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Critical mass renormalization in renormalized phi4 theories in two and
three dimensions: We consider the O(N)-symmetric phi4 theory in two and three dimensions and
determine the nonperturbative mass renormalization needed to obtain the phi4
continuum theory. The required nonperturbative information is obtained by
resumming high-order perturbative series in the massive renormalization scheme,
taking into account their Borel summability and the known large-order behavior
of the coefficients. The results are in good agreement with those obtained in
lattice calculations. | Measurement of the Schrodinger wave of a single particle: We show that it is possible to measure Schrodinger wave of a single quantum
system. This provides a strong argument for associating physical reality with
the quantum state of a single system, and challenges the usual assumption that
the quantum state has physical meaning only for an ensemble of identical
systems. |
Black holes and Bhargava's invariant theory: Attractor black holes in type II string compactifications on $K3 \times T^2$
are in correspondence with equivalence classes of binary quadratic forms. The
discriminant of the quadratic form governs the black hole entropy, and the
count of attractor black holes at a given entropy is given by a class number.
Here, we show this tantalizing relationship between attractors and arithmetic
can be generalized to a rich family, connecting black holes in supergravity and
string models with analogous equivalence classes of more general forms under
the action of arithmetic groups. Many of the physical theories involved have
played an earlier role in the study of "magical" supergravities, while their
mathematical counterparts are directly related to geometry-of-numbers examples
in the work of Bhargava et. al.
This paper is dedicated to the memory of Peter Freund. The last section is
devoted to some of M.G's personal reminiscences of Peter Freund. | Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM
Construction: We study an extension of the ADHM construction to give deformed
anti-self-dual (ASD) instantons in N=1/2 super Yang-Mills theory with U(n)
gauge group. First we extend the exterior algebra on superspace to
non(anti)commutative superspace and show that the N=1/2 super Yang-Mills theory
can be reformulated in a geometrical way. By using this exterior algebra, we
formulate a non(anti)commutative version of the super ADHM construction and
show that the curvature two-form superfields obtained by our construction do
satisfy the deformed ASD equations and thus we establish the deformed super
ADHM construction. We also show that the known deformed U(2) one instanton
solution is obtained by this construction. |
Higher Derivative Correction to the Hawking Flux via Trace Anomaly: In this paper we derive Hawking radiation of black holes with higher
derivative corrections by the method of trace anomaly. Firstly we derive
Hawking radiation for general spherical black holes. We introduce a modified
tortoise coordinate to it and find the analyticity of the coordinate. Secondly
we apply its method to a black hole with a higher derivative correction and
derive the Hawking radiation of it. We found that as an ordinary case the flux
depends only on the surface gravity. | A Doubly Supersymmetric Particle in 3+3 Dimensions: It is shown how in 3+3 dimensions, it is possible to have a superparticle
Lagrangian that has manifest supersymmetry both on the world line and in the
target space. |
Hawking Radiation and Covariant Anomalies: Generalising the method of Wilczek and collaborators we provide a derivation
of Hawking radiation from charged black holes using only covariant gauge and
gravitational anomalies. The reliability and universality of the anomaly
cancellation approach to Hawking radiation is also discussed. | Derivative Expansion and the Effective Action for the Abelian
Chern-Simons Theory at Higher Orders: We study systematically the higher order corrections to the parity violating
part of the effective action for the Abelian Chern-Simons theory in 2+1
dimensions, using the method of derivative expansion. We explicitly calculate
the parity violating parts of the quadratic, cubic and the quartic terms (in
fields) of the effective action. We show that each of these actions can be
summed, in principle, to all orders in the derivatives. However, such a
structure is complicated and not very useful. On the other hand, at every order
in the powers of the derivatives, we show that the effective action can also be
summed to all orders in the fields. The resulting actions can be expressed in
terms of the leading order effective action in the static limit. We prove gauge
invariance, both large and small of the resulting effective actions. Various
other features of the theory are also brought out. |
Connections between reflected entropies and hyperbolic string vertices: In this paper, we establish connections between reflected entropies of
multipartite mixed states in CFT$_{2}$ and hyperbolic string vertices of closed
string field theory (CSFT). We show that the reflected surfaces, which are bulk
duals of the reflected entropies, share the same Riemann surfaces with the
hyperbolic string vertices. This observation enables us to build quantitative
relations between the reflected entropies and hyperbolic string vertices. We
illustrate the connections with several examples. Consequently, we propose that
spacetime structure could be directly generated from the hyperbolic string
vertices. The advantage of the hyperbolic string vertices approach is that we
have a dynamical equation, the Batalin-Vilkoviski master equation, to control
the generating process. | No Area Law in QCD: Wilson's area law in QCD is critically examined. It is shown that the
expectation value of the Wilson loop integral $ \exp(\int iA_\mu dx^\mu) $ in
the strong coupling limit vanishes when we employ the conjugate Wilson action
which has a proper QED action in the continuum limit. The finite value of
Wilson loop with the Wilson action is due to the result of the artifact. The
fact that his area law is obtained even for QED simply indicates that the area
law is unphysical. |
All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies: We give a geometric description of supersymmetric gravity/(non-)abelian
$p$-form hierarchies in superspaces with 4D, $N = 1$ super-Poincare invariance.
These hierarchies give rise to Chern-Simons-like invariants, such as those of
the 5D, $N = 1$ graviphoton and the eleven-dimensional 3-form but also
generalizations such as Green-Schwarz-like/BF-type couplings. Previous
constructions based on prepotential superfields are reinterpreted in terms of
$p$-forms in superspace thereby elucidating the underlying geometry. This
vastly simplifies the calculations of superspace field-strengths, Bianchi
identities, and Chern-Simons invariants. Using this, we prove the validity of a
recursive formula for the conditions defining these actions for any such tensor
hierarchy. Solving it at quadratic and cubic orders, we recover the known
results for the BF-type and cubic Chern-Simons actions. As an application, we
compute the quartic invariant $\sim A dA dA dA + \ldots$ relevant, for example,
to seven-dimensional supergravity compactifications. | 't Hooft-Polyakov Monopoles with Non-Abelian Moduli: We extend the Georgi-Glashow model of the t'Hooft-Polyakov monopoles to
include additional collective coordinates "orientational isospin moduli". The
low-energy theory of these solitonic solutions can be interpreted as dyons with
isospin. |
Permutation Orbifold of N=2 Supersymmetric Minimal Models: In this paper we apply the previously derived formalism of permutation
orbifold conformal field theories to N=2 supersymmetric minimal models. By
interchanging extensions and permutations of the factors we find a very
interesting structure relating various conformal field theories that seems not
to be known in literature. Moreover, unexpected exceptional simple currents
arise in the extended permuted models, coming from off-diagonal fields. In a
few situations they admit fixed points that must be resolved. We determine the
complete CFT data with all fixed point resolution matrices for all simple
currents of all Z_2-permutations orbifolds of all minimal N=2 models with k\neq
2 mod 4. | Quantum mirror symmetry and twistors: Using the twistor approach to hypermultiplet moduli spaces, we derive the
worldsheet, D(-1), and D1-instanton contributions to the generalized mirror
map, relating Type IIA and Type IIB string theory compactified on generic
mirror Calabi-Yau threefolds. For this purpose, we provide a novel description
of the twistor space underlying the Type IIB hypermultiplet moduli space where
the SL(2,Z)-action is found to be free from quantum corrections. The extent to
which instanton effects may resolve the perturbative singularities of the
moduli space metric is discussed. |
Aspects of Integrability in N =4 SYM: Various recently developed connections between supersymmetric Yang-Mills
theories in four dimensions and two dimensional integrable systems serve as
crucial ingredients in improving our understanding of the AdS/CFT
correspondence. In this review, we highlight some connections between
superconformal four dimensional Yang-Mills theory and various integrable
systems. In particular, we focus on the role of Yangian symmetries in studying
the gauge theory dual of closed string excitations. We also briefly review how
the gauge theory connects to Calogero models and open quantum spin chains
through the study of the gauge theory duals of D3 branes and open strings
ending on them. This invited review, written for Modern Physics Letters-A, is
based on a seminar given at the Institute of Advanced Study, Princeton. | Space-time singularities and the axion in the Poincare coset models
ISO(2,1)/H: By promoting an invariant subgroup $H$ of $ISO(2,1)$ to a gauge symmetry of a
WZWN action, we obtain the description of a bosonic string moving either in a
curved 4-dimensional space--time with an axion field and curvature
singularities or in 3-dimensional Minkowski space--time. |
Revisiting the Second Law and Weak Cosmic Censorship Conjecture in
High-Dimensional Charged-AdS Black Hole: an Additional Assumption: The verification of the second law of black hole mechanics and the WCCC in
the context of enthalpy as mass of the black hole and its related thermodynamic
properties has not been tested through a vast number of literature in the
recent past. Such studies are of great physical importance as they provide us
with a large number of information regarding the thermodynamics and the
dynamics of AdS black hole systems. We invest the prior limited surveys of such
analysis to investigate the WCCC for the $D$- dimensional asymptotically
AdS-charged black holes characterized by its mass ($M$), electric charge ($Q$),
and AdS radius ($l$) under the absorption of scalar particles of charge $q$. We
examine the WCCC by analyzing the energy-momentum condition of the electrically
charged particles as absorbed by the black holes. We prove that the conjecture
is well verified irrespective of whether the initial black hole configurations
are extremal or non-extremal by changing its charge, the AdS radius, and their
variations. We show that the first law and the WCCC are valid for all spacetime
dimensions ($D$) independent of the choice of the parameters characterizing the
black holes. But to verify the second law in the extremal and non-extremal
configurations one has to be very cautious as it gets strongly affected by the
choices of the values of the black hole parameters and their variations...
In the context of the extended phase space, taking the grand canonical
potential into account allow us to obtain the missing information about the
variation of the cosmological constant necessary to construct the extended
phase space, namely the notion of the black hole pressure, and which is absent
in the previous literature so far. | Relaxing Lorentz invariance in general perturbative anomalies: We analyze the role of Lorentz symmetry in the perturbative non-gravitational
anomalies for a single family of fermions. The theory is assumed to be
translational invariant, power-counting renormalizable and based on a local
action, but is allowed to have general Lorentz violating operators. We study
the conservation of global and gauge currents associate with general internal
symmetry groups and find, by using a perturbative approach, that Lorentz
symmetry does not participate in the clash of symmetries that leads to the
anomalies. We first analyze the triangle graphs and prove that there are
regulators for which the anomalous part of the Ward identities exactly
reproduces the Lorentz invariant case. Then we show, by means of a regulator
independent argument, that the anomaly cancellation conditions derived in
Lorentz invariant theories remain necessary ingredients for anomaly freedom. |
Perturbative Noncommutative Quantum Gravity: We study perturbative noncommutative quantum gravity by expanding the
gravitational field about a fixed classical background. A calculation of the
one loop gravitational self-energy graph reveals that only the non-planar
graviton loops are damped by oscillating internal momentum dependent factors.
The noncommutative quantum gravity perturbation theory is not renormalizable
beyond one loop for matter-free gravity and all loops for matter interactions.
Comments are made about the nonlocal gravitational interactions produced by the
noncommutative spacetime geometry. | Butterflies on the Stretched Horizon: In this paper I return to the question of what kind of perturbations on
Alice's side of an Einstein-Rosen bridge can send messages to Bob as he enters
the horizon at the other end. By definition "easy" operators do not activate
messages and "hard" operators do, but there are no clear criteria to identify
the difference between easy and hard. In this paper I argue that the difference
is related to the time evolution of a certain measure of computational
complexity, associated with the stretched horizon of Alice's black hole. The
arguments suggest that the AMPSS commutator argument is more connected with
butterflies than with firewalls. |
Coset Models and Differential Geometry: String propagation on a curved background defines an embedding problem of
surfaces in differential geometry. Using this, we show that in a wide class of
backgrounds the classical dynamics of the physical degrees of freedom of the
string involves 2-dim sigma-models corresponding to coset conformal field
theories. | The generalized Abel-Plana formula. Applications to Bessel functions and
Casimir effect: One of the most efficient methods to obtain the vacuum expectation values for
the physical observables in the Casimir effect is based on the using the
Abel-Plana summation formula. This allows to derive the regularized quantities
by manifestly cutoff independent way and to present them in the form of
strongly converging integrals. However the applications of Abel- Plana formula
in usual form is restricted by simple geometries when the eigenmodes have a
simple dependence on quantum numbers. The author generalized the Abel-Plana
formula which essentially enlarges its application range. Based on this
generalization, formulae have been obtained for various types of series over
the zeros of some combinations of Bessel functions and for integrals involving
these functions. It have been shown that these results generalize the special
cases existing in literature. Further the derived summation formulae have been
used to summarize series arising in the mode summation approach to the Casimir
effect for spherically and cylindrically symmetric boundaries. This allows to
extract the divergent parts from the vacuum expectation values for the local
physical observables in the manifestly cutoff independent way. The present
paper reviews these results. Some new considerations are added as well. |
Multi-point Local Height Probabilities in the Integrable RSOS Model: By using the bosonization technique, we derive an integral representation for
multi-point Local Hight Probabilities for the Andrews-Baxter-Forrester model in
the regime III. We argue that the dynamical symmetry of the model is provided
by the deformed Virasoro algebra. | Analytical solutions of pure-spinor superstring field theory: We examine the possibility of constructing analytical solutions describing
marginal deformations in the open superstring field theory that is based on the
non-minimal pure-spinor formalism. It is found out that some methods used for
constructing solutions of bosonic and RNS string field theories do not seem to
generalize to the pure-spinor case, while other methods do lead to reliable
analytical solutions. |
Topological Roots of Black Hole Entropy: We review the insights into black hole entropy that arise from the
formulation of gravitation theory in terms of dimensional continuation. The
role of the horizon area and the deficit angle of a conical singularity at the
horizon as canonically conjugate dynamical variables is analyzed. The path
integral and the extension of the Wheeler-De Witt equation for black holes are
discussed. | Asymmetric interiors for small black holes: We develop the representation of infalling observers and bulk fields in the
CFT as a way to understand the black hole interior in AdS. We first discuss
properties of CFT states which are dual to black holes. We then show that in
the presence of a Killing horizon bulk fields can be decomposed into pieces we
call ingoing and outgoing. The ingoing field admits a simple operator
representation in the CFT, even inside a small black hole at late times, which
leads to a simple CFT description of infalling geodesics. This means classical
infalling observers will experience the classical geometry in the interior. The
outgoing piece of the field is more subtle. In an eternal two-sided geometry it
can be represented as an operator on the left CFT. In a stable one-sided
geometry it can be described using entanglement via the PR construction. But in
an evaporating black hole trans-horizon entanglement breaks down at the Page
time, which means that for old black holes the PR construction fails and the
outgoing field does not see local geometry. This picture of the interior allows
the CFT to reconcile unitary Hawking evaporation with the classical experience
of infalling observers. |
A survey of the electroweak configuration space and the W boson mass: Following the recent work of V. Moncrief, A. Marini, R. Maitra and P. Mondal
on the geometry of field theoretic configuration spaces, this account examines
how the regularized Ricci curvature of the $SU(2)_L \times U(1)_Y$ Yang-Mills
orbit space may provide an intrinsic mass to the W boson which contributes to
the value obtained from the renormalized Higgs mechanism. Though the discussion
is heuristic, one hopes that this infinite-dimensional technology, which does
not postulate extensions to the Standard Model, could explain the mass anomaly
reported by the CDF II collaboration. | Thermal Equilibrium of String Gas in Hagedorn Universe: The thermal equilibrium of string gas is necessary to activate the
Brandenberger-Vafa mechanism, which makes our observed 4-dimensional universe
enlarge. Nevertheless, the thermal equilibrium is not realized in the original
setup, a problem that remains as a critical defect. We study thermal
equilibrium in the Hagedorn universe, and explore possibilities for avoiding
the issue aforementioned flaw. We employ a minimal modification of the original
setup, introducing a dilaton potential. Two types of potential are
investigated: exponential and double-well potentials. For the first type, the
basic evolutions of universe and dilaton are such that both the radius of the
universe and the dilaton asymptotically grow in over a short time, or that the
radius converges to a constant value while the dilaton rolls down toward the
weak coupling limit. For the second type, in addition to the above solutions,
there is another solution in which the dilaton is stabilized at a minimum of
potential and the radius grows in proportion to $t$. Thermal equilibrium is
realized for both cases during the initial phase. These simple setups provide
possible resolutions of the difficulty. |
Entanglement Entropy as a Probe of the Proximity Effect in Holographic
Superconductors: We study the entanglement entropy as a probe of the proximity effect of a
superconducting system by using the gauge/gravity duality in a fully
back-reacted gravity system. While the entanglement entropy in the
superconducting phase is less than the entanglement entropy in the normal
phase, we find that near the contact interface of the superconducting to normal
phase the entanglement entropy has a different behavior due to the leakage of
Cooper pairs to the normal phase. We verify this behavior by calculating the
conductivity near the boundary interface. | Fuzzy Nambu-Goldstone Physics: In spacetime dimensions larger than 2, whenever a global symmetry G is
spontaneously broken to a subgroup H, and G and H are Lie groups, there are
Nambu-Goldstone modes described by fields with values in G/H. In
two-dimensional spacetimes as well, models where fields take values in G/H are
of considerable interest even though in that case there is no spontaneous
breaking of continuous symmetries. We consider such models when the world sheet
is a two-sphere and describe their fuzzy analogues for G=SU(N+1),
H=S(U(N-1)xU(1)) ~ U(N) and G/H=CP^N. More generally our methods give fuzzy
versions of continuum models on S^2 when the target spaces are Grassmannians
and flag manifolds described by (N+1)x(N+1) projectors of rank =< (N+1)/2.
These fuzzy models are finite-dimensional matrix models which nevertheless
retain all the essential continuum topological features like solitonic sectors.
They seem well-suited for numerical work. |
Quantum Aspects of Black Hole Entropy: This survey intends to cover recent approaches to black hole entropy which
attempt to go beyond the standard semiclassical perspective. Quantum
corrections to the semiclassical Bekenstein-Hawking area law for black hole
entropy, obtained within the quantum geometry framework, are treated in some
detail. Their ramification for the holographic entropy bound for bounded
stationary spacetimes is discussed. Four dimensional supersymmetric extremal
black holes in string-based N=2 supergravity are also discussed, albeit more
briefly. | Caustics for Spherical Waves: We study the development of caustics in shift-symmetric scalar field theories
by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of
space dimensions. We show that the pure Galileon, the DBI-Galileon, and the
extreme-relativistic Galileon naturally emerge as the unique set of
caustic-free theories, highlighting a link between the caustic-free condition
for simple $SO(p)$-waves and the existence of either a global Galilean symmetry
or a global (extreme-)relativistic Galilean symmetry. |
A nonperturbative study of three-dimensional phi^4 theory: The spherical field formalism---a nonperturbative approach to quantum field
theory---was recently introduced and applied to phi^4 theory in two dimensions.
The spherical field method reduces a quantum field theory to a
finite-dimensional quantum mechanical system by expanding field configurations
in terms of spherical partial wave modes. We extend the formalism to phi^4
theory in three dimensions and demonstrate the application of the method by
analyzing the phase structure of this theory. | Instanton constraints and renormalization: The renormalization is investigated of one-loop quantum fluctuations around a
constrained instanton in $\phi ^4$-theory with negative coupling. It is found
that the constraint should be renormalized also. This indicates that in general
only renormalizable constraints are permitted. |
Remarks on relativistic scalar models with chemical potential: We discuss selected aspects of classical relativistic scalar field theories
with nonzero chemical potential. First, we offer a review of classical field
theory at nonzero density within the Lagrangian formalism. The aspects covered
include the question of equivalence of descriptions of finite-density states
using a chemical potential or time-dependent field configurations, the choice
of Hamiltonian whose minimization yields the finite-density equilibrium state,
and the issue of breaking of Lorentz invariance. Second, we demonstrate how the
low-energy effective field theory for Nambu-Goldstone (NG) modes arising from
the spontaneous breakdown of global internal symmetries can be worked out
explicitly by integrating out the heavy (Higgs) fields. This makes it possible
to analyze the spectrum of NG modes and their interactions without having to
deal with mixing of NG and Higgs fields, ubiquitous in the linear-sigma-model
description of spontaneous symmetry breaking. | String Theory in Beta Deformed Spacetimes: Fluxbrane-like backgrounds obtained from flat space by a sequence of
T-dualities and shifts of polar coordinates (beta deformations) provide an
interesting class of exactly solvable string theories. We compute the one-loop
partition function for various such deformed spaces and study their spectrum of
D-branes. For rational values of the B-field these models are equivalent to Z_N
\times Z_N orbifolds with discrete torsion. We also obtain an interesting new
class of time-dependent backgrounds which resemble localized closed string
tachyon condensation. |
The Heat Kernel Coefficients to the Matrix Schrödinger Operator: The heat kernel coefficients $H_k$ to the Schr\"odinger operator with a
matrix potential are investigated. We present algorithms and explicit
expressions for the Taylor coefficients of the $H_k$. Special terms are
discussed, and for the one-dimensional case some improved algorithms are
derived. | Spinning Relativistic Particle in an External Electromagnetic Field: The Hamiltonian formulation of the motion of a spinning relativistic particle
in an external electromagnetic field is considered. The approach is based on
the introduction of new coordinates and their conjugated momenta to describe
the spin degrees of freedom together with an appropriate set of constraints in
the Dirac formulation. For particles with gyromagnetic ratio $g=2$, the
equations of motion do not predict any deviation from the standard Lorentz
force, while for $g \neq 2$ an additional force, which corresponds to the
magnetic dipole force, is obtained. |
Gauge-invariant variables, WZW models and (2+1)-dimensional Yang-Mills
theory: Recent progress in understanding (2+1)-dimensional Yang-Mills (YM_{2+1})
theory via the use of gauge-invariant variables is reviewed. Among other
things, we discuss the vacuum wavefunction, an analytic calculation of the
string tension and the propagator mass for gluons and its relation to the
magnetic mass for YM_{3+1} at nonzero temperature. | Israel--Wilson--Perjés Solutions in Heterotic String Theory: We present a simple algorithm to obtain solutions that generalize the
Israel--Wilson--Perj\'es class for the low-energy limit of heterotic string
theory toroidally compactified from D=d+3 to three dimensions. A remarkable map
existing between the Einstein--Maxwell (EM) theory and the theory under
consideration allows us to solve directly the equations of motion making use of
the matrix Ernst potentials connected with the coset matrix of heterotic string
theory. For the particular case d=1 (if we put n=6, the resulting theory can be
considered as the bosonic part of the action of D=4, N=4 supergravity) we
obtain explicitly a dyonic solution in terms of one real 2\times 2--matrix
harmonic function and 2n real constants (n being the number of Abelian vector
fields). By studying the asymptotic behaviour of the field configurations we
define the charges of the system. They satisfy the
Bogomol'nyi--Prasad--Sommmerfeld (BPS) bound. |
On strong integrability of the dressing cosets: We formulate sufficient conditions for the strong integrability of dressing
cosets. We provide several sigma-model backgrounds solving those conditions,
some of them are new and some of them were not so far formulated as the
dressing cosets. The new models are based on the Drinfeld doubles having the
structure of higher order jet bundles of quadratic Lie groups. | Holography and Thermodynamics of 5D Dilaton-gravity: The asymptotically-logarithmically-AdS black-hole solutions of 5D dilaton
gravity with a monotonic dilaton potential are analyzed in detail. Such
theories are holographically very close to pure Yang-Mills theory in four
dimensions. The existence and uniqueness of black-hole solutions is shown. It
is also shown that a Hawking-Page transition exists at finite temperature if
and only if the potential corresponds to a confining theory. The physics of the
transition matches in detail with that of deconfinement of the Yang-Mills
theory. The high-temperature phase asymptotes to a free gluon gas at high
temperature matching the expected behavior from asymptotic freedom. The thermal
gluon condensate is calculated and shown to be crucial for the existence of a
non-trivial deconfining transition. The condensate of the topological charge is
shown to vanish in the deconfined phase. |
Homes' law in Holographic Superconductor with Q-lattices: Homes' law, $\rho_s = C \sigma_{\mathrm{DC}} T_c$, is an empirical law
satisfied by various superconductors with a material independent universal
constant $C$, where $\rho_{s}$ is the superfluid density at zero temperature,
$T_c$ is the critical temperature, and $\sigma_{\mathrm{DC}}$ is the electric
DC conductivity in the normal state close to $T_c$. We study Homes' law in
holographic superconductor with Q-lattices and find that Homes' law is realized
for some parameter regime in insulating phase near the metal-insulator
transition boundary, where momentum relaxation is strong. In computing the
superfluid density, we employ two methods: one is related to the infinite DC
conductivity and the other is related to the magnetic penetration depth. With
finite momentum relaxation both yield the same results, while without momentum
relaxation only the latter gives the superfluid density correctly because the
former has a spurious contribution from the infinite DC conductivity due to
translation invariance. | Charging the Conformal Window: We investigate the properties of near-conformal dynamics in a sector of large
charge when approaching the lower boundary of the conformal window from the
chirally broken phase. To elucidate our approach we use the time-honored
example of the phenomenologically relevant SU(2) color theory featuring $N_f$
Dirac fermions transforming in the fundamental representation of the gauge
group. In the chirally broken phase we employ the effective pion Lagrangian
featuring also a pseudo-dilaton to capture a possible smooth
conformal-to-non-conformal phase transition. We charge the baryon symmetry of
the Lagrangian and study its impact on the ground state and spectrum of the
theory as well as the would-be conformal dimensions of the lowest large-charge
operator. We moreover study the effects of and dependence on the fermion mass
term. |
Dynamical actions and q-representation theory for double-scaled SYK: We show that DSSYK amplitudes are reproduced by considering the quantum
mechanics of a constrained particle on the quantum group SU$_q(1,1)$. We
construct its left-and right-regular representations, and show that the
representation matrices reproduce two-sided wavefunctions and correlation
functions of DSSYK. We then construct a dynamical action and path integral for
a particle on SU$_q(1,1)$, whose quantization reproduces the aforementioned
representation theory. By imposing boundary conditions or constraining the
system we find the $q$-analog of the Schwarzian and Liouville boundary path
integral descriptions. This lays the technical groundwork for identifying the
gravitational bulk description of DSSYK. We find evidence the theory in
question is a sine dilaton gravity, which interestingly is capable of
describing both AdS and dS quantum gravity. | Hayden-Preskill protocol and decoding Hawking radiation at finite
temperature: We study the Hayden-Preskill thought experiment at finite temperature and
obtain the decoupling condition that the information thrown into an old black
hole can be extracted by decoding the Hawking radiation. We then consider the
decoding Hayden-Preskill protocol at finite temperature assuming the observer
outside the black hole who has the access to the full radiation and the unitary
dynamics of the black hole. We also consider the cases when the Hawking
radiation has noise and decoherence in the storage. The decoding probabilities
and the corresponding fidelities are calculated. It is shown that for all the
three cases we have considered, the decoding fidelities are less than unity in
general. This result indicates that at finite temperature, the decoding
strategy and the recovery algorithm is harder to realize than that at infinite
temperature. |
Toroidal Compactification Without Vector Structure: Many important ideas about string duality that appear in conventional $\T^2$
compactification have analogs for $\T^2$ compactification without vector
structure. We analyze some of these issues and show, in particular, how
orientifold planes associated with $Sp(n)$ gauge groups can arise from
T-duality and how they can be interpreted in F-theory. We also, in an appendix,
resolve a longstanding puzzle concerning the computation of $\Tr (-1)^F$ in
four-dimensional supersymmetric Yang-Mills theory with gauge group SO(n). | Tests for C-theorems in 4D: A proof for a non-perturbative C-theorem in four dimensions, capturing the
irreversibility of the renormalization group flow in the space of unitary
quantum field theories, has not been accomplished, yet. We test the conjectured
C-theorems using the exact results recently obtained in N=1 supersymmetric
gauge theories. We find that the flow towards the infrared region is consistent
with the main proposals for a C-theorem. |
Integrability vs. Information Loss: A Simple Example: The half-BPS sector of Yang-Mills theory with 16 supercharges is integrable:
there is a set of commuting conserved charges, whose eigenvalues can completely
identify a state. We show that these charges can be measured in the dual
gravitational description from asymptotic multipole moments of the spacetime.
However, Planck scale measurements are required to separate the charges of
different microstates. Thus, semiclassical observers making coarse-grained
measurements necessarily lose information about the underlying quantum state. | Aharonov-Bohm Effect in the Abelian-Projected SU(3)-QCD with
$Θ$-term: By making use of the path-integral duality transformation, string
representation of the Abelian-projected SU(3)-QCD with the $\Theta$-term is
derived. Besides the short-range (self-)interactions of quarks (which due to
the $\Theta$-term acquire a nonvanishing magnetic charge, i.e. become dyons)
and electric Abrikosov-Nielsen-Olesen strings, the resulting effective action
contains also a long-range topological interaction of dyons with strings. This
interaction, which has the form of the 4D Gauss linking number of the
trajectory of a dyon with the world-sheet of a closed string, is shown to
become nontrivial at $\Theta$ not equal to $3\pi$ times an integer. At these
values of $\Theta$, closed electric Abrikosov-Nielsen-Olesen strings in the
model under study can be viewed as solenoids scattering dyons, which is the 4D
analogue of the Aharonov-Bohm effect. |
Dual Fermion Condensates in Curved Space: In this paper we compute the effective action at finite temperature and
density for the dual fermion condensate in curved space with the fermions
described by an effective field theory with four-point interactions. The
approach we adopt refines a technique developed earlier to study chiral
symmetry breaking in curved space and it is generalized here to include the
U$(1)$-valued boundary conditions necessary to define the dual condensate. The
method we present is general, includes the coupling between the fermion
condensate and the Polyakov loop, and applies to any ultrastatic background
spacetime with a nonsingular base. It also allows one to include inhomogeneous
and anisotropic phases and therefore it is suitable to study situations where
the geometry is not homogeneous. We first illustrate a procedure, based on heat
kernels, useful to deal with situations where the dual and chiral condensates
(as well as any smooth background field eventually present) are slowly or
rapidly varying functions in space. Then we discuss a different approach based
on the density of states method and on the use of Tauberian theorems to handle
the case of arbitrary chemical potentials. As a trial application, we consider
the case of constant curvature spacetimes and show how to compute numerically
the dual fermion condensate in the case of both homogeneous and inhomogeneous
phases. | Spectral geometry approach to Horava-Lifshitz type theories: gravity and
matter sectors in IR regime: We give a brief exposition of the approach based on the methods of spectral
geometry and the spectral action principle to construction and analysis of
models on a foliated space-time. |
Annihilation of the scalar pair into a photon on de Sitter spacetime: The annihilation of massive scalar particles in one photon on de Sitter
expanding universe is studied, using perturbation theory. The amplitude and
probability corresponding to this process is computed using the exact solutions
of the Klein-Gordon and Maxwell equations on de Sitter geometry. Our results
show that the expression of the total probability of photon emission is a
function dependent on the ratio mass/expansion\, factor. We perform a graphical
study of the total probability in terms of the parameter mass/expansion factor,
showing that this effect is significant only in strong gravitational fields. We
also obtain that the total probability for this process vanishes in the
Minkowski limit. | Global Black Branes (Extended Global Defects Surrounded by Horizons),
Brane Worlds and the Cosmological Constant: We study global defects coupled to higher-dimensional gravity with a negative
cosmological constant. This paper is mainly devoted to studying global black
brane solutions which are extended global defects surrounded by horizons. We
find series solutions in a few separated regions and confirm numerically that
they can be mutually connected. When the world volume of the brane is
Ricci-flat, the brane is surrounded by a degenerated horizon, while it is
surrounded by two horizons when the world volume has a positive constant
curvature. Each solution corresponds to an extremal and a non-extremal state,
respectively. Their causal structures resemble those of the
Reissner-Nordstr\"{o}m black holes in anti-de Sitter spacetime. However, the
non-extremal black brane is not a static object, but an inflating brane. In
addition, we briefly discuss a brane world model in the context of the global
black branes. We comment on a few thermodynamic properties of the global black
branes, and discuss a decrease of the cosmological constant on the brane world
through the thermodynamic instability of the non-extremal global black brane. |
Weak Gravity Strongly Constrains Large-Field Axion Inflation: Models of large-field inflation based on axion-like fields with shift
symmetries can be simple and natural, and make a promising prediction of
detectable primordial gravitational waves. The Weak Gravity Conjecture is known
to constrain the simplest case in which a single compact axion descends from a
gauge field in an extra dimension. We argue that the Weak Gravity Conjecture
also constrains a variety of theories of multiple compact axions including
N-flation and some alignment models. We show that other alignment models entail
surprising consequences for how the mass spectrum of the theory varies across
the axion moduli space, and hence can be excluded if further conjectures hold.
In every case that we consider, plausible assumptions lead to field ranges that
cannot be parametrically larger than the Planck scale. Our results are strongly
suggestive of a general inconsistency in models of large-field inflation based
on compact axions, and possibly of a more general principle forbidding
super-Planckian field ranges. | Tetrahedron instantons: We introduce and study tetrahedron instantons, which can be realized in
string theory by D$1$-branes probing a configuration of intersecting
D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they
capture instantons on $\mathbb{C}^{3}$ in the presence of the most general
intersecting real codimension-two supersymmetric defects. Moreover, we
construct the tetrahedron instantons as particular solutions of general
instanton equations in noncommutative field theory. We analyze the moduli space
of tetrahedron instantons and discuss the geometric interpretations. We compute
the instanton partition function both via the equivariant localization on the
moduli space of tetrahedron instantons and via the elliptic genus of the
worldvolume theory on the D$1$-branes probing the intersecting D$7$-branes,
obtaining the same result. The instanton partition function of the tetrahedron
instantons lies between the higher-rank Donaldson-Thomas invariants on
$\mathbb{C}^{3}$ and the partition function of the magnificent four model,
which is conjectured to be the mother of all instanton partition functions.
Finally, we show that the instanton partition function admits a free field
representation, suggesting the existence of a novel kind of symmetry which acts
on the cohomology of the moduli spaces of tetrahedron instantons. |
On Instanton Calculations of N=2 Supersymmetric Yang-Mills Theory: Instanton calculations are demonstrated from a viewpoint of twisted
topological field theory. Various properties become manifest such that
perturbative corrections are terminated at one-loop, and norm cancellations
occur between bosonic and fermionic excitations in any instanton background. We
can easily observe that for a suitable choice of Green functions the infinite
dimensional path integration reduces to a finite dimensional integration over a
supersymmetric instanton moduli space. | Regularization Dependence of Quadratic Divergence Cancellations,
VPI-IHEP-92/10: Certain results related to the cancellation of quadratic divergences, which
had been obtained using dimensional reduction, are reconsidered using a
nonlocal regulator. The results obtained are shown to depend strongly on the
regulator. Specifically, it is shown that a certain result of Al-sarhi, Jack,
and Jones no longer holds, even if a nontrivial measure factor is used; also
that there are no values of the top and Higgs mass for which the one-loop
quadratic divergence in the standard model cancels independently of the
renormalization scale, whether or not strong interaction effects are ignored. |
Fixed points and the spontaneous breaking of scale invariance: We investigate critical $N$-component scalar field theories and the
spontaneous breaking of scale invariance in three dimensions using functional
renormalisation. Global and local renormalisation group flows are solved
analytically in the infinite $N$ limit to establish the phase diagram including
the Wilson-Fisher fixed point and a line of asymptotically safe UV fixed points
characterised by an exactly marginal sextic coupling. We also study the
Bardeen-Moshe-Bander phenomenon of spontaneously broken scale invariance and
the stability of the vacuum for general regularisation. Our findings clarify a
long-standing puzzle about the apparent unboundedness of the effective
potential. Implications for other theories are indicated. | Entanglement Entropy for $TT$ deformed CFT in general dimensions: We consider deformation of a generic $d$ dimensional ($d\geq 2$) large-$N$
CFT on a sphere by a spin-0 operator which is bilinear in the components of the
stress tensor. Such a deformation has been proposed to be holographically dual
to an $AdS_{d+1}$ bulk with a hard radial cut-off. We compute the exact
partition function and find the entanglement entropy from the field theory side
in various dimensions and compare with the corresponding holographic results.
We also compute renormalized entanglement entropy both in field theory and
holography and find complete agreement between them. |
Landau Gauge QCD: Functional Methods versus Lattice Simulations: The infrared behaviour of QCD Green's functions in Landau gauge has been
focus of intense study. Different non-perturbative approaches lead to a
prediction in line with the conditions for confinement in local quantum field
theory as spelled out in the Kugo-Ojima criterion. Detailed comparisons with
lattice studies have revealed small but significant differences, however. But
aren't we comparing apples with oranges when contrasting lattice Landau gauge
simulations with these continuum results? The answer is yes, and we need to
change that. We therefore propose a reformulation of Landau gauge on the
lattice which will allow us to perform gauge-fixed Monte-Carlo simulations
matching the continuum methods of local field theory which will thereby be
elevated to a non-perturbative level at the same time. | Connection between topology and statistics: We introduce topological magnetic field in two-dimensional flat space, which
admits a solution of scalar monopole that describes the nontrivial topology. In
the Chern-Simons gauge field theory of anyons, we interpret the anyons as the
quasi-particles composed of fermions and scalar monopoles in such a form that
each fermion is surrounded by infinite number of scalar monopoles. It is the
monopole charge that determines the statistics of anyons. We re-analyze the
conventional arguments of the connection between topology and statistics in
three-dimensional space, and find that those arguments are based on the global
topology, which is relatively trivial compared with the monopole structure.
Through a simple model, we formulate the three-dimensional anyon field
using infinite number of Dirac's magnetic monopoles that change the ordinary
spacetime topology. The quasi-particle picture of the three-dimensional anyons
is quite similar to that of the usual two-dimensional anyons. However, the
exotic statistics there is not restricted to the usual fractional statistics,
but a functional statistics. |
Continuous Local Symmetry in Ising-type Models: A class of generalized Ising models is examined with a view to extracting a
low energy sector comprising
Dirac fermions coupled to Yang-Mills vectors. The main feature of this
approach is a set of gap equations, covariant with respect to one of the
$4$-dimensional crystallographic space groups. | Tetrahedron equation and the algebraic geometry: The tetrahedron equation arises as a generalization of the famous
Yang--Baxter equation to the 2+1-dimensional quantum field theory and the
3-dimensional statistical mechanics. Very little is still known about its
solutions. Here a systematic method is described that does produce non-trivial
solutions to the tetrahedron equation with spin-like variables on the links.
The essence of the method is the use of the so-called tetrahedral Zamolodchikov
algebras. |
Gamma ray burst delay times probe the geometry of momentum space: We study the application of the recently proposed framework of relative
locality to the problem of energy dependent delays of arrival times of photons
that are produced simultaneously in distant events such as gamma ray bursts.
Within this framework, possible modifications of special relativity are coded
in the geometry of momentum space. The metric of momentum space codes
modifications in the energy momentum relation, while the connection on momentum
space describes possible non-linear modifications in the laws of conservation
of energy and momentum. In this paper, we study effects of first order in the
inverse Planck scale, which are coded in the torsion and non-metricity of
momentum space. We find that time delays of order Distance * Energies/m_p are
coded in the non-metricity of momentum space. Current experimental bounds on
such time delays hence bound the components of this tensor of order 1/m_p. We
also find a new effect, whereby photons from distant sources can appear to
arrive from angles slightly off the direction to the sources, which we call
gravitational lensing. This is found to be coded into the torsion of momentum
space. | Branes from Matrix Theory in PP-Wave Background: Based on the recently proposed action for Matrix theory describing the DLCQ M
theory in the maximally supersymmetric pp-wave background, we obtain the
supersymmetry algebra of supercharge density. Using supersymmetry
transformation rules for fermions, we identify BPS states with the central
charges in the supersymmetry algebra, which can be activated only in the large
N limit. They preserve some fraction of supersymmetries and correspond to
rotating transverse membranes and longitudinal five branes. |
String Theory and Water Waves: We uncover a remarkable role that an infinite hierarchy of non-linear
differential equations plays in organizing and connecting certain {hat c}<1
string theories non-perturbatively. We are able to embed the type 0A and 0B
(A,A) minimal string theories into this single framework. The string theories
arise as special limits of a rich system of equations underpinned by an
integrable system known as the dispersive water wave hierarchy. We observe that
there are several other string-like limits of the system, and conjecture that
some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain
how these and several string-like special points arise and are connected. In
some cases, the framework endows the theories with a non-perturbative
definition for the first time. Notably, we discover that the Painleve IV
equation plays a key role in organizing the string theory physics, joining its
siblings, Painleve I and II, whose roles have previously been identified in
this minimal string context. | Strings in a 2-d Extremal Black Hole: String theory on 2-d charged black holes corresponding to (SL(2)xU(1)_L)/U(1)
exact asymmetric quotient CFTs are investigated. These backgrounds can be
embedded, in particular, in a two dimensional heterotic string. In the extremal
case, the quotient CFT description captures the near horizon physics, and is
equivalent to strings in AdS_2 with a gauge field. Such string vacua possess an
infinite space-time Virasoro symmetry, and hence enhancement of global
space-time Lie symmetries to affine symmetries, in agreement with the
conjectured AdS_2/CFT_1 correspondence. We argue that the entropy of these 2-d
black holes in string theory is compatible with semi-classical results, and
show that in perturbative computations part of an incoming flux is absorbed by
the black hole. Moreover, on the way we find evidence that the 2-d heterotic
string is closely related to the N=(2,1) string, and conjecture that they are
dual. |
Gauging Wess-Zumino-Witten Models: We review some aspects of gauged WZW models. By choosing a nilpotent subgroup
as gauge group, one is lead to three main applications: the construction of
field theories with an extended conformal symmetry, the construction of the
effective action of (extended) 2D gravities and the systematic construction of
string theories with some extended gauge symmetry. | Modifying the Sum Over Topological Sectors and Constraints on
Supergravity: The standard lore about the sum over topological sectors in quantum field
theory is that locality and cluster decomposition uniquely determine the sum
over such sectors, thus leading to the usual theta-vacua. We show that without
changing the local degrees of freedom, a theory can be modified such that the
sum over instantons should be restricted; e.g. one should include only
instanton numbers which are divisible by some integer p. This conclusion about
the configuration space of quantum field theory allows us to carefully
reconsider the quantization of parameters in supergravity. In particular, we
show that FI-terms and nontrivial Kahler forms are quantized. This analysis
also leads to a new derivation of recent results about linearized supergravity. |
Binding Complexity and Multiparty Entanglement: We introduce "binding complexity", a new notion of circuit complexity which
quantifies the difficulty of distributing entanglement among multiple parties,
each consisting of many local degrees of freedom. We define binding complexity
of a given state as the minimal number of quantum gates that must act between
parties to prepare it. To illustrate the new notion we compute it in a toy
model for a scalar field theory, using certain multiparty entangled states
which are analogous to configurations that are known in AdS/CFT to correspond
to multiboundary wormholes. Pursuing this analogy, we show that our states can
be prepared by the Euclidean path integral in $(0+1)$-dimensional quantum
mechanics on graphs with wormhole-like structure. We compute the binding
complexity of our states by adapting the Euler-Arnold approach to Nielsen's
geometrization of gate counting, and find a scaling with entropy that resembles
a result for the interior volume of holographic multiboundary wormholes. We
also compute the binding complexity of general coherent states in perturbation
theory, and show that for "double-trace deformations" of the Hamiltonian the
effects resemble expansion of a wormhole interior in holographic theories. | Gauge Theories Coupled to Fermions in Generation: Gauge theories coupled to fermions in generation are reformulated in a
modified version of extended differential geometry with the symbol $\chi$.
After discussing several toy models, we will reformulate in our framework the
standard model based on Connes' real structure. It is shown that for the most
general bosonic lagrangin which is required to also reconstruct N=2 super
Yang-Mills theory Higgs mechanism operates only for more than one generation as
first pointed out by Connes and Lott. |
Supersymmetric (non-)Abelian Bundles in the Type I and SO(32) Heterotic
String: We discuss perturbative four-dimensional compactifications of both the SO(32)
heterotic and the Type I string on smooth Calabi-Yau manifolds endowed with
general non-abelian and abelian bundles. We analyse the generalized
Green-Schwarz mechanism for multiple anomalous U(1) factors and derive the
generically non-universal one-loop threshold corrections to the gauge kinetic
function as well as the one-loop corrected Fayet-Iliopoulos terms. The latter
can be interpreted as a stringy one-loop correction to the
Donaldson-Uhlenbeck-Yau condition. Applying S-duality, for the Type I string we
obtain the perturbative Pi-stability condition for non-abelian bundles on
curved spaces. Some simple examples are given, and we qualitatively discuss
some generic phenomenological aspects of this kind of string vacua. In
particular, we point out that in principle an intermediate string scale
scenario with TeV scale large extra dimensions might be possible for the
heterotic string. | Universal Bounds on Charged States in 2d CFT and 3d Gravity: We derive an explicit bound on the dimension of the lightest charged state in
two dimensional conformal field theories with a global abelian symmetry. We
find that the bound scales with $c$ and provide examples that parametrically
saturate this bound. We also prove than any such theory must contain a state
with charge-to-mass ratio above a minimal lower bound. We comment on the
implications for charged states in three dimensional theories of gravity. |
5d Conformal Matter: Six-dimensional superconformal field theories (SCFTs) have an atomic
classification in terms of elementary building blocks, conformal systems that
generalize matter and can be fused together to form all known 6d SCFTs in terms
of generalized 6d quivers. It is therefore natural to ask whether 5d SCFTs can
be organized in a similar manner, as the outcome of fusions of certain
elementary building blocks, which we call 5d conformal matter theories. In this
project we begin exploring this idea and we give a systematic construction of
5d generalized ``bifundamental'' SCFTs, building from geometric engineering
techniques in M-theory. In particular, we find several examples of $(\mathfrak
{e}_6,\mathfrak {e}_6)$, $(\mathfrak {e}_7,\mathfrak {e}_7)$ and $(\mathfrak
{e}_8,\mathfrak {e}_8)$ 5d bifundamental SCFTs beyond the ones arising from
(elementary) KK reductions of the 6d conformal matter theories. We show that
these can be fused together giving rise to 5d SCFTs captured by 5d generalized
linear quivers with exceptional gauge groups as nodes, and links given by 5d
conformal matter. As a first application of these models we uncover a large
class of novel 5d dualites, that generalize the well-known fiber/base dualities
outside the toric realm. | Symmetric Space Sigma-model Dynamics: Internal Metric Formalism: For the symmetric space sigma model in the internal metric formalism we
explicitly construct the lagrangian in terms of the axions and the dilatons of
the solvable Lie algebra gauge and then we exactly derive the axion-dilaton
field equations. |
Testing holography using lattice super-Yang--Mills on a 2-torus: We consider maximally supersymmetric SU(N) Yang--Mills theory in Euclidean
signature compactified on a flat two-dimensional torus with anti-periodic
(`thermal') fermion boundary conditions imposed on one cycle. At large N,
holography predicts that this theory describes certain black hole solutions in
Type IIA and IIB supergravity, and we use lattice gauge theory to test this.
Unlike the one-dimensional quantum mechanics case where there is only the
dimensionless temperature to vary, here we emphasize there are two more
parameters which determine the shape of the flat torus. While a rectangular
Euclidean torus yields a thermal interpretation, allowing for skewed tori
modifies the holographic dual black hole predictions and results in another
direction to test holography. Our lattice calculations are based on a
supersymmetric formulation naturally adapted to a particular skewing. Using
this we perform simulations up to N=16 with several lattice spacings for both
skewed and rectangular tori. We observe the two expected black hole phases with
their predicted behavior, with a transition between them that is consistent
with the gravity prediction based on the Gregory--Laflamme transition. | Revisiting the Conformally Soft Sector with Celestial Diamonds: Celestial diamonds encode the structure of global conformal multiplets in 2D
celestial CFT and offer a natural language for describing the conformally soft
sector. The operators appearing at their left and right corners give rise to
conformally soft factorization theorems, the bottom corners correspond to
conserved charges, and the top corners to conformal dressings. We show that
conformally soft charges can be expressed in terms of light ray integrals that
select modes of the appropriate conformal weights. They reside at the bottom
corners of memory diamonds, and ascend to generalized currents. We then
identify the top corners of the associated Goldstone diamonds with conformal
Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings
in gauge theory and gravity which are important for finding nontrivial central
extensions. Finally, we combine these ingredients to speculate on 2D effective
descriptions for the conformally soft sector of celestial CFT. |
Confining Boundary conditions from dynamical Coupling Constants: It is shown that it is possible to consistently and gauge invariantly
formulate models where the coupling constant is a non trivial function of a
scalar field . In the $U(1)$ case the coupling to the gauge field contains a
term of the form $g(\phi)j_\mu (A^{\mu} +\partial^{\mu}B)$ where $B$ is an
auxiliary field and $j_\mu$ is the Dirac current. The scalar field $\phi$
determines the local value of the coupling of the gauge field to the Dirac
particle. The consistency of the equations determine the condition
$\partial^{\mu}\phi j_\mu = 0$ which implies that the Dirac current cannot have
a component in the direction of the gradient of the scalar field. As a
consequence, if $\phi$ has a soliton behaviour, like defining a bubble that
connects two vacuua, we obtain that the Dirac current cannot have a flux
through the wall of the bubble, defining a confinement mechanism where the
fermions are kept inside those bags. Consistent models with time dependent fine
structure constant can be also constructed | Entropy of Near-Extremal Black p-branes: We carry out a thorough survey of entropy for a large class of $p$-branes in
various dimensions. We find that the Bekenstein-Hawking entropy may be given a
simple world volume interpretation only for the non-dilatonic $p$-branes, those
with the dilaton constant throughout spacetime. The entropy of extremal
non-dilatonic $p$-branes is non-vanishing only for the solutions preserving 1/8
of the original supersymmetries. Upon toroidal compactification these reduce to
dyonic black holes in 4 and 5 dimensions. For the self-dual string in 6
dimensions, which preserves 1/4 of the original supersymmetries, the
near-extremal entropy is found to agree with a world sheet calculation, in
support of the existing literature. The remaining 3 interesting cases preserve
1/2 of the original supersymmetries. These are the self-dual 3-brane in 10
dimensions, and the 2- and 5-branes in 11 dimensions. For all of them the
scaling of the near-extremal Bekenstein-Hawking entropy with the Hawking
temperature is in agreement with a statistical description in terms of free
massless fields on the world volume. |
Axial anomaly in nonlinear conformal electrodynamics: We study the axial anomaly of Dirac spinors on gravitational instanton
backgrounds in the context of nonlinear electrodynamics. In order to do so, we
consider Einstein gravity minimally coupled to a recently proposed conformal
electrodynamics that enjoys duality transformation invariance. These symmetries
allow us to generalize the Eguchi-Hanson configuration while preserving its
geometry. We then compute the Dirac index of the nonlinearly charged
Eguchi-Hanson and Taub-NUT configurations. We find that there is an excess of
positive chiral Dirac fermions over the negative ones which triggers the
anomaly. | Born Reciprocity and Cosmic Accelerations: The trans-Planckian theory is a model that realizes concretely the Born
reciprocity idea, which is the postulate of absolute equivalence between
coordinate $x$ and momenta $p$. This model is intrinsically global, and thus it
is naturally implemented in a cosmological setting. Cosmology and Born
reciprocity are made for each other. Inflation provides the essential mechanism
to suppress the terms coming from the dual part of the action. The
trans-Planckian theory provides an explanation for the present acceleration of
the universe scale factor. This is possible just considering a simple model
that contains gravity, one gauge field plus one matter field (to be identified
with dark matter), together with the reciprocity principle. |
Sequential Flows by Irrelevant Operators: We explore whether one can $T \overline{T}$ deform a collection of theories
that are already $T \overline{T}$-deformed. This allows us to define classes of
irrelevant deformations that know about subsystems. In some basic cases, we
explore the spectrum that results from this procedure and we provide numerical
evidence in favor of modular invariance. We also study the flow of the
classical Lagrangian for free bosons and free fermions under successive
deformations. Some of the models found by sequentially flowing are likely to
have interesting holographic interpretations. | Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black
holes: Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we
consider the analog for the Einstein-Maxwell action, which gives Ricci flow
with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell
field. We argue that this flow is well-posed for static spacetimes with pure
electric or magnetic potentialsand show it preserves both non-extremal and
extremal black hole horizons. In the latter case we find the flow of the near
horizon geometry decouples from that of the exterior. The Schwarzschild black
hole is an unstable fixed point of Ricci flow for static spacetimes. Here we
consider flows of the Reissner-Nordstr\"om (RN) fixed point. The magnetic RN
solution becomes a stable fixed point of the flow for sufficient charge.
However we find that the electric RN black hole is always unstable. Numerically
solving the flow starting with a spherically symmetric perturbation of a
non-extremal RN solution, we find similar behaviour in the electric case to the
Ricci flows of perturbed Schwarzschild, namely the horizon shrinks to a
singularity in finite time or expands forever. In the magnetic case, a
perturbed unstable RN solution has a similar expanding behaviour, but a
perturbation that decreases the horizon size flows to a stable black hole
solution rather than a singularity. For extremal RN we solve the near horizon
flow for spherical symmetry exactly, and see in the electric case two unstable
directions which flow to singularities in finite flow time. However, even
turning these off, and fixing the near horizon geometry to be that of RN, we
numerically show that the flows appear to become singular in the vicinity of
its horizon. |
Covariant Map Between Ramond-Neveu-Schwarz and Pure Spinor Formalisms
for the Superstring: A covariant map between the Ramond-Neveu-Schwarz (RNS) and pure spinor
formalisms for the superstring is found which transforms the RNS and pure
spinor BRST operators into each other. The key ingredient is a dynamical
twisting of the ten spin-half RNS fermions into five spin-one and five
spin-zero fermions using bosonic pure spinors that parameterize an SO(10)/U(5)
coset. The map relates massless vertex operators in the two formalisms, and
gives a new description of Ramond states which does not require spin fields. An
argument is proposed for relating the amplitude prescriptions in the two
formalisms. | M-Theory and Stringy Corrections to Anti-de Sitter Black Holes and
Conformal Field Theories: We consider black holes in anti-de Sitter space AdS_{p+2} (p = 2,3,5), which
have hyperbolic, flat or spherical event horizons. The $O(\alpha'^3)$
corrections (or the leading corrections in powers of the eleven-dimensional
Planck length) to the black hole metrics are computed for the various
topologies and dimensions. We investigate the consequences of the stringy or
M-theory corrections for the black hole thermodynamics. In particular, we show
the emergence of a stable branch of small spherical black holes. We obtain the
corrected Hawking-Page transition temperature for black holes with spherical
horizons, and show that for p=3 this phase transition disappears at a value of
$\alpha'$ considerably smaller than that estimated previously by Gao and Li.
Using the AdS/CFT correspondence, we determine the $S^1 x S^3$ N=4 SYM phase
diagram for sufficiently large `t Hooft coupling, and show that the critical
point at which the Hawking-Page transition disappears (the correspondence point
of Horowitz-Polchinski), occurs at $g_{YM}^2N \approx 20.5$. The d=4 and d=7
black hole phase diagrams are also determined, and connection is made with the
corresponding boundary CFTs. Finally, for flat and hyperbolic horizons, we show
that the leading stringy or M-theory corrections do not give rise to any phase
transition. For horizons compactified to a torus $T^p$ or to a quotient of
hyperbolic space, $H^p/\Gamma$, we comment on the effects of light winding
modes. |
Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary
terms: We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary
terms. By exploiting certain functional relations at roots of unity, we propose
the Bethe ansatz solution for the transfer matrix eigenvalues for cases where
atmost two of the boundary parameters are set to be arbitrary and the bulk
anisotropy parameter has values \eta = i \pi/3, i \pi/5,... We present
numerical evidence to demonstrate completeness of the Bethe ansatz solutions
derived for s = 1/2 and s = 1. | Flat connections for Yang-Mills theories on the 3--torus: We discuss the moduli space of flat connections of Yang-Mills theories
formulated on T^3 x R, with periodic boundary conditions. When the gauge group
is SO(N>=7), G_2, F_4, E_6, E_7 or E_8, the moduli space consists of more than
one component. |
Explicit supertring vacua in a background of gravitational waves and
dilaton: We present an explicit solution of superstring effective equations,
represented by gravitational waves and dilaton backgrounds. Particular
solutions will be examined in a forthcoming note. | Entanglement in Theory Space: We propose a new concept of entanglement for quantum systems: entanglement in
theory space. This is defined by decomposing a theory into two by an un-gauging
procedure. We provide two examples where this newly-introduced entanglement is
closely related with conventional geometric entropies: deconstruction and
AGT-type correspondence. |
Deep Quantum Geometry of Matrices: We employ machine learning techniques to provide accurate variational
wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic
matrices. Variational quantum Monte Carlo is implemented with deep generative
flows to search for gauge invariant low energy states. The ground state, and
also long-lived metastable states, of an $\mathrm{SU}(N)$ matrix quantum
mechanics with three bosonic matrices, as well as its supersymmetric `mini-BMN'
extension, are studied as a function of coupling and $N$. Known semiclassical
fuzzy sphere states are recovered, and the collapse of these geometries in more
strongly quantum regimes is probed using the variational wavefunction. We then
describe a factorization of the quantum mechanical Hilbert space that
corresponds to a spatial partition of the emergent geometry. Under this
partition, the fuzzy sphere states show a boundary-law entanglement entropy in
the large $N$ limit. | Non-Critical Bosonic String Corrections to the Black Hole Entropy: We calculate the quantum corrections to the entropy of a very large black
hole, coming from the theory of a $D$-dimensional, non-critical bosonic string.
We show that, for $D >2$, as a result of modular invariance the entropy is
ultraviolet finite, although it diverges in the infrared (while for $D=2$ the
entropy contains both ultraviolet and infrared divergences). The issue of
modular invariance in field theory, in connection with black-hole entropy, is
also investigated. |
Bound State Transfer Matrix for AdS5 x S5 Superstring: We apply the algebraic Bethe ansatz technique to compute the eigenvalues of
the transfer matrix constructed from the general bound state S-matrix of the
light-cone AdS5 x S5 superstring. This allows us to verify certain conjectures
on the quantum characteristic function, and to extend them to the general case. | Conformal, Integrable and Topological Theories, Graphs and Coxeter
Groups: I review three different problems occuring in two dimensional field theory:
1) classification of conformal field theories; 2) construction of lattice
integrable realizations of the latter; 3) solutions to the WDVV equations of
topological field theories. I show that a structure of Coxeter group is hidden
behind these three related problems. |
Axion Inflation in F-theory: We study the dynamics of axion-like fields in F-theory and suggest that they
can serve as inflatons in models of natural inflation. The axions arise from
harmonic three-forms on the F-theory compactification space and parameterize a
complex torus that varies over the geometric moduli space. In particular, this
implies that the axion decay constants depend on the complex structure moduli
that can be fixed by background fluxes. This might allow tuning them to be
super-Planckian in a controlled way and allow for interesting single field
inflationary models. We argue that this requires a localization of the
three-forms near regions of strong string coupling, analogously to the
reasoning that GUT physics requires the use of F-theory. These models can admit
a tensor to scalar ratio r>0.1. | Killing-Yano tensors and generalized supersymmetries in black-hole and
monopole geometries: New kinds of supersymmetry arise in supersymmetric $\sg$-models describing
the motion of spinning point-particles in classical backgrounds, for example
black-holes, or the dynamics of monopoles. Their geometric origin is the
existence of Killing-Yano tensors. The relation between these concepts is
explained and examples are given. --- Contribution to Proceedings Quarks-94;
Vladimir, Russia (1994). |
Superconformal N=2, D=5 matter with and without actions: We investigate N=2, D=5 supersymmetry and matter-coupled supergravity
theories in a superconformal context. In a first stage we do not require the
existence of a Lagrangian. Under this assumption, we already find at the level
of rigid supersymmetry, i.e. before coupling to conformal supergravity, more
general matter couplings than have been considered in the literature. For
instance, we construct new vector-tensor multiplet couplings, theories with an
odd number of tensor multiplets, and hypermultiplets whose scalar manifold
geometry is not hyperkaehler.
Next, we construct rigid superconformal Lagrangians. This requires some extra
ingredients that are not available for all dynamical systems. However, for the
generalizations with tensor multiplets mentioned above, we find corresponding
new actions and scalar potentials. Finally, we extend the supersymmetry to
local superconformal symmetry, making use of the Weyl multiplet. Throughout the
paper, we will indicate the various geometrical concepts that arise, and as an
application we compute the non-vanishing components of the Ricci tensor of
hypercomplex group manifolds. Our results can be used as a starting point to
obtain more general matter-couplings to Poincare supergravity. | Timelike Duality: Several stationary solutions of the low energy string equations are dualized
with respect to their timelike symmetry. Many of the duals have simple physical
interpretations. Those of the nonextremal three dimensional black hole and
black string are negative mass black strings. The extremal cases of these, and
extremal higher dimensional black strings also, give negative energy plane
fronted waves. In fact, all of the duals of positive mass solutions that will
be considered here have nonpositive energies, but an argument is given which
suggests that this is not true in general. |
Inflation and cosmic (super)strings: implications of their intimate
relation revisited: We briefly discuss constraints on supersymmetric hybrid inflation models and
examine the consistency of brane inflation models. We then address the
implications for inflationary scenarios resulting from the strong constraints
on the cosmic (super)string tension imposed from the most recent cosmic
microwave background temperature anisotropies data. | Heterotic non-linear sigma models with anti-de Sitter target spaces: We calculate the beta function of non-linear sigma models with S^{D+1} and
AdS_{D+1} target spaces in a 1/D expansion up to order 1/D^2 and to all orders
in \alpha'. This beta function encodes partial information about the spacetime
effective action for the heterotic string to all orders in \alpha'. We argue
that a zero of the beta function, corresponding to a worldsheet CFT with
AdS_{D+1} target space, arises from competition between the one-loop and
higher-loop terms, similarly to the bosonic and supersymmetric cases studied
previously in hep-th/0512355. Various critical exponents of the non-linear
sigma model are calculated, and checks of the calculation are presented. |
New particle model in extended space-time and covariantization of planar
Landau dynamics: We introduce the Maxwell-invariant extension of D=4 relativistic free
particle model into ten-dimensional Maxwell tensorial space. The new model
after first quantization describes in particular Lorentz frame the planar
dynamics providing Landau orbits in the presence of constant magnetic field. | Spectrum-Generating Algebra for Charged Strings: When an open string ends with charges on a D2-brane, which involves constant
background magnetic field perpendicular to the brane, we construct the
spectrum-generating algebra for this charged string, which assures that our
system is ghost-free under some conditions. The application to the Hall effect
for charged strings is also shortly remarked. |
Emergence of space and cosmic evolution based on entropic force: In this paper, we propose a model in which an additional pressure due to the
effects of the entropic force is added to the ideal fluid. Furthermore, we
obtain the dynamic equation in the FRW universe which contains the quantum
gravitational effects based on the description of entropic force and emergence
of space. Our model can well explain the age of the universe and the effect of
the current accelerating expansion. We give the relation between the luminosity
distance and the redshift factor, and compare this relation with that of lambda
cold dark matter model($\Lambda CDM$ model). | Singlet Couplings and (0,2) Models: We use the quantum symmetries present in string compactification on
Landau-Ginzburg orbifolds to prove the existence of a large class of exactly
marginal (0,2) deformations of (2,2) superconformal theories. Analogous methods
apply to the more general (0,2) models introduced in \DK, lending further
credence to the fact that the corresponding \LG\ models represent bona-fide
(0,2) SCFTs. We also use the large symmetry groups which arise when the
worldsheet superpotential is turned off to constrain the dependence of certain
correlation functions on the untwisted moduli. This allows us to approach the
problem of what happens when one tries to deform away from the \LG\ point. In
particular, we find that the masses and three-point couplings of the massless
$E_{6}$ singlets related to ${\rm H^{1}}(\ET)$ vanish at all points in the
quintic \Ka\ moduli space. Putting these results together, and invoking some
plausible dynamical assumptions about the corresponding linear \sm s, we show
that one can deform these \LG\ theories to arbitrary values of the \Ka\ moduli. |
The Non-Split Scalar Coset in Supergravity Theories: The general non-split scalar coset of supergravity theories is discussed.The
symmetric space sigma model is studied in two equivalent formulations and for
different coset parametrizations.The dualisation and the local first order
formulation is performed for the non-split scalar coset G/K when the rigid
symmetry group G is a real form of a non-compact semisimple Lie group (not
necessarily split) and the local symmetry group K is G's maximal compact
subgroup.A comparison with the scalar cosets arising in the
T^{10-D}-compactification of the heterotic string theory in ten dimensions is
also mentioned. | Phase transition and thermodynamical geometry for Schwarzschild AdS
black hole in $AdS_5\times{S^5}$ spacetime: We study thermodynamics and thermodynamic geometry of a five-dimensional
Schwarzschild AdS black hole in $AdS_5\times{S^5}$ spacetime by treating the
cosmological constant as the number of colors in the boundary gauge theory and
its conjugate quantity as the associated chemical potential. It is found that
the chemical potential is always negative in the stable branch of black hole
thermodynamics and it has a chance to be positive, but appears in the unstable
branch. We calculate scalar curvatures of the thermodynamical Weinhold metric,
Ruppeiner metric and Quevedo metric, respectively and we find that the
divergence of scalar curvature is related to the divergence of specific heat
with fixed chemical potential in the Weinhold metric and Ruppeiner metric,
while in the Quevedo metric the divergence of scalar curvature is related to
the divergence of specific heat with fixed number of colors and the vanishing
of the specific heat with fixed chemical potential. |
Quantum tunneling from scalar fields in rotating black strings: Using the Hamilton-Jacobi method of quantum tunneling and complex path
integration, we study Hawking radiation of scalar particles from rotating black
strings. We discuss tunneling of both charged and uncharged scalar particles
from the event horizons. For this purpose, we use the Klein-Gordon equation and
find the tunneling probability of outging scalar particles. The procedure gives
Hawking temperature for rotating charged black strings as well. | Comments on the Algebraic Properties of Dilaton Actions: We study the relation between the dilaton action and sigma models for the
Goldstone bosons of the spontaneous breaking of the conformal group. We argue
that the relation requires that the sigma model is diffeomorphism invariant.
The origin of the WZW terms for the dilaton is clarified and it is shown that
in this approach the dilaton WZW term is necessarily accompanied by a Weyl
invariant term proposed before from holographic considerations. |
Categorical Foundation of Quantum Mechanics and String Theory: The unification of Quantum Mechanics and General Relativity remains the
primary goal of Theoretical Physics, with string theory appearing as the only
plausible unifying scheme. In the present work, in a search of the conceptual
foundations of string theory, we analyze the relational logic developed by C.
S. Peirce in the late nineteenth century. The Peircean logic has the
mathematical structure of a category with the relation $R_{ij}$ among two
individual terms $S_i$ and $S_j$, serving as an arrow (or morphism). We
introduce a realization of the corresponding categorical algebra of
compositions, which naturally gives rise to the fundamental quantum laws, thus
indicating category theory as the foundation of Quantum Mechanics. The same
relational algebra generates a number of group structures, among them
$W_{\infty}$. The group $W_{\infty}$ is embodied and realized by the matrix
models, themselves closely linked with string theory. It is suggested that
relational logic and in general category theory may provide a new paradigm,
within which to develop modern physical theories. | Quantum corrections during inflation and conservation of adiabatic
perturbations: The possibility that quantum corrections break the conservation of
superhorizon adiabatic perturbations in single field inflation is examined. I
consider the lowest order corrections from massless matter fields in the
Hamiltonian formalism. Particular emphasis is therefore laid on the
renormalization. The counterterms are the same as in the Lagrangian formalism.
The renormalized value of the tadpole is zero. I find a possible secular
dependence of the power spectrum at one loop due to the trace anomaly, but this
result depends on the approximation of the modes and is inconclusive. The
symmetry (not) violated by the quantum corrections is the invariance by
dilatation. Perspectives on the backreaction problem are briefly discussed. |
Mathieu Moonshine and symmetries of K3 sigma models: A recent observation by Eguchi, Ooguri and Tachikawa (EOT) suggests a
relationship between the largest Mathieu group M24 and the elliptic genus of
K3. This correspondence would be naturally explained by the existence of a
non-linear sigma-model on K3 with the Mathieu group as its group of symmetries.
However, all possible symmetry groups of K3 models have been recently
classified and none of them contains M24. We review the evidence in favour of
the EOT conjecture and discuss the open problems in its physical
interpretation. | Stretching the Horizon of a Higher Dimensional Small Black Hole: There is a general scaling argument that shows that the entropy of a small
black hole, representing a half-BPS excitation of an elementary heterotic
string in any dimension, agrees with the statistical entropy up to an overall
numerical factor. We propose that for suitable choice of field variables the
near horizon geometry of the black hole in D space-time dimensions takes the
form of AdS_2\times S^{D-2} and demonstrate how this ansatz can be used to
calculate the numerical factor in the expression for the black hole entropy if
we know the higher derivative corrections to the action. We illustrate this by
computing the entropy of these black holes in a theory where we modify the
supergravity action by adding the Gauss-Bonnet term. The black hole entropy
computed this way is finite and has the right dependence on the charges in
accordance with the general scaling argument, but the overall numerical factor
does not agree with that computed from the statistical entropy except for D=4
and D=5. This is not surprising in view of the fact that we do not use a fully
supersymmetric action in our analysis; however this analysis demonstrates that
higher derivative corrections are capable of stretching the horizon of a small
black hole in arbitrary dimensions. |
Problems and Progress in Covariant High Spin Description: A universal description of particles with spins j greater or equal one ,
transforming in (j,0)+(0,j), is developed by means of representation specific
second order differential wave equations without auxiliary conditions and in
covariant bases such as Lorentz tensors for bosons, Lorentz-tensors with Dirac
spinor components for fermions, or, within the basis of the more fundamental
Weyl-Van-der-Waerden sl(2,C) spinor-tensors. At the root of the method, which
is free from the pathologies suffered by the traditional approaches, are
projectors constructed from the Casimir invariants of the spin-Lorentz group,
and the group of translations in the Minkowski space time. | Modular graph functions and asymptotic expansions of Poincaré series: In this note we study $SL(2,\mathbb{Z})$-invariant functions such as modular
graph functions or coefficient functions of higher derivative corrections in
type IIB string theory. The functions solve inhomogeneous Laplace equations and
we choose to represent them as Poincar\'e series. In this way we can combine
different methods for asymptotic expansions and obtain the perturbative and
non-perturbative contributions to their zero Fourier modes. In the case of the
higher derivative corrections, these terms have an interpretation in terms of
perturbative string loop effects and pairs of instantons/anti-instantons. |
Perturbative Inaccessibility of Conformal Fixed Points in
Nonsupersymmetric Quiver Theories: The possibility that non-supersymmetric quiver theories may have a
renormalization-group fixed point at which there is conformal invariance
requires non-perturbative information. | Multi instanton tests of holography: Gauge theories living on stacks of D7-branes are holographically related to
IIB gravitational backgrounds with a varying axion-dilaton field (F-theory).
The axion-dilaton field is generated by D7, O7 and D-instanton sources and can
be written in terms of the chiral correlators of the eight dimensional gauge
theory living on the D7-branes. Using localization techniques, we prove that
the same correlators determine the gauge coupling of the four-dimensional N=2
supersymmetric SU(2) gauge theories living on the elementary D3-brane which
probes the F-theory geometries. |
Searching for Kerr in the 2PM amplitude: The classical scattering of spinning objects is well described by the
spinor-helicity formalism for heavy particles. Using these variables, we derive
spurious-pole-free, all-spin opposite-helicity Compton amplitudes (factorizing
on physical poles to the minimal, all-spin three-point amplitudes of ref.
\cite{Arkani-Hamed:2017jhn}) in the classical limit for QED, QCD, and gravity.
The cured amplitudes are subject to deformations by contact terms, the vast
majority of whose contributions we can fix by imposing a relation between spin
structures -- motivated by lower spin multipoles of black hole scattering -- at
the second post-Minkowskian (2PM) order. For QED and gravity, this leaves a
modest number of unfixed coefficients parametrizing contact-term deformations,
while the QCD amplitude is uniquely determined. Our gravitational Compton
amplitude allows us to push the state-of-the-art of spinning-2PM scattering to
any order in the spin vectors of both objects; we present results here and in
the auxiliary file \texttt{2PMSpin8Aux.nb} up to eighth order in the spin
vectors. Interestingly, despite leftover coefficients in the Compton amplitude,
imposing the aforementioned relation between spin structures uniquely fixes
some higher-spin parts of the 2PM amplitude. | On The Existence of a Holographic Description of the LHC Quark-Gluon
Plasmas: Peripheral collisions of heavy ions can give rise to extremely intense
magnetic fields. It has been suggested that these fields might invalidate the
holographic description of the corresponding quark-gluon plasmas, assuming that
these can be modelled by strongly coupled field theories. In the case of the
plasmas produced in collisions at the RHIC facility (including in the beam
energy scans), it is known how to deal with this problem: one has to take into
account the large angular momenta generated in these plasmas, and the effects
of the baryonic chemical potential. But this does not work for the plasmas
produced in peripheral collisions at the LHC. However, these results neglect
some (less significant) aspects of bulk physics; could it be that the problem
is resolved by taking into account these lower-order effects? Here we use a
bulk dilatonic field (fully compatible with boundary data, as well as with the
asymptotically AdS character of the bulk geometry) as a model of these effects,
and show that this is unlikely to be the solution. Thus, the existence of a
consistent holographic description of the most extreme LHC plasmas remains open
to question. |
Corner Transfer Matrices and Quantum Affine Algebras: Let H be the corner-transfer-matrix Hamiltonian for the six-vertex model in
the anti-ferroelectric regime. It acts on the infinite tensor product W = V . V
. V ....., where is the 2-dimensional irreducible representation of the quantum
affine sl(2). We observe that H is the derivation of quantum affine sl(2), and
conjecture that the eigenvectors of H form the level-1 vacuum representation of
quantum affine sl(2). We report on checks in support of our conjecture. | On minimal coupling of the ABC-superparticle to supergravity background: By rigorous application of the Hamiltonian methods we show that the
ABC-formulation of the Siegel superparticle admits consistent minimal coupling
to external supergravity. The consistency check proves to involve all the
supergravity constraints. |
Constraint characterization and degree of freedom counting in Lagrangian
field theory: We present a Lagrangian approach to counting degrees of freedom in
first-order field theories. The emphasis is on the systematic attainment of a
complete set of constraints. In particular, we provide the first comprehensive
procedure to ensure the functional independence of all constraints and discuss
in detail the possible closures of the constraint algorithm. We argue degrees
of freedom can but need not correspond to physical modes. The appendix
comprises fully worked out, physically relevant examples of varying complexity. | Coarse Grained Quantum Dynamics: Inspired by holographic Wilsonian renormalization, we consider coarse
graining a quantum system divided between short distance and long distance
degrees of freedom, coupled via the Hamiltonian. Observations using purely long
distance observables are described by the reduced density matrix that arises
from tracing out the short-distance degrees of freedom. The dynamics of this
density matrix is non-Hamiltonian and nonlocal in time, on the order of some
short time scale. We describe this dynamics in a model system with a simple
hierarchy of energy gaps $\Delta E_{UV} > \Delta E_{IR}$, in which the coupling
between high-and low-energy degrees of freedom is treated to second order in
perturbation theory. We then describe the equations of motion under suitable
time averaging, reflecting the limited time resolution of actual experiments,
and find an expansion of the master equation in powers of $\Delta E_{IR}/\Delta
E_{UV}$, after the fashion of effective field theory. The failure of the system
to be Hamiltonian or even Markovian appears at higher orders in this ratio. We
compute the evolution of the density matrix in three specific examples: coupled
spins, linearly coupled simple harmonic oscillators, and an interacting scalar
QFT. Finally, we argue that the logarithm of the Feynman-Vernon influence
functional is the correct analog of the Wilsonian effective action for this
problem. |
Equivalence Principle, Planck Length and Quantum Hamilton-Jacobi
Equation: The Quantum Stationary HJ Equation (QSHJE) that we derived from the
equivalence principle, gives rise to initial conditions which cannot be seen in
the Schroedinger equation. Existence of the classical limit leads to a
dependence of the integration constant $\ell=\ell_1+i\ell_2$ on the Planck
length. Solutions of the QSHJE provide a trajectory representation of quantum
mechanics which, unlike Bohm's theory, has a non-trivial action even for bound
states and no wave guide is present. The quantum potential turns out to be an
intrinsic potential energy of the particle which, similarly to the relativistic
rest energy, is never vanishing. | Anomaly-Induced Magnetic Screening in 2+1 dimensional QED at Finite
Density: We show that in 2+1 dimensional Quantum Electrodynamics an external magnetic
field applied to a finite density of massless fermions is screened, due to a
$2+1$-dimensional realization of the underlying $2$-dimensional axial anomaly
of the space components of the electric current. This is shown to imply
screening of the magnetic field, i.e., the Meissner effect. We discuss the
physical implications of this result. |
$p$-wave holographic superconductors with massive vector condensate in
Born-Infeld electrodynamics: In this paper, we have studied the effect of Born-Infeld electrodynamics in
holographic $p$-wave superconductors with massive vector condensation. We have
analysed this model in the probe limit using a variational method known as the
St\"urm-Liouville eigenvalue approach. For this $p$-wave holographic
superconductor model, we have calculated the critical temperature $T_{c}$ as
well as the value of the condensation operator for two different choices of
$m^{2}$. We have also pointed out the similarities and dissimilarities between
this model for $m^{2} = 0$ and $p$-wave holographic superconductor model
constructed out of Einstein-Yang-Mills theory. We have then computed the
conductivity of these holographic superconductor models using a self-consistent
approach and have shown that the DC conductivity diverges. | General Neveu-Schwarz Correlators in Super Liouville Theory: In this paper we compute the N-point correlation functions of the tachyon
operator from the Neveu Schwarz sector of super Liouville theory coupled to
matter fields (with $\hat c\le 1$) in the super Coulomb gas formulation, on
world sheets with spherical topology. We first integrate over the zero mode
assuming that the $s$ parameter takes an integer value, subsequently we
continue the parameter to an arbitrary real number. We included an arbitrary
number of screening charges (s.c.) and as a result, after renormalizing the
s.c., the external legs and the cosmological constant, the form of the final
amplitudes do not modify. Remarkably, the result is completely parallel to the
bosonic case. We also completed a discussion on the calculation of bosonic
correlators including arbitrary screening charges. |
Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian
Borcherds Algebras: We continue our study of algebraic properties of N=4 topological amplitudes
in heterotic string theory compactified on T^2, initiated in arXiv:1102.1821.
In this work we evaluate a particular one-loop amplitude for any enhanced gauge
group h \subset e_8 + e_8, i.e. for arbitrary choice of Wilson line moduli. We
show that a certain analytic part of the result has an infinite product
representation, where the product is taken over the positive roots of a
Lorentzian Kac-Moody algebra g^{++}. The latter is obtained through double
extension of the complement g= (e_8 + e_8)/h. The infinite product is
automorphic with respect to a finite index subgroup of the full T-duality group
SO(2,18;Z) and, through the philosophy of Borcherds-Gritsenko-Nikulin, this
defines the denominator formula of a generalized Kac-Moody algebra G(g^{++}),
which is an 'automorphic correction' of g^{++}. We explicitly give the root
multiplicities of G(g^{++}) for a number of examples. | Note on Dirac--Kähler massless fields: We obtain the canonical and symmetrical Belinfante energy-momentum tensors of
Dirac--K\"{a}hler's fields. It is shown that the traces of the energy-momentum
tensors are not equal to zero. We find the canonical and Belinfante dilatation
currents which are not conserved, but a new conserved dilatation current is
obtained. It is pointed out that the conformal symmetry is broken. The
canonical quantization is performed and the propagator of the massless fields
in the first-order formalism is found. |
Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure
Term: We investigate a nonperturbative formulation of quantum gravity defined via
Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the
path integral. We are motivated to revisit this older formulation of dynamical
triangulations by hints from renormalization group approaches that gravity may
be asymptotically safe and by the emergence of a semiclassical phase in causal
dynamical triangulations (CDT). We study the phase diagram of this model and
identify the two phases that are well known from previous work: the branched
polymer phase and the collapsed phase. We verify that the order of the phase
transition dividing the branched polymer phase from the collapsed phase is
almost certainly first-order. The nontrivial measure term enlarges the phase
diagram, allowing us to explore a region of the phase diagram that has been
dubbed the crinkled region. Although the collapsed and branched polymer phases
have been studied extensively in the literature, the crinkled region has not
received the same scrutiny. We find that the crinkled region is likely a part
of the collapsed phase with particularly large finite-size effects.
Intriguingly, the behavior of the spectral dimension in the crinkled region at
small volumes is similar to that of CDT, as first reported in arXiv:1104.5505,
but for sufficiently large volumes the crinkled region does not appear to have
4-dimensional semiclassical features. Thus, we find that the crinkled region of
the EDT formulation does not share the good features of the extended phase of
CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent
results of arXiv:1307.2270, in which the authors used a somewhat different
discretization of EDT from the one presented here. | Noncommutative instantons revisited: We find a new gauge in which U(1) noncommutative instantons are explicitly
non-singular on the whole noncommutative R^4, thus resolving the previous
confusions of the author. We start with the pedagogical introduction to the
noncommutative gauge theories. |
Probing the holographic dilaton: Many strongly coupled field theories admit a spectrum of gauge-invariant
bound states that includes scalar particles with the same quantum numbers as
the vacuum. The challenge naturally arises of how to characterise them. In
particular, how can a dilaton---the pseudo-Nambu-Goldstone boson associated
with approximate scale invariance---be distinguished from other generic light
scalars with the same quantum numbers? We address this problem within the
context of gauge-gravity dualities, by analysing the fluctuations of the
higher-dimensional gravitational theory. The diagnostic test that we propose
consists of comparing the results of the complete calculation, performed by
using gauge-invariant fluctuations in the bulk, with the results obtained in
the probe approximation. While the former captures the mixing between scalar
and metric degrees of freedom, the latter removes by hand the fluctuations that
source the dilatation operator of the boundary field-theory. Hence, the probe
approximation cannot capture a possible light dilaton, while it should fare
well for other scalar particles. We test this idea on a number of holographic
models, among which are some of the best known, complete gravity backgrounds
constructed within the top-down approach to gauge-gravity dualities. We compute
the spectra of scalar and tensor fluctuations, that are interpreted as bound
states (glueballs) of the dual field theory, and we highlight those cases in
which the probe approximation yields results close to the correct physical
ones, as well as those cases where significant discrepancies emerge. We
interpret the latter occurrence as an indication that identifying one of the
lightest scalar states with the dilaton is legitimate, at least as a
leading-order approximation. | String Junctions and Non-Simply Connected Gauge Groups: Relations between the global structure of the gauge group in elliptic
F-theory compactifications, fractional null string junctions, and the
Mordell-Weil lattice of rational sections are discussed. We extend results in
the literature, which pertain primarily to rational elliptic surfaces and
obtain pi^1(G) where G is the semi-simple part of the gauge group. We show how
to obtain the full global structure of the gauge group, including all U(1)
factors. Our methods are not restricted to rational elliptic surfaces. We also
consider elliptic K3's and K3-fibered Calabi-Yau three-folds. |
Non-Spherical Horizons, I: We formulate an extension of Maldacena's AdS/CFT conjectures to the case of
branes located at singular points in the ambient transverse space. For
singularities which occur at finite distance in the moduli space of M or F
theory models with spacetime-filling branes, the conjectures identify the
worldvolume theory on the p-branes with a compactification of M or IIB theory
on $AdS_{p+2} \times H^{D-p-2}$. We show how the singularity determines the
horizon H, and demonstrate the relationship between global symmetries on the
worldvolume and gauge symmetries in the AdS model. As a first application, we
study some singularities relevant to the D3-branes required in four-dimensional
F-theory. For these we are able to explicitly derive the low-energy field
theory on the worldvolume and compare its properties to predictions from the
dual AdS model. In particular, we examine the baryon spectra of the models and
the fate of the Abelian factors in the gauge group. | Instanton-soliton loops in 5D super-Yang-Mills: Soliton contributions to perturbative processes in QFT are controlled by a
form factor, which depends on the soliton size. We provide a demonstration of
this fact in a class of scalar theories with generic moduli spaces. We then
argue that for instanton-solitons in 5D super-Yang-Mills theory the analogous
form factor does not lead to faster-than-any-power suppression in the
perturbative coupling. We also discuss the implications of such contributions
for the UV behavior of maximally supersymmetric Yang-Mills in 5D and its
relation to the (2,0) CFT in 6D. This is a contribution to the proceedings of
the "String Math 2013'" conference and is a condensed version of results
appearing in 1404.0016 and 1403.5017. |
Algorithmic construction of SYM multiparticle superfields in the BCJ
gauge: We write down closed formulas for all necessary steps to obtain multiparticle
super Yang--Mills superfields in the so-called BCJ gauge. The superfields in
this gauge have obvious applications in the quest for finding BCJ-satisfying
representations of amplitudes. As a benefit of having these closed formulas, we
identify the explicit finite gauge transformation responsible for attaining the
BCJ gauge. To do this, several combinatorial maps on words are introduced and
associated identities rigorously proven. | Stability of warped AdS3 vacua of topologically massive gravity: AdS3 vacua of topologically massive gravity (TMG) have been shown to be
perturbatively unstable for all values of the coupling constant except the
chiral point \mu l=1. We study the possibility that the warped vacua of TMG,
which exist for all values of \mu, are stable under linearized perturbations.
In this paper, we show that spacelike warped AdS3 vacua with Compere-Detournay
boundary conditions are indeed stable in the range \mu l > 3. This is precisely
the range in which black hole solutions arise as discrete identifications of
the warped AdS3 vacuum. The situation somewhat resembles chiral gravity:
although negative energy modes do exist, they are all excluded by the boundary
conditions, and the perturbative spectrum solely consists of boundary (pure
large gauge) gravitons. |
Fractal Theory Space: Spacetime of Noninteger Dimensionality: We construct matter field theories in ``theory space'' that are fractal, and
invariant under geometrical renormalization group (RG) transformations. We
treat in detail complex scalars, and discuss issues related to fermions,
chirality, and Yang-Mills gauge fields. In the continuum limit these models
describe physics in a noninteger spatial dimension which appears above a RG
invariant ``compactification scale,'' M. The energy distribution of KK modes
above M is controlled by an exponent in a scaling relation of the vacuum energy
(Coleman-Weinberg potential), and corresponds to the dimensionality. For
truncated-s-simplex lattices with coordination number s the spacetime
dimensionality is 1+(3+2ln(s)/ln(s+2)). The computations in theory space
involve subtleties, owing to the 1+3 kinetic terms, yet the resulting
dimensionalites are equivalent to thermal spin systems. Physical implications
are discussed. | Solvable Lie Algebras in Type IIA, Type IIB and M Theories: We study some applications of solvable Lie algebras in type IIA, type IIB and
M theories. RR and NS generators find a natural geometric interpretation in
this framework. Special emphasis is given to the counting of the abelian
nilpotent ideals (translational symmetries of the scalar manifolds) in
arbitrary D dimensions. These are seen to be related, using Dynkin diagram
techniques, to one-form counting in D+1 dimensions. A recipy for gauging
isometries in this framework is also presented. In particular, we list the
gauge groups both for compact and translational isometries. The former agree
with some results already existing in gauged supergravity. The latter should be
possibly related to the study of partial supersymmetry breaking, as suggested
by a similar role played by solvable Lie algebras in N=2 gauged supergravity. |
Non-Abelian bootstrap of primordial magnetism: We point out that a primordial magnetic field can be generated in the
electroweak phase transition by a non-Abelian bootstrap, where the field is
generated by currents of W's, which in turn are extracted from the vacuum by
the magnetic field. This magnetic field is produced as a vortex condensate at
the electroweak phase transition. It becomes stringy as a consequence of the
dynamical evolution due to magnetohydrodynamics. | On space-time noncommutative U(1) model at high temperature: We extend the results of Ref. [arXiv:0705.4294] to noncommutative gauge
theories at finite temperature. In particular, by making use of the background
field method, we analyze renormalization issues and the high-temperature
asymptotics of the one-loop Euclidean free energy of the noncommutative U(1)
gauge model within imaginary time formalism. As a by-product, the heat trace of
the non-minimal photon kinetic operator on noncommutative $S^1 \times R^3$
manifold taken in an arbitrary background gauge is investigated. All possible
types of noncommutativity on $S^1 \times R^3$ are considered. It is
demonstrated that the non-planar sector of the model does not contribute to the
free energy of the system at high temperature. The obtained results are
discussed. |
Supersymmetric Construction of W-Algebras from Super Toda and Wznw
Theories: A systematic construction of super W-algebras in terms of the WZNW model
based on a super Lie algebra is presented. These are shown to be the symmetry
structure of the super Toda models, which can be obtained from the WZNW theory
by Hamiltonian reduction. A classification, according to the conformal spin
defined by an improved energy-momentum tensor, is dicussed in general terms for
all super Lie algebras whose simple roots are fermionic . A detailed discussion
employing the Dirac bracket structure and an explicit construction of
W-algebras for the cases of $OSP(1,2)$, $OSP(2,2)$ , $OSP(3,2)$ and $D(2,1 \mid
\alpha )$ are given. The $N=1$ and $N=2$ super conformal algebras are discussed
in the pertinent cases. | Topology Changing Transitions in Bubbling Geometries: Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x
SO(4) symmetry can be decomposed into a sequence of n elementary transitions.
The half-BPS solution that describes the elementary transition is seeded by a
phase space distribution of fermions filling two diagonal quadrants. We study
the geometry of this solution in some detail. We show that this solution can be
interpreted as a time dependent geometry, interpolating between two asymptotic
pp-waves in the far past and the far future. The singular solution at the
transition can be resolved in two different ways, related by the particle-hole
duality in the effective fermion description. Some universal features of the
topology change are governed by two-dimensional Type 0B string theory, whose
double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at
topological transition. In addition, we present the full class of geometries
describing the vicinity of the most general localized classical singularity
that can occur in this class of half-BPS bubbling geometries. |
Entanglement Negativity in Flat Holography: We advance holographic constructions for the entanglement negativity of
bipartite states in a class of $(1+1)-$dimensional Galilean conformal field
theories dual to asymptotically flat three dimensional bulk geometries
described by Einstein Gravity and Topologically Massive Gravity. The
construction involves specific algebraic sums of the lengths of bulk extremal
curves homologous to certain combinations of the intervals appropriate to such
bipartite states. Our analysis exactly reproduces the corresponding replica
technique results in the large central charge limit. We substantiate our
construction through a semi classical analysis involving the geometric
monodromy technique for the case of two disjoint intervals in such Galilean
conformal field theories dual to bulk Einstein Gravity. | On the Thermodynamic Bethe Ansatz Equation in Sinh-Gordon Model: Two implicit periodic structures in the solution of sinh-Gordon thermodynamic
Bethe ansatz equation are considered. The analytic structure of the solution as
a function of complex $\theta$ is studied to some extent both analytically and
numerically. The results make a hint how the CFT integrable structures can be
relevant in the sinh-Gordon and staircase models. More motivations are figured
out for subsequent studies of the massless sinh-Gordon (i.e. Liouville) TBA
equation. |
Dressing Transformations and the Algebraic--Geometrical Solutions in the
Conformal Affine $sl(2)$ Toda Model: It is shown that the algebraic--geometrical (or quasiperiodic) solutions of
the Conformal Affine $sl(2)$ Toda model are generated from the vacuum via
dressing transformations. This result generalizes the result of Babelon and
Bernard which states that the $N$--soliton solutions are generated from the
vacuum by dressing transformations. | Supersymmetric Yang-Mills Theories in 1 + 1 Dimensions: Supersymmetric Yang-Mills theories are considered in 1+1 dimensions. Firstly
physical mass spectra of supersymmetric Yang-Mills theories in 1+1 dimensions
are evaluated in the light-cone gauge with a compact spatial dimension. The
supercharges are constructed in order to provide a manifestly supersymmetric
infrared regularization for the discretized light-cone approach. By exactly
diagonalizing the supercharge matrix between up to several hundred color
singlet bound states, we find a rapidly increasing density of states as mass
increases. Interpreting this limiting density of states as the stringbehavior,
we obtain the Hagedron temperature $\beta_H=0.676 \sqrt{\pi \over g^2 N}$.
Secondly we have examined the vacuum structure of supersymmetric Yang-Mills
theories in 1+1 dimensions. SUSY allows only periodic boundary conditions for
both fermions and bosons. By using the Born-Oppenheimer approximation for the
weak coupling limit, we find that the vacuum energy vanishes, and hence the
SUSY is unbroken. Other boundary conditions are also studied. The first part is
based on a work in collaboration with Y. Matsumura and T. Sakai. The second
part is based on a work in collaboration with H. Oda and T. Sakai. |
Canonical Quantization for a Relativistic Neutral Scalar Field in
Non-equilibrium Thermo Field Dynamics: A relativistic neutral scalar field is investigated in non-equilibrium thermo
field dynamics. The canonical quantization is applied to the fields out of
equilibrium. Because the thermal Bogoliubov transformation becomes
time-dependent, the equations of motion for the ordinary unperturbed creation
and annihilation operators are modified. This forces us to introduce a thermal
counter term in the interaction Hamiltonian which generates additional
radiative corrections. Imposing the self-consistency renormalization condition
on the total radiative corrections, we obtain the quantum Boltzmann equation
for the relativistic scalar field. | A Safe Beginning for the Universe?: When general relativity is augmented by quadratic gravity terms, it becomes a
renormalisable theory of gravity. This theory may admit a non-Gaussian fixed
point as envisaged in the asymptotic safety program, rendering the theory
trustworthy to energies up to the Planck scale and even beyond. We show that
requiring physical solutions to have a finite action imposes a strong selection
on big-bang-type universes. More precisely we find that, in the approach to
zero volume, both anisotropies and inhomogeneities are suppressed while the
scale factor is required to undergo accelerated expansion. This provides
initial conditions which are favourable to the onset of an inflationary phase
while also providing a suitable starting point for the second law of
thermodynamics in the spirit of the Weyl curvature hypothesis. |
High power Cherenkov radiation from a relativistic particle rotating
around a dielectric ball: Some characteristic features in the radiation from a relativistic electron
uniformly rotating along an equatorial orbit around a dielectric ball have been
studied. It was shown that at some harmonics, in case of weak absorption of
radiation in the ball material, the electron may generate radiation field
quanta exceeding in several dozens of times those generated by electron
rotating in a continuous, infinite and transparent medium having the same real
part of permittivity as the ball material. The rise of high power radiation is
due to the fact that electromagnetic oscillations of Cherenkov radiation
induced along the trajectory of particle are partially locked inside the ball
and superimposed in nondestructive way. | Cosmological Power Spectrum in Non-commutative Space-time: We propose a generalized star product which deviates from the standard
product when the fields at evaluated at different space-time points. This
produces no changes in the standard Lagrangian density in non-commutative
space-time but produces a change in the cosmological power spectrum. We show
that the generalized star product leads to physically consistent results and
can fit the observed data on hemispherical anisotropy in the cosmic microwave
background radiation. |
Vacuum Cherenkov radiation at finite temperature: In this paper we examine the thermal effects of the vacuum Cherenkov
radiation in a Lorentz- and CPT-violating electrodynamics. We compute the
thermal contribution to the Cherenkov radiation rate within the Thermofield
Dynamics approach. Since the model under consideration possess a consistent
canonical quantization and also fulfils the physical constraints in order to
this vacuum process to happen, it is a perfect candidate to implement the study
at finite temperature. We evaluate in details the instantaneous rate of energy
loss for a charge, and show that the radiation rate is significantly modified
at very high temperatures. Intriguingly, we further observe that when the
temperature goes to infinity the radiation rate goes to zero even if the
process is kinematically allowed. | Towards SDp-brane Quantization: The quantum mechanical analysis of the canonical hamiltonian description of
the effective action of a SDp-brane in bosonic ten dimensional Type II
supergravity in a homogeneous background is given. We find exact solutions for
the corresponding quantum theory by solving the Wheeler-deWitt equation in the
late-time limit of the rolling tachyon. The probability densities for several
values of p are shown and their possible interpretation is discussed. In the
process the effects of electromagnetic fields are also incorporated and it is
shown that in this case the interpretation of tachyon regarded as ``matter
clock'' is modified. |
Dynamics of partially localized brane systems: We study dynamical partially localized brane solutions in higher dimensions.
We give new descriptions of the relevant solutions of dynamical branes which
are localized along both the overall and relative transverse directions. The
starting point is a system of p_r-branes ending on a p_s-brane with a
time-dependent warp factor. This system can be related to Dp_r-Dp_s brane
system in string theory, where one brane is localized at the delocalized other
brane. We then show that these give Friedmann-Lemaitre-Robertson-Walker
cosmological solutions. Our approach leads to a new and manifest description of
the brane configurations near the delocalized branes, and new solutions in the
wave or KK-monopole background in terms of certain partial differential
equations in D dimensions including ten and eleven dimensions. | 7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds: We study 7D maximally supersymmetric Yang-Mills theory on 3-Sasakian
manifolds. For manifolds whose hyper-K\"ahler cones are hypertoric we derive
the perturbative part of the partition function. The answer involves a special
function that counts integer lattice points in a rational convex polyhedral
cone determined by hypertoric data. This also gives a more geometric structure
to previous enumeration results of holomorphic functions in the literature.
Based on physics intuition, we provide a factorisation result for such
functions. The full proof of this factorisation using index calculations will
be detailed in a forthcoming paper. |
Quaternionic Groups in Physics: A Panoramic Review: Due to the non-commutative nature of quaternions we introduce the concept of
left and right action for quaternionic numbers. This gives the opportunity to
manipulate appropriately the $H$-field. The standard problems arising in the
definitions of transpose, determinant and trace for quaternionic matrices are
overcome. We investigate the possibility to formulate a new approach to
Quaternionic Group Theory. Our aim is to highlight the possibility of looking
at new quaternionic groups by the use of left and right operators as
fundamental step toward a clear and complete discussion of Unification Theories
in Physics. | de Sitter String Vacua from Perturbative Kahler Corrections and
Consistent D-terms: We present a new way to construct de Sitter vacua in type IIB flux
compactifications, in which moduli stabilization and D-term uplifting can be
combined in a manner consistent with the supergravity constraints. Here, the
closed string fluxes fix the dilaton and the complex structure moduli while
perturbative quantum corrections to the Kahler potential stabilize the volume
Kahler modulus in an AdS_4-vacuum. Then, the presence of magnetized D7-branes
in this setup provide supersymmetric D-terms in a fully consistent way which
uplift the AdS_4-vacuum to a metastable dS-minimum. |
The Relativistic Rindler Hydrodynamics: We consider a (d+2)-dimensional class of Lorentzian geometries
holographically dual to a relativistic fluid flow in (d+1) dimensions. The
fluid is defined on a (d+1)-dimensional time-like surface which is embedded in
the (d+2)-dimensional bulk space-time and equipped with a flat intrinsic
metric. We find two types of geometries that are solutions to the vacuum
Einstein equations: the Rindler metric and the Taub plane symmetric vacuum.
These correspond to dual perfect fluids with vanishing and negative energy
densities respectively. While the Rindler geometry is characterized by a causal
horizon, the Taub geometry has a timelike naked singularity, indicating
pathological behavior. We construct the Rindler hydrodynamics up to the second
order in derivatives of the fluid variables and show the positivity of its
entropy current divergence. | De Sitter from T-branes: Hidden sector D7-branes with non-zero gauge flux are a generic feature of
type IIB compactifications. A non-vanishing Fayet-Iliopoulos term induced by
non-zero gauge flux leads to a T-brane configuration. Expanding the D7-brane
action around this T-brane background in the presence of three-form
supersymmetry breaking fluxes, we obtain a positive definite contribution to
the moduli scalar potential which can be used as an uplifting source for de
Sitter vacua. In this way we provide a higher-dimensional understanding of
known 4D mechanisms of de Sitter uplifting based on hidden sector F-terms which
are non-zero because of D-term stabilisation. |
Scaling Cosmologies from Duality Twisted Compactifications: Oscillating moduli fields can support a cosmological scaling solution in the
presence of a perfect fluid when the scalar field potential satisfies
appropriate conditions. We examine when such conditions arise in
higher-dimensional, non-linear sigma-models that are reduced to four dimensions
under a generalized Scherk-Schwarz compactification. We show explicitly that
scaling behaviour is possible when the higher-dimensional action exhibits a
global SL(n,R) or O(2,2) symmetry. These underlying symmetries can be exploited
to generate non-trivial scaling solutions when the moduli fields have
non-canonical kinetic energy. We also consider the compactification of
eleven-dimensional vacuum Einstein gravity on an elliptic twisted torus. | Stable bound orbits in black lens backgrounds: In contrast to five-dimensional Schwarzschild-Tangherlini and Myers-Perry
backgrounds, we show that there are stable bound orbits of massive/massless
particles in five-dimensional black lens backgrounds, in particular, the
supersymmetric black lens with $L(2,1)$ and $L(3,1)$ topologies. We also show
that in the zero-energy limit of massless particles, there exist stable
circular orbits on the evanescent ergosurfaces. |
A Panorama Of Physical Mathematics c. 2022: What follows is a broad-brush overview of the recent synergistic interactions
between mathematics and theoretical physics of quantum field theory and string
theory. The discussion is forward-looking, suggesting potentially useful and
fruitful directions and problems, some old, some new, for further development
of the subject. This paper is a much extended version of the Snowmass
whitepaper on physical mathematics [1]. | Absence of Black Holes at LHC due to Gravity's Rainbow: In this paper, we investigate the effect of Planckian deformation of quantum
gravity on the production of black holes at colliders using the framework of
gravity's rainbow. We demonstrate that a black hole remnant exists for
Schwarzschild black holes in higher dimensions using gravity's rainbow. The
mass of this remnant is found to be greater than the energy scale at which
experiments were performed at the LHC. We propose this as a possible
explanation for the absence of black holes at the LHC. Furthermore, we
demonstrate that it is possible for black holes in six (and higher) dimensions
to be produced at energy scales that will be accessible in the near future. |
A novel approach to non-commutative gauge theory: We propose a field theoretical model defined on non-commutative space-time
with non-constant non-commutativity parameter $\Theta(x)$, which satisfies two
main requirements: it is gauge invariant and reproduces in the commutative
limit, $\Theta\to 0$, the standard $U(1)$ gauge theory. We work in the slowly
varying field approximation where higher derivatives terms in the star
commutator are neglected and the latter is approximated by the Poisson bracket,
$-i[f,g]_\star\approx\{f,g\}$. We derive an explicit expression for both the NC
deformation of Abelian gauge transformations which close the algebra
$[\delta_f,\delta_g]A=\delta_{\{f,g\}}A$, and the NC field strength ${\cal F}$,
covariant under these transformations, $\delta_f {\cal F}=\{{\cal F},f\}$. NC
Chern-Simons equations are equivalent to the requirement that the NC field
strength, ${\cal F}$, should vanish identically. Such equations are
non-Lagrangian. The NC deformation of Yang-Mills theory is obtained from the
gauge invariant action, $S=\int {\cal F}^2$. As guiding example, the case of
$su(2)$-like non-commutativity, corresponding to rotationally invariant NC
space, is worked out in detail. | Current Algebra and Integrability of Principal Chiral Model on the
World-sheet with General Metric: We study the classical current algebra for principial chiral model defined on
two dimensional world-sheet with general metric. We develop the Hamiltonian
formalism and determine the form of the Poisson brackets between currents. Then
we determine the Poisson bracket for Lax connection and we show that this
Possion bracket does not depend on the world-sheet metric. We also study the
Nambu-Gotto form of this model. We prove an existence of the Lax connection and
determine their Poisson bracket. |
Black holes in Truncated Higher Spin AdS$_3$ Gravity: We study the higher spin black holes in a truncated version of higher spin
gravity in $AdS_3$. This theory contains only finite number of even spins
s=2,4,...,2N. We mainly focus on the simplest case, so-called (Type I and II)
spin ${\tilde 4}$ gravity, which contains only spin 2 and spin 4 fields. This
spin ${\tilde 4}$ gravity is as simple as spin 3 gravity, thus provides another
example to test various ideas on higher spin gravity. We find that the
asymptotical symmetry of this spin ${\tilde 4}$ gravity is a classical
W(2,4)-symmetry. Moreover, we study the black hole solution with pure spin 4
hair and discuss its thermodynamics. One important feature of this black hole
is that its entropy could be written in compact forms. Furthermore, we
investigate a $G_2$ generated higher spin gravity. This higher spin gravity
only contains spin 2 and spin 6 fields which makes it different from other
kinds of higher spin gravity. We find the corresponding black hole with spin 6
hair, and discuss its thermodynamics analytically. It turns out that the black
holes with spin 4 or spin 6 hair constructed in this paper are the only black
holes with single higher spin hair, besides the spin 3 black hole found in
arXiv:1103.4304. | Logarithmic Black Hole Entropy Corrections and Holographic Rényi
Entropy: The entanglement and R\'{e}nyi entropies for spherical entangling surfaces in
CFTs with gravity duals can be explicitly calculated by mapping these entropies
first to the thermal entropy on hyperbolic space and then, using the AdS/CFT
correspondence, to the Wald entropy of topological black holes. Here we extend
this idea by taking into account corrections to the Wald entropy. Using the
method based on horizon symmetries and the asymptotic Cardy formula, we
calculate corrections to the Wald entropy and find that these corrections are
proportional to the logarithm of horizon area. With the corrected black hole
entropy expression, we then find corrections to the R\'{e}nyi entropies. We
calculate these corrections for both Einstein as well as Gauss-Bonnet gravity
duals. Corrections with logarithmic dependence on the area of the entangling
surface naturally occur at the order $G_{D}^0$ and it seems to be a general
feature of entanglement and R\'{e}nyi entropies for CFTs with gravity duals. In
particular, there is a logarithmic correction to the entropy in odd boundary
spacetime dimensions as well. |
Celestial gluon and graviton OPE at loop level: In this paper, we analyze the loop corrections to celestial OPE for gluons
and gravitons. Even at the loop level, the soft gluons and gravitons have
conformal dimensions $\Delta=1-\mathbb Z_{\geq 0}$. The only novelty is the
presence of higher poles. At one loop level, there are two types of conformal
soft gluons with a single pole and a double pole in the $\Delta$ plane. The
celestial OPEs are obtained using the collinear splitting functions. In the
case of gluons, the splitting functions receive loop corrections. After taking
the holomorphic soft limit, we find the OPE of conformal soft gluons. We find a
novel mixing of simple and double poles soft gluon operators in the OPE. In the
case of gravitons, where splitting functions are known to be all loop exact, we
still find a wedge algebra of $w_{\infty}$ which is in addition to the wedge
algebra of $w_{1+\infty}$ already found by Strominger. | Off-Shell ADT Conserved Quantities in Palatini Gravity: In this paper we generalize the off-shell Abbott-Deser-Tekin (ADT) conserved
charge formalism to Palatini theory of gravity with torsion and non-metricity.
Our construction is based on the coordinate formalism and the independent
dynamic fields are the metric and the affine connection. For a general Palatini
theory of gravity, which is diffeomorphism invariant up to a boundary term, we
obtain the most general expression for off-shell ADT potential. As explicit
examples, we derive the off-shell ADT potentials for Einstein-Hilbert action,
the most general $L(g_{\mu\nu}, R^{\lambda}{}_{\nu\alpha\mu},
T^{\lambda}{}_{\alpha\beta}, Q_{\alpha\mu\nu})$ theories and the teleparallel
Palatini gravity. |
The Invariant Charges of the Nambu-Goto String Theory: Quantization of
Non-Additive Composition Laws: We examine and implement the concept of non-additive composition laws in the
quantum theory of closed bosonic strings moving in (3+1)-dimensional Minkowski
space. Such laws supply exact selection rules for the merging and splitting of
closed strings. | All-multiplicity amplitudes with four massive quarks and
identical-helicity gluons: We explore the on-shell recursion for tree-level scattering amplitudes with
massive spinning particles. Based on the factorization structure encoded in the
same way by two different recursion relations, we conjecture an
all-multiplicity formula for two gauged massive particles of arbitrary spin and
any number of identical-helicity gluons. Specializing to quantum chromodynamics
(QCD), we solve the on-shell recursion relations in the presence of two pairs
of massive quarks and an arbitrary number of identical-helicity gluons. We find
closed-form expressions for the two distinct families of color-ordered
four-quark amplitudes, in which all gluons comprise a single color-adjacent
set. We compare the efficiency of the numerical evaluation of the two resulting
analytic formulae against a numerical implementation of the off-shell
Berends-Giele recursion. We find the formulae for both amplitude families to be
faster for large multiplicities, while the simpler of the two is actually
faster for any number of external legs. Our analytic results are provided in a
computer-readable format as two ancillary files. |
Bubbles in Anti-de Sitter Space: We explore the bubble spacetimes which can be obtained from double analytic
continuations of static and rotating black holes in anti-de Sitter space. In
particular, we find that rotating black holes with elliptic horizon lead to
bubble spacetimes only in dimension greater than five. For dimension greater
than seven, the topology of the bubble can be non-spherical. However, a bubble
spacetime is shown to arise from a rotating de Sitter black hole in four
dimensions. In all cases, the evolution of the bubble is of de Sitter type.
Double analytic continuations of hyperbolic black holes and branes are also
discussed. | WZW fusion rings in the limit of infinite level: We show that the WZW fusion rings at finite levels form a projective system
with respect to the partial ordering provided by divisibility of the height,
i.e. the level shifted by a constant. From this projective system we obtain WZW
fusion rings in the limit of infinite level. This projective limit constitutes
a mathematically well-defined prescription for the `classical limit' of WZW
theories which replaces the naive idea of `sending the level to infinity'. The
projective limit can be endowed with a natural topology, which plays an
important role for studying its structure. The representation theory of the
limit can be worked out by considering the associated fusion algebra; this way
we obtain in particular an analogue of the Verlinde formula. |
Partial spontaneous breakdown of 3-dimensional N=2 supersymmetry: The superfield models with the partial spontaneous breaking of the global
D=3, N=2 supersymmetry are discussed. The abelian gauge model describes
low-energy interactions of the real scalar field with the 3D vector and fermion
fields. We introduce the new Goldstone-Maxwell representation of the 3D gauge
superfield and show that the partial spontaneous breaking N=2 to N=1 is
possible for the non-minimal self-interaction of this modified gauge superfield
including the linear Fayet-Iliopoulos term. The dual description of the partial
breaking in the model of the self- interacting Goldstone chiral superfield is
also considered. These models have the constant vacuum solutions and describe,
respectively, the interactions of the N=1 Goldstone multiplets of the D2-brane
or supermembrane with the additional massive multiplets. | Lectures on Holographic Space Time: Summary of three talks on the Holographic Space Time models of early universe
cosmology, particle physics, and the asymptotically de Sitter final state of
our universe. |
The threefold way to quantum periods: WKB, TBA equations and
q-Painlevé: We show that TBA equations defined by the BPS spectrum of $5d$
$\mathcal{N}=1$ $SU(2)$ Yang-Mills on $S^1\times \mathbb{R}^4$ encode the
q-Painlev\'e III$_3$ equation. We find a fine-tuned stratum in the physical
moduli space of the theory where solutions to TBA equations can be obtained
exactly, and verify that they agree with the algebraic solutions to
q-Painlev\'e. Switching from the physical moduli space to that of stability
conditions, we identify a one-parameter deformation of the fine-tuned stratum,
where the general solution of the q-Painlev\'e equation in terms of dual
instanton partition functions continues to provide explicit TBA solutions.
Motivated by these observations, we propose a further extensions of the range
of validity of this correspondence, under a suitable identification of moduli.
As further checks of our proposal, we study the behavior of exact WKB quantum
periods for the quantum curve of local $\mathbb{P}^1\times\mathbb{P}^1$. | Calabi-Yau fourfolds for M- and F-Theory compactifications: We investigate topological properties of Calabi-Yau fourfolds and consider a
wide class of explicit constructions in weighted projective spaces and, more
generally, toric varieties. Divisors which lead to a non-perturbative
superpotential in the effective theory have a very simple description in the
toric construction. Relevant properties of them follow just by counting lattice
points and can be also used to construct examples with negative Euler number.
We study nets of transitions between cases with generically smooth elliptic
fibres and cases with ADE gauge symmetries in the N=1 theory due to
degenerations of the fibre over codimension one loci in the base. Finally we
investigate the quantum cohomology ring of this fourfolds using Frobenius
algebras. |
Non-Relativistic Superstrings: A New Soluble Sector of AdS_5xS^5: We find a new sector of string theory in AdS_5xS^5 describing
non-relativistic superstrings in that geometry. The worldsheet theory of
non-relativistic strings in AdS_5xS^5 is derived and shown to reduce to a
supersymmetric free field theory in AdS_2. Non-relativistic string theory
provides a new calculable setting in which to study holography. | A remark on worldsheet fermions and double-scaled matrix models: We provide a heuristic explanation for the emergence of worldsheet fermions
in the continuum limit of some matrix models. We also argue that turning on
Ramond-Ramond flux confines the fermionic degrees of freedom of the
Ramond-Neveu-Schwarz formalism. |
Closed conformal Killing-Yano tensor and uniqueness of generalized
Kerr-NUT-de Sitter spacetime: The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general
rotating asymptotically de Sitter black hole with NUT parameters. It is known
that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY)
tensor as a ``hidden'' symmetry which provides the separation of variables for
the geodesic equations and Klein-Gordon equations. We present a classification
of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This
provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular,
we show that the Kerr-NUT-de Sitter spacetime is the only spacetime with a
non-degenerate CKY tensor. | Logarithmic Conformal Field Theory: Beyond an Introduction: This article aims to review a selection of central topics and examples in
logarithmic conformal field theory. It begins with a pure Virasoro example,
critical percolation, then continues with a detailed exposition of symplectic
fermions, the fractional level WZW model on SL(2;R) at level -1/2 and the WZW
model on the Lie supergroup GL(1|1). It concludes with a general discussion of
the so-called staggered modules that give these theories their logarithmic
structure, before outlining a proposed strategy to understand more general
logarithmic conformal field theories. Throughout, the emphasis is on continuum
methods and their generalisation from the familiar rational case. In
particular, the modular properties of the characters of the spectrum play a
central role and Verlinde formulae are evaluated with the results compared to
the known fusion rules. Moreover, bulk modular invariants are constructed, the
structures of the corresponding bulk state spaces are elucidated, and a
formalism for computing correlation functions is discussed. |
Holographic Gauge Mediation: We discuss gravitational backgrounds where supersymmetry is broken at the end
of a warped throat, and the SUSY-breaking is transmitted to the Standard Model
via gauginos which live in (part of) the bulk of the throat geometry. We find
that the leading effect arises from splittings of certain "messenger mesons,"
which are adjoint KK-modes of the D-branes supporting the Standard Model gauge
group. This picture is a gravity dual of a strongly coupled field theory where
SUSY is broken in a hidden sector and transmitted to the Standard Model via a
relative of semi-direct gauge mediation. | B-type Landau-Ginzburg models on Stein manifolds: We summarize the description of the open-closed TFT datum for B-type
Landau-Ginzburg models with Stein manifold targets and discuss various
constructions which lead to large classes of examples of such models. |
Three-dimensional Newtonian gravity with cosmological constant and
torsion: In this paper we present an alternative cosmological extension of the
three-dimensional extended Newtonian Chern-Simons gravity by switching on the
torsion. The theory is obtained as a non-relativistic limit of an enhancement
and $U(1)$-enlargement of the so-called teleparallel algebra and can be seen as
the teleparallel analogue of the Newtonian gravity theory. The
infinite-dimensional extension of our result is also explored through the Lie
algebra expansion method. An infinite-dimensional torsional Galilean gravity
model is presented which in the vanishing cosmological constant limit
reproduces the infinite-dimensional extension of the Galilean gravity theory. | The Gribov problem in presence of background field for $SU(2)$
Yang-Mills theory: The Gribov problem in the presence of a background field is analyzed: in
particular, we study the Gribov copies equation in the Landau-De Witt gauge as
well as the semi-classical Gribov gap equation. As background field, we choose
the simplest non-trivial one which corresponds to a constant gauge potential
with non-vanishing component along the Euclidean time direction. This kind of
constant non-Abelian background fields is very relevant in relation with (the
computation of) the Polyakov loop but it also appears when one considers the
non-Abelian Schwinger effect. We show that the Gribov copies equation is
affected directly by the presence of the background field, constructing an
explicit example. The analysis of the Gribov gap equation shows that the larger
the background field, the smaller the Gribov mass parameter. These results
strongly suggest that the relevance of the Gribov copies (from the path
integral point of view) decreases as the size of the background field
increases. |
A Compact Codimension Two Braneworld with Precisely One Brane: Building on earlier work on football shaped extra dimensions, we construct a
compact codimension two braneworld with precisely one brane. The two extra
dimensions topologically represent a 2-torus which is stabilized by a bulk
cosmological constant and magnetic flux. The torus has positive constant
curvature almost everywhere, except for a single conical singularity at the
location of the brane. In contradistinction to the football shaped case, there
is no fine-tuning required for the brane tension. We also present some
plausibility arguments why the model should not suffer from serious stability
issues. | Defining < A^2 > in the finite volume hamiltonian formalism: It is shown how in principle for non-abelian gauge theories it is possible in
the finite volume hamiltonian framework to make sense of calculating the
expectation value of ||A||^2=\int d^3x(A^a_i(x))^2. Gauge invariance requires
one to replace ||A||^2 by its minimum over the gauge orbit, which makes it a
highly non-local quantity. We comment on the difficulty of finding a gauge
invariant expression for ||A||^2_{min} analogous to that found for the abelian
case, and the relation of this question to Gribov copies. We deal with these
issues by implementing the hamiltonian on the so-called fundamental domain,
with appropriate boundary conditions in field space, essential to correctly
represent the physics of the problem. |
Localized Gravitons, Gauge Bosons and Chiral Fermions in Smooth Spaces
Generated by a Bounce: We study five-dimensional solutions to Einstein equations coupled to a scalar
field. Bounce-type solutions for the scalar field are associated with AdS_5
spaces with smooth warp functions. Gravitons are dynamically localized in this
framework in analogy to the Randall-Sundrum solution whereas, a bulk fermion
gives rise to a single chiral zero mode localized at the bounce. Additional
bulk scalar fields are incorporated in this picture. The dilaton, as a bulk
scalar leads, through its coupling, to localized gauge boson fields, something
that holds also in the case that the bounce system is replaced by a brane. | Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains: We present an integrability-preserving recursion relation for the explicit
construction of long-range spin chain Hamiltonians. These chains are
generalizations of the Haldane-Shastry and Inozemtsev models and they play an
important role in recent advances in string/gauge duality. The method is based
on arbitrary nearest-neighbour integrable spin chains and it sheds light on the
moduli space of deformation parameters. We also derive the closed chain
asymptotic Bethe equations. |
Semi-simple enlargement of the $\mathfrak{bms}_3$ algebra from a
$\mathfrak{so}(2,2)\oplus\mathfrak{so}(2,1)$ Chern-Simons theory: In this work we present a BMS-like ansatz for a Chern-Simons theory based on
the semi-simple enlargement of the Poincar\'e symmetry, also known as
AdS-Lorentz algebra. We start by showing that this ansatz is general enough to
contain all the relevant stationary solutions of this theory and provides with
suitable boundary conditions for the corresponding gauge connection. We find an
explicit realization of the asymptotic symmetry at null infinity, which defines
a semi-simple enlargement of the $\mathfrak{bms}_3$ algebra and turns out to be
isomorphic to three copies of the Virasoro algebra. The flat limit of the
theory is discussed at the level of the action, field equations, solutions and
asymptotic symmetry. | Metamorphosis of the Cosmological Constant and 5D Origin of the Fiducial
Metric: In a recently proposed theory, the cosmological constant (CC) does not curve
spacetime in our universe, but instead gets absorbed into another universe
endowed with its own dynamical metric, nonlocally coupled to ours. Thus, one
achieves a long standing goal of removing entirely any cosmological constant
from our universe. Dark energy then cannot be due to a cosmological constant,
but must be obtained via other mechanisms. Here we focus on the scenario in
which dark energy is due to massive gravity and its extensions. We show how the
metric of the other universe, that absorbs our CC, also gives rise to the
fiducial metric known to be necessary for the diffeomorphism invariant
formulation of massive gravity. This is achieved in a framework where the other
universe is described by 5D AdS gravity, while our universe lives on its
boundary and is endowed with dynamical massive gravity. A non-dynamical
pullback of the bulk AdS metric acts as the fiducial metric for massive gravity
on the boundary. This framework also removes a difficulty caused by the quantum
strongly coupled behavior of massive gravity at the Lambda3 scale: in the
present approach, the massive gravity action does not receive any loop-induced
counterterms, despite being strongly coupled. |
Energy distribution in a BTZ black hole spacetime: We evaluate the energy distribution associated with the (2+1)-dimensional
rotating BTZ black hole. The energy-momentum complexes of Landau-Lifshitz and
Weinberg are employed for this computation. Both prescriptions give exactly the
same form of energy distribution. Therefore, these results provide evidence in
support of the claim that, for a given gravitational background, different
energy-momentum complexes can give identical results in three dimensions, as it
is the case in four dimensions. | Current Oscillations, Interacting Hall Discs and Boundary CFTs: In this paper, we discuss the behavior of conformal field theories
interacting at a single point. The edge states of the quantum Hall effect (QHE)
system give rise to a particular representation of a chiral Kac-Moody current
algebra. We show that in the case of QHE systems interacting at one point we
obtain a ``twisted'' representation of the current algebra. The condition for
stationarity of currents is the same as the classical Kirchoff's law applied to
the currents at the interaction point. We find that in the case of two discs
touching at one point, since the currents are chiral, they are not stationary
and one obtains current oscillations between the two discs. We determine the
frequency of these oscillations in terms of an effective parameter
characterizing the interaction. The chiral conformal field theories can be
represented in terms of bosonic Lagrangians with a boundary interaction. We
discuss how these one point interactions can be represented as boundary
conditions on fields, and how the requirement of chirality leads to
restrictions on the interactions described by these Lagrangians. By gauging
these models we find that the theory is naturally coupled to a Chern-Simons
gauge theory in 2+1 dimensions, and this coupling is completely determined by
the requirement of anomaly cancellation. |
Off-shell construction of some trilinear higher spin gauge field
interactions: Several trilinear interactions of higher spin fields involving two equal
($s=s_{1}=s_{2}$) and one higher even ($s_{3}\geq 2s$) spin are presented.
Interactions are constructed on the Lagrangian level using Noether's procedure
together with the corresponding next to free level fields of the gauge
transformations. In certain cases when the number of derivatives in the
transformation is $2s-1$ the interactions lead to the currents constructed from
the generalization of the gravitational Bell-Robinson tensors. In other cases
when the number of derivatives in the transformation is more than $2s-1$ we
obtain the finite tower of interactions with smaller even spins less than
$s_{3}$ in full agreement with our previous results for the interaction of the
higher even spins field with a conformal scalar [1,2]. | Quaternionic Formulation of Supersymmetric Quantum Mechanics: Quaternionic formulation of supersymmetric quantum mechanics has been
developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and
supercharges for free particle and interacting field in one and three
dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are
discussed and it has been shown that the results are consistent with the
results of quantum mechanics. |
Courant Algebroids: This paper is devoted to studying some properties of the Courant algebroids:
we explain the so-called "conducting bundle construction" and use it to attach
the Courant algebroid to Dixmier-Douady gerbe (following ideas of P. Severa).
We remark that WZNW-Poisson condition of Klimcik and Strobl (math.SG/0104189)
is the same as Dirac structure in some particular Courant algebroid. We propose
the construction of the Lie algebroid on the loop space starting from the Lie
algebroid on the manifold and conjecture that this construction applied to the
Dirac structure above should give the Lie algebroid of symmetries in the
WZNW-Poisson $\sigma$-model, we show that it is indeed true in the particular
case of Poisson $\sigma$-model. | Emergent N=4 supersymmetry from N=1: We discover a four-dimensional $\mathcal{N}=1$ supersymmetric field theory
that is dual to the $\mathcal{N}=4$ super Yang-Mills theory with gauge group
$SU(2n+1)$ for each $n$. The dual theory is constructed through the diagonal
gauging of the $SU(2n+1)$ flavor symmetry of three copies of a strongly-coupled
superconformal field theory (SCFT) of Argyres-Douglas type. We find that this
theory flows in the infrared to a strongly-coupled $\mathcal{N}=1$ SCFT that
lies on the same conformal manifold as $\mathcal{N}=4$ super Yang-Mills with
gauge group $SU(2n+1)$. Our construction provides a hint on why certain
$\mathcal{N}=1,2$ SCFTs have identical central charges ($a=c$). |
The Holomorphic Tension of Nonabelian Vortices: We continue the work hep-th/0411075 considering here the case of degenerate
masses. A nonabelian vortex arises in r-vacua upon the breaking by a
superpotential for the adjoint field. We find the BPS tension in the strong
coupling regime computing the dual-quark condensate. Then we find that it is
equal to a simple quantity in the chiral ring of the theory and so we
conjecture the validity of our result out of the strong coupling regime. Our
result gives an interesting hint about the duality r <--> N_f-r, seeing it as
the exchange first <--> second sheet of N=1 Riemann surface. | Lanczos spectrum for random operator growth: Krylov methods have reappeared recently, connecting physically sensible
notions of complexity with quantum chaos and quantum gravity. In these
developments, the Hamiltonian and the Liouvillian are tridiagonalized so that
Schrodinger/Heisenberg time evolution is expressed in the Krylov basis. In the
context of Schrodinger evolution, this tridiagonalization has been carried out
in Random Matrix Theory. We extend these developments to Heisenberg time
evolution, describing how the Liouvillian can be tridiagonalized as well until
the end of Krylov space. We numerically verify the analytical formulas both for
Gaussian and non-Gaussian matrix models. |
Tensionless String in the Notoph Background: We study the interaction between a tensionless (null) string and an
antisymmetric background field B_{ab} using a 2-component spinor formalism. A
geometric condition for the absence of such an interaction is formulated. We
show that only one gauge-invariant degree of freedom of the field B_{ab} does
not satisfy this condition. Identification of this degree of freedom with the
notoph field \phi of Ogievetskii-Polubarinov-Kalb-Ramond is suggested.
Application of a two-component spinor formalism allows us a reduction of the
complete system of non-linear partial differential equations and constraints
governing the interacting null string dynamics to a system of linear
differential equations for the basis spinors of the spin-frame. We find that
total effect of the interaction is contained in a single derivation coefficient
which is identified with the notoph field. | Infrared instability of the de Sitter space: We continue to investigate various instabilities of the fixed backgrounds
related to the de Sitter space. It is shown that in many cases the in/in
perturbation theory contains IR/UV mixing and thus is non-renormalizible. The
application of this result to the global de Sitter space leads to the
conclusion that even massive particles generate IR divergence and the huge back
reaction. The expanding universe is also unstable but in a weaker sense. We
further discuss, the strange features of the Gibbons-Hawking radiation and its
relation to the above instabilities. . |
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