Compactification of F-Theory: We study the elliptic fibrations of some Calabi-Yau three-folds, including
the $Z_2\times Z_2$ orbifold with $(h_{1,1},h_{2,1})=(27,3)$, which is
equivalent to the common framework of realistic free-fermion models, as well as
related orbifold models with $(h_{1,1},h_{2,1})=(51,3)$ and (31,7). However,
two related puzzles arise when one considers the $(h_{1,1},h_{2,1})=(27,3)$
model as an F-theory compactification to six dimensions. The condition for the
vanishing of the gravitational anomaly is not satisfied, suggesting that the
F-theory compactification does not make sense, and the elliptic fibration is
well defined everywhere except at four singular points in the base. We
speculate on the possible existence of N=1 tensor and hypermultiplets at these
points which would cancel the gravitational anomaly in this case. |
Introduction to Spin Networks and Towards a Generalization of the
Decomposition Theorem: The objective of this work is twofold. On one hand, it is intended as a short
introduction to spin networks and invariants of 3-manifolds. It covers the main
areas needed to have a first understanding of the topics involved in the
development of spin networks, which are described in a detailed but not
exhaustive manner and in order of their conceptual development such that the
reader is able to use this work as a first reading. A motivation due to R.
Penrose for considering spin networks as a way of constructing a 3-D Euclidean
space is presented, as well as their relation to Ponzano-Regge theory.
Furthermore, the basic mathematical framework for the algebraic description of
spin networks via quantum groups is described and the notion of a spherical
category and its correspondence to the diagrammatic representation given by the
Temperley-Lieb recoupling theory are presented. In order to give an example of
topological invariants and their relation to TQFT the construction of the
Turaev-Viro invariant is depicted and related to the Kauffman-Lins invariant.
On the other hand, some results aiming at a decomposition theorem for
non-planar spin networks are presented. For this, Moussouris' algorithm and
some basic concepts of topological graph theory are explained and used,
especially Kuratowski's theorem and the Rotation Scheme theorem. | Revisiting modular symmetry in magnetized torus and orbifold
compactifications: We study the modular symmetry in $T^2$ and orbifold comfactifications with
magnetic fluxes. There are $|M|$ zero-modes on $T^2$ with the magnetic flux
$M$. Their wavefunctions as well as massive modes behave as modular forms of
weight $1/2$ and represent the double covering group of $\Gamma \equiv
SL(2,\mathbb{Z})$, $\widetilde{\Gamma} \equiv \widetilde{SL}(2,\mathbb{Z})$.
Each wavefunction on $T^2$ with the magnetic flux $M$ transforms under
$\widetilde{\Gamma}(2|M|)$, which is the normal subgroup of
$\widetilde{SL}(2,\mathbb{Z})$. Then, $|M|$ zero-modes are representations of
the quotient group $\widetilde{\Gamma}'_{2|M|} \equiv
\widetilde{\Gamma}/\widetilde{\Gamma}(2|M|)$. We also study the modular
symmetry on twisted and shifted orbifolds $T^2/\mathbb{Z}_N$. Wavefunctions are
decomposed into smaller representations by eigenvalues of twist and shift. They
provide us with reduction of reducible representations on $T^2$. |
More about Path Integral for Spin: Path integral for the $SU(2)$ spin system is reconsidered. We show that the
Nielsen-Rohrlich(NR) formula is equivalent to the spin coherent state
expression so that the phase space in the NR formalism is not topologically
nontrivial. We also perform the WKB approximation in the NR formula and find
that it gives the exact result. | Correlation Functions in Two-Dimensional Dilaton Gravity: The Liouville approach is applied to the quantum treatment of the dilaton
gravity in two dimensions. The physical states are obtained from the BRST
cohomology and correlation functions are computed up to three-point functions.
For the $N=0$ case (i.e., without matter), the cosmological term operator is
found to have the discrete momentum that plays a special role in the $c=1$
Liouville gravity. The correlation functions for arbitrary numbers of operators
are found in the $N=0$ case, and are nonvanishing only for specific
``chirality'' configurations. |
Fermionic One-Loop Corrections to Soliton Energies in 1+1 Dimensions: We demonstrate an unambiguous and robust method for computing fermionic
corrections to the energies of classical background field configurations. We
consider the particular case of a sequence of background field configurations
that interpolates continuously between the trivial vacuum and a widely
separated soliton/antisoliton pair in 1+1 dimensions. Working in the continuum,
we use phase shifts, the Born approximation, and Levinson's theorem to avoid
ambiguities of renormalization procedure and boundary conditions. We carry out
the calculation analytically at both ends of the interpolation and numerically
in between, and show how the relevant physical quantities vary continuously. In
the process, we elucidate properties of the fermionic phase shifts and zero
modes. | Integrable quantum field theories with OSP(m/2n) symmetries: We conjecture the factorized scattering description for OSP(m/2n)/OSP(m-1/2n)
supersphere sigma models and OSP(m/2n) Gross Neveu models. The non-unitarity of
these field theories translates into a lack of `physical unitarity' of the S
matrices, which are instead unitary with respect to the non-positive scalar
product inherited from the orthosymplectic structure. Nevertheless, we find
that formal thermodynamic Bethe ansatz calculations appear meaningful,
reproduce the correct central charges, and agree with perturbative
calculations. This paves the way to a more thorough study of these and other
models with supergroup symmetries using the S matrix approach. |
Deriving Veneziano Model in a Novel String Field Theory Solving String
Theory by Liberating Right and Left Movers: Bosonic string theory with the possibility for an arbitrary number of strings
- i.e. a string field theory - is formulated by a Hilbert space (a Fock space),
which is just that for massless noninteracting scalars. We earlier presented
this novel type of string field theory, but now we show that it leads to
scattering just given by the Veneziano model amplitude. Generalization to
strings with fermion modes would presumably be rather easy. It is
characteristic for our formulation /model that: 1) We have thrown away some
null set of information compared to usual string field theory, 2)Formulated in
terms of our \objects" (= the non-interacting scalars) there is no interaction
and essentially no time development(Heisenberg picture), 3) so that the
S-matrix is in our Hilbert space given as the unit matrix, S=1, and 4) the
Veneziano scattering amplitude appear as the overlap between the initial and
the final state described in terms of the \objects". 5) The integration in the
Euler beta function making up the Veneziano model appear from the summation
over the number of \objects" from one of the incoming strings which goes into a
certain one of the two outgoing strings. A correction from Weyl anomaly is
needed to get the correct form of the Veneziano amplitude and it only fits for
26 dimensions. | M-Fivebranes Wrapped on Supersymmetric Cycles: We construct supergravity solutions dual to the twisted field theories
arising when M-theory fivebranes wrap general supersymmetric cycles. The
solutions are constructed in maximal D=7 gauged supergravity and then uplifted
to D=11. Our analysis covers Kahler, special Lagrangian and exceptional
calibrated cycles. The metric on the cycles are Einstein, but do not
necessarily have constant curvature. We find many new examples of AdS/CFT
duality, corresponding to the IR superconformal fixed points of the twisted
field theories. |
Instantons from Low Energy String Actions: We look for instanton solutions in a class of two scalar field gravity
models, which includes the low energy string action in four dimensions. In
models where the matter field has a potential with a false vacuum, we find that
non-singular instantons exist as long as the Dilaton field found in string
theory has a potential with a minimum, and provide an example of such an
instanton. The class of singular instanton solutions are also examined, and we
find that depending on the parameter values, the volume factor of the Euclidean
region does not always vanish fast enough at the singularity to make the action
finite. | Electromagnetic Fields in a Thermal Background: The one--loop effective action for a slowly varying electromagnetic field is
computed at finite temperature and density using a real-time formalism. We
discuss the gauge invariance of the result. Corrections to the Debye mass from
an electric field are computed at high temperature and high density. The
effective coupling constant, defined from a purely electric weak--field
expansion, behaves at high temperature very differently from the case of a
magnetic field, and does not satisfy the renormalization group equation. The
issue of pair production in the real--time formalism is discussed and also its
relevance for heavy--ion collisions. |
Dressing Technique for Intermediate Hierarchies: A generalized AKNS systems introduced and discussed recently in \cite{dGHM}
are considered. It was shown that the dressing technique both in matrix
pseudo-differential operators and formal series with respect to the spectral
parameter can be developed for these hierarchies. | D-branes in Little String Theory: We analyze in detail the D-branes in the near-horizon limit of NS5-branes on
a circle, the holographic dual of little string theory in a double scaling
limit. We emphasize their geometry in the background of the NS5-branes and show
the relation with D-branes in coset models. The exact one-point function giving
the coupling of the closed string states with the D-branes and the spectrum of
open strings is computed. Using these results, we analyze several aspects of
Hanany-Witten setups, using exact CFT analysis. In particular we identify the
open string spectrum on the D-branes stretched between NS5-branes which
confirms the low-energy analysis in brane constructions, and that allows to go
to higher energy scales. As an application we show the emergence of the
beta-function of the N=2 gauge theory on D4-branes stretching between
NS5-branes from the boundary states describing the D4-branes. We also speculate
on the possibility of getting a matrix model description of little string
theory from the effective theory on the D1-branes. By considering D3-branes
orthogonal to the NS5-branes we find a CFT incarnation of the Hanany-Witten
effect of anomalous creation of D-branes. Finally we give an brief description
of some non-BPS D-branes. |
An Introduction to the Quantum Supermembrane: We review aspects of quantisation of the 11-dimensional supermembrane world
volume theory. We explicitly construct vertex operators for the massless states
and study interactions of supermembranes. The open supermembrane and its vertex
operators are discussed. We show how our results have direct applications to
Matrix theory by appropriate regularisation of the supermembrane. | Gauge and parametrization dependence in higher derivative quantum
gravity: The structure of counterterms in higher derivative quantum gravity is
reexamined. Nontrivial dependence of charges on the gauge and parametrization
is established. Explicit calculations of two-loop contributions are carried out
with the help of the generalized renormgroup method demonstrating consistency
of the results obtained. |
Electromagnetic and Gravitational Scattering at Planckian Energies: The scattering of pointlike particles at very large center of mass energies
and fixed low momentum transfers, occurring due to both their electromagnetic
and gravitational interactions is re-examined in the particular case when one
of the particles carries magnetic charge. At Planckian center-of-mass energies,
when gravitational dominance is normally expected, the presence of magnetic
charge is shown to produce dramatic modifications to the scattering cross
section as well as to the holomorphic structure of the scattering amplitude. | Holographic Calculations of Euclidean Wilson Loop Correlator in
Euclidean anti-de Sitter Space: The correlation functions of two or more Euclidean Wilson loops of various
shapes in Euclidean anti-de Sitter space are computed by considering the
minimal area surfaces connecting the loops. The surfaces are parametrized by
Riemann theta functions associated with genus three hyperelliptic Riemann
surfaces. In the case of two loops, the distance $L$ by which they are
separated can be adjusted by continuously varying a specific branch point of
the auxiliary Riemann surface. When $L$ is much larger than the characteristic
size of the loops, then the loops are approximately regarded as local operators
and their correlator as the correlator of two local operators. Similarly, when
a loop is very small compared to the size of another loop, the small loop is
considered as a local operator corresponding to a light supergravity mode. |
Termodinámica de agujeros negros y campos escalares: Since the descovery by Stephen Hawking that black holes emit radiation in the
context of the semiclassical approach to gravity, the black hole thermodynamics
has become an active field of research in theoretical physics. In this thesis,
the influence of scalar fields on the black hole thermodynamics in $D=4$
dimensions is studied. On one hand, the role played by scalar fields in the
first law of black hole thermodynamics is elucidated, by using the quasilocal
formalism of Brown and York, which is based on a correct variational principle,
and some concrete examples are provided. On the other, the thermodynamic
stability of asymptotically flat charged hairy black hole exact solutions is
analysed. The solutions considered have a non-trivial scalar field potential
and they can be embebbed in supergravity theories. It is explicitly shown that
these solutions contain thermodynamically stable black holes. | Hawking radiation conference, book of proceedings: Proceedings of the 'Hawking Radiation' conference in Stockholm, Sweden 2015.
It includes a link to the video recording of the conference and all the talks,
discussions, and communications, that took place during the week of the
conference . We hope the recorded discussions will be helpful, especially to
the current and future young researchers and students. |
Effective actions, relative cohomology and Chern Simons forms: The explicit expression of all the WZW effective actions for a simple group G
broken down to a subgroup H is established in a simple and direct way, and the
formal similarity of these actions to the Chern-Simons forms is explained.
Applications are also discussed. | Type IIB Orientifolds without Untwisted Tadpoles, and non-BPS D-branes: We discuss the construction of six- and four-dimensional Type IIB
orientifolds with vanishing untwisted RR tadpoles, but generically non-zero
twisted RR tadpoles. Tadpole cancellation requires the introduction of D-brane
systems with zero untwisted RR charge, but non-zero twisted RR charges. We
construct explicit models containing branes and antibranes at fixed points of
the internal space, or non-BPS branes partially wrapped on it. The models are
non-supersymmetric, but are absolutely stable against decay to supersymmetric
vacua. For particular values of the compactification radii tachyonic modes may
develop, triggering phase transitions between the different types of non-BPS
configurations of branes, which we study in detail in a particular example. As
an interesting spin-off, we show that the $\IT^6/\IZ_4$ orientifold without
vector structure, previously considered inconsistent due to uncancellable
twisted tadpoles, can actually be made consistent by introducing a set of
brane-antibrane pairs whose twisted charge cancels the problematic tadpole. |
Nonabelian solutions in N=4, D=5 gauged supergravity: We consider static, nonabelian solutions in N=4, D=5 Romans' gauged
supergravity model. Numerical arguments are presented for the existence of
asymptotically anti-de Sitter configurations in the $N=4^+$ version of the
theory, with a dilaton potential presenting a stationary point. Considering the
version of the theory with a Liouville dilaton potential, we look for
configurations with unusual topology. A new exact solution is presented, and a
counterterm method is proposed to compute the mass and action. | String Kaluza-Klein cosmologies with RR-fields: We construct 4-dimensional cosmological FRW--models by compactifying a black
5-brane solution of type IIB supergravity, which carries both magnetic
NS-NS-charge and RR-charge. The influence of nontrivial RR-fields on the
dynamics of the cosmological models is investigated. |
Duality Symmetric Actions with Manifest Space-Time Symmetries: We consider a space-time invariant duality symmetric action for a free
Maxwell field and an $SL(2,{\bf R})\times SO(6,22)$ invariant effective action
describing a low-energy bosonic sector of the heterotic string compactified on
a six-dimensional torus. The manifest Lorentz and general coordinate invariant
formulation of the models is achieved by coupling dual gauge fields to an
auxiliary vector field from an axionic sector of the theory. | Duality Phase Transition in Type I String Theory: We show that the duality phase transition in the unoriented type I theory of
open and closed strings is_first order_. The order parameter is the
semiclassical approximation to the heavy quark-antiquark potential at finite
temperature, extracted from the covariant off-shell string amplitude with
Wilson loop boundaries wrapped around the Euclidean time direction. Remarkably,
precise calculations can be carried out on either side of the phase boundary at
the string scale T_C = 1/2\pi \alpha^{'1/2} by utilizing the T-dual, type IB
and type I', descriptions of the short string gas of massless gluon radiation.
We will calculate the change in the duality transition temperature in the
presence of an electromagnetic background field. |
Lagrangian description of N=2 minimal models as critical points of
Landau-Ginzburg theories.: We discuss a two-dimensional lagrangian model with $N=2$ supersymmetry
described by a K\"{a}hler potential $K(X,\bar{X})$ and superpotential $gX^k$
which explicitly exhibits renormalization group flows to infrared fixed points
where the central charge has a value equal that of the $N=2$, $A_{k-1}$ minimal
model. We consider the dressing of such models by N=2 supergravity: in
contradistinction to bosonic or $N=1$ models, no modification of the
$\b$-function takes place. | The Gauge-Fixing Fermion in BRST Quantisation: Conditions which must be satisfied by the gauge-fixing fermion $\chi$ used in
the BRST quantisation of constrained systems are established. These ensure that
the extension of the Hamiltonian by the gauge-fixing term $[\Omega, \chi]$
(where $\Omega$ is the BRST charge) gives the correct path integral. (Lecture
given at the conference Constrained Dynamics and Quantum Gravity II, Santa
Margherita, Italy, September 1996) |
Stationary bubbles and their tunneling channels toward trivial geometry: In the path integral approach, one has to sum over all histories that start
from the same initial condition in order to obtain the final condition as a
superposition of histories. Applying this into black hole dynamics, we consider
stable and unstable stationary bubbles as a reasonable and regular initial
condition. We find examples where the bubble can either form a black hole or
tunnel toward a trivial geometry, i.e., with no singularity nor event horizon.
We investigate the dynamics and tunneling channels of true vacuum bubbles for
various tensions. In particular, in line with the idea of superposition of
geometries, we build a classically stable stationary thin-shell solution in a
Minkowski background where its fate is probabilistically given by
non-perturbative effects. Since there exists a tunneling channel toward a
trivial geometry in the entire path integral, the entire information is encoded
in the wave function. This demonstrates that the unitarity is preserved and
there is no loss of information when viewed from the entire wave function of
the universe, whereas a semi-classical observer, who can see only a definitive
geometry, would find an effective loss of information. This may provide a
resolution to the information loss dilemma. | Update of D3/D7-Brane Inflation on K3 x T^2/Z_2: We update the D3/D7-brane inflation model on K3 x T^2/Z_2 with branes and
fluxes. For this purpose, we study the low energy theory including g_s
corrections to the gaugino condensate superpotential that stabilizes the K3
volume modulus. The gauge kinetic function is verified to become holomorphic
when the original N=2 supersymmetry is spontaneously broken to N=1 by bulk
fluxes. From the underlying classical N=2 supergravity, the theory inherits a
shift symmetry which provides the inflaton with a naturally flat potential. We
analyze the fate of this shift symmetry after the inclusion of quantum
corrections. The field range of the inflaton is found to depend significantly
on the complex structure of the torus but is independent of its volume. This
allows for a large kinematical field range for the inflaton. Furthermore, we
show that the D3/D7 model may lead to a realization of the recent CMB fit by
Hindmarsh et al. with an 11% contribution from cosmic strings and a spectral
index close to n_s=1. On the other hand, by a slight change of the parameters
of the model one can strongly suppress the cosmic string contribution and
reduce the spectral index n_s to fit the WMAP5 data in the absence of cosmic
strings. We also demonstrate that the inclusion of quantum corrections allows
for a regime of eternal D3/D7 inflation. |
Topological Ward Identity and Anti-de Sitter Space/CFT Correspondence: The dual relationship between the supergravity in the anti-de Sitter(AdS)
space and the superconformal field theory is discussed in the simplest form. We
show that a topological Ward identity holds in the three dimensional
Chern-Simons gravity. In this simple case the proposed dual relationship can be
understood as the topological Ward identity. Extensions to the supersymmetric
theories and higher dimensional ones are also briefly discussed. | Relativistic dynamics, Green function and pseudodifferential operators: The central role played by pseudodifferential operators in relativistic
dynamics is very well know. In this work, operators as the Schrodinger one
(e.g: square root) are treated from the point of view of the non-local
pseudodifferential Green functions. Starting from the explicit construction of
the Green (semigroup) theoretical kernel, a theorem linking the integrability
conditions and their dependence on the spacetime dimensions is given.
Relativistic wave equations with arbitrary spin and the causality problem are
discussed with the algebraic interpretation of the radical operator and their
relation with coherent and squeezed states. Also we perform by mean of pure
theoretical procedures (based in physical concepts and symmetry) the
relativistic position operator which satisfies the conditions of integrability
: it is non-local, Lorentz invariant and does not have the same problems as the
"local"position operator proposed by Newton and Wigner. Physical examples, as
Zitterbewegung and rogue waves, are presented and deeply analysed in this
theoretical framework. |
Lorentz Violation and the Higgs Mechanism: We consider scalar quantum electrodynamics in the Higgs phase and in the
presence of Lorentz violation. Spontaneous breaking of the gauge symmetry gives
rise to Lorentz-violating gauge field mass terms. These may cause the
longitudinal mode of the gauge field to propagate superluminally. The theory
may be quantized by the Faddeev-Popov procedure, although the Lagrangian for
the ghost fields also needs to be Lorentz violating. | S-parameter, Technimesons, and Phase Transitions in Holographic Tachyon
DBI Models: We investigate some phenomenological aspects of the holographic models based
on the tachyon Dirac-Born-Infeld action in the AdS space-time. These
holographic theories model strongly interacting fermions and feature dynamical
mass generation and symmetry breaking. We show that they can be viewed as
models of holographic walking technicolor and compute the Peskin-Takeuchi
S-parameter and masses of lightest technimesons for a variety of the tachyon
potentials. We also investigate the phase structure at finite temperature and
charge density. Finally, we comment on the holographic Wilsonian RG in the
context of holographic tachyon DBI models. |
Large-$N$ nonlinear $σ$ models on $R^2\times S^1$: The large-$N$ nonlinear $O(N)$, $CP^{N-1}$ $\sigma$ models are studied on
$R^2 \times S^1$. The $N$-components scalar fields of the models are supposed
to acquire a phase $e^{i2\pi\delta}$ $(0\leq \delta <1)$, along the circulation
of the circle, $S^1$. We evaluate the effective potentials to the leading order
of the $1/N$ expansion. It is shown that, on $R^2\times S^1$ the $O(N)$ model
has rich phase structure while the phase of $CP^{N-1}$ model is just that of
the model at finite temperature. | TASI lectures on AdS/CFT: We introduce the AdS/CFT correspondence as a natural extension of QFT in a
fixed AdS background. We start by reviewing some general concepts of CFT,
including the embedding space formalism. We then consider QFT in a fixed AdS
background and show that one can define boundary operators that enjoy very
similar properties as in a CFT, except for the lack of a stress tensor.
Including a dynamical metric in AdS generates a boundary stress tensor and
completes the CFT axioms. We also discuss some applications of the bulk
geometric intuition to strongly coupled QFT. Finally, we end with a review of
the main properties of Mellin amplitudes for CFT correlation functions and
their uses in the context of AdS/CFT. |
Why some stars seem to be older than the Universe?: There is some experimental evidence that some stars are older than the
Universe in General Relativity based cosmology. In TGD based cosmology the
paradox has explanation. Photons can be either topologically condensed on
background spacetime surface or in 'vapour phase' that is progate in
$M^4_+\times CP_2$ as small surfaces. The time for propagation from A to B is
in general larger in condensate than in vapour phase. In principle observer
detects from a given astrophysical object both vapour phase and condensate
photons, vapour phase photons being emitted later than condensate photons.
Therefore the erraneous identification of vapour phase photons as condensate
photons leads to an over estimate for the age of the star and star can look
older than the Universe. The Hubble constant for vapour phase photons is that
associated with $M^4_+$ and smaller than the Hubble constant of matter
dominated cosmology. This could explain the measured two widely different
values of Hubble constant if smaller Hubble constant corresponds to the Hubble
constant of the future light cone $M^4_+$. The ratio of propagation velocities
of vapour phase and condensate photons equals to ratio of the two Hubble
constants, which in turn is depends on the ratio of mass density and critical
mass density, only. Anomalously large redshifts are possible since vapour phase
photons can come also from region outside the horizon. | Quasi-normal modes for doubly rotating black holes: Based on the work of Chen, L\"u and Pope, we derive expressions for the
$D\geq 6$ dimensional metric for Kerr-(A)dS black holes with two independent
rotation parameters and all others set equal to zero: $a_1\neq 0, a_2\neq0,
a_3=a_4=...=0$. The Klein-Gordon equation is then explicitly separated on this
background. For $D\geq 6$ this separation results in a radial equation coupled
to two generalized spheroidal angular equations. We then develop a full
numerical approach that utilizes the Asymptotic Iteration Method (AIM) to find
radial Quasi-Normal Modes (QNMs) of doubly rotating flat Myers-Perry black
holes for slow rotations. We also develop perturbative expansions for the
angular quantum numbers in powers of the rotation parameters up to second
order. |
Bose-Einstein Condensation in Compactified Spaces: We discuss the thermodynamic potential of a charged Bose gas with the
chemical potential in arbitrary dimensions. The critical temperature for
Bose-Einstein condensation is investigated. In the case of the compactified
background metric, it is shown that the critical temperature depends on the
size of the extra spaces. The asymmetry of the "Kaluza-Klein charge" is also
discussed. | Spectral Networks and Snakes: We apply and illustrate the techniques of spectral networks in a large
collection of A_{K-1} theories of class S, which we call "lifted A_1 theories."
Our construction makes contact with Fock and Goncharov's work on higher
Teichmuller theory. In particular we show that the Darboux coordinates on
moduli spaces of flat connections which come from certain special spectral
networks coincide with the Fock-Goncharov coordinates. We show, moreover, how
these techniques can be used to study the BPS spectra of lifted A_1 theories.
In particular, we determine the spectrum generators for all the lifts of a
simple superconformal field theory. |
Aspects of moduli stabilization in type IIB string theory: We review moduli stabilization in type IIB string theory compactification
with fluxes. We focus on the KKLT and Large Volume Scenario (LVS). We show that
the predicted soft SUSY breaking terms in KKLT model are not phenomenological
viable. In LVS, the following result for scalar mass, gaugino mass, and
trilinear term is obtained: $m_0 =m_{1/2}= - A_0=m_{3/2}$, which may account
for Higgs mass limit if $m_{3/2} \sim {\cal O}(1.5)$ TeV. However, in this case
the relic abundance of the lightest neutralino can not be consistent with the
measured limits. We also study the cosmological consequences of moduli
stabilization in both models. In particular, the associated inflation models
such as racetrack inflation and K\"ahler inflation are analyzed. Finally the
problem of moduli destabilization and the effect of string moduli backreaction
on the inflation models are discussed. | 3d Expansions of 5d Instanton Partition Functions: We propose a set of novel expansions of Nekrasov's instanton partition
functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary
gauge group on $\mathbb{C}^2_{q,t^{-1}} \times \mathbb{S}^1$, we show that the
instanton partition function admits expansions in terms of partition functions
of unitary gauge theories living on the 3d subspaces $\mathbb{C}_{q} \times
\mathbb{S}^1$, $\mathbb{C}_{t^{-1}} \times \mathbb{S}^1$ and their intersection
along $\mathbb{S}^1$. These new expansions are natural from the BPS/CFT
viewpoint, as they can be matched with $W_{q,t}$ correlators involving an
arbitrary number of screening charges of two kinds. Our constructions
generalize and interpolate existing results in the literature. |
Equivariant Localization of Path Integrals: We review equivariant localization techniques for the evaluation of Feynman
path integrals. We develop systematic geometric methods for studying the
semi-classical properties of phase space path integrals for dynamical systems,
emphasizing the relations with integrable and topological quantum field
theories. Beginning with a detailed review of the relevant mathematical
background -- equivariant cohomology and the Duistermaat-Heckman theorem, we
demonstrate how the localization ideas are related to classical integrability
and how they can be formally extended to derive explicit localization formulas
for path integrals in special instances using BRST quantization techniques.
Various loop space localizations are presented and related to notions in
quantum integrability and topological field theory. We emphasize the common
symmetries that such localizable models always possess and use these symmetries
to discuss the range of applicability of the localization formulas. A number of
physical and mathematical applications are presented in connection with
elementary quantum mechanics, Morse theory, index theorems, character formulas
for semi-simple Lie groups, quantization of spin systems, unitary integrations
in matrix models, modular invariants of Riemann surfaces, supersymmetric
quantum field theories, two-dimensional Yang-Mills theory, conformal field
theory, cohomological field theories and the loop expansion in quantum field
theory. Some modern techniques of path integral quantization, such as coherent
state methods, are also discussed. The relations between equivariant
localization and other ideas in topological field theory, such as the
Batalin-Fradkin-Vilkovisky and Mathai-Quillen formalisms, are presented. | A note on transition in discrete gauge groups in F-theory: We observe a new puzzling physical phenomenon in F-theory on the multisection
geometry, wherein a model without a gauge group transitions to another model
with a discrete $\mathbb{Z}_n$ gauge group via Higgsing. This phenomenon may
suggest an unknown aspect of F-theory compactification on multisection geometry
lacking a global section. A possible interpretation of this puzzling physical
phenomenon is proposed in this note. We also propose a possible interpretation
of another unnatural physical phenomenon observed for F-theory on four-section
geometry, wherein a discrete $\mathbb{Z}_2$ gauge group transitions to a
discrete $\mathbb{Z}_4$ gauge group via Higgsing as described in the previous
literature. |
Critical and Tricritical Points for the Massless 2d Gross-Neveu Model
Beyond Large N: Using optimized perturbation theory, we evaluate the effective potential for
the massless two dimensional Gross-Neveu model at finite temperature and
density containing corrections beyond the leading large-N contribution. For
large-N, our results exactly reproduce the well known 1/N leading order results
for the critical temperature, chemical potential and tricritical points. For
finite N, our critical values are smaller than the ones predicted by the
large-N approximation and seem to observe Landau's theorem for phase
transitions in one space dimension. New analytical results are presented for
the tricritical points that include 1/N corrections. The easiness with which
the calculations and renormalization are carried out allied to the seemingly
convergent optimized results displayed, in this particular application, show
the robustness of this method and allows us to obtain neat analytical
expressions for the critical as well as tricritical values beyond the results
currently known. | Schrödinger Functional and Quantization of Gauge Theories in the
Temporal Gauge: In the language of Feynman path integrals the quantization of gauge theories
is most easily carried out with the help of the Schr\"odinger Functional (SF).
Within this formalism the essentially unique gauge fixing condition is
$A_{\circ} = 0$ (temporal gauge), as any other rotationally invariant gauge
choice can be shown to be functionally equivalent to the former. In the
temporal gauge Gauss' law is automatically implemented as a constraint on the
states. States not annihilated by the Gauss operator describe the situation in
which external (infinitely heavy) colour sources interact with the gauge field.
The SF in the presence of an arbitrary distribution of external colour sources
can be expressed in an elegant and concise way. |
High energy QCD from Planckian scattering in AdS and the Froissart bound: We reanalyze high energy QCD scattering regimes from scattering in cut-off
AdS via gravity-gauge dualities (a la Polchinski-Strassler). We look at 't
Hooft scattering, Regge behaviour and black hole creation in AdS. Black hole
creation in the gravity dual is analyzed via gravitational shockwave
collisions. We prove the saturation of the QCD Froissart unitarity bound,
corresponding to the creation of black holes of AdS size, as suggested by
Giddings. | On the Entanglement of Multiple CFTs via Rotating Black Hole Interior: We study the minimal surfaces between two of the multiple boundaries of 3d
maximally extended rotating eternal black hole. Via AdS/CFT, this corresponds
to investigating the behavior of entanglements of the boundary CFT with
multiple sectors. Non-trivial time evolutions of such entanglements detect the
geometry inside the horizon, and behave differently depending on the choice of
the two boundaries. |
Conjectures for Large N Superconformal N=4 Chiral Primary Four Point
Functions: An expression for the four point function for half-BPS operators belonging to
the [0,p,0] SU(4) representation in N=4 superconformal theories at strong
coupling in the large N limit is suggested for any p. It is expressed in terms
of the four point integrals defined by integration over AdS_5 and agrees with,
and was motivated by, results for p=2,3,4 obtained via the AdS/CFT
correspondence. Using crossing symmetry and unitarity, the detailed form is
dictated by the requirement that at large N the contribution of long multiplets
with twist less than 2p, which do not have anomalous dimensions, should cancel
corresponding free field contributions. | Near BPS Skyrmions and Restricted Harmonic Maps: Motivated by a class of near BPS Skyrme models introduced by Adam,
S\'anchez-Guill\'en and Wereszczy\'nski, the following variant of the harmonic
map problem is introduced: a map $\phi:(M,g)\rightarrow (N,h)$ between
Riemannian manifolds is restricted harmonic (RH) if it locally extremizes $E_2$
on its $SDiff(M)$ orbit, where $SDiff(M)$ denotes the group of volume
preserving diffeomorphisms of $(M,g)$, and $E_2$ denotes the Dirichlet energy.
It is conjectured that near BPS skyrmions tend to RH maps in the BPS limit. It
is shown that $\phi$ is RH if and only if $\phi^*h$ has exact divergence, and a
linear stability theory of RH maps is developed, whence it follows that all
weakly conformal maps, for example, are stable RH. Examples of RH maps in every
degree class $R^3\to SU(2)$ and $R^2\to S^2$ are constructed. It is shown that
the axially symmetric BPS skyrmions on which all previous analytic studies of
near BPS Skyrme models have been based, are not RH, so each such field can be
deformed along $SDiff(R^3)$ to yield BPS skyrmions with lower $E_2$, casting
doubt on the predictions of such studies. The problem of minimizing $E_2$ for
$\phi:R^k\to N$ over all linear volume preserving diffeomorphisms is solved
explicitly, and a deformed axially symmetric family of Skyrme fields
constructed which are candidates for approximate near BPS skyrmions at low
baryon number. The notion of restricted harmonicity is generalized to
restricted $F$-criticality where $F$ is any functional on maps $(M,g)\to (N,h)$
which is, in a precise sense, geometrically natural. The case where $F$ is a
linear combination of $E_2$ and $E_4$, the usual Skyrme term, is studied in
detail, and it is shown that inverse stereographic projection $R^3\to S^3\equiv
SU(2)$ is stable restricted $F$-critical for every such $F$. |
On $p$-adic string amplitudes in the limit $p$ approaches to one: In this article we discuss the limit $p$ approaches to one of tree-level
$p$-adic open string amplitudes and its connections with the topological zeta
functions. There is empirical evidence that $p$-adic strings are related to the
ordinary strings in the $p \to 1$ limit. Previously, we established that
$p$-adic Koba-Nielsen string amplitudes are finite sums of multivariate Igusa's
local zeta functions, consequently, they are convergent integrals that admit
meromorphic continuations as rational functions. The meromorphic continuation
of local zeta functions has been used for several authors to regularize
parametric Feynman amplitudes in field and string theories. Denef and Loeser
established that the limit $p \to 1$ of a Igusa's local zeta function gives
rise to an object called topological zeta function. By using Denef-Loeser's
theory of topological zeta functions, we show that limit $p \to 1$ of
tree-level $p$-adic string amplitudes give rise to certain amplitudes, that we
have named Denef-Loeser string amplitudes. Gerasimov and Shatashvili showed
that in limit $p \to 1$ the well-known non-local effective Lagrangian
(reproducing the tree-level $p$-adic string amplitudes) gives rise to a simple
Lagrangian with a logarithmic potential. We show that the Feynman amplitudes of
this last Lagrangian are precisely the amplitudes introduced here. Finally, the
amplitudes for four and five points are computed explicitly. | The Nonperturbative Gauge Coupling of N=2 Supersymmetric Theories: We argue that the topology of the quantum coupling space and the low energy
effective action on the Coulomb branch of scale invariant N=2 SU(n) gauge
theories pick out a preferred nonperturbative definition of the gauge coupling
up to non-singular holomorphic reparametrizations. |
Evaluation of the Free Energy of Two-Dimensional Yang-Mills Theory: The free energy in the weak-coupling phase of two-dimensional Yang-Mills
theory on a sphere for SO(N) and Sp(N) is evaluated in the 1/N expansion using
the techniques of Gross and Matytsin. Many features of Yang-Mills theory are
universal among different gauge groups in the large N limit, but significant
differences arise in subleading order in 1/N. | Statistical mechanics of strings with Y-junctions: We investigate the Hagedorn transitions of string networks with Y-junctions
as may occur, for example, with (p,q) cosmic superstrings. In a simplified
model with three different types of string, the partition function reduces to
three generalised coupled XY models. We calculate the phase diagram and show
that, as the system is heated, the lightest strings first undergo the Hagedorn
transition despite the junctions. There is then a second, higher, critical
temperature above which infinite strings of all tensions, and junctions, exist.
Conversely, on cooling to low temperatures, only the lightest strings remain,
but they collapse into small loops. |
Non-perturbative 2d quantum gravity and hamiltonians unbounded from
below: We show how the stochastic stabilization provides both the weak coupling
genus expansion and a strong coupling expansion of 2d quantum gravity. The
double scaling limit is described by a hamiltonian which is unbounded from
below, but which has a discrete spectrum. | Black Hole Superpartners and Fixed Scalars: Some bosonic solutions of supergravities admit Killing spinors of unbroken
supersymmetry. The anti-Killing spinors of broken supersymmetry can be used to
generate the superpartners of stringy black holes. This has a consequent
feedback on the metric and the graviphoton. We have found however that the
fixed scalars for the black hole superpartners remain the same as for the
original black holes. Possible phenomenological implications of this result are
discussed. |
Conformal Field Theory and Geometry of Strings: What is quantum geometry? This question is becoming a popular leitmotiv in
theoretical physics and in mathematics. Conformal field theory may catch a
glimpse of the right answer. We review global aspects of the geometry of
conformal fields, such as duality and mirror symmetry, and interpret them
within Connes' non-commutative geometry. Extended version of lectures given by
the 2nd author at the Mathematical Quantum Theory Conference, Vancouver,
Canada, August 4 to 8, 1993 | Supergravity and M-Theory: Supergravity provides the effective field theories for string
compactifications. The deformation of the maximal supergravities by non-abelian
gauge interactions is only possible for a restricted class of charges.
Generically these `gaugings' involve a hierarchy of p-form fields which belong
to specific representations of the duality group. The group-theoretical
structure of this p-form hierarchy exhibits many interesting features. In the
case of maximal supergravity the class of allowed deformations has intriguing
connections with M/string theory. |
Three-generation Asymmetric Orbifold Models from Heterotic String Theory: Using Z3 asymmetric orbifolds in heterotic string theory, we construct N=1
SUSY three-generation models with the standard model gauge group SU(3)_C \times
SU(2)_L \times U(1)_Y and the left-right symmetric group SU(3)_C \times SU(2)_L
\times SU(2)_R \times U(1)_{B-L}. One of the models possesses a gauge flavor
symmetry for the Z3 twisted matter. | Degenerate Rotating Black Holes, Chiral CFTs and Fermi Surfaces I -
Analytic Results for Quasinormal Modes: In this work we discuss charged rotating black holes in $AdS_5 \times S^5$
that degenerate to extremal black holes with zero entropy. These black holes
have scaling properties between charge and angular momentum similar to those of
Fermi surface operators in a subsector of $\mathcal{N}=4$ SYM. We add a
massless uncharged scalar to the five dimensional supergravity theory, such
that it still forms a consistent truncation of the type IIB ten dimensional
supergravity and analyze its quasinormal modes. Separating the equation of
motion to a radial and angular part, we proceed to solve the radial equation
using the asymptotic matching expansion method applied to a Heun equation with
two nearby singularities. We use the continued fraction method for the angular
Heun equation and obtain numerical results for the quasinormal modes. In the
case of the supersymmetric black hole we present some analytic results for the
decay rates of the scalar perturbations. The spectrum of quasinormal modes
obtained is similar to that of a chiral 1+1 CFT, which is consistent with the
conjectured field-theoretic dual. In addition, some of the modes can be found
analytically. |
Yang-Mills condensates in cosmology: We discuss homogeneous and isotropic cosmological models driven by SU(2)
gauge fields in the framework of Einstein gravity. There exists a Yang-Mills
field configuration, parametrized by a single scalar function, which consists
of parallel electric and magnetic fields and has the stress tensor mimicking an
homogeneous and isotropic fluid. The unique SU(2) gauge theory with spontaneous
symmetry breaking sharing the same property is the Yang-Mills coupled to the
complex doublet Higgs, this exists only in the case of the closed universe.
This model contains an intrinsic mechanism for inflation due to the Higgs
potential. Our second goal is to show that a successful inflation can be
achieved also within the pure Yang-Mills theory adding an appropriate
theta-term. | Compensating Fields and Anomalies in Supergravity: We discuss the quantization of theories which are formulated using
compensating fields. In particular, we discuss the relation between the
components formulation and the superspace formulation of supergravity theories.
The requirement that the compensating field can be eliminated at the quantum
level gives rise to on-shell constraints on the operators of the theory. In
some cases, the constraints turn out to be physically unacceptable. Using these
considerations we show that new minimal supergravity is in general anomalous. |
The crossing multiplier for solvable lattice models: We study the large class of solvable lattice models, based on the data of
conformal field theory.
These models are constructed from any conformal field theory.
We consider the lattice models based on affine algebras described by Jimbo et
al., for the algebras $ABCD$ and by Kuniba et al. for $G_2$. We find a general
formula for the crossing multipliers of these models. It is shown that these
crossing multipliers are also given by the principally specialized characters
of the model in question. Therefore we conjecture that the crossing multipliers
in this large class of solvable interaction round the face lattice models are
given by the characters of the conformal field theory on which they are based.
We use this result to study the local state probabilities of these models and
show that they are given by the branching rule, in regime III. | On the Symmetry Foundation of Double Soft Theorems: Double-soft theorems, like its single-soft counterparts, arises from the
underlying symmetry principles that constrain the interactions of massless
particles. While single soft theorems can be derived in a non-perturbative
fashion by employing current algebras, recent attempts of extending such an
approach to known double soft theorems has been met with difficulties. In this
work, we have traced the difficulty to two inequivalent expansion schemes,
depending on whether the soft limit is taken asymmetrically or symmetrically,
which we denote as type A and B respectively. We show that soft-behaviour for
type A scheme can simply be derived from single soft theorems, and are thus
non-preturbatively protected. For type B, the information of the four-point
vertex is required to determine the corresponding soft theorems, and thus are
in general not protected. This argument can be readily extended to general
multi-soft theorems. We also ask whether unitarity can be emergent from
locality together with the two kinds of soft theorems, which has not been fully
investigated before. |
Lorentz-invariant CPT violation: A Lorentz-invariant CPT violation, which may be termed as long-distance CPT
violation in contrast to the familiar short-distance CPT violation, has been
recently proposed. This scheme is based on a non-local interaction vertex and
characterized by an infrared divergent form factor. We show that the Lorentz
covariant $T^{\star}$-product is consistently defined and the energy-momentum
conservation is preserved in perturbation theory if the path integral is
suitably defined for this non-local theory, although unitarity is generally
lost. It is illustrated that T violation is realized in the decay and formation
processes. It is also argued that the equality of masses and decay widths of
the particle and anti-particle is preserved if the non-local CPT violation is
incorporated either directly or as perturbation by starting with the
conventional CPT-even local Lagrangian. However, we also explicitly show that
the present non-local scheme can induce the splitting of particle and
anti-particle mass eigenvalues if one considers a more general class of
Lagrangians. | Rotational Invariance in the M(atrix) Formulation of Type IIB Theory: The matrix model formulation of M-theory can be generalized by
compactification to ten-dimensional type II string theory, formulated in the
infinite momentum frame. Both the type IIA and IIB string theories can be
formulated in this way. In the M-theory and type IIA cases, the transverse
rotational invariance is manifest, but in the IIB case, one of the transverse
dimensions materializes in a completely different way from the other seven. The
full O(8) rotational symmetry then follows in a surprising way from the
electric-magnetic duality of supersymmetric Yang-Mills field theory. |
Topological Defects and the Trial Orbit Method: We deal with the presence of topological defects in models for two real
scalar fields. We comment on defects hosting topological defects, and we search
for explicit defect solutions using the trial orbit method. As we know, under
certain circumstances the second order equations of motion can be solved by
first order differential equations. In this case we show that the trial orbit
method can be used very efficiently to obtain explicit solutions. | Chiral approach to partially-massless fields: We propose a new (chiral) description of partially-massless fields in $4d$,
including the partially-massless graviton, that is similar to the pure
connection formulation for gravity and massless higher spin fields, the latter
having a clear twistor origin. The new approach allows us to construct complete
examples of higher spin gravities with (partially-)massless fields that feature
Yang--Mills and current interactions. |
AdS$_3$/AdS$_2$ degression of massless particles: We study a 3d/2d dimensional degression which is a Kaluza-Klein type
mechanism in AdS$_3$ space foliated into AdS$_2$ hypersurfaces. It is shown
that an AdS$_3$ massless particle of spin $s=1,2,...,\infty$ degresses into a
couple of AdS$_2$ particles of equal energies $E=s$. Note that the Kaluza-Klein
spectra in higher dimensions are always infinite. To formulate the
AdS$_3$/AdS$_2$ degression we consider branching rules for AdS$_3$ isometry
algebra o$(2,2)$ representations decomposed with respect to AdS$_2$ isometry
algebra o$(1,2)$. We find that a given o$(2,2)$ higher-spin representation
lying on the unitary bound (i.e. massless) decomposes into two equal o$(1,2)$
modules. In the field-theoretical terms, this phenomenon is demonstrated for
spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can
be seen by using particular mode expansions, (partial) diagonalizations, and
identities specific to two dimensions. | Incoherent conductivity of holographic charge density waves: The DC resistivity of charge density waves weakly-pinned by disorder is
controlled by diffusive, incoherent processes rather than slow momentum
relaxation. The corresponding incoherent conductivity can be computed in the
limit of zero disorder. We compute this transport coefficient in holographic
spatially modulated breaking translations spontaneously. As a by-product of our
analysis, we clarify how the boundary heat current is obtained from a conserved
bulk current, defined as a suitable generalization of the Iyer-Wald Noether
current of the appropriate Killing vector. |
Superconformal Indices for ${\cal N}=6$ Chern Simons Theories: Aharony, Bergman, Jafferis and Maldacena have recently proposed a dual
gravitational description for a family of superconformal Chern Simons theories
in three spacetime dimensions. In this note we perform the one loop computation
that determines the field theory superconformal index of this theory and
compare with the index computed over the Fock space of dual supersymmetric
gravitons. In the appropriate limit (large $N$ and large $k$) we find a perfect
match. | Holographic OPE Coefficients from AdS Black Holes with Matters: We study the OPE coefficients $c_{\Delta, J}$ for heavy-light scalar
four-point functions, which can be obtained holographically from the two-point
function of a light scalar of some non-integer conformal dimension $\Delta_L$
in an AdS black hole. We verify that the OPE coefficient $c_{d,0}=0$ for pure
gravity black holes, consistent with the tracelessness of the holographic
energy-momentum tensor. We then study the OPE coefficients from black holes
involving matter fields. We first consider general charged AdS black holes and
we give some explicit low-lying examples of the OPE coefficients. We also
obtain the recursion formula for the lowest-twist OPE coefficients with at most
two current operators. For integer $\Delta_L$, although the OPE coefficients
are not fully determined, we set up a framework to read off the coefficients
$\gamma_{\Delta,J}$ of the $\log(z\bar{z})$ terms that are associated with the
anomalous dimensions of the exchange operators and obtain a general formula for
$\gamma_{\Delta,J}$. We then consider charged AdS black holes in gauged
supergravity STU models in $D=5$ and $D=7$, and their higher-dimensional
generalizations. The scalar fields in the STU models are conformally massless,
dual to light operators with $\Delta_L=d-2$. We derive the linear perturbation
of such a scalar in the STU charged AdS black holes and obtain the explicit OPE
coefficient $c_{d-2,0}$. Finally, we analyse the asymptotic properties of
scalar hairy AdS black holes and show how $c_{d,0}$ can be nonzero with
exchanging scalar operators in these backgrounds. |
Hamiltonian cosmology in bigravity and massive gravity: In the Hamiltonian language we provide a study of flat-space cosmology in
bigravity and massive gravity constructed mostly with de Rham, Gabadadze,
Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are
powerful not only in proving the absence of the Boulware-Deser ghost, but also
in solving other problems. The purpose of this work is to give an introduction
both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch
three roads to the Hamiltonian of bigravity with the dRGT potential: the
metric, the tetrad and the minisuperspace approaches. | Perturbative unitarity of Lee-Wick quantum field theory: We study the perturbative unitarity of the Lee-Wick models, formulated as
nonanalytically Wick rotated Euclidean theories. The complex energy plane is
divided into disconnected regions and the values of a loop integral in the
various regions are related to one another by a nonanalytic procedure. We show
that the one-loop diagrams satisfy the expected, unitary cutting equations in
each region: only the physical degrees of freedom propagate through the cuts.
The goal can be achieved by working in suitable subsets of each region and
proving that the cutting equations can be analytically continued as a whole. We
make explicit calculations in the cases of the bubble and triangle diagrams and
address the generality of our approach. We also show that the same
higher-derivative models violate unitarity if they are formulated directly in
Minkowski spacetime. |
On unitarity of the Coon amplitude: The Coon amplitude is a one-parameter deformation of the Veneziano amplitude.
We explore the unitarity of the Coon amplitude through its partial wave
expansion using tools from $q$-calculus. Our analysis establishes manifest
positivity on the leading and sub-leading Regge trajectories in arbitrary
spacetime dimensions $D$, while revealing a violation of unitarity in a certain
region of $(q,D)$ parameter space starting at the sub-sub-leading Regge order.
A combination of numerical studies and analytic arguments allows us to argue
for the manifest positivity of the partial wave coefficients in fixed spin and
Regge asymptotics. | M Theory Extensions of T Duality: T duality expresses the equivalence of a superstring theory compactified on a
manifold K to another (possibly the same) superstring theory compactified on a
dual manifold K'. The volumes of K and K' are inversely proportional. In this
talk we consider two M theory generalizations of T duality: (i) M theory
compactified on a torus is equivalent to type IIB superstring theory
compactified on a circle and (ii) M theory compactified on a cylinder is
equivalent to SO(32) superstring theory compactified on a circle. In both cases
the size of the circle is proportional to the -3/4 power of the area of the
dual manifold. |
Stringy effect of the holographic correspondence for Dp-brane
backgrounds: Based on the holographic conjecture for superstrings on Dp-brane backgrounds
and the dual (p+1)-dimensional gauge theory ($0\le p\le 4$) given in
hep-th/0308024 and hep-th/0405203, we continue the study of superstring
amplitudes including string higher modes ($n\ne 0$). We give a prediction to
the two-point functions of operators with large R-charge J. The effect of
stringy modes do not appear as the form of anomalous dimensions except for p=3.
Instead, it gives non-trivial correction to the two-point functions for
supergravity modes. For p=4, the scalar two-point functions for any n behave
like free fields of the effective dimension d_{eff}=6 in the infra-red limit. | Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA
perspective: We revisit the correspondence between Calabi-Yau (CY) threefold isolated
singularities $\mathbf{X}$ and five-dimensional superconformal field theories
(SCFTs), which arise at low energy in M-theory on the space-time transverse to
$\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the
"gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA
duality. In this setup, the low-energy gauge group simply arises on stacks of
coincident D6-branes wrapping 2-cycles in some ALE space of type $A_{M-1}$
fibered over a real line, and the map between the K\"ahler parameters of
$\mathbf{X}$ and the Coulomb branch parameters of the field theory (masses and
VEVs) can be read off systematically. Different type IIA "reductions" give rise
to different gauge theory phases, whose existence depends on the particular
(partial) resolutions of the isolated singularity $\mathbf{X}$. We also comment
on the case of non-isolated toric singularities. Incidentally, we propose a
slightly modified expression for the Coulomb-branch prepotential of 5d
$\mathcal{N}=1$ gauge theories. |
Weak Separation, Positivity and Extremal Yangian Invariants: We classify all positive n-particle N^kMHV Yangian invariants in N=4
Yang-Mills theory with n=5k, which we call extremal because none exist for
n>5k. We show that this problem is equivalent to that of enumerating plane
cactus graphs with k pentagons. We use the known solution of that problem to
provide an exact expression for the number of cyclic classes of such invariants
for any k, and a simple rule for writing them down explicitly. As a byproduct,
we provide an alternative (but equivalent) classification by showing that a
product of k five-brackets with disjoint sets of indices is a positive Yangian
invariant if and only if the sets are all weakly separated. | Excited state Rényi entropy and subsystem distance in two-dimensional
non-compact bosonic theory. Part II. Multi-particle states: We study the excited state R\'enyi entropy and subsystem Schatten distance in
the two-dimensional free massless non-compact bosonic field theory, which is a
conformal field theory. The discretization of the free non-compact bosonic
theory gives the harmonic chain with local couplings. We consider the field
theory excited states that correspond to the harmonic chain states with
excitations of more than one quasiparticle, which we call multi-particle
states. This extends the previous work by the same authors to more general
excited states. In the field theory we obtain the exact R\'enyi entropy and
subsystem Schatten distance for several low-lying states. We also obtain the
short interval expansion of the R\'enyi entropy and subsystem Schatten distance
for general excited states. In the locally coupled harmonic chain we calculate
numerically the excited state R\'enyi entropy and subsystem Schatten distance
using the wave function method. We find excellent matches of the analytical
results in the field theory and numerical results in the gapless limit of the
harmonic chain. We also make some preliminary investigations of the R\'enyi
entropy and the subsystem Schatten distance in the extremely gapped limit of
the harmonic chain. |
Challenges for D-brane large-field inflation with stabilizer fields: We study possible string theory compactifications which, in the low-energy
limit, describe chaotic inflation with a stabilizer field. We first analyze
type IIA setups where the inflationary potential arises from a D6-brane
wrapping an internal three-cycle, and where the stabilizer field is either an
open-string or bulk K\"ahler modulus. We find that after integrating out the
relevant closed-string moduli consistently, tachyonic directions arise during
inflation which cannot be lifted. This is ultimately due to the shift
symmetries of the type IIA K\"ahler potential at large compactification volume.
This motivates us to search for stabilizer candidates in the complex structure
sector of type IIB orientifolds, since these fields couple to D7-brane Wilson
lines and their shift symmetries are generically broken away from the large
complex structure limit. However, we find that in these setups the challenge is
to obtain the necessary hierarchy between the inflationary and Kaluza-Klein
scales. | Schwarzschild-Tangherlini Metric from Scattering Amplitudes: We present a general framework with which the Schwarzschild-Tangherlini
metric of a point particle in arbitrary dimensions can be derived from a
scattering amplitude to all orders in the gravitational constant, $G_N$, in
covariant gauge (i.e. $R_\xi$-gauge) with a generalized de Donder-type gauge
function, $G_\sigma$. The metric is independent of the covariant gauge
parameter $\xi$ and obeys the classical gauge condition $G_\sigma=0$. We
compute the metric with the generalized gauge choice explicitly to second order
in $G_N$ where gravitational self-interactions become important and these
results verify the general framework to one-loop order. Interestingly, after
generalizing to arbitrary dimension, a logarithmic dependence on the radial
coordinate appears in space-time dimension $D=5$. |
Collective Coordinates in String Theory: The emergence of violations of conformal invariance in the form of non-local
operators in the two-dimensional action describing solitons inevitably leads to
the introduction of collective coordinates as two dimensional ``wormhole
parameters''. | A new approach to the complex-action problem and its application to a
nonperturbative study of superstring theory: Monte Carlo simulations of a system whose action has an imaginary part are
considered to be extremely difficult. We propose a new approach to this
`complex-action problem', which utilizes a factorization property of
distribution functions. The basic idea is quite general, and it removes the
so-called overlap problem completely. Here we apply the method to a
nonperturbative study of superstring theory using its matrix formulation. In
this particular example, the distribution function turns out to be positive
definite, which allows us to reduce the problem even further. Our numerical
results suggest an intuitive explanation for the dynamical generation of 4d
space-time. |
Virasoro Representations on (Diff S1)/S1 Coadjoint Orbits: A new set of realizations of the Virasoro algebra on a bosonic Fock space are
found by explicitly computing the Virasoro representations associated with
coadjoint orbits of the form (Diff S1) / S1. Some progress is made in
understanding the unitary structure of these representations. The characters of
these representations are exactly the bosonic partition functions calculated
previously by Witten using perturbative and fixed-point methods. The
representations corresponding to the discrete series of unitary Virasoro
representations with c <= 1 are found to be reducible in this formulation,
confirming a conjecture by Aldaya and Navarro-Salas. | Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality: Motivated by applications to black hole physics and duality, we study the
effect of higher derivative corrections on the dimensional reduction of
four-dimensional Einstein, Einstein Liouville and Einstein-Maxwell gravity to
one direction, as appropriate for stationary, spherically symmetric solutions.
We construct a field redefinition scheme such that the one-dimensional
Lagrangian is corrected only by powers of first derivatives of the fields,
eliminating spurious modes and providing a suitable starting point for
quantization. We show that the Ehlers symmetry, broken by the leading $R^2$
corrections in Einstein-Liouville gravity, can be restored by including
contributions of Taub-NUT instantons. Finally, we give a preliminary discussion
of the duality between higher-derivative F-term corrections on the vector and
hypermultiplet branches in N=2 supergravity in four dimensions. |
Weight Systems from Feynman Diagrams: We find that the overall UV divergences of a renormalizable field theory with
trivalent vertices fulfil a four-term relation. They thus come close to
establish a weight system. This provides a first explanation of the recent
successful association of renormalization theory with knot theory. | On the Evaluation of the Ray-Singer Torsion Path Integral: There are very few explicit evaluations of path integrals for topological
gauge theories in more than 3 dimensions. Here we provide such a calculation
for the path integral representation of the Ray-Singer Torsion of a flat
connection on a vector bundle on base manifolds that are themselves $S^{1}$
bundles of any dimension. The calculation relies on a suitable algebraic choice
of gauge which leads to a convenient factorisation of the path integral into
horizontal and vertical parts. |
Is there a breakdown of effective field theory at the horizon of an
extremal black hole?: Linear perturbations of extremal black holes exhibit the Aretakis
instability, in which higher derivatives of a scalar field grow polynomially
with time along the event horizon. This suggests that higher derivative
corrections to the classical equations of motion may become large, indicating a
breakdown of effective field theory at late time on the event horizon. We
investigate whether or not this happens. For extremal Reissner-Nordstrom we
argue that, for a large class of theories, general covariance ensures that the
higher derivative corrections to the equations of motion appear only in
combinations that remain small compared to two derivative terms so effective
field theory remains valid. For extremal Kerr, the situation is more
complicated since backreaction of the scalar field is not understood even in
the two derivative theory. Nevertheless we argue that the effects of the higher
derivative terms will be small compared to the two derivative terms as long as
the spacetime remains close to extremal Kerr. | Three-point correlators for giant magnons: Three-point correlation functions in the strong-coupling regime of the
AdS/CFT correspondence can be analyzed within a semiclassical approximation
when two of the vertex operators correspond to heavy string states having large
quantum numbers while the third vertex corresponds to a light state with fixed
charges. We consider the case where the heavy string states are chosen to be
giant magnon solitons with either a single or two different angular momenta,
for various different choices of light string states. |
Quiver gauge theories and integrable lattice models: We discuss connections between certain classes of supersymmetric quiver gauge
theories and integrable lattice models from the point of view of topological
quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} =
1$ theories known as brane box and brane tilling models, 3d $\mathcal{N} = 2$
and 2d $\mathcal{N} = (2,2)$ theories obtained from them by compactification,
and 2d $\mathcal{N} = (0,2)$ theories closely related to these theories. We
argue that their supersymmetric indices carry structures of TQFTs equipped with
line operators, and as a consequence, are equal to the partition functions of
lattice models. The integrability of these models follows from the existence of
extra dimension in the TQFTs, which emerges after the theories are embedded in
M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric
indices under Seiberg duality and its lower-dimensional analogs. | Towards a holographic realization of the quarkyonic phase: Large-N_c QCD matter at intermediate baryon density and low temperatures has
been conjectured to be in the so-called quarkyonic phase, i.e., to have a quark
Fermi surface and on top of it a confined spectrum of excitations. It has been
suggested that the presence of the quark Fermi surface leads to a homogeneous
phase with restored chiral symmetry, which is unstable towards creating
condensates breaking both the chiral and translational symmetry. Motivated by
these exotic features, we investigate properties of cold baryonic matter in the
single flavor Sakai-Sugimoto model searching for a holographic realization of
the quarkyonic phase. We use a simplified mean-field description and focus on
the regime of parametrically large baryon densities, of the order of the square
of the 't Hooft coupling, as they turn out to lead to new physical effects
similar to the ones occurring in the quarkyonic phase. One effect, the
appearance of a particular marginally stable mode breaking translational
invariance and linked with the presence of the Chern-Simons term in the flavor
brane Lagrangian, is known to occur in the deconfined phase of the
Sakai-Sugimoto model, but turns out to be absent here. The other, completely
new phenomenon that we, preliminarily, study using strong simplifying
assumptions are density-enhanced interactions of the flavor brane gauge field
with holographically represented baryons. These seem to significantly affect
the spectrum of vector and axial mesons and might lead to approximate chiral
symmetry restoration in the lowest part of the spectrum, where the mesons start
to qualitatively behave like collective excitations of the dense baryonic
medium. We discuss the relevance of these effects for holographic searches of
the quarkyonic phase and conclude with a discussion of various subtleties
involved in constructing a mean-field holographic description of a dense
baryonic medium. |
On a new type of orbifold equivalence and M-theoretic AdS4/CFT3 duality: We consider the large-N limit of \mathcal{N}=6 U(N) \times U(N)
superconformal Chern-Simons (ABJM) theory with fixed level k, which is
conjectured to be dual to M-theory on AdS4\times (S^7/Z_k) background. We point
out that the so-called orbifold equivalence on the gravity side, combined with
the AdS4/CFT3 duality, predicts a hitherto unknown type of duality on the gauge
theory side. It establishes the equivalence between a class of observables,
which are not necessarily protected by supersymmetry, in strongly coupled ABJM
theories away from the planar approximation, with different values of k and N
but sharing common kN. This limit is vastly different from the planar limit,
and hence from the gauge theory point of view the duality is more difficult to
explain compared to the previously known analogous equivalence between planar
gauge theories, where one can explicitly prove the equivalence diagrammatically
using the dominance of the planar diagrams. | Universality of the universal R-matrix and applications to quantum
integrable systems: Results obtained by us are overviewed from a general set up. The universal
$R$-matrix is exploited to obtain various important relations and structures
involved in quantum group algebra, which are used subsequently for generating
different classes of quantum integrable systems through a systematic scheme.
This recovers known models as well as discovers a series of new ones. |
Scattering Amplitudes and the Navier-Stokes Equation: We explore the scattering amplitudes of fluid quanta described by the
Navier-Stokes equation and its non-Abelian generalization. These amplitudes
exhibit universal infrared structures analogous to the Weinberg soft theorem
and the Adler zero. Furthermore, they satisfy on-shell recursion relations
which together with the three-point scattering amplitude furnish a pure
S-matrix formulation of incompressible fluid mechanics. Remarkably, the
amplitudes of the non-Abelian Navier-Stokes equation also exhibit
color-kinematics duality as an off-shell symmetry, for which the associated
kinematic algebra is literally the algebra of spatial diffeomorphisms. Applying
the double copy prescription, we then arrive at a new theory of a tensor
bi-fluid. Finally, we present monopole solutions of the non-Abelian and tensor
Navier-Stokes equations and observe a classical double copy structure. | Supersymmetry and Lorentzian holonomy in various dimensions: We present a systematic method for constructing manifolds with Lorentzian
holonomy group that are non-static supersymmetric vacua admitting covariantly
constant light-like spinors. It is based on the metric of their Riemannian
counterparts and the realization that, when certain conditions are satisfied,
it is possible to promote constant moduli parameters into arbitrary functions
of the light-cone time. Besides the general formalism, we present in detail
several examples in various dimensions. |
Analytic Solution for Tachyon Condensation in Berkovits' Open
Superstring Field Theory: We present an analytic solution for tachyon condensation on a non-BPS D-brane
in Berkovits' open superstring field theory. The solution is presented as a
product of $2\times 2$ matrices in two distinct $GL_2$ subgroups of the open
string star algebra. All string fields needed for computation of the
nonpolynomial action can be derived in closed form, and the action produces the
expected non-BPS D-brane tension in accordance with Sen's conjecture. We also
comment on how D-brane charges may be encoded in the topology of the tachyon
vacuum gauge orbit. | On aspects of 2-dim dilaton gravity, dimensional reduction and
holography: We discuss aspects of generic 2-dimensional dilaton gravity theories. The
2-dim geometry is in general conformal to $AdS_2$ and has IR curvature
singularities at zero temperature: this can be regulated by a black hole. The
on-shell action is divergent: we discuss the holographic energy-momentum tensor
by adding appropriate counterterms. For theories obtained by dimensional
reduction of the gravitational sector of higher dimensional theories, for
instance higher dimensional $AdS$ gravity as a concrete example, the
2-dimensional description dovetails with the higher dimensional one. We also
discuss more general theories containing an extra scalar field which now drives
nontrivial dynamics. Finally we discuss aspects of the 2-dimensional
cosmological singularities discussed in earlier work. These studies suggest
that generic 2-dim dilaton gravity theories are somewhat distinct from JT
gravity and theories "near JT". |
Microstate Renormalization in Deformed D1-D5 SCFT: We derive the corrections to the conformal dimensions of twisted Ramond
ground states in the deformed two-dimensional $\mathcal N = (4,4)$
superconformal $(\mathbb T^4)^N/S_N$ orbifold theory describing bound states of
the D1-D5 brane system in type IIB superstring theory. Our result holds to
second order in the deformation parameter, and at the large $N$ planar limit.
The method of calculation involves the analytic evaluation of integrals of
four-point functions of two R-charged twisted Ramond fields and two marginal
deformation operators. We also calculate the deviation from zero, at first
order in the considered marginal perturbation, of the structure constant of the
three-point function of two Ramond fields and one deformation operator. | Spinning Kerr black holes with stationary massive scalar clouds: The
large-coupling regime: We study analytically the Klein-Gordon wave equation for stationary massive
scalar fields linearly coupled to spinning Kerr black holes. In particular,
using the WKB approximation, we derive a compact formula for the discrete
spectrum of scalar field masses which characterize the stationary composed
Kerr-black-hole-massive-scalar-field configurations in the large-coupling
regime $M\mu\gg1$ (here $M$ and $\mu$ are respectively the mass of the central
black hole and the proper mass of the scalar field). We confirm our
analytically derived formula for the Kerr-scalar-field mass spectrum with
numerical data that recently appeared in the literature. |
BPS Skyrme Submodels of The Five Dimensional Skyrme Model: In this paper, we search for the BPS skyrmions in some BPS submodels of the
generalized Skyrme model in five-dimensional spacetime using the BPS Lagrangian
method. We focus on the static solutions of the Bogomolny's equations and their
corresponding energies with topological charge $B>0$ is an integer. We consider
two main cases based on the symmetry of the effective Lagrangian of the BPS
submodels, i.e. the spherically symmetric and non-spherically symmetric cases.
For the spherically symmetric case, we find two BPS submodels. The first BPS
submodels consist of a potential term and a term proportional to the square of
the topological current. The second BPS submodels consist of only the Skyrme
term. The second BPS submodel has BPS skyrmions with the same topological
charge $B>1$, but with different energies, that we shall call "topological
degenerate" BPS skyrmions. It also has the usual BPS skyrmions with equal
energies, if the topological charge is a prime number. Another interesting
feature of the BPS skyrmions, with $B>1$, in this BPS submodel, is that these
BPS skyrmions have non-zero pressures in the angular direction. For the
non-spherically symmetric case, there is only one BPS submodel, which is
similar to the first BPS submodel in the spherically symmetric case. We find
that the BPS skyrmions depend on a constant $k$ and for a particular value of
$k$ we obtain the BPS skyrmions of the first BPS submodel in the spherically
symmetric case. The total static energy and the topological charge of these BPS
skyrmions also depend on this constant. We also show that all the results found
in this paper satisfy the full field equations of motions of the corresponding
BPS submodels. | Hierarchical structure of physical Yukawa couplings from matter field
Kähler metric: We study the impacts of matter field K\"ahler metric on physical Yukawa
couplings in string compactifications. Since the K\"ahler metric is non-trivial
in general, the kinetic mixing of matter fields opens a new avenue for
realizing a hierarchical structure of physical Yukawa couplings, even when
holomorphic Yukawa couplings have the trivial structure. The hierarchical
Yukawa couplings are demonstrated by couplings of pure untwisted modes on
toroidal orbifolds and their resolutions in the context of heterotic string
theory with standard embedding. Also, we study the hierarchical couplings among
untwisted and twisted modes on resolved orbifolds. |
Dualities from higher-spin supergravity: We study the vacuum structure of spin-3 higher-spin supergravity in AdS_3
spacetime. The theory can be written as a Chern-Simons theory based on the Lie
superalgebra sl(3|2). We find three distinct AdS_3 vacua, AdS^(1), AdS^(2) and
AdS^(p), each corresponding to one embedding of the osp(1|2) subalgebra into
the sl(3|2) algebra. We explicitly construct the RG flows from AdS^(1) to
AdS^(p) and from AdS^(2) to AdS^(p), which identifies AdS^(p) as an IR vacuum
and AdS^(1), AdS^(2) as two different UV vacua. Thus a duality is found between
the two UV theories in the sense that the two theories, each with a chemical
potential turned on, flow to the same IR theory. Moreover, we identify a
similar structure in the Hamiltonian reductions of the 2d Wess-Zumino-Witten
(WZW) model with sl(3|2)-valued currents by matching the chiral symmetries
there with the asymptotic symmetries of the three different embeddings. Our
computation gives an RG interpretation of (certain types of) the Hamiltonian
reductions. In addition, it gives a hint of a duality between the 3d
higher-spin supergravity and some conformally extended super-Toda theory as
suggested by Mansfield and Spence for the bosonic case. | Interferometric evidence for brane world cosmologies: The hypothesis of brane-embedded matter appears to gain increasing
credibility in astrophysics. However, it can only be truly successful if its
implications on particle interaction are consistent with existing knowledge.
This letter focuses on the issue of optical interference, and shows that at
least one brane-world model can offer plausible interpretations for both
Young's double-slit experiment, and the experiments that fit less neatly with
it. The basic assumption is that particles can interact at a distance through
the vibrations induced by their motion on the brane. The qualitative analysis
of this mechanism suggests that fringe visibility in single photon interference
depends on the energy levels and the interval between interacting particles. A
double-slit experiment, performed with coherent single red photons should
reveal the disappearance of interference when the time delay between individual
particles is increased over 2.18 seconds. In the case of infrared photons with
the frequency of $9\cdot 10^{13}$ Hz, interference must vanish already at the
interval of one second. |
Gaussian Wavefunctional Approach in Thermofield Dynamics: The Gaussian wavefunctional approach is developed in thermofield dynamics. We
manufacture thermal vacuum wavefunctional, its creation as well as annihilation
operators,and accordingly thermo-particle excited states. For a
(D+1)-dimensional scalar field system with an arbitrary potential whose Fourier
representation exists in a sense of tempered distributions, we calculate the
finite temperature Gaussian effective potential (FTGEP), one- and
two-thermo-particle-state energies. The zero-temperature limit of each of them
is just the corresponding result in quantum field theory, and the FTGEP can
lead to the same one of each of some concrete models as calculated by the
imaginary time Green function. | Open Inflation With Scalar-tensor Gravity: The open inflation model recently proposed by Hawking and Turok is
investigated in scalar-tensor gravity context. If the dilaton-like field has no
potential, the instanton of our model is singular but has a finite action. The
Gibbons-Hawking surface term vanishes and hence, can not be used to make
$\Omega_0$ nonzero. To obtain a successful open inflation one should introduce
other matter fields or a potential for the dilaton-like fields. |
Duffin-Kemmer-Petiau equation on the quaternion field: We show that the Klein-Gordon equation on the quaternion field is equivalent
to a pair of DKP equations. We shall also prove that this pair of DKP equations
can be taken back to a pair of new KG equations. We shall emphasize the
important difference between the standard and the new KG equations. We also
present some qualitative arguments, concerning the possibility of interpreting
anomalous solution, within a quaternion quantum field theory. | On the Stratified Classical Configuration Space of Lattice QCD: The stratified structure of the configuration space $\mb G^N = G \times ...
\times G$ reduced with respect to the action of $G$ by inner automorphisms is
investigated for $G = SU(3) .$ This is a finite dimensional model coming from
lattice QCD. First, the stratification is characterized algebraically, for
arbitrary $N$. Next, the full algebra of invariants is discussed for the cases
$N = 1$ and $N =2 .$ Finally, for $N = 1$ and $N =2 ,$ the stratified structure
is investigated in some detail, both in terms of invariants and relations and
in more geometric terms. Moreover, the strata are characterized explicitly
using local cross sections. |
Normalized Observational Probabilities from Unnormalizable Quantum
States or Phase-Space Distributions: Often it is assumed that a quantum state or a phase-space distribution must
be normalizable. Here it is shown that even if it is not normalizable, one may
be able to extract normalized observational probabilities from it. | New Example of Infinite Family of Quiver Gauge Theories: We construct a new infinite family of quiver gauge theories which blow down
to the X^{p,q} quiver gauge theories found by Hanany, Kazakopoulos and Wecht.
This family includes a quiver gauge theory for the third del Pezzo surface. We
show, using Z-minimaization, that these theories generically have irrational
R-charges. The AdS/CFT correspondence implies that the dual geometries are
irregular toric Sasaki-Einstein manifolds, although we do not know the explicit
metrics. |
Gauge/string duality and hadronic physics: We review some recent results on phenomenological approaches to strong
interactions inspired in gauge/string duality. In particular, we discuss how
such models lead to very good estimates for hadronic masses. | Geometric Quantization of the Phase Space of a Particle in a Yang-Mills
Field: The method of geometric quantization is applied to a particle moving on an
arbitrary Riemannian manifold $Q$ in an external gauge field, that is a
connection on a principal $H$-bundle $N$ over $Q$. The phase space of the
particle is a Marsden-Weinstein reduction of $T^*N$, hence this space can also
be considered to be the reduced phase space of a particular type of constrained
mechanical system. An explicit map is found from a subalgebra of the classical
observables to the corresponding quantum operators. These operators are found
to be the generators of a representation of the semi-direct product group,
Aut~$N\lx C^\infty_c(Q)$. A generalised Aharanov-Bohm effect is shown to be a
natural consequence of the quantization procedure. In particular the r\^ole of
the connection in the quantum mechanical system is made clear. The quantization
of the Hamiltonian is also considered. Additionally, our approach allows the
related quantization procedures proposed by Mackey and by Isham to be fully
understood.\\ |
Bridging the Chiral symmetry and Confinement with Singularity: We consider a holographic quark model where the confinement is a consequence
of the quark condensate. Surprisingly, the equation of motion of our
holographic model can be mapped to the old spin-less bag model. Both models
correctly reproduce the linear Regge trajectory of hadrons for zero quark mass.
For the case of non-zero quark mass, the model lead us to Heun's equation. The
mass term is precisely the origin of the higher singularity, which changes the
system behavior drastically. Our result can shed some light on why the chiral
transition is so close to the confinement transition. In the massive case, the
Schroedinger equation is exactly solvable, but only if a surprising new
quantization condition, additional to the energy quantization, is applied. | Perturbation Theory for Antisymmetric Tensor Fields in Four Dimensions: Perturbation theory for a class of topological field theories containing
antisymmetric tensor fields is considered. These models are characterized by a
supersymmetric structure which allows to establish their perturbative
finiteness. |
Fast Scramblers and Non-Commutative Gauge Theories: Fast scramblers are quantum systems which thermalize in a time scale
logarithmic in the number of degrees of freedom of the system. Non-locality has
been argued to be an essential feature of fast scramblers. We provide evidence
in support of the crucial role of non-locality in such systems by considering
the approach to thermalization in a (strongly-coupled) high temperature
non-commutative gauge theory. We show that non-locality inherent to
non-commutative gauge theories does indeed accelerate the rate of dissipation
in the heat bath in stark contrast to the slow random walk diffusive behavior
prevalent in local field theories. | Quantum dress for a naked singularity: We investigate semiclassical backreaction on a conical naked singularity
space-time with a negative cosmological constant in (2+1)-dimensions. In
particular, we calculate the renormalized quantum stress-energy tensor for a
conformally coupled scalar field on such naked singularity space-time. We then
obtain the backreacted metric via the semiclassical Einstein equations. We show
that, in the regime where the semiclassical approximation can be trusted,
backreaction dresses the naked singularity with an event horizon, thus
enforcing cosmic censorship. |
Generalized Vanishing Theorems for Yukawa Couplings in Heterotic
Compactifications: Heterotic compactifications on Calabi-Yau threefolds frequently exhibit
textures of vanishing Yukawa couplings in their low energy description. The
vanishing of these couplings is often not enforced by any obvious symmetry and
appears to be topological in nature. Recent results in the literature used
differential geometric methods to explain the origin of some of this structure.
A vanishing theorem was given which showed that the effect could be attributed,
in part, to the embedding of the Calabi-Yau manifolds of interest inside higher
dimensional ambient spaces, if the gauge bundles involved descended from vector
bundles on those larger manifolds. In this paper, we utilize an
algebro-geometric approach to provide an alternative derivation of some of
these results, and are thus able to generalize them to a much wider arena than
has been considered before. For example, we consider cases where the vector
bundles of interest do not descend from bundles on the ambient space. In such a
manner we are able to highlight the ubiquity with which textures of vanishing
Yukawa couplings can be expected to arise in heterotic compactifications, with
multiple different constraints arising from a plethora of different geometric
features associated to the gauge bundle. | Nonlinear Realization of Supersymmetry and Superconformal Symmetry: Nonlinear realizations describing the spontaneous breakown of supersymmetry
and R symmetry are constructed using the Goldstino and R axion fields. The
associated R current, supersymmetry current and energy-momentum tensor are
shown to be related under the nonlinear supersymmetry transformations.
Nonlinear realizations of the superconformal algebra carried by these degrees
of freedom are also displayed. The divergences of the R and dilatation currents
are related to the divergence of the superconformal currents through nonlinear
supersymmetry transformations which in turn relates the explicit breakings of
these symmetries. |
ADE Double Scaled Little String Theories, Mock Modular Forms and Umbral
Moonshine: We consider double scaled little string theory on $K3$. These theories are
labelled by a positive integer $k \ge 2$ and an $ADE$ root lattice with Coxeter
number $k$. We count BPS fundamental string states in the holographic dual of
this theory using the superconformal field theory $K3 \times \left(
\frac{SL(2,\mathbb{R})_k}{U(1)} \times \frac{SU(2)_k}{U(1)} \right) \big/
\mathbb{Z}_k$. We show that the BPS fundamental string states that are counted
by the second helicity supertrace of this theory give rise to weight two mixed
mock modular forms. We compute the helicity supertraces using two separate
techniques: a path integral analysis that leads to a modular invariant but
non-holomorphic answer, and a Hamiltonian analysis of the contribution from
discrete states which leads to a holomorphic but not modular invariant answer.
From a mathematical point of view the Hamiltonian analysis leads to a mixed
mock modular form while the path integral gives the completion of this mixed
mock modular form. We also compare these weight two mixed mock modular forms to
those that appear in instances of Umbral Moonshine labelled by Niemeier root
lattices $X$ that are powers of $ADE$ root lattices and find that they are
equal up to a constant factor that we determine. In the course of the analysis
we encounter an interesting generalization of Appell-Lerch sums and
generalizations of the Riemann relations of Jacobi theta functions that they
obey. | Electric Dipole Moments of Dyon and `Electron': The electric and magnetic dipole moments of dyon fermions are calculated
within N=2 supersymmetric Yang-Mills theory including the theta-term. It is
found, in particular, that the gyroelectric ratio deviates from the canonical
value of 2 for the monopole fermion (n_m=1,n_e=0) in the case theta\not=0.
Then, applying the S-duality transformation to the result for the dyon
fermions, we obtain an explicit prediction for the electric dipole moment (EDM)
of the charged fermion (`electron'). It is thus seen that the approach
presented here provides a novel method for computing the EDM induced by the
theta-term. |
The Berkovits Method for Conformally Invariant Non-linear Sigma-models
on G/H: We discuss 2-dimmensional non-linear sigma-models on the Kaehler manifold G/H
in the first order formalisim. Using the Berkovits method we explicitly
construct the G-symmetry currents and primaries, when G/H are irreducible. It
is a variant of the Wakimoto realization of the affine Lie algebra using a
particular reducible Kaehler manifold G/U(1)^r with r the rank of G. | On the scattering of gluons in the GKP string: We compute the one-loop S-matrix for the light bosonic excitations of the GKP
string at strong coupling. These correspond, on the gauge theory side, to gluon
insertions in the GKP vacuum. We perform the calculation by Feynman diagrams in
the worldsheet theory and we compare the result to the integrability
prediction, finding perfect agreement for the scheme independent part. For
scheme dependent rational terms we test different schemes and find that a
recent proposal reproduces exactly the integrability prediction. |
Holographic s-wave condensate with non-linear electrodynamics: A
nontrivial boundary value problem: In this paper, considering the probe limit, we analytically study the onset
of holographic s-wave condensate in the planar Schwarzschild-AdS background.
Inspired by various low energy features of string theory, in the present work
we replace the conventional Maxwell action by a (non-linear) Born-Infeld (BI)
action which essentially corresponds to the higher derivative corrections of
the gauge fields. Based on a variational method, which is commonly known as the
Sturm-Liouville (SL) eigenvalue problem and considering a non-trivial
asymptotic solution for the scalar field, we compute the critical temperature
for the s-wave condensation. The results thus obtained analytically agree well
with the numerical findings\cite{hs19}. As a next step, we extend our
perturbative technique to compute the order parameter for the condensation.
Interestingly our analytic results are found to be of the same order as the
numerical values obtained earlier. | Symmetries of generalized soliton models and submodels on target space
$S^2$: Some physically relevant non-linear models with solitons, which have target
space $S^2$, are known to have submodels with infinitly many conservation laws
defined by the eikonal equation. Here we calculate all the symmetries of these
models and their submodels by the prolongation method. We find that for some
models, like the Baby Skyrme model, the submodels have additional symmetries,
whereas for others, like the Faddeev--Niemi model, they do not. |
W_{1+\infty} and W(gl_N) with central charge N: We study representations of the central extension of the Lie algebra of
differential operators on the circle, the W-infinity algebra. We obtain
complete and specialized character formulas for a large class of
representations, which we call primitive; these include all quasi-finite
irreducible unitary representations. We show that any primitive representation
with central charge N has a canonical structure of an irreducible
representation of the W-algebra W(gl_N) with the same central charge and that
all irreducible representations of W(gl_N) with central charge N arise in this
way. We also establish a duality between "integral" modules of W(gl_N) and
finite-dimensional irreducible modules of gl_N, and conjecture their fusion
rules. | The Rational Higher Structure of M-theory: We review how core structures of string/M-theory emerge as higher structures
in super homotopy theory; namely from systematic analysis of the brane bouquet
of universal invariant higher central extensions growing out of the superpoint.
Since super homotopy theory is immensely rich, to start with we consider this
in the rational/infinitesimal approximation which ignores torsion-subgroups in
brane charges and focuses on tangent spaces of super space-time. Already at
this level, super homotopy theory discovers all super $p$-brane species, their
intersection laws, their M/IIA-, T- and S-duality relations, their black brane
avatars at ADE-singularities, including their instanton contributions, and,
last not least, Dirac charge quantization: for the D-branes it recovers twisted
K-theory, rationally, but for the M-branes it gives cohomotopy cohomology
theory. We close with an outlook on the lift of these results beyond the
rational/infinitesimal approximation to a candidate formalization of
microscopic M-theory in super homotopy theory. |
On Finite-Size D-Branes in Superstring Theory: We test exact marginality of the deformation describing the blow-up of a
zero-size D(-1) brane bound to a background of D3-branes by analyzing the
equations of motion of superstring field theory to third order in the size. In
the process we review the derivation of the instanton profile from string
theory, extending it to include $\alpha'$- corrections. | Leading all-loop quantum contribution to the effective potential in the
inflationary cosmology: In this paper, we have constructed quantum effective potentials and used them
to study slow-roll inflationary cosmology. We derived the generalised RG
equation for the effective potential in the leading logarithmic approximation
and applied it to evaluate the potentials of the $T^2$ and $T^4$-models, which
are often used in modern models of slow-roll inflation. We found that while the
one-loop correction strongly affects the potential, breaking its original
symmetry, the contribution of higher loops smoothes the behaviour of the
potential. However, unlike the $\phi^4$-case, we found that the effective
potentials preserve spontaneous symmetry breaking when summing all the leading
corrections. We calculated the spectral indices $n_s$ and $r$ for the effective
potentials of both models and found that they are consistent with the
observational data for a wide range of parameters of the models. |
Massless hook field in AdS(d+1) from the holographic perspective: We systematically consider the AdS/CFT correspondence for a simplest
mixed-symmetry massless gauge field described by hook Young diagram. We
introduce the radial gauge fixing and explicitly solve the Dirichlet problem
for the hook field equations. Solution finding conveniently splits in two
steps. We first define an incomplete solution characterized by a functional
freedom and then impose the boundary conditions. The resulting complete
solution is fixed unambiguously up to boundary values. Two-point correlation
function of hook primary operators is found via the corresponding boundary
effective action computed separately in even and odd boundary dimensions. In
particular, the higher-derivative action for boundary conformal hook fields is
identified with a singular part of the effective action in even dimensions. The
bulk/boundary symmetry transmutation within the Dirichlet boundary problem is
explicitly studied. It is shown that traces of boundary fields are
Stueckelberg-like modes that can be algebraically gauged away so that boundary
fields are traceless. | The ${\cal N} = 8$ Superconformal Bootstrap in Three Dimensions: We analyze the constraints imposed by unitarity and crossing symmetry on the
four-point function of the stress-tensor multiplet of ${\cal N}=8$
superconformal field theories in three dimensions. We first derive the
superconformal blocks by analyzing the superconformal Ward identity. Our
results imply that the OPE of the primary operator of the stress-tensor
multiplet with itself must have parity symmetry. We then analyze the relations
between the crossing equations, and we find that these equations are mostly
redundant. We implement the independent crossing constraints numerically and
find bounds on OPE coefficients and operator dimensions as a function of the
stress-tensor central charge. To make contact with known ${\cal N}=8$
superconformal field theories, we compute this central charge in a few
particular cases using supersymmetric localization. For limiting values of the
central charge, our numerical bounds are nearly saturated by the large $N$
limit of ABJM theory and also by the free $U(1)\times U(1)$ ABJM theory. |
Unitary Rules for Black Hole Evaporation: Hawking has proposed non-unitary rules for computing the probabilistic
outcome of black hole formation. It is shown that the usual interpretation of
these rules violates the superposition principle and energy conservation.
Refinements of Hawking's rules are found which restore both the superposition
principle and energy conservation, but leave completely unaltered Hawking's
prediction of a thermal emission spectrum prior to the endpoint of black hole
evaporation. These new rules violate clustering. They further imply the
existence of superselection sectors, within each of which clustering is
restored and a unitary $S$-matrix is shown to exist. -- This is an expanded
version of a talk given at the Seventh Marcel Grossman Meeting on General
Relativity, Stanford CA. | Higher Spin Black Holes in Three Dimensions: Comments on Asymptotics and
Regularity: In the context of (2+1)--dimensional SL(N,R)\times SL(N,R) Chern-Simons
theory we explore issues related to regularity and asymptotics on the solid
torus, for stationary and circularly symmetric solutions. We display and solve
all necessary conditions to ensure a regular metric and metric-like higher spin
fields. We prove that holonomy conditions are necessary but not sufficient
conditions to ensure regularity, and that Hawking conditions do not necessarily
follow from them. Finally we give a general proof that once the chemical
potentials are turn on -- as demanded by regularity -- the asymptotics cannot
be that of Brown-Henneaux. |
Holographic Flavor Transport in Schroedinger Spacetime: We use gauge-gravity duality to study the transport properties of a finite
density of charge carriers in a strongly-coupled theory with non-relativistic
symmetry. The field theory is N=4 supersymmetric SU(Nc) Yang-Mills theory in
the limit of large Nc and with large 't Hooft coupling, deformed by an
irrelevant operator, coupled to a number Nf of massive N=2 supersymmetric
hypermultiplets in the fundamental representation of the gauge group, i.e.
flavor fields. The irrelevant deformation breaks the relativistic conformal
group down to the Schroedinger group, which has non-relativistic scale
invariance with dynamical exponent z=2. Introducing a finite baryon number
density of the flavor fields provides us with charge carriers. We compute the
associated DC and AC conductivities using the dual gravitational description of
probe D7-branes in an asymptotically Schroedinger spacetime. We generically
find that in the infrared the conductivity exhibits scaling with temperature or
frequency that is relativistic, while in the ultraviolet the scalings appear to
be non-relativistic with dynamical exponent z=2, as expected in the presence of
the irrelevant deformation. | Generalised Virasoro Constructions from Affine Inonu-Wigner Contractions: We present a new method to find solutions of the Virasoro master equations
for any affine Lie algebra $\widehat{g}$. The basic idea is to consider first
the simplified case of an In\"on\"u-Wigner contraction $\widehat{g}_c$ of
$\widehat{g}$ and to extend the Virasoro constructions of $\widehat{g}_c$ to
$\widehat{g}$ by a perturbative expansion in the contraction parameter. The
method is then applied to the orthogonal algebras, leading to fixed-level
multi-parameter Virasoro constructions, which are the generalisations of the
one-parameter Virasoro construction of $\widehat{su}(2)$ at level four. |
Fractional and noncommutative spacetimes: We establish a mapping between fractional and noncommutative spacetimes in
configuration space. Depending on the scale at which the relation is
considered, there arise two possibilities. For a fractional spacetime with
log-oscillatory measure, the effective measure near the fundamental scale
determining the log-period coincides with the non-rotation-invariant but
cyclicity-preserving measure of \kappa-Minkowski. At scales larger than the
log-period, the fractional measure is averaged and becomes a power-law with
real exponent. This can be also regarded as the cyclicity-inducing measure in a
noncommutative spacetime defined by a certain nonlinear algebra of the
coordinates, which interpolates between \kappa-Minkowski and canonical
spacetime. These results are based upon a braiding formula valid for any
nonlinear algebra which can be mapped onto the Heisenberg algebra. | One-Loop Divergences in Simple Supergravity: Boundary Effects: This paper studies the semiclassical approximation of simple supergravity in
Riemannian four-manifolds with boundary, within the framework of
$\zeta$-function regularization. The massless nature of gravitinos, jointly
with the presence of a boundary and a local description in terms of potentials
for spin ${3\over 2}$, force the background to be totally flat. First, nonlocal
boundary conditions of the spectral type are imposed on spin-${3\over 2}$
potentials, jointly with boundary conditions on metric perturbations which are
completely invariant under infinitesimal diffeomorphisms. The axial
gauge-averaging functional is used, which is then sufficient to ensure
self-adjointness. One thus finds that the contributions of ghost and gauge
modes vanish separately. Hence the contributions to the one-loop wave function
of the universe reduce to those $\zeta(0)$ values resulting from physical modes
only. Another set of mixed boundary conditions, motivated instead by local
supersymmetry and first proposed by Luckock, Moss and Poletti, is also
analyzed. In this case the contributions of gauge and ghost modes do not cancel
each other. Both sets of boundary conditions lead to a nonvanishing $\zeta(0)$
value, and spectral boundary conditions are also studied when two concentric
three-sphere boundaries occur. These results seem to point out that simple
supergravity is not even one-loop finite in the presence of boundaries. |
A note on the Hamiltonian structure of transgression forms: By incorporating two gauge connections, transgression forms provide a
generalization of Chern-Simons actions that are genuinely gauge-invariant on
bounded manifolds. In this work, we show that, when defined on a manifold with
a boundary, the Hamiltonian formulation of a transgression field theory can be
consistently carried out without the need to implement regularizing boundary
terms at the level of first-class constraints. By considering boundary
variations of the relevant functionals in the Poisson brackets, the surface
integral in the very definition of a transgression action can be translated
into boundary contributions in the generators of gauge transformations and
diffeomorphisms. This prescription systematically leads to the corresponding
surface charges of the theory, reducing to the general expression for conserved
charges in (higher-dimensional) Chern-Simons theories when one of the gauge
connections in the transgression form is set to zero. | Bosonic (p - 1)-forms in Einstein-Cartan theory of gravity: We introduce bosonic (p - 1)-form fields that couple to the spin connection
of the Einstein-Cartan theory of gravity thus becoming a non-trivial source of
space-time torsion. We analyze all the general features of both the matter and
the gravitational sectors of the theory. Finally we briefly consider the
implications of the existence of such fields in different physical settings. |
Noncommutative deformation of four dimensional Einstein gravity: We construct a model for noncommutative gravity in four dimensions, which
reduces to the Einstein-Hilbert action in the commutative limit. Our proposal
is based on a gauge formulation of gravity with constraints. While the action
is metric independent, the constraints insure that it is not topological. We
find that the choice of the gauge group and of the constraints are crucial to
recover a correct deformation of standard gravity. Using the Seiberg-Witten map
the whole theory is described in terms of the vierbeins and of the Lorentz
transformations of its commutative counterpart. We solve explicitly the
constraints and exhibit the first order noncommutative corrections to the
Einstein-Hilbert action. | Quantising Higher-spin String Theories: In this paper, we examine the conditions under which a higher-spin string
theory can be quantised. The quantisability is crucially dependent on the way
in which the matter currents are realised at the classical level. In
particular, we construct classical realisations for the $W_{2,s}$ algebra,
which is generated by a primary spin-$s$ current in addition to the
energy-momentum tensor, and discuss the quantisation for $s\le8$. From these
examples we see that quantum BRST operators can exist even when there is no
quantum generalisation of the classical $W_{2,s}$ algebra. Moreover, we find
that there can be several inequivalent ways of quantising a given classical
theory, leading to different BRST operators with inequivalent cohomologies. We
discuss their relation to certain minimal models. We also consider the
hierarchical embeddings of string theories proposed recently by Berkovits and
Vafa, and show how the already-known $W$ strings provide examples of this
phenomenon. Attempts to find higher-spin fermionic generalisations lead us to
examine the whether classical BRST operators for $W_{2,{n\over 2}}$ ($n$ odd)
algebras can exist. We find that even though such fermionic algebras close up
to null fields, one cannot build nilpotent BRST operators, at least of the
standard form. |
Spectral functions in the $φ^4$-theory from the spectral DSE: We develop a non-perturbative functional framework for computing real-time
correlation functions in strongly correlated systems. The framework is based on
the spectral representation of correlation functions and dimensional
regularisation. Therefore, the non-perturbative spectral renormalisation setup
here respects all symmetries of the theories at hand. In particular this
includes space-time symmetries as well as internal symmetries such as chiral
symmetry, and gauge symmetries. Spectral renormalisation can be applied within
general functional approaches such as the functional renormalisation group,
Dyson-Schwinger equations, and two- or $n$-particle irreducible approaches. As
an application we compute the full, non-perturbative, spectral function of the
scalar field in the $\phi^4$-theory in $2+1$ dimensions from spectral
Dyson-Schwinger equations. We also compute the $s$-channel spectral function of
the full $\phi^4$-vertex in this theory. | Structural aspects of FRG in quantum tunnelling computations: We probe both the unidimensional quartic harmonic oscillator and the double
well potential through a numerical analysis of the Functional Renormalization
Group flow equations truncated at first order in the derivative expansion. The
two partial differential equations for the potential V_k(varphi) and the wave
function renormalization Z_k(varphi), as obtained in different schemes and with
distinct regulators, are studied down to k=0, and the energy gap between lowest
and first excited state is computed, in order to test the reliability of the
approach in a strongly non-perturbative regime. Our findings point out at least
three ranges of the quartic coupling lambda, one with higher lambda where the
lowest order approximation is already accurate, the intermediate one where the
inclusion of the first correction produces a good agreement with the exact
results and, finally, the one with smallest lambda where presumably the higher
order correction of the flow is needed. Some details of the specifics of the
infrared regulator are also discussed. |
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