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Operator geometry and algebraic gravity: An algebraic formulation of general relativity is proposed. The formulation
is applicable to quantum gravity and noncommutative space. To investigate
quantum gravity we develop the canonical formalism of operator geometry, after
reconstructing an algebraic canonical formulation on analytical dynamics. The
remarkable fact is that the constraint equation and evolution equation of the
gravitational system are algebraically unified. From the discussion of
regularization we find the quantum correction of the semi-classical gravity is
same as that already known in quantum field theory. | Soliton Solutions in Noncritical String Field Theory?: We look for soliton solutions in $c=0$ noncritical string field theory
constructed by the authors and collaborators. It is shown that the string field
action itself is very complicated in our formalism but it satisfies a very
simple equation. We derive an equation which a solution to the equation of
motion should satisfy. Using this equation, we conjecture the form of a soliton
solution which is responsible for the nonperturbative effects of order
$e^{-A/\kappa}$. (Talk given by N.I. at ``Inauguration Conference of APCTP'',
4-10 June, 1996) |
Integrating Geometry in General 2D Dilaton Gravity with Matter: General 2d dilaton theories, containing spherically symmetric gravity and
hence the Schwarzschild black hole as a special case, are quantized by an exact
path integral of their geometric (Cartan-) variables. Matter, represented by
minimally coupled massless scalar fields is treated in terms of a systematic
perturbation theory. The crucial prerequisite for our approach is the use of a
temporal gauge for the spin connection and for light cone components of the
zweibeine which amounts to an Eddington Finkelstein gauge for the metric. We
derive the generating functional in its most general form which allows a
perturbation theory in the scalar fields. The relation of the zero order
functional to the classical solution is established. As an example we derive
the effective (gravitationally) induced 4-vertex for scalar fields. | Phase transitions in the logarithmic Maxwell O(3)-sigma model: We investigate the presence of topological structures and multiple phase
transitions in the O(3)-sigma model with the gauge field governed by Maxwell's
term and subject to a so-called Gausson's self-dual potential. To carry out
this study, it is numerically shown that this model supports topological
solutions in 3-dimensional spacetime. In fact, to obtain the topological
solutions, we assume a spherically symmetrical ansatz to find the solutions, as
well as some physical behaviors of the vortex, as energy and magnetic field. It
is presented a planar view of the magnetic field as an interesting
configuration of a ring-like profile. To calculate the differential
configurational complexity (DCC) of structures, the spatial energy density of
the vortex is used. In fact, the DCC is important because it provides us with
information about the possible phase transitions associated with the structures
located in the Maxwell-Gausson model in 3D. Finally, we note from the DCC
profile an infinite set of kink-like solutions associated with the parameter
that controls the vacuum expectation value. |
Infrared Behaviour of Landau Gauge Yang-Mills Theory with a
Fundamentally Charged Scalar Field: The infrared behaviour of the n-point functions of a Yang-Mills theory with a
charged scalar field in the fundamental representation of SU(N) is studied in
the formalism of Dyson-Schwinger equations. Assuming a stable skeleton
expansion solutions in form of power laws for the Green functions are obtained.
For a massless scalar field the uniform limit is sufficient to describe the
infrared scaling behaviour of vertices. Not taking into account a possible
Higgs-phase it turns out that kinematic singularities play an important role
for the scaling solutions of massive scalars. On a qualitative level scalar
Yang-Mills theory yields similar scaling solutions as recently obtained for
QCD. | Regular Representation of the Quantum Heisenberg Double $U_q(sl(2))$,
$Fun_{q}(SL(2))$ ($q$ is a root of unity): Pairing between the universal enveloping algebra $U_q(sl(2))$ and the algebra
of functions over $SL_q(2)$ is obtained in explicit terms. The regular
representation of the quantum double is constructed and investigated. The
structure of the root subspaces of the Casimir operator is revealed and
described in terms of $SL_q(2)$ elements. |
Supersymmetric Multiple Basin Attractors: We explain that supersymmetric attractors in general have several critical
points due to the algebraic nature of the stabilization equations. We show that
the critical values of the cosmological constant of the adS_5 vacua are given
by the topological (moduli independent) formulae analogous to the entropy of
the d=5 supersymmetric black holes. We present conditions under which more than
one critical point is available (for black hole entropy as well as to the
cosmological constant) so that the system tends to its own locally stable
attractor point. We have found several families of Z_2-symmetric critical
points where the central charge has equal absolute values but opposite signs in
two attractor points. We present examples of interpolating solutions and
discuss their generic features. | A parafermionic hypergeometric function and supersymmetric 6j-symbols: We study properties of a parafermionic generalization of the hyperbolic
hypergeometric function appearing as the most important part in the fusion
matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev
modular double. We show that this generalized hypergeometric function is a
limiting form of the rarefied elliptic hypergeometric function $V^{(r)}$ and
derive its transformation properties and a mixed difference-recurrence equation
satisfied by it. At the intermediate level we describe symmetries of a more
general rarefied hyperbolic hypergeometric function. An important $r=2$ case
corresponds to the supersymmetric hypergeometric function given by the integral
appearing in the fusion matrix of $N=1$ super Liouville field theory and the
Racah-Wigner symbols of the quantum algebra ${\rm U}_q({\rm osp}(1|2))$. We
indicate relations to the standard Regge symmetry and prove some previous
conjectures for the supersymmetric Racah-Wigner symbols by establishing their
different parametrizations. |
Low-energy next-to-leading contributions to the effective action in
${\cal N}=4$ SYM theory: Using formulation of ${\cal N}=4$ SYM theory in terms of ${\cal N}=1$
superfields superfields we construct the derivative expansion of the one-loop
${\cal N}=4$ SYM effective action in background fields corresponding to
constant Abelian strength $F_{mn}$ and constant hypermultiplet. Any term of the
effective action derivative expansion can be rewritten in terms of ${\cal N}=2$
superfields. The action is manifestly ${\cal N}=2$ supersymmetric but on-shell
hidden ${\cal N}=2$ supersymmetry is violated. We propose a procedure which
allows to restore the hidden ${\cal N}=2$ invariance. | Anthropic interpretation of quantum theory: The problem of interpreting quantum theory on a large (e.g. cosmological)
scale has been commonly conceived as a search for objective reality in a
framework that is fundamentally probabilistic. The Everett programme attempts
to evade the issue by the reintroduction of determinism at the global level of
a ``state vector of the universe''. The present approach is based on the
recognition that, like determinism, objective reality is an unrealistic
objective. It is shown how an objective theory of an essentially subjective
reality can be set up using an appropriately weighted probability measure on
the relevant set of Hilbert subspaces. It is suggested that an entropy
principle (superseding the weak anthropic principle) should be used to provide
the weighting that is needed. |
Gauge Fields Condensation at Finite Temperature: The two-loop effective action for the SU(3) gauge model in a constant
background field ${\bar A}_0(x,t)=B_0^3T_3+B_0^8T_8$ is recalculated for a
gauge with an arbitrary $\xi$-parameter. The gauge-invariant thermodynamical
potential is found and its extremum points are investigated. Within a two-loop
order we find that the stable nontrivial vacuum is completely equivalent to the
trivial one but when the high order corrections being taken into account the
indifferent equilibrium seems to be broken. Briefly we also discuss the
infrared peculiarities and their status for the gauge models with a nonzero
condensate. | Quantum deformation of the Dirac bracket: The quantum deformation of the Poisson bracket is the Moyal bracket. We
construct quantum deformation of the Dirac bracket for systems which admit
global symplectic basis for constraint functions. Equivalently, it can be
considered as an extension of the Moyal bracket to second-class constraints
systems and to gauge-invariant systems which become second class when
gauge-fixing conditions are imposed. |
High Energy Field Theory in Truncated AdS Backgrounds: In this letter we show that, in five-dimensional anti-deSitter space (AdS)
truncated by boundary branes, effective field theory techniques are reliable at
high energy (much higher than the scale suggested by the Kaluza-Klein mass
gap), provided one computes suitable observables. We argue that in the model of
Randall and Sundrum for generating the weak scale from the AdS warp factor, the
high energy behavior of gauge fields can be calculated in a {\em cutoff
independent manner}, provided one restricts Green's functions to external
points on the Planck brane. Using the AdS/CFT correspondence, we calculate the
one-loop correction to the Planck brane gauge propagator due to charged bulk
fields. These effects give rise to non-universal logarithmic energy dependence
for a range of scales above the Kaluza-Klein gap. | Star Integrals, Convolutions and Simplices: We explore single and multi-loop conformal integrals, such as the ones
appearing in dual conformal theories in flat space. Using Mellin amplitudes, a
large class of higher loop integrals can be written as simple
integro-differential operators on star integrals: one-loop $n$-gon integrals in
$n$ dimensions. These are known to be given by volumes of hyperbolic simplices.
We explicitly compute the five-dimensional pentagon integral in full generality
using Schl\"afli's formula. Then, as a first step to understanding higher
loops, we use spline technology to construct explicitly the $6d$ hexagon and
$8d$ octagon integrals in two-dimensional kinematics. The fully massive hexagon
and octagon integrals are then related to the double box and triple box
integrals respectively. We comment on the classes of functions needed to
express these integrals in general kinematics, involving elliptic functions and
beyond. |
SU(5) Monopoles and the Dual Standard Model: We find the spectrum of magnetic monopoles produced in the symmetry breaking
SU(5) to [SU(3)\times SU(2)\times U(1)']/Z_6 by constructing classical bound
states of the fundamental monopoles. The spectrum of monopoles is found to
correspond to the spectrum of one family of standard model fermions and hence,
is a starting point for constructing the dual standard model. At this level,
however, there is an extra monopole state - the ``diquark'' monopole - with no
corresponding standard model fermion. If the SU(3) factor now breaks down to
Z_3, the monopoles with non-trivial SU(3) charge get confined by strings in
SU(3) singlets. Another outcome of this symmetry breaking is that the diquark
monopole becomes unstable (metastable) to fragmentation into fundamental
monopoles and the one-one correspondence with the standard model fermions is
restored. We discuss the fate of the monopoles if the [SU(2)\times U(1)']/Z_2
factor breaks down to U(1)_Q by a Higgs mechanism as in the electroweak model.
Here we find that monopoles that are misaligned with the vacuum get connected
by strings even though the electroweak symmetry breaking does not admit
topological strings. We discuss the lowest order quantum corrections to the
mass spectrum of monopoles. | Higher-Order Derivative Susy in Quantum Mechanics with Large Energy
Shifts: Within the framework of second order derivative (one dimensional) SUSYQM we
discuss particular realizations which incorporate large energy shifts between
the lowest states of the spectrum of the superhamiltonian (of Schr\"odinger
type). The technique used in this construction is based on the "gluing"
procedure. We study the limit of infinite energy shift for the charges of the
Higher Derivative SUSY Algebra, and compare the results with those of the
standard SUSY Algebra. We conjecture that our results can suggest a
construction of a toy model where large energy splittings between fermionic and
bosonic partners do not affect the SUSY at low energies. |
On Generalized Axion Reductions: Recently interest in using generalized reductions to construct massive
supergravity theories has been revived in the context of M-theory and
superstring theory. These compactifications produce mass parameters by
introducing a linear dependence on internal coordinates in various axionic
fields. Here we point out that by extending the form of this simple ansatz, it
is always possible to introduce the various mass parameters simultaneously.
This suggests that the various ``distinct'' massive supergravities in the
literature should all be a part of a single massive theory. | Towards traversable wormholes from force-free plasmas: The near-horizon region of magnetically charged black holes can have very
strong magnetic fields. A useful low-energy effective theory for fluctuations
of the fields, coupled to electrically charged particles, is force-free
electrodynamics. The low energy collective excitations include a large number
of Alfven wave modes, which have a massless dispersion relation along the field
worldlines. We attempt to construct traversable wormhole solutions using the
negative Casimir energy of the Alfven wave modes, analogously to the recent
construction using charged massless fermions. The behaviour of massless scalars
in the near-horizon region implies that the size of the wormholes is strongly
restricted and cannot be made large, even though the force free description is
valid in a larger regime. |
New conformal-like symmetry of strictly massless fermions in
four-dimensional de Sitter space: We present new infinitesimal `conformal-like' symmetries for the field
equations of strictly massless spin-$s \geq 3/2$ totally symmetric
tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime
($dS_{4}$). The corresponding symmetry transformations are generated by the
five conformal Killing vectors of $dS_{4}$, but they are not conventional
conformal transformations. We show that the algebra generated by the ten de
Sitter (dS) symmetries and the five conformal-like symmetries closes on the
conformal-like algebra $so(4,2)$ up to gauge transformations of the gauge
potentials. Furthermore, we demonstrate that the two sets of physical mode
solutions, corresponding to the two helicities $\pm s$ of the strictly massless
theories, form a direct sum of Unitary Irreducible Representations (UIRs) of
the conformal-like algebra. We also fill a gap in the literature by explaining
how these physical modes form a direct sum of Discrete Series UIRs of the dS
algebra $so(4,1)$. | Propagator identities, holographic conformal blocks, and higher-point
AdS diagrams: Conformal blocks are the fundamental, theory-independent building blocks in
any CFT, so it is important to understand their holographic representation in
the context of AdS/CFT. We describe how to systematically extract the
holographic objects which compute higher-point global (scalar) conformal blocks
in arbitrary spacetime dimensions, extending the result for the four-point
block, known in the literature as a geodesic Witten diagram, to five- and
six-point blocks. The main new tools which allow us to obtain such
representations are various higher-point propagator identities, which can be
interpreted as generalizations of the well-known flat space star-triangle
identity, and which compute integrals over products of three bulk-to-bulk
and/or bulk-to-boundary propagators in negatively curved spacetime. Using the
holographic representation of the higher-point conformal blocks and
higher-point propagator identities, we develop geodesic diagram techniques to
obtain the explicit direct-channel conformal block decomposition of a broad
class of higher-point AdS diagrams in a scalar effective bulk theory, with
closed-form expressions for the decomposition coefficients. These methods
require only certain elementary manipulations and no bulk integration, and
furthermore provide quite trivially a simple algebraic origin of the
logarithmic singularities of higher-point tree-level AdS diagrams. We also
provide a more compact repackaging in terms of the spectral decomposition of
the same diagrams, as well as an independent discussion on the closely related
but computationally simpler framework over $p$-adics which admits comparable
statements for all previously mentioned results. |
Conformal Partial Waves: Further Mathematical Results: Further results for conformal partial waves for four point functions for
conformal primary scalar fields in conformally invariant theories are obtained.
They are defined as eigenfunctions of the differential Casimir operators for
the conformal group acting on two variable functions subject to appropriate
boundary conditions. As well as the scale dimension $\Delta$ and spin $\ell$
the conformal partial waves depend on two parameters $a,b$ related to the
dimensions of the operators in the four point function. Expressions for the
Mellin transform of conformal partial waves are obtained in terms of
polynomials of the Mellin transform variables given in terms of finite sums.
Differential operators which change $a,b$ by $\pm 1$, shift the dimension $d$
by $\pm 2$ and also change $\Delta,\ell$ are found. Previous results for
$d=2,4,6$ are recovered. The trivial case of $d=1$ and also $d=3$ are also
discussed. For $d=3$ formulae for the conformal partial waves in some
restricted cases as a single variable integral representation based on the
Bateman transform are found. | Creating 3, 4, 6 and 10-dimensional spacetime from W3 symmetry: We describe a model where breaking of W3 symmetry will lead to the emergence
of time and subsequently of space. Surprisingly the simplest such models which
lead to higher dimensional spacetimes are based on the four "magical" Jordan
algebras of 3x3 Hermitian matrices with real, complex, quaternion and octonion
entries, respectively. The simplest symmetry breaking leads to universes with
spacetime dimensions 3, 4, 6, and 10. |
Fiber-base duality from the algebraic perspective: Quiver 5D $\mathcal{N}=1$ gauge theories describe the low-energy dynamics on
webs of $(p,q)$-branes in type IIB string theory. S-duality exchanges NS5 and
D5 branes, mapping $(p,q)$-branes to branes of charge $(-q,p)$, and, in this
way, induces several dualities between 5D gauge theories. On the other hand,
these theories can also be obtained from the compactification of topological
strings on a Calabi-Yau manifold, for which the S-duality is realized as a
fiber-base duality. Recently, a third point of view has emerged in which 5D
gauge theories are engineered using algebraic objects from the Ding-Iohara-Miki
(DIM) algebra. Specifically, the instanton partition function is obtained as
the vacuum expectation value of an operator $\mathcal{T}$ constructed by gluing
the algebra's intertwiners (the equivalent of topological vertices) following
the rules of the toric diagram/brane web. Intertwiners and
$\mathcal{T}$-operators are deeply connected to the co-algebraic structure of
the DIM algebra. We show here that S-duality can be realized as the twist of
this structure by Miki's automorphism. | Categories of quantum liquids I: We develop a mathematical theory of separable higher categories based on
Gaiotto and Johnson-Freyd's work on condensation completion. Based on this
theory, we prove some fundamental results on $E_m$-multi-fusion higher
categories and their higher centers. We also outline a theory of unitary higher
categories based on a $*$-version of condensation completion. After these
mathematical preparations, based on the idea of topological Wick rotation, we
develop a unified mathematical theory of all quantum liquids, which include
topological orders, SPT/SET orders, symmetry-breaking orders and CFT-like
gapless phases. We explain that a quantum liquid consists of two parts, the
topological skeleton and the local quantum symmetry, and show that all $n$D
quantum liquids form a $*$-condensation complete higher category whose
equivalence type can be computed explicitly from a simple coslice 1-category. |
Einstein-Yang-Mills Sphalerons and Level Crossing: The fermion energy spectrum along paths which connect topologically distinct
vacua in the Einstein-Yang-Mills theory passing through the gravitational
sphaleron equilibrium solutions is investigated. | Correspondence between Holographic and Gauss-Bonnet dark energy models: In the present work we investigate the cosmological implications of
holographic dark energy density in the Gauss-Bonnet framework. By formulating
independently the two cosmological scenarios, and by enforcing their
simultaneous validity, we show that there is a correspondence between the
holographic dark energy scenario in flat universe and the phantom dark energy
model in the framework of Gauss-Bonnet theory with a potential. This
correspondence leads consistently to an accelerating universe. However, in
general one has not full freedom of constructing independently the two
cosmological scenarios. Specific constraints must be imposed on the coupling
with gravity and on the potential. |
On the Existence of Meta-stable Vacua in Klebanov-Strassler: We solve for the complete space of linearized deformations of the
Klebanov-Strassler background consistent with the symmetries preserved by a
stack of anti-D3 branes smeared on the $S^3$ of the deformed conifold. We find
that the only solution whose UV physics is consistent with that of a
perturbation produced by anti-D3 branes must have a singularity in the
infrared, coming from NS and RR three-form field strengths whose energy density
diverges. If this singularity is admissible, our solution describes the
backreaction of the anti-D3 branes, and is thus likely to be dual to the
conjectured metastable vacuum in the Klebanov-Strassler field theory. If this
singularity is not admissible, then our analysis strongly suggests that anti-D3
branes do not give rise to metastable Klebanov-Strassler vacua, which would
have dramatic consequences for some string theory constructions of de Sitter
space. Key to this result is a simple, universal form for the force on a probe
D3-brane in our ansatz. | Tunnelling phenomenon near an apparent horizon in two-dimensional
dilaton gravity: Based on the definition of the apparent horizon in a general two-dimensional
dilaton gravity theory, we analyze the tunnelling phenomenon of the apparent
horizon by using Hamilton-Jacobi method. In this theory the definition of the
horizon is very different from those in higher-dimensional gravity theories.
The spectrum of the radiation is obtained and the temperature of the radiation
is read out from this spectrum and it satisfies the usual relationship with the
surface gravity. Besides, the calculation with Parikh's null geodesic method
for a simple example conforms to our result in general stationary cases. |
Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models: We continue the investigation of coupled Sachdev-Ye-Kitaev(SYK) models
without Schwarzian action dominance. Like the original SYK, at large N and low
energies these models have an approximate reparametrization symmetry. However,
the dominant action for reparametrizations is non-local due to the presence of
irrelevant local operator with small conformal dimension. We semi-analytically
study different thermodynamic properties and the 4-point function and
demonstrate that they significantly differ from the Schwarzian prediction.
However, the residual entropy and maximal chaos exponent are the same as in
Majorana SYK. We also discuss chain models and finite N corrections. | Contractions and deformations of quasi-classical Lie algebras preserving
a non-degenerate quadratic Casimir operator: By means of contractions of Lie algebras, we obtain new classes of
indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter
equations in its reformulation in terms of triple products. These algebras are
shown to arise naturally from non-compact real simple algebras with non-simple
complexification, where we impose that a non-degenerate quadratic Casimir
operator is preserved by the limiting process. We further consider the converse
problem, and obtain sufficient conditions on integrable cocycles of
quasi-classical Lie algebras in order to preserve non-degenerate quadratic
Casimir operators by the associated linear deformations. |
Effect of the deformation operator in the D1D5 CFT: The D1D5 CFT gives a holographic dual description of a near-extremal black
hole in string theory. The interaction in this theory is given by a marginal
deformation operator, which is composed of supercharges acting on a twist
operator. The twist operator links together different copies of a free CFT. We
study the effect of this deformation operator when it links together CFT copies
with winding numbers M and N to produce a copy with winding M+N, populated with
excitations of a particular form. We compute the effect of the deformation
operator in the full supersymmetric theory, firstly on a Ramond-Ramond ground
state and secondly on states with an initial bosonic or fermionic excitation.
Our results generalize recent work which studied only the bosonic sector of the
CFT. Our findings are a step towards understanding thermalization in the D1D5
CFT, which is related to black hole formation and evaporation in the bulk. | Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge: We investigate the Laplacian Abelian gauge on the sphere S^4 in the
background of a single `t Hooft instanton. To this end we solve the eigenvalue
problem of the covariant Laplace operator in the adjoint representation. The
ground state wave function serves as an auxiliary Higgs field. We find that the
ground state is always degenerate and has nodes. Upon diagonalisation, these
zeros induce toplogical defects in the gauge potentials. The nature of the
defects crucially depends on the order of the zeros. For first-order zeros one
obtains magnetic monopoles. The generic defects, however, arise from zeros of
second order and are pointlike. Their topological invariant is the Hopf index
S^3 -> S^2. These findings are corroborated by an analysis of the Laplacian
gauge in the fundamental representation where similar defects occur. Possible
implications for the confinement scenario are discussed. |
f(R)-Einstein-Palatini Formalism and smooth branes: In this work, we present the f(R)-Einstein-Palatini formalism in arbitrary
dimensions and the study of consistency applied to brane models, the so-called
braneworld sum rules. We show that it is possible a scenario of thick branes in
five dimensions with compact extra dimension in the framework of the
f(R)-Einstein-Palatini theory by the accomplishment of an assertive criteria. | Diagnostics of plasma photoemission at strong coupling: We compute the spectrum of photons emitted by the finite-temperature large-N
SU(N) ${\cal {N}}=4$ supersymmetric Yang-Mills plasma coupled to
electromagnetism, at strong yet finite 't Hooft coupling. We work in the
holographic dual description, extended by the inclusion of the full set of
${\cal{O}}(\alpha'^3)$ type IIB string theory operators that correct the
minimal supergravity action. We find that, as the t' Hooft coupling decreases,
the peak of the spectrum increases, and the momentum of maximal emission shifts
towards the infra-red, as expected from weak-coupling computations. The total
number of emitted photons also increases as the 't Hooft coupling weakens. |
Form Factors of the Elementary Field in the Bullough-Dodd Model: We derive the recursive equations for the form factors of the local hermitian
operators in the Bullough-Dodd model. At the self-dual point of the theory, the
form factors of the fundamental field of the Bullough-Dodd model are equal to
those of the fundamental field of the Sinh-Gordon model at a specific value of
the coupling constant. | Polar decomposition of a Dirac spinor: Local decompositions of a Dirac spinor into `charged' and `real' pieces
psi(x) = M(x) chi(x) are considered. chi(x) is a Majorana spinor, and M(x) a
suitable Dirac-algebra valued field. Specific examples of the decomposition in
2+1 dimensions are developed, along with kinematical implications, and
constraints on the component fields within M(x) sufficient to encompass the
correct degree of freedom count. Overall local reparametrisation and
electromagnetic phase invariances are identified, and a dynamical framework of
nonabelian gauge theories of noncompact groups is proposed. Connections with
supersymmetric composite models are noted (including, for 2+1 dimensions,
infrared effective theories of spin-charge separation in models of high-Tc
superconductivity). |
On Ising Correlation Functions with Boundary Magnetic Field: Exact expressions of the boundary state and the form factors of the Ising
model are used to derive differential equations for the one-point functions of
the energy and magnetization operators of the model in the presence of a
boundary magnetic field. We also obtain explicit formulas for the massless
limit of the one-point and two-point functions of the energy operator. | Infrared behavior of graviton-graviton scattering: The quantum effective theory of general relativity, independent of the
eventual full theory at high energy, expresses graviton-graviton scattering at
one loop order O(E^4) with only one parameter, Newton's constant. Dunbar and
Norridge have calculated the one loop amplitude using string based techniques.
We complete the calculation by showing that the 1/(d-4) divergence which
remains in their result comes from the infrared sector and that the cross
section is finite and model independent when the usual bremsstrahlung diagrams
are included. |
Two Splits, Three Ways: Advances in Double Splitting Quenches: In this work we introduce a method for calculating holographic duals of BCFTs
with more than two boundaries. We apply it to calculating the dynamics of
entanglement entropy in a 1+1d CFT that is instantaneously split into multiple
segments and calculate the entanglement entropy as a function of time for the
case of two splits, showing that our approach reproduces earlier results for
the double split case. Our manuscript lays the groundwork for future
calculations of the entanglement entropy for more than two splits and systems
at nonzero temperature. | Algebra of Observables for Identical Particles in One Dimension: The algebra of observables for identical particles on a line is formulated
starting from postulated basic commutation relations. A realization of this
algebra in the Calogero model was previously known. New realizations are
presented here in terms of differentiation operators and in terms of
SU(N)-invariant observables of the Hermitian matrix models. Some particular
structure properties of the algebra are briefly discussed. |
The generating function of amplitudes with N twisted and M untwisted
states: We show that the generating function of all amplitudes with N twisted and M
untwisted states, i.e. the Reggeon vertex for magnetized branes on R^2 can be
computed once the correlator of N non excited twisted states and the
corresponding Green function are known and we give an explicit expression as a
functional of the these objects | Superpotentials, A-infinity Relations and WDVV Equations for Open
Topological Strings: We give a systematic derivation of the consistency conditions which constrain
open-closed disk amplitudes of topological strings. They include the A-infinity
relations (which generalize associativity of the boundary product of
topological field theory), as well as certain homotopy versions of
bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability
of amplitudes with respect to bulk and boundary deformations, and write down
the analogs of WDVV equations for the space-time superpotential. We also study
the structure of these equations from a string field theory point of view. As
an application, we determine the effective superpotential for certain families
of D-branes in B-twisted topological minimal models, as a function of both
closed and open string moduli. This provides an exact description of tachyon
condensation in such models, which allows one to determine the truncation of
the open string spectrum in a simple manner. |
The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear
quantum mechanical supersymmetry: We show that the Ginzburg-Landau expansion of the grand potential for the
Bogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinear
equations of the AKNS hierarchy, and that this provides the natural
mathematical framework for a hidden nonlinear quantum mechanical supersymmetry
underlying the dynamics. | Renormalization Scheme Dependence with Renormalization Group Summation: We consider all radiative corrections to the total electron-positron cross
section showing how the renormalization group equation can be used to sum the
logarithmic contributions in two ways. First of all, one can sum leading-log
etc. contributions. A second summation shows how all logarithmic corrections
can be expressed in terms of log-independent contributions. Next, using
Stevenson's characterization of renormalization scheme, we examine scheme
dependence when using the second way of summing logarithms. The renormalization
scheme invariants that arise are then related to those of Stevenson. We
consider two choices of renormalization scheme, one resulting in two powers of
a running coupling, the second in an infinite series in the two loop running
constant. We then establish how the coupling constant arising in one
renormalization scheme can be expressed as a power series of the coupling in
any other scheme. Next we establish how by using different mass scale at each
order of perturbation theory, all renormalization scheme dependence can be
absorbed into these mass scales when one uses the second way of summing
logarithmic corrections. We then employ this approach to renormalization scheme
dependency to the effective potential in a scalar model, showing the result
that it is independent of the background field is scheme independent. The way
in which the "principle of minimal sensitivity" can be applied after summation
is then discussed. |
Constructing Space From Entanglement Entropy: We explicitly reconstruct the metric of a gravity dual to field theories
using known entanglement entropies using the Ryu-Takayanagi formula. We use for
examples CFT's in $d = 1$, 2 and 3 as well as CFT on a circle of length $L$ and
a thermal CFT at temperature $\beta^{-1}$. We also give the first several
coefficients in the Taylor series of the metric for a general entanglement
entropy in 1+1 dimensions as well as some examples (Appendix B). The beginnings
of a dictionary between the dual theories appears naturally and does not need
to be inserted by hand. For example, the dictionary entries $c=3R/2G_N$ for 1+1
dimensional CFT and $N^2 = \pi R^3/2G_N$ for $\mathcal{N}=4$ SYM in 3+1
dimensions are forced upon us. After uploading this paper I was made aware of
(arXiv:1012.1812) which solves the same problem in a similar way. | 't Hooft surface operators in five dimensions and elliptic Ruijsenaars
operators: We introduce codimension three magnetically charged surface operators in
five-dimensional (5d) $\mathcal{N}=1$ supersymmetric gauge on $T^2 \times
\mathbb{R}^3$. We evaluate the vacuum expectation values (vevs) of surface
operators by supersymmetric localization techniques. Contributions of Monopole
bubbling effects to the path integral are given by elliptic genera of world
volume theories on D-branes. Our result gives an elliptic deformation of the
SUSY localization formula \cite{Ito:2011ea} (resp. \cite{Okuda:2019emk,
Assel:2019yzd}) of BPS 't Hooft loops (resp. bare monopole operators) in 4d
$\mathcal{N}=2$ (resp. 3d $\mathcal{N}=4$) gauge theories. We define
deformation quantizations of vevs of surface operators in terms of the
Weyl-Wigner transform, where the $\Omega$-background parameter plays the role
of the Planck constant. For 5d $\mathcal{N}=1^*$ gauge theory, we find that the
deformation quantization of the surface operators in the anti-symmetric
representations agrees with the type A elliptic Ruijsenaars operators. The
mutual commutativity of these difference operators is related to the
commutativity of products of 't Hooft surface operators. |
Three-Dimensional Solutions of Supersymmetrical Intertwining Relations
and Pairs of Isospectral Hamiltonians: The general solution of SUSY intertwining relations for three-dimensional
Schr\"odinger operators is built using the class of second order supercharges
with nondegenerate constant metric. This solution includes several models with
arbitrary parameters. We are interested only in quantum systems which are not
amenable to separation of variables, i.e. can not be reduced to lower
dimensional problems. All constructed Hamiltonians are partially integrable -
each of them commutes with a symmetry operator of fourth order in momenta. The
same models can be considered also for complex values of parameters leading to
a class of non-Hermitian isospectral Hamiltonians. | Higher-degree Dirac Currents of Twistor and Killing Spinors in
Supergravity Theories: We show that higher degree Dirac currents of twistor and Killing spinors
correspond to the hidden symmetries of the background spacetime which are
generalizations of conformal Killing and Killing vector fields respectively.
They are the generalizations of 1-form Dirac currents to higher degrees which
are used in constructing the bosonic supercharges in supergravity theories. In
the case of Killing spinors, we find that the equations satisfied by the higher
degree Dirac currents are related to Maxwell-like and Duffin-Kemmer-Petiau
equations. Correspondence between the Dirac currents and harmonic forms for
parallel and pure spinor cases is determined. We also analyze the supergravity
twistor and Killing spinor cases in 10 and 11-dimensional supergravity theories
and find that although different inner product classes induce different
involutions on spinors, the higher degree Dirac currents still correspond to
the hidden symmetries of the spacetime. |
A double copy for ${\cal N}=2$ supergravity: a linearised tale told
on-shell: We construct the on-shell double copy for linearised four-dimensional ${\cal
N}=2$ supergravity coupled to one vector multiplet with a quadratic
prepotential. We apply this dictionary to the weak-field approximation of
dyonic BPS black holes in this theory. | Baryon as dyonic instanton-II. Baryon mass versus chiral condensate: We discuss the description of baryon as the dyonic instanton in holographic
QCD. The solution generalizes the Skyrmion taking into account the infinite
tower of vector and axial mesons as well as the chiral condensate. We construct
the solution with unit baryon charge and study the dependence of its mass on
the chiral condensate. The elegant explanation of the Ioffe's formula has been
found and we speculate on the relation between physical scales of the chiral
and conformal symmetry breaking. |
On the stability of open-string orbifold models with broken
supersymmetry: We consider an open-string realisation of $\mathcal{N}=2\to \mathcal{N}=0$
spontaneous breaking of supersymmetry in four-dimensional Minkowski spacetime.
It is based on type IIB orientifold theory compactified on $T^2\times
T^4/\mathbb{Z}_2$, with Scherk--Schwarz supersymmetry breaking implemented
along $T^2$. We show that in the regions of moduli space where the
supersymmetry breaking scale is lower than the other scales, there exist
configurations with minima that have massless Bose-Fermi degeneracy and hence
vanishing one-loop effective potential, up to exponentially suppressed
corrections. These backgrounds describe non-Abelian gauge theories, with all
open-string moduli and blowing up modes of $T^4/\mathbb{Z}_2$ stabilized, while
all untwisted closed-string moduli remain flat directions. Other backgrounds
with strictly positive effective potentials exist, where the only instabilities
arising at one loop are associated with the supersymmetry breaking scale, which
runs away. All of these backgrounds are consistent non-perturbatively. | N=4 superconformal mechanics as a Non linear Realization: An action for a superconformal particle is constructed using the non linear
realization method for the group PSU(1,1|2), without introducing superfields.
The connection between PSU(1,1|2) and black hole physics is discussed. The
lagrangian contains six arbitrary constants and describes a non-BPS
superconformal particle. The BPS case is obtained if a precise relation between
the constants in the lagrangian is verified, which implies that the action
becomes kappa-symmetric. |
Gravity and the stability of the Higgs vacuum: We discuss the effect of gravitational interactions on the lifetime of the
Higgs vacuum where generic quantum gravity corrections are taken into account.
We show how small black holes can act as seeds for vacuum decay, spontaneously
nucleating a new Higgs phase centered on the black hole with a lifetime
measured in millions of Planck times rather than billions of years. The
constraints on parameter space of corrections to the Higgs potential are
outlined, and implications for collider black holes discussed. | An Update on Perturbative N=8 Supergravity: According to the recent pure spinor analysis of the UV divergences by
Karlsson, there are no divergent 1PI structures beyond 6 loops in D=4 N=8
supergravity. In combination with the common expectation that the UV
divergences do not appear at less than 7 loops, this may imply that the 4-point
amplitude in D=4 N=8 supergravity is all-loop finite. This differs from the
result of the previous studies of pure spinors, which suggested that there is a
UV divergence at 7 loops in D=4. Therefore an independent investigation of the
pure spinor formalism predictions is desirable, as well as continuation of
explicit loop computations. In the meantime, we revisit here our earlier
arguments on UV finiteness of N=8 supergravity based on the absence of the
off-shell light-cone superspace counterterms, as well as on the E_{7(7)}
current conservation. We believe that both arguments remain valid in view of
the developments in this area during the last few years. |
Reflected entropy is not a correlation measure: By explicit counterexample, we show that the "reflected entropy" defined by
Dutta and Faulkner is not monotonically decreasing under partial trace, and so
is not a measure of physical correlations. In fact, our counterexamples show
that none of the R\'enyi reflected entropies $S_{R}^{(\alpha)}$ for $0 < \alpha
< 2$ is a correlation measure; the usual reflected entropy is realized as the
$\alpha=1$ member of this family. The counterexamples are given by quantum
states that correspond to classical probability distributions, so reflected
entropy fails to measure correlations even at the classical level. | Quantum Quench and Double Trace Couplings: We consider quantum quench by a time dependent double trace coupling in a
strongly coupled large N field theory which has a gravity dual via the AdS/CFT
correspondence. The bulk theory contains a self coupled neutral scalar field
coupled to gravity with negative cosmological constant. We study the scalar
dynamics in the probe approximation in two backgrounds: AdS soliton and AdS
black brane. In either case we find that in equilibrium there is a critical
phase transition at a {\em negative} value of the double trace coupling
$\kappa$ below which the scalar condenses. For a slowly varying homogeneous
time dependent coupling crossing the critical point, we show that the dynamics
in the critical region is dominated by a single mode of the bulk field. This
mode satisfies a Landau-Ginsburg equation with a time dependent mass, and leads
to Kibble Zurek type scaling behavior. For the AdS soliton the system is
non-dissipative and has $z=1$, while for the black brane one has dissipative
$z=2$ dynamics. We also discuss the features of a holographic model which would
describe the non-equilibrium dynamics around quantum critical points with
arbitrary dynamical critical exponent $z$ and correlation length exponent
$\nu$. These analytical results are supported by direct numerical solutions. |
The Physics of Q-balls: In this thesis we investigate the stationary properties and formation process
of a class of nontopological solitons, namely Q-balls. We explore both the
quantum-mechanical and classical stability of Q-balls that appear in
polynomial, gravity-mediated and gauge-mediated potentials. By presenting our
detailed analytic and numerical results, we show that absolutely stable
non-thermal Q-balls may exist in any kinds of the above potentials. The latter
two types of potentials are motivated by Affleck-Dine baryogenesis, which is
one of the best candidate theories to solve the present baryon asymmetry. By
including quantum corrections in the scalar potentials, a naturally formed
condensate in a post-inflationary era can be classically unstable and fragment
into Q-balls that can be long-lived or decay into the usual baryons/leptons as
well as the lightest supersymmeric particles. This scenario naturally provides
the baryon asymmetry and the similarity of the energy density between baryons
and dark matter in the Universe. Introducing detailed lattice simulations, we
argue that the formation, thermalisation and stability of these Q-balls depend
on the properties of models involved with supersymmetry breaking. | On an alternative quantization of R-NS strings: We investigate an alternative quantization of R-NS string theory. In the
alternative quantization, we define the distinct vacuum for the left-moving
mode and the right-moving mode by exchanging the role of creation operators and
annihilation operators in the left-moving sector. The resulting string theory
has only a finite number of propagating degrees of freedom. We show that an
appropriate choice of the GSO projection makes the theory tachyon free. The
spectrum coincides with the massless sector of type IIA or type IIB superstring
theory without any massive excitations. |
A String Theory Which Isn't About Strings: Quantization of closed string proceeds with a suitable choice of worldsheet
vacuum. A priori, the vacuum may be chosen independently for left-moving and
right-moving sectors. We construct {\sl ab initio} quantized bosonic string
theory with left-right asymmetric worldsheet vacuum and explore its
consequences and implications. We critically examine the validity of new vacuum
and carry out first-quantization using standard operator formalism. Remarkably,
the string spectrum consists only of a finite number of degrees of freedom:
string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two
massive spin-two Fierz-Pauli fields. The massive spin-two fields have negative
norm, opposite mass-squared, and provides a Lee-Wick type extension of string
gravity. We compute two physical observables: tree-level scattering amplitudes
and one-loop cosmological constant. Scattering amplitude of four dilatons is
shown to be a rational function of kinematic invariants, and in $D=26$
factorizes into contributions of massless spin-two and a pair of massive
spin-two fields. The string one loop partition function is shown to perfectly
agree with one loop Feynman diagram of string gravity and two massive spin-two
fields. In particular, it does not exhibit modular invariance. We critically
compare our construction with recent studies and contrast differences. | Hamiltonian analysis of nonprojectable Hořava-Lifshitz gravity with
$U(1)$ symmetry: We study the nature of constraints and count the number of degrees of freedom
in the nonprojectable version of the $U(1)$ extension of Ho\v{r}ava-Lifshitz
gravity, using the standard method of Hamiltonian analysis in the classical
field theory. This makes it possible for us to investigate the condition under
which the scalar graviton is absent at a fully nonlinear level. We show that
the scalar graviton does not exist at the classical level if and only if two
specific coupling constants are exactly zero. The operators corresponding to
these two coupling constants are marginal for any values of the dynamical
critical exponent of the Lifshitz scaling and thus should be generated by
quantum corrections even if they are eliminated from the bare action. We thus
conclude that the theory in general contains the scalar graviton. |
New Aspects of Heterotic--F Theory Duality: In order to understand both up-type and down-type Yukawa couplings, F-theory
is a better framework than the perturbative Type IIB string theory. The duality
between the Heterotic and F-theory is a powerful tool in gaining more insights
into F-theory description of low-energy chiral multiplets. Because chiral
multiplets from bundles /\^2 V and /\^2 V^x as well as those from a bundle V
are all involved in Yukawa couplings in Heterotic compactification, we need to
translate descriptions of all those kinds of matter multiplets into F-theory
language through the duality. We find that chiral matter multiplets in F-theory
are global holomorphic sections of line bundles on what we call covering matter
curves. The covering matter curves are formulated in Heterotic theory in
association with normalization of spectral surface, while they are where
M2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality
formulae are given purely in terms of (possibly primitive) four-form flux. In
order to complete the translation, the dictionary of the Heterotic--F theory
duality has to be refined in some aspects. A precise map of spectral surface
and complex structure moduli is obtained, and with the map, we find that
divisors specifying the line bundles correspond precisely to codimension-3
singularities in F-theory. | Exceptional Seiberg-Witten Geometry with Massive Fundamental Matters: We propose Seiberg-Witten geometry for N=2 gauge theory with gauge group
$E_6$ with massive $N_f$ fundamental hypermultiplets. The relevant manifold is
described as a fibration of the ALE space of $E_6$ type. It is observed that
the fibering data over the base ${\bf CP}^1$ has an intricate dependence on
hypermultiplet bare masses. |
Higher derivative extension of the functional renormalization group: We study higher derivative extension of the functional renormalization group
(FRG). We consider FRG equations for a scalar field that consist of terms with
higher functional derivatives of the effective action and arbitrary cutoff
functions. We show that the epsilon expansion around the Wilson-Fisher fixed
point is indeed reproduced by the local potential approximation of the FRG
equations. | Conformal Dimensions of Two-Derivative BMN Operators: We compute the anomalous dimensions of BMN operators with two covariant
derivative impurities at the planar level up to first order in the effective
coupling lambda'. The result equals those for two scalar impurities as well as
for mixed scalar and vector impurities given in the literature. Though the
results are the same, the computation is very different from the scalar case.
This is basically due to the existence of a non-vanishing overlap between the
derivative impurity and the ``background'' field Z. We present details of these
differences and their consequences. |
Localization of 4d $\mathcal{N}=1$ theories on $\mathbb{D}^2\times
\mathbb{T}^2$: We consider 4d $\mathcal{N}=1$ gauge theories with R-symmetry on a hemisphere
times a torus. We apply localization techniques to evaluate the exact partition
function through a cohomological reformulation of the supersymmetry
transformations. Our results represent the natural elliptic lifts of the lower
dimensional analogs as well as a field theoretic derivation of the conjectured
4d holomorphic blocks, from which partition functions of compact spaces with
diverse topology can be recovered through gluing. We also analyze the different
boundary conditions which can naturally be imposed on the chiral multiplets,
which turn out to be either Dirichlet or Robin-like. We show that different
boundary conditions are related to each other by coupling the bulk to 3d
$\mathcal{N}=1$ degrees of freedom on the boundary three-torus, for which we
derive explicit 1-loop determinants. | Berry's Phase and Euclidean Path Integral: A method for finding Berry's phase is proposed under the Euclidean path
integral formalism. It is characterized by picking up the imaginary part from
the resultant exponent. Discussion is made on the generalized harmonic
oscillator which is shown being so universal in a single degree case. The spin
model expressed by creation and annihilation operators is also discussed. A
systematic way of expansion in the adiabatic approximation is presented in
every example. |
Stationarity of Inflation and Predictions of Quantum Cosmology: We describe several different regimes which are possible in inflationary
cosmology. The simplest one is inflation without self-reproduction of the
universe. In this scenario the universe is not stationary. The second regime,
which exists in a broad class of inflationary models, is eternal inflation with
the self-reproduction of inflationary domains. In this regime local properties
of domains with a given density and given values of fields do not depend on the
time when these domains were produced. The probability distribution to find a
domain with given properties in a self-reproducing universe may or may not be
stationary, depending on the choice of an inflationary model. We give examples
of models where each of these possibilities can be realized, and discuss some
implications of our results for quantum cosmology. In particular, we propose a
new mechanism which may help solving the cosmological constant problem. | Triangle UD integrals in the position space: We investigate triangle UD ladder integrals in the position space. The
investigation is necessary to find an all-order in loop solution for an
auxiliary Lcc correlator in Wess-Zumino-Landau gauge of the maximally
supersymmetric Yang-Mills theory and to present correlators of dressed mean
gluons in terms of it in all loops. We show that triangle UD ladder diagrams in
the position space can be expressed in terms of the same UD functions Phi^(L)
in terms of which they were represented in the momentum space, for an arbitrary
number of rungs. |
Properties of solutions of the "naive" functional Schroedinger equation
for QCD: In this paper we consider the simplest functional Schroedinger equation of a
quantum field theory (in particular QCD) and study its solutions. We observe
that the solutions to this equation must possess a number of properties. Its
Taylor coefficients are multivalued functions with rational and logarithmic
branchings and essential singularities of exponential type. These singularities
occur along a locus defined by polynomial equations. The conditions we find
define a class of functions that generalizes to multiple dimensions meromorphic
functions with finite Nevanlinna type. We note that in perturbation theory
these functions have local asymptotics that is given by multidimensional
confluent hypergeometric functions in the sense of Gelfand-Kapranov-Zelevinsky. | Hidden horizons in non-relativistic AdS/CFT: We study boundary Green's functions for spacetimes with non-relativistic
scaling symmetry. For this class of backgrounds, scalar modes with large
transverse momentum, or equivalently low frequency, have an exponentially
suppressed imprint on the boundary. We investigate the effect of these modes on
holographic two-point functions. We find that the boundary Green's function is
generically insensitive to horizon features on small transverse length scales.
We explicitly demonstrate this insensitivity for Lifshitz z=2, and then use the
WKB approximation to generalize our findings to Lifshitz z>1 and RG flows with
a Lifshitz-like region. We also comment on the analogous situation in
Schroedinger spacetimes. Finally, we exhibit the analytic properties of the
Green's function in these spacetimes. |
Tachyon Condensation on Separated Brane-Antibrane System: We study the effect of tachyon condensation on a brane antibrane pair in
superstring theory separated in the transverse direction. The static properties
of the tachyon potential analyzed using level truncated string field theory
reproduces the desired property that the dependence of the minimum value of the
potential on the initial distance of separation between the branes decreases as
we include higher level terms. The rolling tachyon solution constructed using
the conformal field theory methods shows that if the initial separation between
the branes is less than a critical distance then the solution is described by
an exactly marginal deformation of the original conformal field theory where
the correlation functions of the deformed theory are determined completely in
terms of the correlation functions of the undeformed theory without any need to
regularize the theory. Using this we give an expression for the pressure on the
brane-antibrane system as a power series expansion in \exp(C x^0) for an
appropriate constant C. | On covariant phase space methods: It is well known that the Lagrangian and the Hamiltonian formalisms can be
combined and lead to "covariant symplectic" methods. For that purpose a
"pre-symplectic form" has been constructed from the Lagrangian using the
so-called Noether form. However, analogously to the standard Noether currents,
this symplectic form is only determined up to total divergences which are
however essential ingredients in gauge theories.
We propose a new definition of the symplectic form which is covariant and
free of ambiguities in a general first order formulation. Indeed, our
construction depends on the equations of motion but not on the Lagrangian. We
then define a generalized Hamiltonian which generates the equations of motions
in a covariant way. Applications to Yang-Mills, general relativity,
Chern-Simons and supergravity theories are given. We also consider nice sets of
possible boundary conditions that imply the closure and conservation of the
total symplectic form.
We finally revisit the construction of conserved charges associated with
gauge symmetries, from both the "covariant symplectic" and the "covariantized
Regge-Teitelboim" points of view. We find that both constructions coincide when
the ambiguity in the Noetherian pre-symplectic form is fixed using our new
prescription. We also present a condition of integrability of the equations
that lead to these quantities. |
Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry
Breaking: Without Lorentz invariance, spontaneous global symmetry breaking can lead to
multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion
$\omega\sim k^n$ ($n=2,3,\ldots$), whose naturalness is protected by polynomial
shift symmetries. Here we investigate the role of infrared divergences and the
nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW)
theorem. We find novel cascading phenomena with large hierarchies between the
scales at which the value of $n$ changes, leading to an evasion of the "no-go"
consequences of the relativistic CHMW theorem. | Classical N=2 W-superalgebras From Superpseudodifferential Operators: We study the supersymmetric Gelfand-Dickey algebras associated with the
superpseudodifferential operators of positive as well as negative leading
order. We show that, upon the usual constraint, these algebras contain the N=2
super Virasoro algebra as a subalgebra as long as the leading order is odd. The
decompositions of the coefficient functions into N=1 primary fields are then
obtained by covariantizing the superpseudodifferential operators. We discuss
the problem of identifying N=2 supermultiplets and work out a couple of
supermultiplets by explicit computations. |
Thoughts on Tachyon Cosmology: After a pedagogical review of elementary cosmology, I go on to discuss some
obstacles to obtaining inflationary or accelerating universes in M/String
Theory. In particular, I give an account of an old No-Go Theorem to this
effect. I then describe some recent ideas about the possible r\^ole of the
tachyon in cosmology. I stress that there are many objections to a naive
inflationary model based on the tachyon, but there remains the possiblity that
the tachyon was important in a possible pre-inflationary Open-String Era
preceding our present Closed String Era. | Precision Islands in the Ising and $O(N)$ Models: We make precise determinations of the leading scaling dimensions and operator
product expansion (OPE) coefficients in the 3d Ising, $O(2)$, and $O(3)$ models
from the conformal bootstrap with mixed correlators. We improve on previous
studies by scanning over possible relative values of the leading OPE
coefficients, which incorporates the physical information that there is only a
single operator at a given scaling dimension. The scaling dimensions and OPE
coefficients obtained for the 3d Ising model, $(\Delta_{\sigma},
\Delta_{\epsilon},\lambda_{\sigma\sigma\epsilon},
\lambda_{\epsilon\epsilon\epsilon}) = (0.5181489(10), 1.412625(10),
1.0518537(41), 1.532435(19))$, give the most precise determinations of these
quantities to date. |
Negative mode of Schwarzschild black hole from the thermodynamic
instability: The thermodynamic instability, for example the negative heat capacity, of a
black hole implies the existence of off-shell negative mode(s) (tachyonic
mode(s)) around the black hole geometry in the Euclidean path integral
formalism of quantum gravity. We explicitly construct an off-shell negative
mode inspired from the negative heat capacity in the case of Schwarzschild
black hole with/without a cosmological constant. We carefully check the
boundary conditions, i.e. the regularity at the horizon, the traceless
condition, and the normalizability. | Pseudoclassical mechanics and hidden symmetries of 3d particle models: We discuss hidden symmetries of three-dimensional field configurations
revealed at the one-particle level by the use of pseudoclassical particle
models. We argue that at the quantum field theory level, these can be naturally
explained in terms of manifest symmetries of the reduced phase space
Hamiltonian of the corresponding field systems. |
Entanglement of the $3$-State Potts Model via Form Factor Bootstrap:
Total and Symmetry Resolved Entropies: In this paper, we apply the form factor bootstrap approach to branch point
twist fields in the $q$-state Potts model for $q\leq 3$. For $q=3$ this is an
integrable interacting quantum field theory with an internal discrete
$\mathbb{Z}_3$ symmetry and therefore provides an ideal starting point for the
investigation of the symmetry resolved entanglement entropies. However, more
generally, for $q\leq 3$ the standard R\'enyi and entanglement entropies are
also accessible through the bootstrap programme. In our work we present form
factor solutions both for the standard branch point twist field with $q\leq 3$
and for the composite (or symmetry resolved) branch point twist field with
$q=3$. In both cases, the form factor equations are solved for two particles
and the solutions are carefully checked via the $\Delta$-sum rule. Using our
analytic predictions, we compute the leading finite-size corrections to the
entanglement entropy and entanglement equipartition for a single interval in
the ground state. | Standard Model and SU(5) GUT with Local Scale Invariance and the Weylon: Weyl's scale invariance is introduced as an additional local symmetry in the
standard model of electroweak interactions. An inevitable consequence is the
introduction of general relativity coupled to scalar fields a la Dirac and an
additional vector particle we call the Weylon. Once Weyl's scale invariance is
broken, the phenomenon (a) generates Newton's gravitational constant G_N and
(b) triggers the conventional spontaneous symmetry breaking mechanism that
results in masses for all the fermions and bosons. The scale at which Weyl's
scale symmetry breaks is of order Planck mass. If right-handed neutrinos are
also introduced, their absence at present energy scales is attributed to their
mass which is tied to the scale where scale invariance breaks. Some
implications of these ideas are noted in grand unification based on the gauge
symmetry SU(5). |
Evolution method and "differential hierarchy" of colored knot
polynomials: We consider braids with repeating patterns inside arbitrary knots which
provides a multi-parametric family of knots, depending on the "evolution"
parameter, which controls the number of repetitions. The dependence of knot
(super)polynomials on such evolution parameters is very easy to find. We apply
this evolution method to study of the families of knots and links which include
the cases with just two parallel and anti-parallel strands in the braid, like
the ordinary twist and 2-strand torus knots/links and counter-oriented 2-strand
links. When the answers were available before, they are immediately reproduced,
and an essentially new example is added of the "double braid", which is a
combination of parallel and anti-parallel 2-strand braids. This study helps us
to reveal with the full clarity and partly investigate a mysterious
hierarchical structure of the colored HOMFLY polynomials, at least, in
(anti)symmetric representations, which extends the original observation for the
figure-eight knot to many (presumably all) knots. We demonstrate that this
structure is typically respected by the t-deformation to the superpolynomials. | On the theory of coherent pair production in crystals in presence of
acoustic waves: The influence of hypersonic waves excited in a single crystal is investigated
on the process of electron-positron pair creation by high-energy photons. The
coherent part of the corresponding differential cross-section is derived as a
function of the amplitude and wave number of the hypersound. The values of the
parameters are specified for which the latter affects remarkably on the pair
creation cross-section. It is shown that under certain conditions the presence
of hypersonic waves can result in enhancement of the process cross-section. |
Coset Realization of Unifying W-Algebras: We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and
sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely
generated. Furthermore, we discuss in detail their role as unifying W-algebras
of Casimir W-algebras. We show that it is possible to give coset realizations
of various types of unifying W-algebras, e.g. the diagonal cosets based on the
symplectic Lie algebras sp(2n) realize the unifying W-algebras which have
previously been introduced as `WD_{-n}'. In addition, minimal models of WD_{-n}
are studied. The coset realizations provide a generalization of
level-rank-duality of dual coset pairs. As further examples of finitely
nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras
which on the quantum level has different properties than in the classical case.
We demonstrate in some examples that the classical limit according to Bowcock
and Watts of these nonfreely finitely generated quantum W-algebras probably
yields infinitely nonfreely generated classical W-algebras. | IIB flux non-commutativity and the global structure of field theories: We discuss the origin of the choice of global structure for six dimensional
$(2,0)$ theories and their compactifications in terms of their realization from
IIB string theory on ALE spaces. We find that the ambiguity in the choice of
global structure on the field theory side can be traced back to a subtle effect
that needs to be taken into account when specifying boundary conditions at
infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes
in spaces with torsion. As an example, we show how the classification of
$\mathcal{N}=4$ theories by Aharony, Seiberg and Tachikawa can be understood in
terms of choices of boundary conditions for RR fields in IIB. Along the way we
encounter a formula for the fractional instanton number of $\mathcal{N}=4$ ADE
theories in terms of the torsional linking pairing for rational homology
spheres. We also consider six-dimensional $(1,0)$ theories, clarifying the
rules for determining commutators of flux operators for discrete 2-form
symmetries. Finally, we analyze the issue of global structure for four
dimensional theories in the presence of duality defects. |
Riemann Tensor of the Ambient Universe, the Dilaton and the Newton's
Constant: We investigate a four-dimensional world, embedded into a five-dimensional
spacetime, and find the five-dimensional Riemann tensor via generalisation of
the Gauss (--Codacci) equations. We then derive the generalised equations of
the four-dimensional world and also show that the square of the dilaton field
is equal to the Newton's constant. We find plausable constant and non-constant
solutions for the dilaton. | Colliding branes and big crunches: We examine the global structure of colliding domain walls in AdS spacetime
and come to the conclusion that singularities forming from such collisions are
of the big-crunch type rather than that of a black brane. |
Supergravity Solution for Three-String Junction in M-Theory: Three-String junctions are allowed configurations in II B string theory which
preserve one-fourth supersymmetry. We obtain the 11-dimensional supergravity
solution for curved membranes corresponding to these three-string junctions. | Inflationary universe from anomaly-free $F(R)$-gravity: By adding a three dimensional manifold to an eleven dimensional manifold in
supergravity, we obtain the action of $F(R)$-gravity and find that it is
anomaly free. We calculate the scale factor of the inflationary universe in
this model, and observe that it is related to the slow-roll parameters. The
scalar-tensor ratio R\_(scalar-tensor) is in good agreement with experimental
data. |
Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2
Supersymmetric QCD: We consider non-Abelian semilocal strings (vortices, or vortex-strings)
arising in N=2 supersymmetric U(N) gauge theory with Nf=N+\~N matter
hypermultiplets in the fundamental representation (quarks), and a
Fayet-Iliopoulos term {\xi}. We present, for the first time ever, a systematic
field-theoretic derivation of the world-sheet theory for such strings,
describing dynamics of both, orientational and size zero modes. Our derivation
is complete in the limit, ln(L)\rightarrow \infty, where L is an infrared (IR)
regulator in the transverse plane. In this limit the world-sheet theory is
obtained exactly. It is presented by a so far unknown N=2 two-dimensional sigma
model, to which we refer as the zn model, with or without twisted masses.
Alternative formulations of the zn model are worked out: conventional and
extended gauged formulations and a geometric formulation. We compare the exact
metric of the zn model with that of the weighted CP(Nf-1) model conjectured by
Hanany and Tong, through D-branes, as the world-sheet theory for the
non-Abelian semilocal strings. The Hanany-Tong set-up has no parallel for the
field-theoretic IR parameter and metrics of the weighted CP(Nf-1) model and zn
model are different. Still their quasiclassical excitation spectra coincide. | Linking the Supersymmetric Standard Model to the Cosmological Constant: String theory has no parameter except the string scale $M_S$, so the Planck
scale $M_\text{Pl}$, the supersymmetry-breaking scale, the EW scale
$m_\text{EW}$ as well as the vacuum energy density (cosmological constant)
$\Lambda$ are to be determined dynamically at any local minimum solution in the
string theory landscape. Here we consider a model that links the supersymmetric
electroweak phenomenology (bottom up) to the string theory motivated flux
compactification approach (top down). In this model, supersymmetry is broken by
a combination of the racetrack K\"ahler uplift mechanism, which naturally
allows an exponentially small positive $\Lambda$ in a local minimum, and the
anti-D3-brane in the KKLT scenario. In the absence of the Higgs doublets in the
supersymmetric standard model, one has either a small $\Lambda$ or a big enough
SUSY-breaking scale, but not both. The introduction of the Higgs fields (with
their soft terms) allows a small $\Lambda$ and a big enough SUSY-breaking scale
simultaneously. Since an exponentially small $\Lambda$ is statistically
preferred (as the properly normalized probability distribution $P(\Lambda)$
diverges at $\Lambda=0^{+}$), identifying the observed $\Lambda_{\rm obs}$ to
the median value $\Lambda_{50\%}$ yields $m_{\rm EW} \sim 100$ GeV. We also
find that the warped anti-D3-brane tension has a SUSY-breaking scale of
$100m_{\rm EW}$ in the landscape while the SUSY-breaking scale that directly
correlates with the Higgs fields in the visible sector has a value of $m_{\rm
EW}$. |
Completion of standard-like embeddings: Inequivalent standard-like observable sector embeddings in $Z_3$ orbifolds
with two discrete Wilson lines, as determined by Casas, Mondragon and Mu\~noz,
are completed by examining all possible ways of embedding the hidden sector.
The hidden sector embeddings are relevant to twisted matter in nontrivial
representations of the Standard Model and to scenarios where supersymmetry
breaking is generated in a hidden sector. We find a set of 175 models which
have a hidden sector gauge group which is viable for dynamical supersymmetry
breaking. Only four different hidden sector gauge groups are possible in these
models. | Scalar charges and the first law of black hole thermodynamics: We present a variational formulation of Einstein-Maxwell-dilaton theory in
flat spacetime, when the asymptotic value of the scalar field is not fixed. We
obtain the boundary terms that make the variational principle well posed and
then compute the finite gravitational action and corresponding Brown-York
stress tensor. We show that the total energy has a new contribution that
depends of the asymptotic value of the scalar field and discuss the role of
scalar charges for the first law of thermodynamics. We also extend our analysis
to hairy black holes in Anti-de Sitter spacetime and investigate the
thermodynamics of an exact solution that breaks the conformal symmetry of the
boundary. |
Unimodular Gravity and the lepton anomalous magnetic moment at one-loop: We work out the one-loop contribution to the lepton anomalous magnetic moment
coming from Unimodular Gravity. We use Dimensional Regularization and
Dimensional Reduction to carry out the computations. In either case, we find
that Unimodular Gravity gives rise to the same one-loop correction as that of
General Relativity. | TFT construction of RCFT correlators IV: Structure constants and
correlation functions: We compute the fundamental correlation functions in two-dimensional rational
conformal field theory, from which all other correlators can be obtained by
sewing: the correlators of three bulk fields on the sphere, one bulk and one
boundary field on the disk, three boundary fields on the disk, and one bulk
field on the cross cap. We also consider conformal defects and calculate the
correlators of three defect fields on the sphere and of one defect field on the
cross cap.
Each of these correlators is presented as the product of a structure constant
and the appropriate conformal two- or three-point block. The structure
constants are expressed as invariants of ribbon graphs in three-manifolds. |
$T\bar{T}$ Flows and (2,2) Supersymmetry: We construct a solvable deformation of two-dimensional theories with $(2,2)$
supersymmetry using an irrelevant operator which is a bilinear in the
supercurrents. This supercurrent-squared operator is manifestly supersymmetric,
and equivalent to $T\bar{T}$ after using conservation laws. As illustrative
examples, we deform theories involving a single $(2,2)$ chiral superfield. We
show that the deformed free theory is on-shell equivalent to the $(2,2)$
Nambu-Goto action. At the classical level, models with a superpotential exhibit
more surprising behavior: the deformed theory exhibits poles in the physical
potential which modify the vacuum structure. This suggests that irrelevant
deformations of $T\overline{T}$ type might also affect infrared physics. | Closed String Tachyons on AdS Orbifolds and Dual Yang-Mills Instantons: We study the condensation of localized closed string tachyons on AdS
orbifolds both from the bulk and boundary theory viewpoints. We first extend
the known results for AdS_5/Z_k to AdS_3/Z_k case, and we proposed that the
AdS_3/Z_k decays into AdS_3/Z_k' with k' < k. From the bulk viewpoint, we
obtain a time-dependent gravity solution describing the decay of AdS orbifold
numerically. From the dual gauge theory viewpoint, we calculated the Casimir
energies of gauge theory vacua and it is found that their values are exactly
the same as the masses of dual geometries, even though they are in different
parameter regimes of 't Hooft coupling. We also consider AdS_5 orbifold. The
decay of AdS_5/Z_k is dual to the transition between the dual gauge theory
vacua on R_t x S^3/Z_k, parametrized by different holonomies along the
orbifolded spatial cycle. We constructed the instanton solutions describing the
transitions by making use of instanton solutions on R_t x S^2. |
Discrete Symmetry and GUT Breaking: We study the supersymmetric GUT models where the supersymmetry and GUT gauge
symmetry can be broken by the discrete symmetry. First, with the ansatz that
there exist discrete symmetries in the branes' neighborhoods, we discuss the
general reflection $Z_2$ symmetries and GUT breaking on $M^4\times M^1$ and
$M^4\times M^1\times M^1$. In those models, the extra dimensions can be large
and the KK states can be set arbitrarily heavy. Second, considering the extra
space manifold is the annulus $A^2$ or disc $D^2$, we can define any $Z_n$
symmetry and break any 6-dimensional N=2 supersymmetric SU(M) models down to
the 4-dimensional N=1 supersymmetric $SU(3)\times SU(2)\times U(1)^{M-4}$
models for the zero modes. In particular, there might exist the interesting
scenario on $M^4\times A^2$ where just a few KK states are light, while the
others are relatively heavy. Third, we discuss the complete global discrete
symmetries on $M^4\times T^2$ and study the GUT breaking. | Torsion in quantum field theory through time-loops on Dirac materials: Assuming dislocations could be meaningfully described by torsion, we propose
here a scenario based on the role of time in the low-energy regime of
two-dimensional Dirac materials, for which coupling of the fully antisymmetric
component of the torsion with the emergent spinor is not necessarily zero.
Appropriate inclusion of time is our proposal to overcome well-known
geometrical obstructions to such a program, that stopped further research of
this kind. In particular, our approach is based on the realization of an exotic
$time-loop$, that could be seen as oscillating particle-hole pairs. Although
this is a theoretical paper, we moved the first steps toward testing the
realization of these scenarios, by envisaging $Gedankenexperiments$ on the
interplay between an external electromagnetic field (to excite the pair
particle-hole and realize the time-loops), and a suitable distribution of
dislocations described as torsion (responsible for the measurable holonomy in
the time-loop, hence a current). Our general analysis here establishes that we
need to move to a nonlinear response regime. We then conclude by pointing to
recent results from the interaction laser-graphene that could be used to look
for manifestations of the torsion-induced holonomy of the time-loop, e.g., as
specific patterns of suppression/generation of higher harmonics. |
A World without Pythons would be so Simple: We show that bulk operators lying between the outermost extremal surface and
the asymptotic boundary admit a simple boundary reconstruction in the classical
limit. This is the converse of the Python's lunch conjecture, which proposes
that operators with support between the minimal and outermost (quantum)
extremal surfaces - e.g. the interior Hawking partners - are highly complex.
Our procedure for reconstructing this "simple wedge" is based on the HKLL
construction, but uses causal bulk propagation of perturbed boundary conditions
on Lorentzian timefolds to expand the causal wedge as far as the outermost
extremal surface. As a corollary, we establish the Simple Entropy proposal for
the holographic dual of the area of a marginally trapped surface as well as a
similar holographic dual for the outermost extremal surface. We find that the
simple wedge is dual to a particular coarse-grained CFT state, obtained via
averaging over all possible Python's lunches. An efficient quantum circuit
converts this coarse-grained state into a "simple state" that is
indistinguishable in finite time from a state with a local modular Hamiltonian.
Under certain circumstances, the simple state modular Hamiltonian generates an
exactly local flow; we interpret this result as a holographic dual of black
hole uniqueness. | Closed Bosonic String Field Theory at Quintic Order II: Marginal
Deformations and Effective Potential: We verify that the dilaton together with one exactly marginal field, form a
moduli space of marginal deformations of closed bosonic string field theory to
polynomial order five. We use the results of this successful check in order to
find the best functional form of a fit of quintic amplitudes. We then use this
fit in order to accurately compute the tachyon and dilaton effective potential
in the limit of infinite level. We observe that to order four, the effective
potential gives unexpectedly accurate results for the vacuum. We are thus led
to conjecture that the effective potential, to a given order, is a good
approximation to the whole potential including all interactions from the
vertices up to this order from the untruncated string field. We then go on and
compute the effective potential to order five. We analyze its vacuum structure
and find that it has several saddle points, including the Yang-Zwiebach vacuum,
but also a local minimum. We discuss the possible physical meanings of these
vacua. |
Constraints on a Massive Double-Copy and Applications to Massive Gravity: We propose and study a BCJ double-copy of massive particles, showing that it
is equivalent to a KLT formula with a kernel given by the inverse of a matrix
of massive bi-adjoint scalar amplitudes. For models with a uniform non-zero
mass spectrum we demonstrate that the resulting double-copy factors on physical
poles and that up to at least 5-particle scattering, color-kinematics
satisfying numerators always exist. For the scattering of 5 or more particles,
the procedure generically introduces spurious singularities that must be
cancelled by imposing additional constraints. When massive particles are
present, color-kinematics duality is not enough to guarantee a physical
double-copy. As an example, we apply the formalism to massive Yang-Mills and
show that up to 4-particle scattering the double-copy construction generates
physical amplitudes of a model of dRGT massive gravity coupled to a dilaton and
a two-form with dilaton parity violating couplings. We show that the spurious
singularities in the 5-particle double-copy do not cancel in this example, and
the construction fails to generate physically sensible amplitudes. We
conjecture sufficient constraints on the mass spectrum, which in addition to
massive BCJ relations, guarantee the absence of spurious singularities. | Nonlinear Transport in a Two Dimensional Holographic Superconductor: The problem of nonlinear transport in a two dimensional superconductor with
an applied oscillating electric field is solved by the holographic method. The
complex conductivity can be computed from the dynamics of the current for both
near- and non-equilibrium regimes. The limit of weak electric field corresponds
to the near equilibrium superconducting regime, where the charge response is
linear and the conductivity develops a gap determined by the condensate. A
larger electric field drives the system into a superconducting non-equilibrium
steady state, where the nonlinear conductivity is quadratic with respect to the
electric field. Keeping increasing the amplitude of applied electric field
results in a far-from-equilibrium non-superconducting steady state with a
universal linear conductivity of one. In lower temperature regime we also find
chaotic behavior of superconducting gap, which results in a non-monotonic field
dependent nonlinear conductivity. |
Functionals and the Quantum Master Equation: The quantum master equation is usually formulated in terms of functionals of
the components of mappings from a space-time manifold M into a
finite-dimensional vector space. The master equation is the sum of two terms
one of which is the anti-bracket (odd Poisson bracket) of functionals and the
other is the Laplacian of a functional. Both of these terms seem to depend on
the fact that the mappings on which the functionals act are vector-valued. It
turns out that neither this Laplacian nor the anti-bracket is well-defined for
sections of an arbitrary vector bundle. We show that if the functionals are
permitted to have their values in an appropriate graded tensor algebra whose
factors are the dual of the space of smooth functions on M, then both the
anti-bracket and the Laplace operator can be invariantly defined. Additionally,
one obtains a new anti-bracket for ordinary functionals. | On the Construction of SL(2,Z) Type IIB 5-Branes: This talk reviews our recent work on the construction of SL(2,Z) multiplets
of type IIB superfivebranes. We here pay particular attention to the methods
employed and some salient features of the solutions. |
Comments on I1-branes: We explore the supergravity solution of D5-branes intersecting as an
I1-brane. In a suitable near-horizon limit the geometry is in qualitative
agreement with that found in the microscopic open-string analysis as well as
the NS5-brane analysis of Itzhaki, Kutasov and Seiberg. In particular, the
ISO(1,1) Lorentz symmetry of the intersection domain is enhanced to ISO(1,2).
The discussion is generalised to the T-dual configuration of a D4-brane
intersecting a D6-brane. In this case the ISO(1,1) symmetry is not enhanced.
This is true both in the supergravity approximation to the weakly coupled
string theory and to the M-theory limit. | Upper bound on the Abelian gauge coupling from asymptotic safety: We explore the impact of asymptotically safe quantum gravity on the Abelian
gauge coupling in a model including a charged scalar, confirming indications
that asymptotically safe quantum fluctuations of gravity could trigger a
power-law running towards a free fixed point for the gauge coupling above the
Planck scale. Simultaneously, quantum gravity fluctuations balance against
matter fluctuations to generate an interacting fixed point, which acts as a
boundary of the basin of attraction of the free fixed point. This enforces an
upper bound on the infrared value of the Abelian gauge coupling. In the regime
of gravity couplings which in our approximation also allows for a prediction of
the top quark and Higgs mass close to the experimental value [1], we obtain an
upper bound approximately 35% above the infrared value of the hypercharge
coupling in the Standard Model. |
Free Boson Realization of $U_q(\widehat{sl_N})$: We construct a realization of the quantum affine algebra
$U_q(\widehat{sl_N})$ of an arbitrary level $k$ in terms of free boson fields.
In the $q\!\rightarrow\! 1$ limit this realization becomes the Wakimoto
realization of $\widehat{sl_N}$. The screening currents and the vertex
operators(primary fields) are also constructed; the former commutes with
$U_q(\widehat{sl_N})$ modulo total difference, and the latter creates the
$U_q(\widehat{sl_N})$ highest weight state from the vacuum state of the boson
Fock space. | The Off-Shell Boundary State and Cross-Caps in the Genus Expansion of
String Theory: We use the boundary state formalism for the bosonic string to calculate the
emission amplitude for closed string states from particular D-branes. We show
that the amplitudes obtained are exactly the same as those obtained from the
world-sheet sigma model calculation, and that the construction enforces the
requirement for integrated vertex operators, even in the off-shell case. Using
the expressions obtained for the boundary state we propose higher order terms
in the string loop expansion for the background considered. |
On the hydrodynamic attractor of Yang-Mills plasma: There is mounting evidence suggesting that relativistic hydrodynamics becomes
relevant for the physics of quark-gluon plasma as the result of nonhydrodynamic
modes decaying to an attractor apparent even when the system is far from local
equilibrium. Here we determine this attractor for Bjorken flow in N=4
supersymmetric Yang-Mills theory using Borel summation of the gradient
expansion of the expectation value of the energy momentum tensor. By comparing
the result to numerical simulations of the flow based on the AdS/CFT
correspondence we show that it provides an accurate and unambiguous
approximation of the hydrodynamic attractor in this system. This development
has important implications for the formulation of effective theories of
hydrodynamics. | Resurgence, Operator Product Expansion, and Remarks on Renormalons in
Supersymmetric Yang-Mills: I discuss similarities and differences between the resurgence program in
quantum mechanics and the operator product expansion in strongly coupled
Yang-Mills theories. In ${\mathcal N}=1$ super-Yang-Mills renormalons possess
peculiar features that make them different from renormalons in QCD. Their
conventional QCD interpretation does not seem to be applicable in
supersymmetric Yang-Mills in a straightforward manner. |
Black Holes and D-branes: D-branes have been used to describe many properties of extremal and near
extremal black holes. These lecture notes provide a short review of these
developments. | General self-tuning solutions and no-go theorem: We consider brane world models with one extra dimension. In the bulk there is
in addition to gravity a three form gauge potential or equivalently a scalar
(by generalisation of electric magnetic duality). We find classical solutions
for which the 4d effective cosmological constant is adjusted by choice of
integration constants. No go theorems for such self-tuning mechanism are
circumvented by unorthodox Lagrangians for the three form respectively the
scalar. It is argued that the corresponding effective 4d theory always includes
tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended
to a general class of models with unorthodox Lagrangians. |
Quantum mechanics on Riemannian Manifold in Schwinger's Quantization
Approach I: Schwinger's quantization scheme is extended in order to solve the problem of
the formulation of quantum mechanics on a space with a group structure. The
importance of Killing vectors in a quantization scheme is showed. Usage of
these vectors provides algebraic properties of operators to be consistent with
the geometrical structure of a manifold. The procedure of the definition of the
quantum Lagrangian of a free particle and the norm of velocity (momentum)
operators is given. These constructions are invariant under a general
coordinate transformation. The unified procedure for constructing the quantum
theory on a space with a group structure is developed. Using it quantum
mechanics on a Riemannian manifold with a simply transitive group acting on it
is investigated. | Black holes as quantum membranes: path integral approach: We describe the horizon of a quantum black hole in terms of a dynamical
surface which defines the boundary of space-time as seen by external static
observers, and we define a path integral in the presence of this dynamical
boundary. Using renormalization group arguments, we find that the dynamics of
the horizon is governed by the action of the relativistic bosonic membrane.
{}From the thermodynamical properties of this bosonic membrane we derive the
entropy and the temperature of black holes, and we find agreement with the
standard results. With this formalism we can also discuss the corrections to
the Hawking temperature when the mass $M$ of the black hole approaches the
Planck mass $M_{\rm Pl}$. When $M$ becomes as low as $(10-100) M_{\rm Pl}$ a
phase transition takes place and the specific heat of the black hole becomes
positive. |
Matrix model partition function by a single constraint: In the recent study of Virasoro action on characters, we discovered that it
gets especially simple for peculiar linear combinations of the Virasoro
operators: particular harmonics of $\hat w$-operators. In this letter, we
demonstrate that even more is true: a {\it single} $w$-constraint is sufficient
to uniquely specify the partition functions provided one assumes that it is a
power series in time-variables. This substitutes the previous specifications in
terms of {\it two} requirements: either a string equation imposed on the
KP/Toda $\tau$-function or a pair of Virasoro generators. This mysterious {\it
single}-entry definition holds for a variety of theories, including Hermitian
and complex matrix models, and also matrix models with external matrix: the
unitary and cubic Kontsevich models. In these cases, it is equivalent to
W-representation and is closely related to {\it super}\,integrability. However,
a similar single equation that completely determines the partition function
exists also in the case of the generalized Kontsevich model (GKM) with the
potential of higher degree, when the constraint algebra is a larger
$W$-algebra, and neither W-representation nor superintegrability are understood
well enough. | Brane World Dynamics and Conformal Bulk Fields: In the Randall-Sundrum scenario we investigate the dynamics of a spherically
symmetric 3-brane world when matter fields are present in the bulk. To analyze
the 5-dimensional Einstein equations we employ a global conformal
transformation whose factor characterizes the $Z_2$ symmetric warp. We find a
new set of exact dynamical collapse solutions which localize gravity in the
vicinity of the brane for a stress-energy tensor of conformal weight -4 and a
warp factor that depends only on the coordinate of the fifth dimension.
Geometries which describe the dynamics of inhomogeneous dust and generalized
dark radiation on the brane are shown to belong to this set. The conditions for
singular or globally regular behavior and the static marginally bound limits
are discussed for these examples. Also explicitly demonstrated is complete
consistency with the effective point of view of a 4-dimensional observer who is
confined to the brane and makes the same assumptions about the bulk degrees of
freedom. |
Deformation Quantization of Fermi Fields: Deformation quantization for any Grassmann scalar free field is described via
the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal
$\star$-product and the Wigner functional are obtained by extending the
formalism proposed recently in [35] to the fermionic systems of infinite number
of degrees of freedom. In particular, this formalism is applied to quantize the
Dirac free field. It is observed that the use of suitable oscillator variables
facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the
Moyal $\star$-product, the Wigner functional, the normal ordering operator, and
finally, the Dirac propagator have been found with the use of these variables. | The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized
Double Copy: We use the recently developed generalized double-copy procedure to construct
an integrand for the five-loop four-point amplitude of N=8 supergravity. This
construction starts from a naive double copy of the previously computed
corresponding amplitude of N=4 super-Yang-Mills theory. This is then
systematically modified by adding contact terms generated in the context of the
method of maximal unitarity cuts. For the simpler generalized cuts, whose
corresponding contact terms tend to be the most complicated, we derive a set of
formulas relating the contact contributions to the violations of the dual
Jacobi identities in the relevant gauge-theory amplitudes. For more complex
generalized unitarity cuts, which tend to have simpler contact terms associated
with them, we use the method of maximal cuts more directly. The five-loop
four-point integrand is a crucial ingredient towards future studies of
ultraviolet properties of N=8 supergravity at five loops and beyond. We also
present a nontrivial check of the consistency of the integrand, based on modern
approaches for integrating over the loop momenta in the ultraviolet region. |
Quantum Chains with $GL_q(2)$ Symmetry: Usually quantum chains with quantum group symmetry are associated with
representations of quantized universal algebras $U_q(g) $ . Here we propose a
method for constructing quantum chains with $C_q(G)$ global symmetry , where
$C_q(G)$ is the algebra of functions on the quantum group. In particular we
will construct a quantum chain with $GL_q(2)$ symmetry which interpolates
between two classical Ising chains.It is shown that the Hamiltonian of this
chain satisfies in the generalised braid group algebra. | Integrable systems and supersymmetric gauge theory: After the work of Seiberg and Witten, it has been seen that the dynamics of
N=2 Yang-Mills theory is governed by a Riemann surface $\Sigma$. In particular,
the integral of a special differential $\lambda_{SW}$ over (a subset of) the
periods of $\Sigma$ gives the mass formula for BPS-saturated states. We show
that, for each simple group $G$, the Riemann surface is a spectral curve of the
periodic Toda lattice for the dual group, $G^\vee$, whose affine Dynkin diagram
is the dual of that of $G$. This curve is not unique, rather it depends on the
choice of a representation $\rho$ of $G^\vee$; however, different choices of
$\rho$ lead to equivalent constructions. The Seiberg-Witten differential
$\lambda_{SW}$ is naturally expressed in Toda variables, and the N=2 Yang-Mills
pre-potential is the free energy of a topological field theory defined by the
data $\Sigma_{\gg,\rho}$ and $\lambda_{SW}$. |
Deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3
from supersymmetric matrix quantum mechanics: We test the recent claim that supersymmetric matrix quantum mechanics with
mass deformation preserving maximal supersymmetry can be used to study N=4
super Yang-Mills theory on RxS^3 in the planar limit. When the mass parameter
is large, we can integrate out all the massive fluctuations around a particular
classical solution, which corresponds to RxS^3. The resulting effective theory
for the gauge field moduli at finite temperature is studied both analytically
and numerically, and shown to reproduce the deconfinement phase transition in
N=4 super Yang-Mills theory on RxS^3 at weak coupling. This transition was
speculated to be a continuation of the conjectured phase transition at strong
coupling, which corresponds to the Hawking-Page transition based on the
gauge-gravity duality. By choosing a different classical solution of the same
model, one can also reproduce results for gauge theories on other space-time
such as RxS^3/Z_q and RxS^2. All these theories can be studied at strong
coupling by the new simulation method, which was used successfully for
supersymmetric matrix quantum mechanics without mass deformation. | The elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ and its bosonization
at level one: We extend the work of Foda et al and propose an elliptic quantum algebra
$A_{q,p}(\hat {sl_n})$. Similar to the case of $A_{q,p}(\hat {sl_2})$, our
presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and
$R^*$ are $Z_n$ symmetric R-matrices with the elliptic moduli chosen
differently and a factor is also involved. With the help of the results
obtained by Asai et al, we realize type I and type II vertex operators in terms
of bosonic free fields for $Z_n$ symmetric Belavin model. We also give a
bosonization for the elliptic quantum algebra $A_{q,p}(\hat {sl_n})$ at level
one. |
The theory of superstring with flux on non-Kahler manifolds and the
complex Monge-Ampere equation: The purpose of this paper is to solve a problem posed by Strominger in
constructing smooth models of superstring theory with flux. These are given by
non-Kahler manifolds with torsion. | Path Integral Junctions: We propose path integral description for quantum mechanical systems on
compact graphs consisting of N segments of the same length. Provided the bulk
Hamiltonian is segment-independent, scale-invariant boundary conditions given
by self-adjoint extension of a Hamiltonian operator turn out to be in
one-to-one correspondence with N \times N matrix-valued weight factors on the
path integral side. We show that these weight factors are given by
N-dimensional unitary representations of the infinite dihedral group. |
Wess-Zumino Terms for Relativistic Fluids, Superfluids, Solids, and
Supersolids: We use the coset construction of low-energy effective actions to
systematically derive Wess-Zumino (WZ) terms for fluid and isotropic solid
systems in two, three and four spacetime dimensions. We recover the known WZ
term for fluids in two dimensions as well as the very recently found WZ term
for fluids in three dimensions. We find two new WZ terms for supersolids that
have not previously appeared in the literature. In addition, by relaxing
certain assumptions about the symmetry group of fluids we find a number of new
WZ terms for fluids with and without charge, in all dimensions. We find no WZ
terms for solids and superfluids. | Deformed Intersecting D6-Brane GUTS I: By employing D6-branes intersecting at angles in $D = 4$ type IIA strings, we
construct {\em four stack string GUT models} (PS-I class), that contain at low
energy {\em exactly the three generation Standard model} with no extra matter
and/or extra gauge group factors. These classes of models are based on the
Pati-Salam (PS) gauge group $SU(4)_C \times SU(2)_L \times SU(2)_R$. They
represent deformations around the quark and lepton basic intersection number
structure. The models possess the same phenomenological characteristics of some
recently discussed examples (PS-A class) of four stack PS GUTS. Namely, there
are no colour triplet couplings to mediate proton decay and proton is stable as
baryon number is a gauged symmetry. Neutrinos get masses of the correct sizes.
Also the mass relation
$m_e = m_d$ at the GUT scale is recovered.
Moreover, we clarify the novel role of {\em extra} branes, the latter having
non-trivial intersection numbers with quarks and leptons and creating scalar
singlets, needed for the satisfaction of RR tadpole cancellation conditions.
The presence of N=1 supersymmetry in sectors involving the {\em extra} branes
is equivalent to the, model dependent, orthogonality conditions of the U(1)'s
surviving massless the generalized Green-Schwarz mechanism.
The use of
{\em extra} branes creates mass couplings that predict the appearance of
light fermion doublets up to the scale of electroweak scale symmetry breaking. |
Note on Quantum Periods and a TBA-like System: There is an interesting relation between the quantum periods on a certain
limit of local $\mathbb{P}^1\times \mathbb{P}^1$ Calabi-Yau space and a TBA
(Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM
(Aharony-Bergman-Jafferis-Maldacena) theory. We propose a one-parameter
generalization of the relation. Furthermore, we derive the differential
operators for quantum periods and the TBA-like equation in various limits of
the generalized relation. | Notes on nonabelian (0,2) theories and dualities: In this paper we explore basic aspects of nonabelian (0,2) GLSM's in two
dimensions for unitary gauge groups, an arena that until recently has largely
been unexplored. We begin by discussing general aspects of (0,2) theories,
including checks of dynamical supersymmetry breaking, spectators and weak
coupling limits, and also build some toy models of (0,2) theories for bundles
on Grassmannians, which gives us an opportunity to relate physical anomalies
and trace conditions to mathematical properties. We apply these ideas to study
(0,2) theories on Pfaffians, applying recent perturbative constructions of
Pfaffians of Jockers et al. We discuss how existing dualities in (2,2)
nonabelian gauge theories have a simple mathematical understanding, and make
predictions for additional dualities in (2,2) and (0,2) gauge theories.
Finally, we outline how duality works in open strings in unitary gauge
theories, and also describe why, in general terms, we expect analogous
dualities in (0,2) theories to be comparatively rare. |
Fock-space projection operators for semi-inclusive final states: We present explicit expressions for Fock-space projection operators that
correspond to realistic final states in scattering experiments. Our operators
automatically sum over unobserved quanta and account for non-emission into
sub-regions of momentum space. | Conformal Symmetry in Field Theory and in Quantum Gravity: Conformal symmetry always played an important role in field theory (both
quantum and classical) and in gravity. We present construction of quantum
conformal gravity and discuss its features regarding scattering amplitudes and
quantum effective action. First, the long and complicated story of
UV-divergences is recalled. With the development of UV-finite higher derivative
(or non-local) gravitational theory, all problems with infinities and spacetime
singularities are solved. Moreover, the non-local quantum conformal theory
reveals itself to be ghost-free, so the unitarity of the theory is safe. After
the construction of UV-finite theory, we focused on making it manifestly
conformally invariant using the dilaton trick. We also argue that in this class
of theories conformal anomaly vanishes by fine-tuning the couplings. As
applications of this theory, the constraints of the conformal symmetry on the
form of the effective action and on the scattering amplitudes are shown. We
also remark about the preservation of the unitarity bound for scattering.
Finally, the old model of conformal supergravity by Fradkin and Tseytlin is
briefly presented. |
Non-Abelian Vortices in N=1* Gauge Theory: We consider the N=1* supersymmetric SU(2) gauge theory and demonstrate that
the Z_2 vortices in this theory acquire orientational zero modes, associated
with the rotation of magnetic flux inside SU(2) group, and turn into the
non-Abelian strings, when the masses of all chiral fields become equal. These
non-Abelian strings are not BPS-saturated. We study the effective theory on the
string world sheet and show that it is given by two-dimensional
non-supersymmetric O(3) sigma model. The confined 't Hooft-Polyakov monopole is
seen as a junction of the Z_2-string and anti-string, and as a kink in the
effective world sheet sigma model. We calculate its mass and show that besides
the four-dimensional confinement of monopoles, they are also confined in the
two-dimensional theory: the monopoles stick to anti-monopoles to form the
meson-like configurations on the strings they are attached to. | $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear
$σ$-models: A new symmetry of $(1,0)$ supersymmetric non-linear $\sigma$-models in two
dimensions with Fermi and mass sectors is introduced. It is a generalisation of
the so-called special holonomy $W$-symmetry of Howe and Papadopoulos associated
with structure group reductions of the target space $\mathcal{M}$. Our symmetry
allows in particular non-trivial flux and instanton-like connections on vector
bundles over $\mathcal{M}$. We also investigate potential anomalies and show
that cohomologically non-trivial terms in the quantum effective action are
invariant under a corrected version of our symmetry. Consistency with heterotic
supergravity at first order in $\alpha'$ is manifest and discussed. |
3D gravity, point particles and deformed symmetries: It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons
theory, with the gauge group given by the local isometry group, depending on
the metric signature and the cosmological constant. Point particles are added
into spacetime as (spinning) conical defects. Then, in principle, one may
integrate out the gravitational degrees of freedom to obtain the effective
particle action; the most interesting consequence is that the momentum space of
a particle turns out to be curved. This is still not completely understood in
the case of non-zero cosmological constant. | CFTs on Non-Critical Braneworlds: We examine the cosmological evolution equations of de Sitter, flat and
anti-de Sitter braneworlds sandwiched in between two n dimensional
AdS-Schwarzschild spacetimes. We are careful to use the correct form for the
induced Newton's constant on the brane, and show that it would be naive to
assume the energy of the bulk spacetime is just given by the sum of the black
hole masses. By carefully calculating the energy of the bulk for large mass we
show that the induced geometry of the braneworld is just a radiation dominated
FRW universe with the radiation coming from a CFT that is dual to the AdS bulk. |
Holographic computation of Wilson loops in a background with broken
conformal invariance and finite chemical potential: In this paper, we follow a `bottom-up' AdS/QCD approach to holographically
probe the dynamics of a moving $q\bar{q}$ pair inside a strongly coupled plasma
at the boundary. We consider a deformed AdS-Reissner Nordstr\"om metric in the
bulk in order to introduce nonconformality and finite quark density in the dual
field theory. By boosting the gravity solution in a specific direction we
consider two extreme cases of orientation, parallel and perpendicular, for the
Wilson loop which in turn fixes the relative position of the $q\bar{q}$ pair
with respect to the direction of boost in the plasma. By utilizing this set-up,
we holographically compute the vacuum expectation value of the time-like Wilson
loop in order to obtain real part of the $q\bar{q}$ potential and the effects
of nonconformality (deformation parameter $c$), chemical potential $\mu$ and
rapidity $\beta$ are observed on this potential. We then compute the in-medium
energy loss of the moving parton (jet quenching parameter $q_m$) by setting
$\beta\rightarrow\infty$ which in turn makes the Wilson loop light-like. We
also use the jet quenching as an order parameter to probe the strongly-coupled
domain of the dual field theory. Finally, we compute the imaginary part of the
$q\bar{q}$ potential ($\mathrm{Im}(V_{q\bar{q}})$) by considering the thermal
fluctuation (arbitrary long wavelength) of the string world-sheet. It is
observed that for fixed values of the chemical potential and rapidity, increase
in the nonconformality parameter leads to an increase in the real and imaginary
potentials as well as the jet quenching parameter. | D-instanton, threshold corrections, and topological string: In this note, we prove that the one-loop pfaffian of the non-perturbative
superpotential generated by Euclidean D-branes in type II compactifications on
orientifolds of Calabi-Yau threefolds is determined by the moduli integral of
the new supersymmetric index defined by Cecotti, Fendley, Intriligator, and
Vafa. As this quantity can be computed via topological string theory,
Chern-Simons theory, matrix models, or by solving the holomorphic anomaly
equation, this result provides a method to directly compute the one-loop
pfaffian of the non-perturbative superpotential. The relation between the
one-loop pfaffian, threshold corrections to the gauge coupling, and the
one-loop partition function of open topological string theory is discussed. |
Exact Multi-Instanton Solutions to Selfdual Yang-Mills Equation on
Curved Spaces: We find exact multi-instanton solutions to the selfdual Yang-Mills equation
on a large class of curved spaces with $SO(3)$ isometry, generalizing the
results previously found on $\mathbb{R}^4$. The solutions are featured with
explicit multi-centered expressions and topological properties. As examples, we
demonstrate the approach on several different curved spaces, including the
Einstein static universe and $\mathbb{R} \times$ dS$_3^E$, and show that the
exact multi-instanton solutions exist on these curved backgrounds. | (2+1)-Dimensional Yang-Mills Theory and Form Factor Perturbation Theory: We study Yang Mills theory in 2+1 dimensions, as an array of coupled
(1+1)-dimensional principal chiral sigma models. This can be understood as an
anisotropic limit where one of the space-time dimensions is discrete and the
others are continuous. The $SU(N)\times SU(N)$ principal chiral sigma model in
1+1 dimensions is integrable, asymptotically free and has massive excitations.
New exact form factors and correlation functions of the sigma model have
recently been found by the author and P. Orland. In this paper, we use these
new results to calculate physical quantities in (2+1)-dimensional Yang-Mills
theory, generalizing previous $SU(2)$ results by Orland, which include the
string tensions and the low-lying glueball spectrum. We also present a new
approach to calculate two-point correlation functions of operators using the
light glueball states. The anisotropy of the theory yields different
correlation functions for operators separated in the $x^1$ and
$x^2$-directions. |
Orbifold Constructions of K3: A Link between Conformal Field Theory and
Geometry: We discuss geometric aspects of orbifold conformal field theories in the
moduli space of N=(4,4) superconformal field theories with central charge c=6.
Part of this note consists of a summary of our earlier results on the location
of these theories within the moduli space [NW01,Wen] and the action of a
specific version of mirror symmetry on them [NW]. We argue that these results
allow for a direct translation from geometric to conformal field theoretic
data. Additionally, this work contains a detailed discussion of an example
which allows the application of various versions of mirror symmetry on K3. We
show that all of them agree in that point of the moduli space. | Holographic Hierarchy in the Gaussian Matrix Model via the Fuzzy Sphere: The Gaussian Hermitian matrix model was recently proposed to have a dual
string description with worldsheets mapping to a sphere target space. The
correlators were written as sums over holomorphic (Belyi) maps from worldsheets
to the two-dimensional sphere, branched over three points. We express the
matrix model correlators by using the fuzzy sphere construction of matrix
algebras, which can be interpreted as a string field theory description of the
Belyi strings. This gives the correlators in terms of trivalent ribbon graphs
that represent the couplings of irreducible representations of su(2), which can
be evaluated in terms of 3j and 6j symbols. The Gaussian model perturbed by a
cubic potential is then recognised as a generating function for Ponzano-Regge
partition functions for 3-manifolds having the worldsheet as boundary, and
equipped with boundary data determined by the ribbon graphs. This can be viewed
as a holographic extension of the Belyi string worldsheets to membrane
worldvolumes, forming part of a holographic hierarchy linking, via the large N
expansion, the zero-dimensional QFT of the Matrix model to 2D strings and 3D
membranes. |
Mass-Deformed Bagger-Lambert Theory and its BPS Objects: We find a sixteen supersymmetric mass-deformed Bagger-Lambert theory with
$SO(4)\times SO(4)$ global R-symmetry. The R-charge plays the `non-central'
term in the superalgebra. This theory has one symmetric vacuum and two
in-equivalent broken sectors of vacua. Each sector of the broken symmetry has
the SO(4) geometry. We find the 1/2 BPS domain walls connecting the symmetric
phase and any broken phase, and 1/4 BPS supertube-like objects, which may
appear as anyonic q-balls in the symmetric phase or vortices in the broken
phase. We also discuss mass deformations which reduces the number of
supersymmetries. | Penrose Limit of AdS_4 x V_{5,2} and Operators with Large R Charge: We consider M-theory on AdS_4 x V_{5,2} where V_{5,2}= SO(5)/SO(3) is a
Stiefel manifold. We construct a Penrose limit of AdS_4 x V_{5,2} that provides
the pp-wave geometry. There exists a subsector of three dimensional N=2 dual
gauge theory, by taking both the conformal dimension and R charge large with
the finiteness of their difference, which has enhanced N=8 maximal
supersymmetry. We identify operators in the N=2 gauge theory with supergravity
KK excitations in the pp-wave geometry and describe how the gauge theory
operators made out of chiral field of conformal dimension 1/3 fall into N=8
supermultiplets. |
Quantum Hall Liquid on a Noncommutative Superplane: Supersymmetric quantum Hall liquids are constructed on a noncommutative
superplane.
We explore a supersymmetric formalism of the Landau problem. In the lowest
Landau level, there appear spin-less bosonic states and spin-1/2 down fermionic
states, which exhibit a super-chiral property. It is shown the Laughlin
wavefunction and topological excitations have their superpartners. Similarities
between supersymmetric quantum Hall systems and bilayer quantum Hall systems
are discussed. | Brane Configurations and 4D Field Theory Dualities: We study brane configurations which correspond to field theories in four
dimension with N=2 and N=1 supersymmetry. In particular we discuss brane
motions that translate to Seiberg's duality in N=1 models recently studied by
Elitzur, Giveon and Kutasov. We investigate, using the brane picture, the
moduli spaces of the dual theories. Deformations of these models like mass
terms and vacuum expectation values of scalar fields can be identified with
positions of branes. The map of these deformations between the electric and
dual magnetic theories is clarified. The models we study reproduce known field
theory results and we provide an example of new dual pairs with N=1
supersymmetry. Possible relations between brane configurations and
non-supersymmetric field theories are discussed. |
Superfluous Physics: A superweapon of modern physics superscribes a wide superset of phenomena,
ranging from supernumerary rainbows to superfluidity and even possible
supermultiplets. | Canonical approach to the WZNW model: The chiral Wess-Zumino-Novikov-Witten (WZNW) model provides the simplest
class of rational conformal field theories which exhibit a non-abelian
braid-group statistics and an associated "quantum symmetry". The canonical
derivation of the Poisson-Lie symmetry of the classical chiral WZNW theory
(originally studied by Faddeev, Alekseev, Shatashvili and Gawedzki, among
others) is reviewed along with subsequent work on a covariant quantization of
the theory which displays its quantum group symmetry. |
Finite size effect from classical strings in $AdS_3 \times S^3$ with
NS-NS flux: We study the finite size effect of rigidly rotating strings and closed folded
strings in $AdS_3\times S^3$ geometry with NS-NS B-field. We calculate the
classical exponential corrections to the dispersion relation of infinite size
giant magnon and single spike in terms of Lambert $\mathbf{W}-$function. We
also write the analytic expression for the dispersion relation of finite size
Gubser-Klebanov-Polyakov (GKP) string in the form of Lambert
$\mathbf{W}-$function. | Open spin chains for giant gravitons and relativity: We study open spin chains for strings stretched between giant graviton states
in the N=4 SYM field theory in the collective coordinate approach. We study the
boundary conditions and the effective Hamiltonian of the corresponding spin
chain to two loop order.
The ground states of the spin chain have energies that match the relativistic
dispersion relation characteristic of massive W boson particles on the
worldvolume of the giant graviton configurations, up to second order in the
limit where the momentum is much larger than the mass. We find evidence for a
non-renormalization theorem for the ground state wave function of this spin
chain system. We also conjecture a generalization of this result to all loop
orders which makes it compatible with a fully relativistic dispersion relation.
We show that the conjecture follows if one assumes that the spin chain admits a
central charge extension that is sourced by the giant gravitons, generalizing
the giant magnon dispersion relation for closed string excitations. This
provides evidence for ten dimensional local physics mixing AdS directions and
the five-sphere emerging from an N=4 SYM computation in the presence of a
non-trivial background (made of D-branes) that break the conformal field theory
of the system. |
D=6 massive spinning particle: The massive spinning particle in six-dimensional Minkowski space is described
as a mechanical system with the configuration space ${\ R}% ^{5,1}\times {\
CP}^3$. The action functional of the model is unambigiously determined by the
requirement of identical (off-shell) conservation for the phase-space
counterparts of three Casimir operators of Poincar\'e group. The model is shown
to be exactly solvable. Canonical quantization of the model leads to the
equations on wave functions which prove to be equivalent to the relativistic
wave equations for the irreducible $6d$ fields. | Nonlocal regularisation of noncommutative field theories: We study noncommutative field theories, which are inherently nonlocal, using
a Poincar\'e-invariant regularisation scheme which yields an effective,
nonlocal theory for energies below a cut-off scale. After discussing the
general features and the peculiar advantages of this regularisation scheme for
theories defined in noncommutative spaces, we focus our attention onto the
particular case when the noncommutativity parameter is inversely proportional
to the square of the cut-off, via a dimensionless parameter $\eta$. We work out
the perturbative corrections at one-loop order for a scalar theory with quartic
interactions, where the signature of noncommutativity appears in
$\eta$-dependent terms. The implications of this approach, which avoids the
problems related to UV-IR mixing, are discussed from the perspective of the
Wilson renormalisation program. Finally, we remark about the generality of the
method, arguing that it may lead to phenomenologically relevant predictions,
when applied to realistic field theories. |
The Fate of Monsters in Anti-de Sitter Spacetime: Black hole entropy remains a deep puzzle: where does such enormous amount of
entropy come from? Curiously, there exist gravitational configurations that
possess even larger entropy than a black hole of the same mass, in fact,
arbitrarily high entropy. These are the so-called monsters, which are
problematic to the Anti-de Sitter/Conformal Field Theory (AdS/CFT)
correspondence paradigm since there is far insufficient degrees of freedom on
the field theory side to account for the enormous entropy of monsters in AdS
bulk. The physics of the bulk however may be considerably modified at
semi-classical level due to the presence of branes. We show that this is
especially so since monster spacetimes are unstable due to brane nucleation. As
a consequence, it is not clear what the final fate of monsters is. We argue
that in some cases there is no real threat from monsters since although they
are solutions to Einstein's Field Equations, they are very likely to be
completely unstable when embedded in string theory, and thus probably are not
solutions to the full quantum theory of gravity. Our analysis, while suggestive
and supportive of the claim that such pathological objects are not allowed in
the final theory, by itself does not rule out all monsters. We comment on
various kin of monsters such as the bag-of-gold spacetime, and also discuss
briefly the implications of our work to some puzzles related to black hole
entropy. | Relative scale separation in orbifolds of $S^2$ and $S^5$: In orbifold vacua containing an $S^q/\Gamma$ factor, we compute the relative
order of scale separation, $r$, defined as the ratio of the eigenvalue of the
lowest-lying $\Gamma$-invariant state of the scalar Laplacian on $S^q$, to the
eigenvalue of the lowest-lying state. For $q=2$ and $\Gamma$ finite subgroup of
$SO(3)$, or $q=5$ and $\Gamma$ finite subgroup of $SU(3)$, the maximal relative
order of scale separation that can be achieved is $r=21$ or $r=12$,
respectively. For smooth $S^5$ orbifolds, the maximal relative scale separation
is $r=4.2$. Methods from invariant theory are very efficient in constructing
$\Gamma$-invariant spherical harmonics, and can be readily generalized to other
orbifolds. |
Chiral symmetry in $SU(N_c)$ gauge theories at high density: We study $SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless
staggered fermions in the presence of quark chemical potential $\mu$. A recent
exact result that in the strong coupling limit (vanishing inverse gauge
coupling $\beta$) and for sufficiently large $\mu$ the theory is in a chiral
symmetric phase is here extended into the finite gauge coupling region. A
cluster expansion combining a fermion spacelike hopping expansion and a strong
coupling plaquette expansion is shown to converge for sufficiently large $\mu$
and small $\beta$ at any temperature $T$. All expectations of chirally
non-invariant local fermion operators vanish identically, or, equivalently,
their correlations cluster exponentially within the expansion implying absence
of spontaneous chiral symmetry breaking. The resulting phase at low $T$ may be
described as a "quarkyonic" matter phase. Some implications for the phase
diagram of $SU(N_c)$ theories are discussed. | D-Strings on D-Manifolds: We study the mechanism for appearance of massless solitons in type II string
compactifications. We find that by combining $T$-duality with strong/weak
duality of type IIB in 10 dimensions enhanced gauge symmetries and massless
solitonic hypermultiplets encountered in Calabi-Yau compactifications can be
studied perturbatively using D-strings (the strong/weak dual to type IIB
string) compactified on ``D-manifolds''. In particular the nearly massless
solitonic states of the type IIB compactifications correspond to elementary
states of D-strings. As examples we consider the D-string description of
enhanced gauge symmetries for type IIA string compactification on ALE spaces
with $A_n$ singularities and type IIB on a class of singular Calabi-Yau
threefolds. The class we study includes as a special case the conifold
singularity in which case the perturbative spectrum of the D-string includes
the expected massless hypermultiplet with degeneracy one. |
A Monte-Carlo study of the AdS/CFT correspondence: an exploration of
quantum gravity effects: In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge
group U(N), compactified on S^3 in four dimensions using Monte-Carlo
techniques. The simulation is based on a particular reduction of degrees of
freedom to commuting matrices of constant fields, and in particular, we can
write the wave functions of these degrees of freedom exactly. The square of the
wave function is equivalent to a probability density for a Boltzman gas of
interacting particles in six dimensions. From the simulation we can extract the
density particle distribution for each wave function, and this distribution can
be interpreted as a special geometric locus in the gravitational dual. Studying
the wave functions associated to half-BPS giant gravitons, we are able to show
that the matrix model can measure the Planck scale directly. We also show that
the output of our simulation seems to match various theoretical expectations in
the large N limit and that it captures 1/N effects as statistical fluctuations
of the Boltzman gas with the expected scaling. Our results suggest that this is
a very promising approach to explore quantum corrections and effects in
gravitational physics on AdS spaces. | The LHC String Hunter's Companion (II): Five-Particle Amplitudes and
Universal Properties: We extend the study of scattering amplitudes presented in ``The LHC String
Hunter's Companion'' to the case of five-point processes that may reveal the
signals of low mass strings at the LHC and are potentially useful for detailed
investigations of fundamental Regge excitations. In particular, we compute the
full-fledged string disk amplitudes describing all 2->3 parton scattering
subprocesses leading to the production of three hadronic jets. We cast our
results in a form suitable for the implementation of stringy partonic cross
sections in the LHC data analysis. We discuss the universal, model-independent
features of multi-parton processes and point out the existence of even stronger
universality relating N-gluon amplitudes to the amplitudes involving N-2 gluons
and one quark-antiquark pair. We construct a particularly simple basis of two
functions describing all universal five-point amplitudes. We also discuss
model-dependent amplitudes involving four fermions and one gauge boson that may
be relevant for studying jets associated to Drell-Yan pairs and other processes
depending on the spectrum of Kaluza-Klein particles, thus on the geometry of
compact dimensions. |
Super-exceptional geometry: origin of heterotic M-theory and
super-exceptional embedding construction of M5: In the quest for the mathematical formulation of M-theory, we consider three
major open problems: a first-principles construction of the single (abelian)
M5-brane Lagrangian density, the origin of the gauge field in heterotic
M-theory, and the supersymmetric enhancement of exceptional M-geometry. By
combining techniques from homotopy theory and from supergeometry to what we
call super-exceptional geometry within super-homotopy theory, we present an
elegant joint solution to all three problems. This leads to a unified
description of the Nambu-Goto, Perry-Schwarz, and topological Yang-Mills
Lagrangians in the topologically nontrivial setting. After explaining how
charge quantization of the C-field in Cohomotopy reveals D'Auria-Fre's "hidden
supergroup" of 11d supergravity as the super-exceptional target space, in the
sense of Bandos, for M5-brane sigma-models, we prove, in exceptional
generalization of the doubly-supersymmetric super-embedding formalism, that a
Perry-Schwarz-type Lagrangian for single (abelian) M5-branes emerges as the
super-exceptional trivialization of the M5-brane cocycle along the
super-exceptional embedding of the "half" M5-brane locus, super-exceptionally
compactified on the Horava-Witten circle fiber. From inspection of the
resulting 5d super Yang-Mills Lagrangian we find that the extra fermion field
appearing in super-exceptional M-geometry, whose physical interpretation had
remained open, is the M-theoretic avatar of the gaugino field. | A note on noncommutative scalar multisolitons: We prove that there do not exist multisoliton solutions of noncommutative
scalar field theory in the Moyal plane which interpolate smoothly between $n$
overlapping solitons and $n$ solitons with an infinite separation. |
On-shell constructibility of Born amplitudes in spontaneously broken
gauge theories: We perform a comprehensive study of on-shell recursion relations for Born
amplitudes in spontaneously broken gauge theories and identify the minimal
shifts required to construct amplitudes with a given particle content and spin
quantum numbers. We show that two-line or three-line shifts are sufficient to
construct all amplitudes with five or more particles, apart from amplitudes
involving longitudinal vector bosons or scalars, which may require at most
five-line shifts. As an application, we revisit selection rules for multi-boson
amplitudes using on-shell recursion and little-group transformations. | Finite Temperature Effects for Massive Fields in D-dimensional
Rindler-like Spaces: The first quantum corrections to the free energy for massive fields in
$D$-dimensional space-times of the form $\R\times\R^+\times\M^{N-1}$, where
$D=N+1$ and $\M^{N-1}$ is a constant curvature manifold, is investigated by
means of the $\zeta$-function regularization. It is suggested that the nature
of the divergences, which are present in the thermodynamical quantities, might
be better understood making use of the conformal related optical metric and
associated techniques. The general form of the horizon divercences of the free
energy is obtained as a function of free energy densities of fields having
negative square masses (absence of the gap in the Laplace operator spectrum) on
ultrastatic manifolds with hyperbolic spatial section $H^{N-2n}$ and of the
Seeley-DeWitt coefficients of the Laplace operator on the manifold $\M^{N-1}$.
Furthermore, recurrence relations are found relating higher and lower
dimensions. The cases of Rindler space, where $\M^{N-1}=\R^{N-1}$ and very
massive $D$-dimensional black holes, where $\M^{N-1}=S^{N-1}$ are treated as
examples. The renormalization of the internal energy is also discussed. |
The non-planar contribution to the four-loop anomalous dimension of
twist-2 operators: first moments in N=4 SYM and non-singlet QCD: We present the result of a full direct component calculation for the first
three even moments of the non-planar contribution into the four-loop anomalous
dimension of twist-2 operators in maximally extended N=4 supersymmetric
Yang-Mills theory. Obtained result complete our previous calculations in
arXiv:0902.4646 and gives the usual result for the higher moments on the
contrary to degenerate one in the case of Konishi. We have proposed a general
form of zeta(5) and zeta(3) parts of the full non-planar anomalous dimension of
twist-2 operators. As by product, we have obtained the first moment of the
non-planar contribution to the non-singlet four-loop anomalous dimension of
Wilson twist-2 operators in QCD. | Numerical determination of the entanglement entropy for a Maxwell field
in the cylinder: We calculate numerically the logarithmic contribution to the entanglement
entropy of a cylindrical region in three spatial dimensions for a Maxwell
field. Our result does not agree with the analytical predictions concerning any
conformal field theory in four dimensions according to which the coefficient is
universal and proportional to the type c conformal anomaly. In cylindrical
coordinates the problem decomposes into one dimensional ones along the radial
coordinate for each angular momentum. The entanglement entropy of a Maxwell
field is equivalent to the one of two identical decoupled scalars with an extra
self interaction term. |
Analytic Solutions for Tachyon Condensation with General Projectors: The tachyon vacuum solution of Schnabl is based on the wedge states, which
close under the star product and interpolate between the identity state and the
sliver projector. We use reparameterizations to solve the long-standing problem
of finding an analogous family of states for arbitrary projectors and to
construct analytic solutions based on them. The solutions simplify for special
projectors and allow explicit calculations in the level expansion. We test the
solutions in detail for a one-parameter family of special projectors that
includes the sliver and the butterfly. Reparameterizations further allow a
one-parameter deformation of the solution for a given projector, and in a
certain limit the solution takes the form of an operator insertion on the
projector. We discuss implications of our work for vacuum string field theory. | Physical Properties of Four Dimensional Superstring Gravity Black Hole
Solutions: We consider the physical properties of four dimensional black hole solutions
to the effective action describing the low energy dynamics of the gravitational
sector of heterotic superstring theory. We compare the properties of the
external field strengths in the perturbative solution to the full $O(\alpha')$
string effective action equations, to those of exact solutions in a truncated
action for charged black holes, and to the Kerr-Newman family of solutions of
Einstein-Maxwell theory. We contrast the numerical results obtained in these
approaches, and discuss limitations of the analyses. Finally we discuss how the
new features of classical string gravity affect the standard tests of general
relativity. |
Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter: All solvable two-dimensional quantum gravity models have non-trivial BRST
cohomology with vanishing ghost number. These states form a ring and all the
other states in the theory fall into modules of this ring. The relations in the
ring and in the modules have a physical interpretation. The existence of these
rings and modules leads to nontrivial constraints on the correlation functions
and goes a long way toward solving these theories in the continuum approach. | Vector boson scattering and boundary conditions in Kaluza-Klein toy
model: We study a simple higher-dimensional toy model of electroweak symmetry
breaking, in particular a pure gauge 5D theory on flat background with one
extra finite space dimension. The principle of least action and the requirement
of gauge independence of scattering amplitudes are used to determine the
possible choices of boundary conditions. We demonstrate that for any of these
choices the scattering amplitudes of vector bosons do not exhibit power-like
growth in the high energy limit. Our analysis is an extension and
generalization of the results obtained previously by other authors. |
The geometry of W3 algebra: a twofold way for the rebirth of a symmetry: The purpose of this note is to show that W3 algebras originate from an
unusual interplay between the breakings of the reparametrization invariance
under the diffemorphism action on the cotangent bundle of a Riemann surface. It
is recalled how a set of smooth changes of local complex coordinates on the
base space are collectively related to a background within a symplectic
framework. The power of the method allows to calculate explicitly some primary
fields whose OPEs generate the algebra as explicit functions in the
coordinates: this is achieved only if well defined conditions are satisfied,
and new symmetries emerge from the construction. Moreoverer, when primary
flelds are introduced outside of a coordinate description the W3 symmetry
byproducts acquire a good geometrical definition with respect to holomorphic
changes of charts. | Dyon degeneracies from Mathieu moonshine: We construct the Siegel modular forms associated with the theta lift of
twisted elliptic genera of $K3$ orbifolded with $g'$ corresponding to the
conjugacy classes of the Mathieu group $M_{24}$. We complete the construction
for all the classes which belong to $M_{23} \subset M_{24}$ and two other
classes outside the subgroup $M_{23}$. For this purpose we provide the explicit
expressions for all the twisted elliptic genera in all the sectors of these
classes.
We show that the Siegel modular forms satisfy the required properties for
them to be generating functions of $1/4$ BPS dyons of type II string theories
compactified on $K3\times T^2$ and orbifolded by $g'$ which acts as a
$\mathbb{Z}_N$ automorphism on $K3$ together with a $1/N$ shift on a circle of
$T^2$. In particular the inverse of these Siegel modular forms admit a Fourier
expansion with integer coefficients together with the right sign as predicted
from black hole physics. Our analysis completes the construction of the
partition function for dyons as well as the twisted elliptic genera for all the
$7$ CHL compactifications. |
Multi-band structure of the quantum bound states for a generalized
nonlinear Schrodinger model: By using the method of coordinate Bethe ansatz, we study N-body bound states
of a generalized nonlinear Schrodinger model having two real coupling constants
c and \eta. It is found that such bound states exist for all possible values of
c and within several nonoverlapping ranges (called bands) of \eta. The ranges
of \eta within each band can be determined completely using Farey sequences in
number theory. We observe that N-body bound states appearing within each band
can have both positive and negative values of the momentum and binding energy. | The Swampland: Introduction and Review: The Swampland program aims to distinguish effective theories which can be
completed into quantum gravity in the ultraviolet from those which cannot. This
article forms an introduction to the field, assuming only a knowledge of
quantum field theory and general relativity. It also forms a comprehensive
review, covering the range of ideas that are part of the field, from the Weak
Gravity Conjecture, through compactifications of String Theory, to the de
Sitter conjecture. |
A Modified Cosmic Brane Proposal for Holographic Renyi Entropy: We propose a new formula for computing holographic Renyi entropies in the
presence of multiple extremal surfaces. Our proposal is based on computing the
wave function in the basis of fixed-area states and assuming a diagonal
approximation for the Renyi entropy. For Renyi index $n\geq1$, our proposal
agrees with the existing cosmic brane proposal for holographic Renyi entropy.
For $n<1$, however, our proposal predicts a new phase with leading order (in
Newton's constant $G$) corrections to the cosmic brane proposal, even far from
entanglement phase transitions and when bulk quantum corrections are
unimportant. Recast in terms of optimization over fixed-area states, the
difference between the two proposals can be understood to come from the order
of optimization: for $n<1$, the cosmic brane proposal is a minimax prescription
whereas our proposal is a maximin prescription. We demonstrate the presence of
such leading order corrections using illustrative examples. In particular, our
proposal reproduces existing results in the literature for the PSSY model and
high-energy eigenstates, providing a universal explanation for previously found
leading order corrections to the $n<1$ Renyi entropies. | Topological modes in relativistic hydrodynamics: We show that gapless modes in relativistic hydrodynamics could become
topologically nontrivial by weakly breaking the conservation of energy momentum
tensor in a specific way. This system has topological semimetal-like crossing
nodes in the spectrum of hydrodynamic modes that require the protection of a
special combination of translational and boost symmetries in two spatial
directions. We confirm the nontrivial topology from the existence of an
undetermined Berry phase. These energy momentum non-conservation terms could
naturally be produced by an external gravitational field that comes from a
reference frame change from the original inertial frame, i.e. by fictitious
forces in a non-inertial reference frame. This non-inertial frame is the rest
frame of an accelerating observer moving along a trajectory of a helix. This
suggests that topologically trivial modes could become nontrivial by being
observed in a special non-inertial reference frame, and this fact could be
verified in laboratories, in principle. Finally, we propose a holographic
realization of this system. |
On the Statistical Origin of Topological Symmetries: We investigate a quantum system possessing a parasupersymmetry of order 2, an
orthosupersymmetry of order $p$, a fractional supersymmetry of order $p+1$, and
topological symmetries of type $(1,p)$ and $(1,1,...,1)$. We obtain the
corresponding symmetry generators, explore their relationship, and show that
they may be expressed in terms of the creation and annihilation operators for
an ordinary boson and orthofermions of order $p$. We give a realization of
parafermions of order~2 using orthofermions of arbitrary order $p$, discuss a
$p=2$ parasupersymmetry between $p=2$ parafermions and parabosons of arbitrary
order, and show that every orthosupersymmetric system possesses topological
symmetries. We also reveal a correspondence between the orthosupersymmetry of
order $p$ and the fractional supersymmetry of order $p+1$. | On ADE Quiver Models and F-Theory Compactification: Based on mirror symmetry, we discuss geometric engineering of N=1 ADE quiver
models from F-theory compactifications on elliptic K3 surfaces fibered over
certain four-dimensional base spaces. The latter are constructed as
intersecting 4-cycles according to ADE Dynkin diagrams, thereby mimicking the
construction of Calabi-Yau threefolds used in geometric engineering in type II
superstring theory. Matter is incorporated by considering D7-branes wrapping
these 4-cycles. Using a geometric procedure referred to as folding, we discuss
how the corresponding physics can be converted into a scenario with D5-branes
wrapping 2-cycles of ALE spaces. |
M-brane interpolations and (2,0) Renormalization Group flow: We obtain the M5-M2-MW bound state solutions of 11-dimensional supergravity
corresponding to the 1/2 supersymmetric vacua of the M5-brane equations with
constant background fields. In the `near-horizon' case the solution
interpolates between the $adS_7\times S^4$ Kaluza-Klein vacuum and D=11
Minkowski spacetime via a Domain Wall spacetime. We discuss implications for
renormalization group flow of (2,0) D=6 field theories. | Finite size effects in classical string solutions of the Schrodinger
geometry: We study finite size corrections to the semiclassical string solutions of the
Schrodinger spacetime. We compute the leading order exponential corrections to
the infinite size dispersion relation of the single spin giant magnon and of
the single spin single spike solutions. The solutions live in a $S^3$ subspace
of the five-sphere and extent in the Schrodinger part of the metric. In the
limit of zero deformation the finite size dispersion relations flow to the
undeformed $AdS_5 \times S^5$ counterparts and in the infinite size limit the
correction term vanishes and the known infinite size dispersion relations are
obtained. |
QCD with Bosonic Quarks at Nonzero Chemical Potential: We formulate the low energy limit of QCD like partition functions with
bosonic quarks at nonzero chemical potential. The partition functions are
evaluated in the parameter domain that is dominated by the zero momentum modes
of the Goldstone fields. We find that partition functions with bosonic quarks
differ structurally from partition functions with fermionic quarks. Contrary to
the theory with one fermionic flavor, where the partition function in this
domain does not depend on the chemical potential, a phase transition takes
place in the theory with one bosonic flavor when the chemical potential is
equal to $m_\pi/2$. For a pair of conjugate bosonic flavors the partition
function shows no phase transition, whereas the fermionic counterpart has a
phase transition at $\mu = m_\pi/2$. The difference between the bosonic
theories and the fermionic ones originates from the convergence requirements of
bosonic integrals resulting in a noncompact Goldstone manifold and a covariant
derivative with the commutator replaced by an anti-commutator. | Rotating Spacetimes with Asymptotic Non-Flat Structure and the
Gyromagnetic Ratio: In general relativity, the gyromagnetic ratio for all stationary,
axisymmetric and asymptotically flat Einstein-Maxwell fields is known to be
g=2. In this paper, we continue our previous works of examination this result
for rotating charged spacetimes with asymptotic non-flat structure. We first
consider two instructive examples of these spacetimes: The spacetime of a
Kerr-Newman black hole with a straight cosmic string on its axis of symmetry
and the Kerr-Newman Taub-NUT spacetime. We show that for both spacetimes the
gyromagnetic ratio g=2 independent of their asymptotic structure. We also
extend this result to a general class of metrics which admit separation of
variables for the Hamilton-Jacobi and wave equations. We proceed with the study
of the gyromagnetic ratio in higher dimensions by considering the general
solution for rotating charged black holes in minimal five-dimensional gauged
supergravity. We obtain the analytic expressions for two distinct gyromagnetic
ratios of these black holes that are associated with their two independent
rotation parameters. These expressions reveal the dependence of the
gyromagnetic ratio on both the curvature radius of the AdS background and the
parameters of the black holes: The mass, electric charge and two rotation
parameters. We explore some special cases of interest and show that when the
two rotation parameters are equal to each other and the rotation occurs at the
maximum angular velocity, the gyromagnetic ratio g=4 regardless of the value of
the electric charge. This agrees precisely with our earlier result obtained for
general Kerr-AdS black holes with a test electric charge. We also show that in
the BPS limit the gyromagnetic ratio for a supersymmetric black hole with equal
rotation parameters ranges between 2 and 4. |
LIV Dimensional Regularization and Quantum Gravity effects in the
Standard Model: Recently, we have remarked that the main effect of Quantum Gravity(QG) will
be to modify the measure of integration of loop integrals in a renormalizable
Quantum Field Theory. In the Standard Model this approach leads to definite
predictions, depending on only one arbitrary parameter. In particular, we found
that the maximal attainable velocity for particles is not the speed of light,
but depends on the specific couplings of the particles within the Standard
Model. Also birrefringence occurs for charged leptons, but not for gauge
bosons. Our predictions could be tested in the next generation of neutrino
detectors such as NUBE. In this paper, we elaborate more on this proposal. In
particular, we extend the dimensional regularization prescription to include
Lorentz invariance violations(LIV) of the measure, preserving gauge invariance.
Then we comment on the consistency of our proposal. | Euclidean Path Integral of the Gauge Field -- Holomorphic Representation: Basing on the canonical quantization of a BRS invariant Lagrangian, we
construct holomorphic representation of path integrals for Faddeev-Popov(FP)
ghosts as well as for unphysical degrees of the gauge field from covariant
operator formalism. A thorough investigation of a simple soluble gauge model
with finite degrees will explain the metric structure of the Fock space and
constructions of path integrals for quantized gauge fields with FP ghosts. We
define fermionic coherent states even for a Fock space equipped with indefinite
metric to obtain path integral representations of a generating functional and
an effective action. The same technique will also be developed for path
integrals of unphysical degrees in the gauge field to find complete
correspondence, that insures cancellation of FP determinant, between FP ghosts
and unphysical components of the gauge field. As a byproduct, we obtain an
explicit form of Kugo-Ojima projection, $P^{(n)}$, to the subspace with
$n$-unphysical particles in terms of creation and annihilation operators for
the abelian gauge theory. |
Vertical D4-D2-D0 bound states on K3 fibrations and modularity: An explicit formula is derived for the generating function of vertical
D4-D2-D0 bound states on smooth K3 fibered Calabi-Yau threefolds, generalizing
previous results of Gholampour and Sheshmani. It is also shown that this
formula satisfies strong modularity properties, as predicted by string theory.
This leads to a new construction of vector valued modular forms which exhibits
some of the features of a generalized Hecke transform. | Deformed integrable $σ$-models, classical $R$-matrices and
classical exchange algebra on Drinfel'd doubles: We describe a unifying framework for the systematic construction of
integrable deformations of integrable $\sigma$-models within the Hamiltonian
formalism. It applies equally to both the `Yang-Baxter' type as well as `gauged
WZW' type deformations which were considered recently in the literature. As a
byproduct, these two families of integrable deformations are shown to be
Poisson-Lie T-dual of one another. |
Lax pairs for deformed Minkowski spacetimes: We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based
on a conformal embedding. We first revisit a Melvin background and argue a Lax
pair by adopting a simple replacement law invented in 1509.00173. This argument
enables us to deduce a general expression of Lax pair. Then the anticipated Lax
pair is shown to work for arbitrary classical $r$-matrices with Poinca\'e
generators. As other examples, we present Lax pairs for pp-wave backgrounds,
the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background. | Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate: The rate of entropy production in a classical dynamical system is
characterized by the Kolmogorov-Sinai entropy rate $h_{\mathrm{KS}}$ given by
the sum of all positive Lyapunov exponents of the system. We prove a quantum
version of this result valid for bosonic systems with unstable quadratic
Hamiltonian. The derivation takes into account the case of time-dependent
Hamiltonians with Floquet instabilities. We show that the entanglement entropy
$S_A$ of a Gaussian state grows linearly for large times in unstable systems,
with a rate $\Lambda_A \leq h_{KS}$ determined by the Lyapunov exponents and
the choice of the subsystem $A$. We apply our results to the analysis of
entanglement production in unstable quadratic potentials and due to periodic
quantum quenches in many-body quantum systems. Our results are relevant for
quantum field theory, for which we present three applications: a scalar field
in a symmetry-breaking potential, parametric resonance during post-inflationary
reheating and cosmological perturbations during inflation. Finally, we
conjecture that the same rate $\Lambda_A$ appears in the entanglement growth of
chaotic quantum systems prepared in a semiclassical state. |
Phase Transitions in NJL and super-NJL models: An elementary method of determination of the character of the hot phase
transition in 4d four-fermion NJL-type models is applied to non-supersymmetric
and supersymmetric versions of simple NJL model. We find that in the non-susy
case the transition is usually of the second order. It is weakly first order
only in the region of parameters which correspond to fermion masses comparable
to the cut-off. In the supersymmetric case both kinds of phase transitions are
possible. For sufficiently strong coupling and sufficiently large susy-breaking
scale the transition is always of the first order. | Ghost inflation and de Sitter entropy: In the setup of ghost condensation model the generalized second law of black
hole thermodynamics can be respected under a radiatively stable assumption that
couplings between the field responsible for ghost condensate and matter fields
such as those in the Standard Model are suppressed by the Planck scale. Since
not only black holes but also cosmology are expected to play important roles
towards our better understanding of gravity, we consider a cosmological setup
to test the theory of ghost condensation. In particular we shall show that the
de Sitter entropy bound proposed by Arkani-Hamed, et.al. is satisfied if ghost
inflation happened in the early epoch of our universe and if there remains a
tiny positive cosmological constant in the future infinity. We then propose a
notion of cosmological Page time after inflation. |
Bootstrapping gauge theories: We consider asymptotically free gauge theories with gauge group $SU(N_c)$ and
$N_f$ quarks with mass $m_q\ll \Lambda_{\text{QCD}}$ that undergo chiral
symmetry breaking and confinement. We propose a bootstrap method to compute the
S-matrix of the pseudo-Goldstone bosons (pions) that dominate the low energy
physics. For the important case of $N_c=3$, $N_f=2$, a numerical implementation
of the method gives the phase shifts of the $S0$, $P1$ and $S2$ waves in good
agreement with experimental results. The method incorporates gauge theory
information ($N_c$, $N_f$, $m_q$, $\Lambda_{\text{QCD}}$) by using the
form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones
together with a finite energy version of the SVZ sum rules. At low energy we
impose constraints from chiral symmetry breaking. The only low energy numerical
inputs are the pion mass $m_\pi$ and the quark and gluon condensates. | The Two-Loop Euler-Heisenberg Lagrangian in Dimensional Renormalization: We clarify a discrepancy between two previous calculations of the two-loop
QED Euler-Heisenberg Lagrangian, both performed in proper-time regularization,
by calculating this quantity in dimensional regularization. |
Strong Coupling BCS Superconductivity and Holography: We attempt to give a holographic description of the microscopic theory of a
BCS superconductor. Exploiting the analogy with chiral symmetry breaking in QCD
we use the Sakai-Sugimoto model of two D8 branes in a D4 brane background with
finite baryon number. In this case there is a new tachyonic instability which
is plausibly the bulk analog of the Cooper pairing instability. We analyze the
Yang-Mills approximation to the non-Abelian Born-Infeld action. We give some
exact solutions of the non-linear Yang-Mills equations in flat space and also
give a stability analysis, showing that the instability disappears in the
presence of an electric field. The holograhic picture also suggests a
dependence of $T_c$ on the number density which is different from the usual
(weak coupling) BCS. The flat space solutions are then generalized to curved
space numerically and also, in an approximate way, analytically. This
configuration should then correspond to the ground state of the boundary
superconducting (superfluid) ground state. We also give some preliminary
results on Green functions computations in the Sakai - Sugimoto model without
any chemical potential | Spectral representation of the shear viscosity for local scalar QFTs at
finite temperature: In local scalar quantum field theories (QFTs) at finite temperature
correlation functions are known to satisfy certain non-perturbative
constraints, which for two-point functions in particular implies the existence
of a generalisation of the standard K\"{a}ll\'{e}n-Lehmann representation. In
this work, we use these constraints in order to derive a spectral
representation for the shear viscosity arising from the thermal asymptotic
states, $\eta_{0}$. As an example, we calculate $\eta_{0}$ in $\phi^{4}$
theory, establishing its leading behaviour in the small and large coupling
regimes. |
Four-dimensional M-theory and supersymmetry breaking: We investigate compactifications of M-theory from $11\to 5\to 4$ dimensions
and discuss geometrical properties of 4-d moduli fields related to the
structure of 5-d theory. We study supersymmetry breaking by compactification of
the fifth dimension and find that an universal superpotential is generated for
the axion-dilaton superfield $S$. The resulting theory has a vacuum with
$<S>=1$, zero cosmological constant and a gravitino mass depending on the fifth
radius as $m_{3/2} \sim R_5^{-2}/M_{Pl}$. We discuss phenomenological aspects
of this scenario, mainly the string unification and the decompactification
problem. | A new exactly solvable Eckart-type potential: A new exact analytically solvable Eckart-type potential is presented, a
generalisation of the Hulthen potential. The study through Supersymmetric
Quantum Mechanics is presented together with the hierarchy of Hamiltonians and
the shape invariance property. |
Convexity and Liberation at Large Spin: We consider several aspects of unitary higher-dimensional conformal field
theories (CFTs). We first study massive deformations that trigger a flow to a
gapped phase. Deep inelastic scattering in the gapped phase leads to a
convexity property of dimensions of spinning operators of the original CFT. We
further investigate the dimensions of spinning operators via the crossing
equations in the light-cone limit. We find that, in a sense, CFTs become free
at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys
additivity: if two twists tau_1, tau_2 appear in the spectrum, there are
operators whose twists are arbitrarily close to tau_1+tau_2. We characterize
how tau_1+tau_2 is approached at large spin by solving the crossing equations
analytically. We find the precise form of the leading correction, including the
prefactor. We compare with examples where these observables were computed in
perturbation theory, or via gauge-gravity duality, and find complete agreement.
The crossing equations show that certain operators have a convex spectrum in
twist space. We also observe a connection between convexity and the ratio of
dimension to charge. Applications include the 3d Ising model, theories with a
gravity dual, SCFTs, and patterns of higher spin symmetry breaking. | Covariantly Quantized Spinning Particle and its Possible Connection to
Non-Commutative Space-Time: Covariant quantization of the Nambu-Goto spinning particle in 2+1-dimensions
is studied. The model is relevant in the context of recent activities in
non-commutative space-time. From a technical point of view also covariant
quantization of the model poses an interesting problem: the set of second class
constraints (in the Dirac classification scheme) is {\it reducible}. The
reducibility problem is analyzed from two contrasting approaches: (i) the
auxiliary variable method [bn] and (ii) the projection operator method [blm].
Finally in the former scheme, a Batalin-Tyutin quantization has been done. This
induces a mapping between the non-commutative and the ordinary space-time. BRST
quantization programme in the latter scheme has also been discussed. |
T-duality and The Gravitational Description Of Gauge Theories: This is a review of some basic features on the relation between supergravity
and pure gauge theories with special emphasis on the relation between T-duality
and supersymmetry. Some new results concerning the interplay between T-duality
and near horizon geometries are presented | 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories: We propose 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories. From a
Higgsing of the $SO(7)$ gauge theory with a hypermultiplet in the spinor
representation, we construct two types of 5-brane web configurations for the
pure $G_2$ gauge theory using an O5-plane or an $\widetilde{\text{O5}}$-plane.
Adding flavors to the 5-brane web for the pure $G_2$ gauge theory is also
discussed. Based on the obtained 5-brane webs, we compute the partition
functions for the 5d $G_2$ gauge theories using the recently suggested
topological vertex formulation with an O5-plane, and we find agreement with
known results. |
Split Supersymmetry Breaking from Stuckelberg Mixing of Multiple U(1)'s: We show that multiple Abelian sectors with Stuckelberg mass-mixing simply
break supersymmetry via Fayet-Iliopoulos D-terms and straightforwardly mediate
it to the other sectors. This mechanism naturally realizes a split
supersymmetry spectrum for soft parameters. Scalar squared-masses (holomorphic
and non-holomorphic) are induced through sizable portals and are not
suppressed. Gaugino masses, a-terms and a mu-like term are generated by
higher-dimensional operators and are suppressed. The hypercharge is mixed with
extra U(1)'s, it's D-term in non-vanishing and supersymmetry is broken in the
visible sector too. Scalar tachyonic directions are removed by unsuppressed
interactions and hypercharge is preserved as supersymmetry is broken. Moreover,
if a singlet chiral field is charged under additional $U(1)$'s proportional to
its hypercharge, new interaction terms in the Kahler potential and the
superpotential are added through Stuckelberg compensation. In this case
supersymmetry is broken via F-terms or mixed F and D-terms. | The Hamilton-Jacobi Equation and Holographic Renormalization Group Flows
on Sphere: We study the Hamilton-Jacobi formulation of effective mechanical actions
associated with holographic renormalization group flows when the field theory
is put on the sphere and mass terms are turned on. Although the system is
supersymmetric and it is described by a superpotential, Hamilton's
characteristic function is not readily given by the superpotential when the
boundary of AdS is curved. We propose a method to construct the solution as a
series expansion in scalar field degrees of freedom. The coefficients are
functions of the warp factor to be determined by a differential equation one
obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We
also show how the solution can be derived from the BPS equations without having
to solve differential equations. The characteristic function readily provides
information on holographic counterterms which cancel divergences of the
on-shell action near the boundary of AdS. |
Local E(11) and the gauging of the trombone symmetry: In any dimension, the positive level generators of the very-extended
Kac-Moody algebra $E_{11}$ with completely antisymmetric spacetime indices are
associated to the form fields of the corresponding maximal supergravity. We
consider the local $E_{11}$ algebra, that is the algebra obtained enlarging
these generators of $E_{11}$ in such a way that the global $E_{11}$ symmetries
are promoted to gauge symmetries. These are the gauge symmetries of the
corresponding massless maximal supergravity. We show the existence of a new
type of deformation of the local $E_{11}$ algebra, which corresponds to the
gauging of the symmetry under rescaling of the fields. In particular, we show
how the gauged IIA theory of Howe, Lambert and West is obtained from an
eleven-dimensional group element that only depends on the eleventh coordinate
via a linear rescaling. We then show how this results in ten dimensions in a
deformed local $E_{11}$ algebra of a new type. | Multicritical hypercubic models: We study renormalization group multicritical fixed points in the
$\epsilon$-expansion of scalar field theories characterized by the symmetry of
the (hyper)cubic point group $H_N$. After reviewing the algebra of
$H_N$-invariant polynomials and arguing that there can be an entire family of
multicritical (hyper)cubic solutions with $\phi^{2n}$ interactions in
$d=\frac{2n}{n-1}-\epsilon$ dimensions, we use the general multicomponent beta
functionals formalism to study the special cases $d = 3-\epsilon$ and $d
=\frac{8}{3}-\epsilon$, deriving explicitly the beta functions describing the
flow of three- and four-critical (hyper)cubic models. We perform a study of
their fixed points, critical exponents and quadratic deformations for various
values of $N$, including the limit $N=0$, that was reported in another paper in
relation to the randomly diluted single-spin models, and an analysis of the
large $N$ limit, which turns out to be particularly interesting since it
depends on the specific multicriticality. We see that, in general, the
continuation in $N$ of the random solutions is different from the continuation
coming from large-$N$, and only the latter interpolates with the physically
interesting cases of low-$N$ such as $N=3$. Finally, we also include an
analysis of a theory with quintic interactions in $d =\frac{10}{3}-\epsilon$
and, for completeness, the NNLO computations in $d=4-\epsilon$. |
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