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Self-dual vortex-like configurations in SU(2) Yang-Mills Theory: We show that there are solutions of the SU(2) Yang-Mills classical equations
of motion in R^4, which are self-dual and vortex-like(fluxons). The action
density is concentrated along a thick two-dimensional wall (the world sheet of
a straight infinite vortex line). The configurations are constructed from
self-dual R^2 x T^2 configurations. | Avoiding Haag's theorem with parameterized quantum field theory: Under the normal assumptions of quantum field theory, Haag's theorem states
that any field unitarily equivalent to a free field must itself be a free
field. Unfortunately, the derivation of the Dyson series perturbation expansion
relies on the use of the interaction picture, in which the interacting field is
unitarily equivalent to the free field but must still account for interactions.
Thus, the traditional perturbative derivation of the scattering matrix in
quantum field theory is mathematically ill defined. Nevertheless, perturbative
quantum field theory is currently the only practical approach for addressing
scattering for realistic interactions, and it has been spectacularly successful
in making empirical predictions. This paper explains this success by showing
Haag's Theorem can be avoided when quantum field theory is formulated using an
invariant, fifth path parameter in addition to the usual four position
parameters, such that the Dyson perturbation expansion for the scattering
matrix can still be reproduced. As a result, the parameterized formalism
provides a consistent foundation for the interpretation of quantum field theory
as used in practice and, perhaps, for better dealing with other mathematical
issues. |
Structure constants for the D-series Virasoro minimal models: In this paper expressions are given for the bulk and boundary structure
constants of D-series Virasoro minimal models on the upper half plane. It is
the continuation of an earlier work on the A-series. The solution for the
boundary theory is found first and then extended to the bulk. The modular
invariant bulk field content is recovered as the maximal set of bulk fields
consistent with the boundary theory. It is found that the structure constants
are unique up to redefinition of the fields and in the chosen normalisation
exhibit a manifest Z_2-symmetry associated to the D-diagram. The solution has
been subjected to random numerical tests against the constraints it has to
fulfill. | Brane-Antibrane Dynamics From the Tachyon DBI Action: The Tachyon-Dirac-Born-Infeld (TDBI) action captures some aspects of the
dynamics of non-BPS D-branes in type II string theory. We show that it can also
be used to study the classical interactions of BPS branes and antibranes. Our
analysis sheds light on real time D-Dbar tachyon condensation, on the proposal
that the tachyon field can be thought of as an extra spatial dimension whose
role is similar to the radial direction in holography, and on A. Sen's open
string completeness conjecture. |
Braneworld solutions from scalar field in bimetric theory: We investigate the presence of braneworld solutions in a bimetric theory,
with gravity and the scalar field coupling differently. We consider a
non-standard model, with a Cuscuton-like scalar field, and we show how to
generate braneworld solutions in this new scenario. In particular, we found no
gravitational instabilities for the braneworld solutions. | Eternal Chaotic Inflation is Prohibited by Weak Gravity Conjecture: We investigate whether the eternal chaotic inflation can be achieved when the
weak gravity conjecture is taken into account. We show that even the assisted
chaotic inflation with potential $\lambda\phi^4$ or $m^2\phi^2$ can not be
eternal. The effective field theory description for the inflaton field breaks
down before inflation reaches the eternal regime. We also find that the total
number of e-folds is still bounded by the inflationary entropy for the assisted
inflation. |
Group Theoretical Approach to the Construction of Conformal Field
Theories: A conformal field theory (CFT) is a quantum field theory which is invariant
under conformal transformations; a group action that preserve angles but not
necessarily lengths. There are two traditional approaches to the construction
of CFTs: analyzing a statistical system near a critical point as a euclidean
field theory, and in holographic duality within the context of string theory.
This pedagogical paper presents a construction of CFTs using purely group
theoretic techniques. Starting with the basic definition of a Lie algebra and
quantum field theory, we generalize to affine Lie algebras and form a energy
momentum tensor via the Sugawara construction. | Conformal Blocks of Coset Construction: Zero Ghost Number: It is shown that zero ghost conformal blocks of coset theory G/H are
determined uniquely by those of G and H theories. G/G theories are considered
as an example, their structure constants and correlation functions on sphere
are calculated. |
New local symmetry for QED in two dimensions: A new local, covariant and nilpotent symmetry is shown to exist for the
interacting BRST invariant U(1) gauge theory in two dimensions of space-time.
Under this new symmetry, it is the gauge-fixing term that remains invariant and
the corresponding transformations on the Dirac fields turn out to be the
analogue of chiral transformations. The extended BRST algebra is derived for
the generators of all the underlying symmetries, present in the theory. This
algebra turns out to be the analogue of the algebra obeyed by the de Rham
cohomology operators of differential geometry. Possible interpretations and
implications of this symmetry are pointed out in the context of BRST cohomology
and Hodge decomposition theorem. | Long Multiplet Bootstrap: Applications of the bootstrap program to superconformal field theories
promise unique new insights into their landscape and could even lead to the
discovery of new models. Most existing results of the superconformal bootstrap
were obtained form correlation functions of very special fields in short (BPS)
representations of the superconformal algebra. Our main goal is to initiate a
superconformal bootstrap for long multiplets, one that exploits all constraints
from superprimaries and their descendants. To this end, we work out the Casimir
equations for four-point correlators of long multiplets of the two-dimensional
global $\mathcal{N}=2$ superconformal algebra. After constructing the full set
of conformal blocks we discuss two different applications. The first one
concerns two-dimensional (2,0) theories. The numerical bootstrap analysis we
perform serves a twofold purpose, as a feasibility study of our long multiplet
bootstrap and also as an exploration of (2,0) theories. A second line of
applications is directed towards four-dimensional $\mathcal{N}=3$ SCFTs. In
this context, our results imply a new bound $c \geqslant \tfrac{13}{24}$ for
the central charge of such models, which we argue cannot be saturated by an
interacting SCFT. |
A $\hbar$-deformation of the $W_{N}$ algebra and its vertex operators: In this paper,we derive a $\hbar$-deformation of the $W_{N}$ algebra and its
quantum Miura tranformation. The vertex operators for this $\hbar$-deformed
$W_{N}$ algebra and its commutation relations are also obtained. | Integral expression for a topological charge in the Faddeev-Niemi
non-linear sigma model: We have introduced Faddeev-Niemi type variables for static SU(3) Yang-Mills
theory. The variables suggest that a non-linear sigma model whose sigma fields
take values in SU(3)/(U(1)xU(1)) and SU(3)/(SU(2)xU(1)) may be relevant to
infrared limit of the theory. Shabanov showed that the energy functional of the
non-linear sigma model is bounded from below by certain functional. However,
the Shabanov's functional is not homotopy invariant, and its value can be an
arbitrary real number -- therefore it is not a topological charge. Since the
third homotopy group of SU(3)/(U(1)xU(1)) is isomorphic to the group of integer
numbers, there is a non-trivial topological charge (given by the isomorphism).
We apply Novikov's procedure to obtain integral expression for this charge. The
resulting formula is analogous to the Whitehead's realization of the Hopf
invariant. |
Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons: We investigate the existence of double copy structure, or the lack thereof,
in higher derivative operators for Nambu-Goldstone bosons. At the leading
${\cal O}(p^2)$, tree amplitudes of Nambu-Goldstone bosons in the adjoint
representation can be (trivially) expressed as the double copy of itself and
the cubic bi-adjoint scalar theory, through the Kawai-Lewellen-Tye bilinear
kernel. At the next-to-leading ${\cal O}(p^4)$ there exist four operators in
general, among which we identify one operator whose amplitudes exhibit the
flavor-kinematics duality and can be written as the double copy of ${\cal
O}(p^2)$ Nambu-Goldstone amplitudes and the Yang-Mills+$\phi^3$ theory,
involving both gluons and gauged cubic bi-adjoint scalars. The specific
operator turns out to coincide with the scalar ${\cal O}(p^4)$ operator in the
so-called extended Dirac-Born-Infeld theory, for which the aforementioned
double copy relation holds more generally. | Drinfel'd algebra deformations, homotopy comodules and the associahedra: The aim of this work is to construct a cohomology theory controlling the
deformations of a general Drinfel'd algebra. The task is accomplished in three
steps. The first step is the construction of a modified cobar complex adapted
to a non-coassociative comultiplication. The following two steps each involve a
new, highly non-trivial, construction. The first construction, essentially
combinatorial, defines a differential graded Lie algebra structure on the
simplicial chain complex of the associahedra. The second construction, of a
more algebraic nature, is the definition of map of differential graded Lie
algebras from the complex defined above to the algebra of derivations on the
bar resolution. Using the existence of this map and the acyclicity of the
associahedra we can define a so-called homotopy comodule structure on the bar
resolution of a general Drinfeld algebra. This in turn allows us to define the
desired cohomology theory in terms of a complex which consists, roughly
speaking, of the bimodule and bicomodule maps from the bar resolution to the
modified cobar resolution. The complex is bigraded but not a bicomplex as in
the Gerstenhaber-Schack theory for bialgebra deformations. The new components
of the coboundary operator are defined via the constructions mentioned above.
As an application we show that the Drinfel'd deformation of the universal
enveloping algebra of a simple Lie algebra is not a jump deformation. The
results of the paper were announced in the paper "Drinfel'd algebra
deformations and the associahedra" (IMRN, Duke Math. Journal, 4(1994), 169-176,
appeared also as preprint hep-th/9312196). |
Dynamics of a Dirac Fermion in the presence of spin noncommutativity: Recently, it has been proposed a spacetime noncommutativity that involves
spin degrees of freedom, here called "spin noncommutativity". One of the
motivations for such a construction is that it preserves Lorentz invariance,
which is deformed or simply broken in other approaches to spacetime
noncommutativity. In this work, we gain further insight in the physical aspects
of the spin noncommutativity. The noncommutative Dirac equation is derived from
an action principle, and it is found to lead to the conservation of a modified
current, which involves the background electromagnetic field. Finally, we study
the Landau problem in the presence of spin noncommutativity. For this scenario
of a constant magnetic field, we are able to derive a simple Hermitean
non-commutative correction to the Hamiltonian operator, and show that the
degeneracy of the excited states is lifted by the noncommutativity at the
second order or perturbation theory. | The semiclassical limit of W_N CFTs and Vasiliev theory: We propose a refinement of the Gaberdiel-Gopakumar duality conjecture between
W_N conformal field theories and 2+1-dimensional higher spin gravity. We make
an identification of generic representations of the W_N CFT in the
semiclassical limit with bulk configurations. By studying the spectrum of the
semiclassical limit of the W_N theories and mapping to solutions of Euclidean
Vasiliev gravity at \lambda=-N, we propose that the `light states' of the W_N
minimal models in the 't Hooft limit map not to the conical defects of the
Vasiliev theory, but rather to bound states of perturbative scalar fields with
these defects. Evidence for this identification comes from comparing charges
and from holographic relations between CFT null states and bulk symmetries. We
also make progress in understanding the coupling of scalar matter to sl(N)
gauge fields. |
Beyond $N=\infty$ in Large $N$ Conformal Vector Models at Finite
Temperature: We investigate finite-temperature observables in three-dimensional large $N$
critical vector models taking into account the effects suppressed by $1\over
N$. Such subleading contributions are captured by the fluctuations of the
Hubbard-Stratonovich auxiliary field which need to be handled with care due to
a subtle divergence structure which we clarify. The examples we consider
include the scalar $O(N)$ model, the Gross-Neveu model, the Nambu-Jona-Lasinio
model and the massless Chern-Simons Quantum Electrodynamics. We present
explicit results for the free energy density to the subleading order, which
also captures the one-point function of the stress-energy tensor, and include
the dependence on a chemical potential. We further provide a formula from
diagrammatics for the one-point functions of general single-trace higher-spin
currents. We observe that in most cases considered, these subleading effects
lift the apparent degeneracies between observables in different models at
infinite $N$, while in special cases the discrepancies only start to appear at
the next-to-subleading order. | Integrable Structure of Conformal Field Theory, Quantum KdV Theory and
Thermodynamic Bethe Ansatz: We construct the quantum versions of the monodromy matrices of KdV theory.
The traces of these quantum monodromy matrices, which will be called as ``${\bf
T}$-operators'', act in highest weight Virasoro modules. The ${\bf
T}$-operators depend on the spectral parameter $\lambda$ and their expansion
around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians
of the quantum KdV system. The ${\bf T}$-operators can be viewed as the
continuous field theory versions of the commuting transfer-matrices of
integrable lattice theory. In particular, we show that for the values
$c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,... $of the Virasoro central charge
the eigenvalues of the ${\bf T}$-operators satisfy a closed system of
functional equations sufficient for determining the spectrum. For the
ground-state eigenvalue these functional equations are equivalent to those of
massless Thermodynamic Bethe Ansatz for the minimal conformal field theory
${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique
of Thermodynamic Bethe Ansatz to the excited states. We discuss a
generalization of our approach to the cases of massive field theories obtained
by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$.
The relation of these ${\bf T}$-operators to the boundary states is also
briefly described. |
Comment on "The relativistic particle with curvature and torsion of
world trajectory": Gogilidze and Surovtsev have claimed recently (hep-th/9809191) that the
tachyonic sector can be removed from the spectrum of the relativistic particle
with curvature and torsion by a proper gauge choice. We show that the mass-spin
dependence obtained by them is incorrect and point out that their gauge surface
does not cross all the gauge orbits. We discuss the nature of the tachyonic
sector of the model and argue why it cannot be removed by any gauge fixing
procedure. | Kaluza-Klein Black Holes in String Theory: Non-supersymmetric black holes carrying both electric and magnetic charge
with respect to a single Kaluza-Klein gauge field have much in common with
supersymmetric black holes. Angular momentum conservation and other general
physics principles underlies some of their basic features. Kaluza-Klein black
holes are interpreted in string theory as bound states of D6-branes and
D0-branes. The microscopic theory reproduces the full nonlinear mass formula of
the extremal black holes. |
Yang-Mills solutions on Minkowski space via non-compact coset spaces: We find a two-parameter family of solutions of the Yang-Mills equations for
gauge group SO(1,3) on Minkowski space by foliating different parts of it with
non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone
is foliated with hyperbolic space $H^3\cong \text{SO}(1,3)/\text{SO}(3)$, while
the exterior of the lightcone employs de Sitter space dS$_3\cong
\text{SO}(1,3)/\text{SO}(1,2)$. The lightcone itself is parametrized by
SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3)
Yang-Mills system on the first two coset spaces yields a mechanical system with
inverted double-well potential and the foliation parameter serving as an
evolution parameter. Its known analytic solutions are periodic or runaway
except for the kink. On the lightcone, only the vacuum solution remains. The
constructed Yang-Mills field strength is singular across the lightcone and of
infinite action due to the noncompact cosets. Its energy-momentum tensor takes
a very simple form, with energy density of opposite signs inside and outside
the lightcone. | Emergent geometry, thermal CFT and surface/state correspondence: We study a conjectured correspondence between any codimension two convex
surface and a quantum state (SS-duality for short). By generalizing thermofield
double formalism to continuum version of the multi-scale entanglement
renormalization ansatz (cMERA) and using the SS-duality, we show that thermal
geometries naturally emerge as a result of hidden quantum entanglement between
boundary CFTs. We therefore propose a general framework to emerge the thermal
geometry from CFT at finite temperature. As an example, the case of $2d$ CFT is
considered. We calculate its information metric and show that it is either BTZ
black hole or thermal AdS as expected. |
Non-Invertible Symmetry in Calabi-Yau Conformal Field Theories: We construct examples of non-invertible global symmetries in two-dimensional
superconformal field theories described by sigma models into Calabi-Yau target
spaces. Our construction provides some of the first examples of non-invertible
symmetry in irrational conformal field theories. Our approach begins at a
Gepner point in the conformal manifold where the sigma model specializes to a
rational conformal field theory and we can identify all supersymmetric
topological Verlinde lines. By deforming away from this special locus using
exactly marginal operators, we then identify submanifolds in moduli space where
some non-invertible symmetry persists. For instance, along ten-dimensional loci
in the complex structure moduli space of quintic Calabi-Yau threefolds there is
a symmetry characterized by a Fibonacci fusion category. The symmetries we
identify provide new constraints on spectra and correlation functions. As an
application we show how they constrain conformal perturbation theory,
consistent with recent results about scaling dimensions in the K3 sigma model
near its Gepner point. | String in Horava-Lifshitz Gravity: We generalize recent analysis of the dynamics of point particle in
Horava-Lifshitz background to the case of string probe when we replace the
Hamiltonian constraint of the Polyakov string with the constraint that breaks
Lorentz invariance of target space-time. Then we find corresponding Lagrangian
and argue that the world-sheet theory is invariant under foliation preserving
diffeomorphism. Finally we discuss the Hamiltonian dynamics and show that this
is well defined on condition that the world-sheet lapse function obeys the
projectability condition. |
Non-extremal Localised Branes and Vacuum Solutions in M-Theory: Non-extremal overlapping p-brane supergravity solutions localised in their
relative transverse coordinates are constructed. The construction uses an
algebraic method of solving the bosonic equations of motion. It is shown that
these non-extremal solutions can be obtained from the extremal solutions by
means of the superposition of two deformation functions defined by vacuum
solutions of M-theory. Vacuum solutions of M-theory including irrational powers
of harmonic functions are discussed. | Supergroup BF action for supergravity: General relativity can be formulated as a SU(2) BF-theory with constraints,
as has been shown, by Pleba\'nski. The cosmological constant term can be
obtained from the constraint term, following from the consistency of the
equations of motion, as recently shown by Krasnov. We consider an $OSp(2|1)$
invariant, supergravity extension of this theory, for which the consistency of
the equations of motion and the constraints contribute as well to the
cosmological constant terms of Townsend's supergravity. The Kalb-Ramond
invariance is shortly discussed. |
Energy returns in global AdS_4: Recent studies of the weakly nonlinear dynamics of probe fields in global
AdS$_4$ (and of the nonrelativistic limit of AdS resulting in the
Gross-Pitaevskii equation) have revealed a number of cases with exact dynamical
returns for two-mode initial data. In this paper, we address the question
whether similar exact returns are present in the weakly nonlinear dynamics of
gravitationally backreacting perturbations in global AdS$_4$. In the
literature, approximate returns were first pointed out numerically and with
limited precision. We first provide a thorough numerical analysis and discover
returns that are so accurate that it would be tantalizing to sign off the small
imperfections as an artifact of numerics. To clarify the situation, we
introduce a systematic analytic approach by focusing on solutions with spectra
localized around one of the two lowest modes. This allows us to demonstrate
that in the gravitational case the returns are not exact. Furthermore, our
analysis predicts and explains specific integer numbers of direct-reverse
cascade sequences that result in particularly accurate energy returns
(elaborate hierarchies of more and less precise returns arise if one waits for
appropriate longer multiple periods in this manner). In addition, we explain,
at least in this regime, the ubiquitous appearance of direct-reverse cascades
in the weakly nonlinear dynamics of AdS-like systems. | Unimodular cosmology and the weight of energy: Some models are presented in which the strength of the gravitational coupling
of the potential energy relative to the same coupling for the kinetic energy
is, in a precise sense, adjustable. The gauge symmetry of these models consists
of those coordinate changes with unit jacobian. |
BRST quantization of Matrix Chern-Simons Theory: The BRST quantization of matrix Chern-Simons theory is carried out, the
symmetries of the theory are analysed and used to constrain the form of the
effective action. | On the validity of the 'New ansatz for metric operator calculation in
pseudo-Hermitian field theory'": This paper has been withdrawn by the author(s), due a mistake of factor 1/2. |
The One-Loop H^2R^3 and H^2(DH)^2R Terms in the Effective Action: We consider the one-loop B^2h^3 and B^4h amplitudes in type II string theory,
where B is the NS-NS two-form and h the graviton, and expand to lowest order in
alpha'. After subtracting diagrams due to quartic terms in the effective
action, we determine the presence and structure of both an H^2R^3 and
H^2(DH)^2R term. We show that both terms are multiplied by the usual
(t_8t_8\pm{1/8}\epsilon_{10}\epsilon_{10}) factor. | S-Duality, SL(2,Z) Multiplets and Killing Spinors: The S-duality transformations in type IIB string theory can be seen as local
U(1) transformations in type IIB supergravity. We use this approach to
construct the $SL(2,Z)$ multiplets associated to supersymmetric backgrounds of
type IIB string theory and the transformation laws of their corresponding
Killing spinors. |
Four-point Amplitudes in N=8 Supergravity and Wilson Loops: Prompted by recent progress in the study of N=4 super Yang-Mills amplitudes,
and evidence that similar approaches might be relevant to N=8 supergravity, we
investigate possible iterative structures and applications of Wilson loop
techniques in maximal supergravity. We first consider the two-loop, four-point
MHV scattering amplitude in N=8 supergravity, confirming that the infrared
divergent parts exponentiate, and we give the explicit expression which
represents the failure for this to occur for the finite part. We observe that
each term in the expansion of the one- and two-loop amplitudes in the
dimensional regularisation parameter epsilon has a uniform degree of
transcendentality. We then turn to consider Wilson loops in supergravity,
showing that a natural definition of the loop, involving the Christoffel
connection, fails to reproduce the one-loop amplitude. An alternative
expression, which involves the metric explicitly, is shown to have a close
relationship with the physical amplitude. We find that in a gauge in which the
cusp diagrams vanish, the remaining diagrams for this Wilson loop correctly
generate the full one-loop, four-point N=8 supergravity amplitude. | Noncommutative Black Hole Thermodynamics: We give a general derivation, for any static spherically symmetric metric, of
the relation $T_h=\frac{\cal K}{2\pi}$ connecting the black hole temperature
($T_h$) with the surface gravity ($\cal K$), following the tunneling
interpretation of Hawking radiation. This derivation is valid even beyond the
semi classical regime i. e. when quantum effects are not negligible. The
formalism is then applied to a spherically symmetric, stationary noncommutative
Schwarzschild space time. The effects of back reaction are also included. For
such a black hole the Hawking temperature is computed in a closed form. A
graphical analysis reveals interesting features regarding the variation of the
Hawking temperature (including corrections due to noncommutativity and back
reaction) with the small radius of the black hole. The entropy and tunneling
rate valid for the leading order in the noncommutative parameter are
calculated. We also show that the noncommutative Bekenstein-Hawking area law
has the same functional form as the usual one. |
Comments on the Casimir energy in supersymmetric field theories: We study the Casimir energy of four-dimensional supersymmetric gauge theories
in the context of the rigid limit of new minimal supergravity. Firstly,
revisiting the computation of the localized partition function on $S^1\times
S^3$, we recover the supersymmetric Casimir energy. Secondly, we consider the
same theories in the Hamiltonian formalism on $\mathbb{R}\times S^3$, focussing
on the free limit and including a one-parameter family of background gauge
fields along $\mathbb{R}$. We compute the vacuum expectation value of the
canonical Hamiltonian using zeta function regularization, and show that this
interpolates between the supersymmetric Casimir energy and the ordinary Casimir
energy of a supersymmetric free field theory. | Notes on D-branes in 2D Type 0 String Theory: In this paper we construct complete macroscopic operators in two dimensional
type 0 string theory. They represent D-branes localized in the time direction.
We give another equivalent description of them as deformed Fermi surfaces. We
also discuss a continuous array of such D-branes and show that it can be
described by a matrix model with a deformed potential. For appropriate values
of parameters, we find that it has an additional new sector hidden inside its
strongly coupled region. |
More on the scalar-tensor B-F theory: This work is based on an earlier proposal \cite{hs} that the membrane B-F
theory consists of matter fields alongwith Chern-Simons fields as well as the
auxiliary pairs of scalar and tensor fields. We especially discuss the
supersymmetry aspects of such a membrane theory. It is concluded that the
theory possesses maximal supersymmetry and it is related to the L-BLG theory
via a field map. We obtain fuzzy-sphere solution and corresponding tensor field
configuration is given. | Open-closed homotopy algebra in mathematical physics: In this paper we discuss various aspects of open-closed homotopy algebras
(OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed
string field theory, but that first paper concentrated on the mathematical
aspects. Here we show how an OCHA is obtained by extracting the tree part of
Zwiebach's quantum open-closed string field theory. We clarify the explicit
relation of an OCHA with Kontsevich's deformation quantization and with the
B-models of homological mirror symmetry. An explicit form of the minimal model
for an OCHA is given as well as its relation to the perturbative expansion of
open-closed string field theory. We show that our open-closed homotopy algebra
gives us a general scheme for deformation of open string structures
($A_\infty$-algebras) by closed strings ($L_\infty$-algebras). |
Discrete D-branes in AdS3 and in the 2d black hole: I show how the AdS2 D-branes in the Euclidean AdS3 string theory are related
to the continuous D-branes in Liouville theory. I then propose new discrete
D-branes in the Euclidean AdS3 which correspond to the discrete D-branes in
Liouville theory. These new D-branes satisfy the appropriate shift equations.
They give rise to two families of discrete D-branes in the 2d black hole, which
preserve different symmetries. | KALUZA-KLEIN BLACK HOLES WITHIN HETEROTIC STRING THEORY ON A TORUS: We point out that in heterotic string theory compactified on a 6-torus, after
a consistent truncation of the 10-d gauge fields and the antisymmetric tensor
fields, 4-dimensional black holes of Kaluza-Klein theory on a 6-torus
constitute a subset of solutions. |
One loop divergences and anomalies from chiral superfields in
supergravity: We apply the heat kernel method (using Avramidi's non-recursive technique) to
the study of the effective action of chiral matter in a complex representation
of an arbitrary gauge sector coupled to background U(1) supergravity. This
generalizes previous methods, which restricted to 1) real representations of
the gauge sector in traditional Poincar\'e supergravity or 2) vanishing
supergravity background. In this new scheme, we identify a classical ambiguity
in these theories which mixes the supergravity U(1) with the gauge U(1). At the
quantum level, this ambiguity is maintained since the effective action changes
only by a local counterterm as one shifts a U(1) factor between the
supergravity and gauge sectors.
An immediate application of our formalism is the calculation of the one-loop
gauge, Kahler, and reparametrization anomalies of chiral matter coupled to
minimal supergravity from purely chiral loops. Our approach gives an anomaly
whose covariant part is both manifestly supersymmetric and non-perturbative in
the Kahler potential. | LINEAR CONNECTIONS ON EXTENDED SPACE-TIME: A modification of Kaluza-Klein theory is proposed which is general enough to
admit an arbitrary finite noncommutative internal geometry. It is shown that
the existence of a non-trival extension to the total geometry of a linear
connection on space-time places severe restrictions on the structure of the
noncommutative factor. A counter-example is given. |
High-Order Corrections to the Entropy and Area of Quantum Black Holes: The celebrated area-entropy formula for black holes has provided the most
important clue in the search for the elusive theory of quantum gravity. We
explore the possibility that the (linear) area-entropy relation acquires some
smaller corrections. Using the Boltzmann-Einstein formula, we rule out the
possibility for a power-law correction, and provide severe constraints on the
coefficient of a possible log-area correction. We argue that a non-zero
logarithmic correction to the area-entropy relation, would also imply a
modification of the area-mass relation for quantum black holes. | Generalized BIons in M-theory: In string theory, stacks of D1-branes can expand into intersecting D3-branes.
These configurations are called (generalized) BIons. We show how the analogous
constructions in M-theory, where M2-branes blow up into calibrated
intersections of M5-branes, arise from some of the membrane theories. |
On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic
string theories: We show that the low-energy effective actions of two ten-dimensional
supersymmetric heterotic strings are different by a $\mathbb{Z}_3$-valued
discrete topological term even after we turn off the $E_8\times E_8$ and
$Spin(32)/\mathbb{Z}_2$ gauge fields. This will be demonstrated by considering
the inflow of normal bundle anomaly to the respective NS5-branes from the bulk.
We also find that the $Spin(16)\times Spin(16)$ non-tachyonic
non-supersymmetric heterotic string has the same non-zero $\mathbb{Z}_3$-valued
discrete topological term. We will also explain the relation of our findings to
the theory of topological modular forms.
The paper is written as a string theory paper, except for an appendix
translating the content in mathematical terms. We will explain there that our
finding identifies a representative of the $\mathbb{Z}/3$-torsion element of
$\pi_{-32}\mathrm{TMF}$ as a particular self-dual vertex operator superalgebra
of $c=16$ and how we utilize string duality to arrive at this statement. | Momentum-carrying waves on D1-D5 microstate geometries: If one attempts to add momentum-carrying waves to a black string then the
solution develops a singularity at the horizon; this is a manifestation of the
'no hair theorem' for black objects. However individual microstates of a black
string do not have a horizon, and so the above theorem does not apply. We
construct a perturbation that adds momentum to a family of microstates of the
extremal D1-D5 string. This perturbation is analogous to the 'singleton' mode
localized at the boundary of AdS; to leading order it is pure gauge in the AdS
interior of the geometry. |
Matter Coupled AdS_3 Supergravities and Their Black Strings: We couple n copies of N=(2,0) scalar multiplets to a gauged N=(2,0)
supergravity in 2+1 dimensions which admits AdS_3 as a vacuum. The scalar
fields are charged under the gauged R-symmetry group U(1) and parametrize
certain Kahler manifolds with compact or non-compact isometries. The radii of
these manifolds are quantized in the compact case, but arbitrary otherwise. In
the compact case, we find half-supersymmetry preserving and asymptotically
Minkowskian black string solutions. For a particular value of the scalar
manifold radius, the solution coincides with that of Horne and Horowitz found
in the context of a string theory in 2+1 dimensions. In the non-compact case,
we find half-supersymmetry preserving and asymptotically AdS_3 string solutions
which have naked singularities. We also obtain two distinct AdS_3
supergravities coupled to n copies of N=(1,0) scalar multiplets either by the
truncation of the (2,0) model or by a direct construction. | Gaugino Condensates and Fluxes in N = 1 Effective Superpotentials: In the framework of orbifold compactifications of heterotic and type II
orientifolds, we study effective N = 1 supergravity potentials arising from
fluxes and gaugino condensates. These string solutions display a broad
phenomenology which we analyze using the method of N = 4 supergravity gaugings.
We give examples in type II and heterotic compactifications of combined fluxes
and condensates leading to vacua with naturally small supersymmetry breaking
scale controlled by the condensate, cases where the supersymmetry breaking
scale is specified by the fluxes even in the presence of a condensate and also
examples where fluxes and condensates conspire to preserve supersymmetry. |
Induced Action for Conformal Higher Spins from Worldline Path Integrals: Conformal higher spin (CHS) fields, despite being non unitary, provide a
remarkable example of a consistent interacting higher spin theory in flat space
background, that is local to all orders. The non-linear action is defined as
the logarithmically UV divergent part of a one-loop scalar effective action. In
this paper we take a particle model, that describes the interaction of a scalar
particle to the CHS background, and compute its path integral on the circle. We
thus provide a worldline representation for the CHS action, and rederive its
quadratic part. We plan to come back to the subject, to compute cubic and
higher vertices, in a future work. | Rigid supersymmetric theories in 4d Riemannian space: We consider rigid supersymmetric theories in four-dimensional Riemannian spin
manifolds. We build the Lagrangian directly in Euclidean signature from the
outset, keeping track of potential boundary terms. We reformulate the
conditions for supersymmetry as a set of conditions on the torsion classes of a
suitable SU(2) or trivial G-structure. We illustrate the formalism with a
number of examples including supersymmetric backgrounds with non-vanishing Weyl
tensor. |
Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice
model: We investigate feasible holography with the Kitaev model using dilatonic
gravity in AdS$_2$. We propose a generic dual theory of gravity in the AdS$_2$
and suggest that this bulk action is a suitable toy model in studying quantum
mechanics in the Kitaev model using gauge/gravity duality. This gives a
possible equivalent description for the Kitaev model in the dual gravity bulk.
Scalar and tensor perturbations are investigated in detail. In the case of near
AdS perturbation, we show that the geometry still "freezes" as is AdS, while
the dilation perturbation decays at the AdS boundary safely. The time-dependent
part of the perturbation is an oscillatory model. We discover that the dual
gravity induces an effective and renormalizable quantum action. The
entanglement entropy for bulk theory is computed using extremal surfaces. We
prove that these surfaces have a fold bifurcation regime of criticality. Our
approach shows directly that chaos in AdS$_2$ can be understood via fold
bifurcation minimal surfaces. | Recombination of Intersecting D-Branes and Cosmological Inflation: We consider the interactions between Dp-branes intersecting at an arbitrary
number of angles in the context of type II string theory. For cosmology
purposes we concentrate in the theory on R^{3,1} x T^6. Interpreting the
distance between the branes as the inflaton field, the branes can intersect at
most at two angles on the compact space. If the configuration is
non-supersymmetric we will have an interbrane potential that provides an
effective cosmological inflationary epoch at the four dimensional intersection
between the branes. The end of inflation occurs when the interbrane distance
becomes small compared with the string scale, where a tachyon develops
triggering the recombination of the branes. We study this recombination due to
tachyon instabilities and we find the possibility for the final configuration
to be again branes intersecting at two angles. This preserves the interesting
features that are present in the intersecting brane models from the string
model building point of view also after the end of inflation. This fact was not
present in the models of branes intersecting at just one angle. This kind of
recombination can be also important in other string contexts. |
Dilatations Revisited: Dilatation, i.e. scale, symmetry in the presence of the dilaton in Minkowski
space is derived from diffeomorphism symmetry in curved spacetime,
incorporating the volume-preserving diffeomorphisms. The conditions for scale
invariance are derived and their relation to conformal invariance is examined.
In the presence of the dilaton scale invariance automatically guarantees
conformal invariance due to diffeomorphism symmetry. Low energy scale-invariant
phenomenological Lagrangians are derived in terms of dilaton-dressed fields,
which are identified as the fields satisfying the usual scaling properties. The
notion of spontaneous scale symmetry breaking is defined in the presence of the
dilaton. In this context, possible phenomenological implications are advocated
and by computing the dilaton mass the idea of PCDC (partially conserved
dilatation current) is further explored. | Bulk-brane supergravity: We point out a limitation of the existing supergravity tensor calculus on the
$S^1/Z_2$ orbifold that prevents its use for constructing general
supersymmetric bulk-plus-brane actions. We report on the progress achieved in
removing this limitation via the development of ``supersymmetry without
boundary conditions.'' |
Fermion Self-energy and Pseudovector Condensate in NJL Model with
External Magnetic Field: In this paper, we aim to study the complete self-energy in the fermion
propagator within two-flavor NJL model in the case of finite temperature,
chemical potential and external magnetic field. Through Fierz transformation we
prove that the self-energy is not simply proportional to dynamical mass in the
presence of chemical potential, moreover, it contains four kinds of condensates
after introducing external magnetic field. We find out the appropriate and
complete form of self-energy and establish new gap equations. We take two of
the four condensates (scalar and pseudovector condensates) to make an
approximation and simplify the gap equations. The numerical results show that
not only the dynamical mass get quantitative modification, but also the
properties of Nambu phase and Wigner phase are significantly different with
classic results. Instead of classic Wigner phase with zero dynamic mass in the
massless NJL model, we propose a new phase - quasi-Wigner phase in this
article, it has small but nonzero dynamic mass, with increasing chemical
potential, eventually Nambu phase will turn into quasi-Wigner phase with
first-order phase transition, therefore the chiral symmetry can never be fully
restored but be partially restored. Furthermore, we prove that pseudovector
condensate in self-energy can generate energy splitting in dispersion relation,
it will cause minor differences of particle numbers with the split energy
levels. | Quantum oscillator and a bound system of two dyons: It is shown that $U(1)$--Hamiltonian reduction of a four--dimensional
isotropic quantum oscillator results in a bound system of two spinless
Schwinger's dyons. Its wavefunctions and spectrum are constructed. |
Two-Dimensional Dilaton Gravity and Toda - Liouville Integrable Models: General properties of a class of two-dimensional dilaton gravity (DG)
theories with multi-exponential potentials are studied and a subclass of these
theories, in which the equations of motion reduce to Toda and Liouville
equations, is treated in detail. A combination of parameters of the equations
should satisfy a certain constraint that is identified and solved for the
general multi-exponential model. From the constraint it follows that in DG
theories the integrable Toda equations, generally, cannot appear without
accompanying Liouville equations.
We also show how the wave-like solutions of the general Toda-Liouville
systems can be simply derived. In the dilaton gravity theory, these solutions
describe nonlinear waves coupled to gravity as well as static states and
cosmologies. A special attention is paid to making the analytic structure of
the solutions of the Toda equations as simple and transparent as possible, with
the aim to gain a better understanding of realistic theories reduced to
dimensions 1+1 and 1+0 or 0+1. | Lectures on Spectrum Generating Symmetries and U-duality in
Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic
Superspace: We review the underlying algebraic structures of supergravity theories with
symmetric scalar manifolds in five and four dimensions, orbits of their
extremal black hole solutions and the spectrum generating extensions of their
U-duality groups. For 5D, N=2 Maxwell-Einstein supergravity theories (MESGT)
defined by Euclidean Jordan algebras, J, the spectrum generating symmetry
groups are the conformal groups Conf(J) of J which are isomorphic to their
U-duality groups in four dimensions. Similarly, the spectrum generating
symmetry groups of 4D, N=2 MESGTs are the quasiconformal groups QConf(J)
associated with J that are isomorphic to their U-duality groups in three
dimensions. We then review the work on spectrum generating symmetries of
spherically symmetric stationary 4D BPS black holes, based on the equivalence
of their attractor equations and the equations for geodesic motion of a
fiducial particle on the target spaces of corresponding 3D supergravity
theories obtained by timelike reduction. We also discuss the connection between
harmonic superspace formulation of 4D, N=2 sigma models coupled to supergravity
and the minimal unitary representations of their isometry groups obtained by
quantizing their quasiconformal realizations. We discuss the relevance of this
connection to spectrum generating symmetries and conclude with a brief summary
of more recent results. |
Towards a stringy extension of self-dual super Yang-Mills: Motivated by the search for a space-time supersymmetric extension of the N=2
string, we construct a particle model which, upon quantization, describes
(abelian) self-dual super Yang-Mills in 2+2 dimensions. The local symmetries of
the theory are shown to involve both world-line supersymmetry and kappa
symmetry. | Small Fluctuations in $λφ^{n+1}$ Theory in a Finite Domain: An
Hirota's Method Approach: We present a method to calculate small stationary fluctuations around static
solutions describing bound states in a $(1+1)$-dimensional $\lambda \phi^{n+1}$
theory in a finite domain. We also calculate explicitly fluctuations for the
$\lambda \phi^4$. These solutions are written in terms of Jacobi Elliptic
functions and are obtained from both linear and nonlinear equations. For the
linear case we get eingenvalues of a Lam\'e type Equation and the nonlinear one
relies on Hirota's Method. |
Primordial perturbations from inflation with a hyperbolic field-space: We study primordial perturbations from hyperinflation, proposed recently and
based on a hyperbolic field-space. In the previous work, it was shown that the
field-space angular momentum supported by the negative curvature modifies the
background dynamics and enhances fluctuations of the scalar fields
qualitatively, assuming that the inflationary background is almost de Sitter.
In this work, we confirm and extend the analysis based on the standard approach
of cosmological perturbation in multi-field inflation. At the background level,
to quantify the deviation from de Sitter, we introduce the slow-varying
parameters and show that steep potentials, which usually can not drive
inflation, can drive inflation. At the linear perturbation level, we obtain the
power spectrum of primordial curvature perturbation and express the spectral
tilt and running in terms of the slow-varying parameters. We show that
hyperinflation with power-law type potentials has already been excluded by the
recent Planck observations, while exponential-type potential with the exponent
of order unity can be made consistent with observations as far as the power
spectrum is concerned. We also argue that, in the context of a simple $D$-brane
inflation, the hyperinflation requires exponentially large hyperbolic extra
dimensions but that masses of Kaluza-Klein gravitons can be kept relatively
heavy. | ADHM Construction of Noncommutative Instantons: We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N)
instantons in noncommutative (NC) space and prove the one-to-one correspondence
between moduli spaces of the noncommutative instantons and the ADHM data,
together with an origin of the instanton number for U(1). We also give a
derivation of the ADHM construction from the viewpoint of the Nahm
transformation of instantons on four-tori. This article is a composite version
of [23] and [24]. |
On $W$-representations of $β$- and $q,t$-deformed matrix models: $W$-representation realizes partition functions by an action of a
cut-and-join-like operator on the vacuum state with a zero-mode background. We
provide explicit formulas of this kind for $\beta$- and $q,t$-deformations of
the simplest rectangular complex matrix model. In the latter case, instead of
the complicated definition in terms of multiple Jackson integrals, we define
partition functions as the weight-two series, made from Macdonald polynomials,
which are evaluated at different loci in the space of time variables. Resulting
expression for the $\hat W$ operator appears related to the problem of simple
Hurwitz numbers (contributing are also the Young diagrams with all but one
lines of length two and one). This problem is known to exhibit nice
integrability properties. Still the answer for $\hat W$ can seem unexpectedly
sophisticated and calls for improvements. Since matrix models lie at the very
basis of all gauge- and string-theory constructions, our exercise provides a
good illustration of the jump in complexity between $\beta$- and
$q,t$-deformations -- which is not always seen at the accidently simple level
of Calogero-Ruijsenaars Hamiltonians (where both deformations are equally
straightforward). This complexity is, however, quite familiar in the theories
of network models, topological vertices and knots. | The box integrals in momentum-twistor geometry: An account is given of how the 'box integrals', as used for one-loop
calculations in massless field theory, appear in momentum-twistor geometry.
Particular attention is paid to the role of compact contour integration in
representing the Feynman propagator in twistor space. An explicit calculation
of all the box integrals, using only elementary methods, is included. |
Heterotic-Type II duality in the hypermultiplet sector: We revisit the duality between heterotic string theory compactified on K3 x
T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet
sector. We derive an explicit map between the field variables of the respective
moduli spaces at the level of the classical effective actions. We determine the
parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal
form. From the expression of the holomorphic prepotential we are led to
conjecture that both X and its mirror must be K3 fibrations in order for the
type IIA theory to have an heterotic dual. We then focus on the region of the
moduli space where the metric is expressed in terms of a prepotential on both
sides of the duality. Applying the duality we derive the heterotic
hypermultiplet metric for a gauge bundle which is reduced to 24 point-like
instantons. This result is confirmed by using the duality between the heterotic
theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on
the moduli space of an SU(2) bundle on K3. | High-energy String Scatterings of Compactified Open String: We calculate high-energy massive string scattering amplitudes of compactified
open string. We derive infinite linear relations, or stringy symmetries, among
soft high-energy string scattering amplitudes of different string states in the
Gross kinematic regime (GR). In addition, we systematically analyze all hard
power-law and soft exponential fall-off regimes of high-energy compactified
open string scatterings by comparing the scatterings with their 26D
noncompactified counterparts. In particular, we discover the existence of a
power-law regime at fixed angle and an exponential fall-off regime at small
angle for high-energy compactified open string scatterings. The linear
relations break down as expected in all power-law regimes. The analysis can be
extended to the high-energy scatterings of the compactified closed string,
which corrects and extends the previous results in [28] . |
The Coset Spin-4 Casimir Operator and Its Three-Point Functions with
Scalars: We find the GKO coset construction of the dimension 4 Casimir operator that
contains the quartic WZW currents contracted with completely symmetric SU(N)
invariant tensors of ranks 4, 3, and 2. The requirements, that the operator
product expansion with the diagonal current is regular and it should be primary
under the coset Virasoro generator of dimension 2, fix all the coefficients in
spin-4 current, up to two unknown coefficients. The operator product expansion
of coset primary spin-3 field with itself fixes them completely. We compute the
three-point functions with scalars for all values of the 't Hooft coupling in
the large N limit. At fixed 't Hooft coupling, these three-point functions are
dual to that found by Chang and Yin recently in the undeformed AdS_3 bulk
theory (higher spin gravity with matter). | A fifth order perturbative solution to the Gribov - Lipatov equation: Fifth order exact corrections to the non-singlet electron structure function
in QED are the leading logarithmic approximation using the ad hoc
exponentiation prescription proposed by Jadach and Ward and a recurence formula
for the elements of the Jadach-Ward series. A comparison with existing third
order solutions is also presented. The three next elements of the Jadac Ward
series were calculated numerically and parametrized with an accuracy better
than 5x10^-6 in the range of x between 0.01 and 1. |
Unruh effect without Rindler horizon: We investigate the Unruh effect for a massless scalar field in the two
dimensional Minkowski space in the presence of a uniformly accelerated perfect
mirror, with the trajectory of the mirror chosen in such a way that the mirror
completely masks the Rindler horizon from the space-time region of interest. We
find that the characteristic thermodynamical properties of the effect remain
unchanged, i.e. the response of a uniformly co-accelerated Unruh detector and
the distribution of the Rindler particles retain their thermal form. However,
since in this setup there are no unobserved degrees of freedom of the field the
thermal statistics of the Rindler particles is inconsistent with an initial
pure vacuum, which leads us to reconsider the problem for the more physical
case when the mirror is inertial in the past. In these conditions we find that
the distribution of the Rindler particles is non-thermal even in the limit of
infinite acceleration times, but an effective thermal statistics can be
recovered provided that one restricts to the expectation values of smeared
operators associated to finite norm Rindler states. We explain how the thermal
statistics in our problem can be understood in analogy with that in the
conventional version of the effect. | Topologically twisted index of $T[SU(N)]$ at large $N$: We compute, in the large $N$ limit, the topologically twisted index of the 3d
$T[SU(N)]$ theory, namely the partition function on $\Sigma_{\mathfrak{g}}
\times S^1$, with a topological twist on the Riemann surface
$\Sigma_{\mathfrak{g}}$. To provide an expression for this quantity, we take
advantage of some recent results obtained for five dimensional quiver gauge
theories. In case of a universal twist, we correctly reproduce the entropy of
the universal black hole that can be embedded in the holographically dual
solution. |
PSU(2,2|4) transformations of IIB superstring in AdS_5 x S^5: The PSU(2,2|4) transformation laws of the IIB superstring theory in the AdS_5
x S^5 background are explicitly obtained for the light-cone gauge in the
Green-Schwarz formalism. | Comment on "Cosmological Topological Massive Gravitons and Photons": In a recent paper (arXiv: 0801.4566) it was shown that all global energy
eigenstates of asymptotically $AdS_3$ chiral gravity have non-negative energy
at the linearized level. This result was questioned (arXiv: 0803.3998) by
Carlip, Deser, Waldron and Wise (CDWW), who work on the Poincare patch. They
exhibit a linearized solution of chiral gravity and claim that it has negative
energy and is smooth at the boundary. We show that the solution of CDWW is
smooth only on that part of the boundary of $AdS_3$ included in the Poincare
patch. Extended to global $AdS_3$, it is divergent at the boundary point not
included in the Poincare patch. Hence it is consistent with the results of
(arXiv: 0801.4566). |
Factorization of Mellin amplitudes: We introduce Mellin amplitudes for correlation functions of $k$ scalar
operators and one operator with spin in conformal field theories (CFT) in
general dimension. We show that Mellin amplitudes for scalar operators have
simple poles with residues that factorize in terms of lower point Mellin
amplitudes, similarly to what happens for scattering amplitudes in flat space.
Finally, we study the flat space limit of Anti-de Sitter (AdS) space, in the
context of the AdS/CFT correspondence, and generalize a formula relating CFT
Mellin amplitudes to scattering amplitudes of the bulk theory, including
particles with spin. | Lattice realizations of unitary minimal modular invariant partition
functions: The conformal spectra of the critical dilute A-D-E lattice models are studied
numerically. The results strongly indicate that, in branches 1 and 2, these
models provide realizations of the complete A-D-E classification of unitary
minimal modular invariant partition functions given by Cappelli, Itzykson and
Zuber. In branches 3 and 4 the results indicate that the modular invariant
partition functions factorize. Similar factorization results are also obtained
for two-colour lattice models. |
The role of mathematics in contemporary theoretical physics: Talk given at the 6th Philosophy-and-Physics-Workshop ``Epistemological
Aspects of the Role of Mathematics in Physical Science'', FEST, Heidelberg,
Feb. 1993 | Anomalous Casimir effect in axion electrodynamics: We study the Casimir effect in axion electrodynamics. A finite $\theta$-term
affects the energy dispersion relation of photon if $\theta$ is time and/or
space dependent. We focus on a special case with linearly inhomogeneous
$\theta$ along the $z$-axis. Then we demonstrate that the Casimir force between
two parallel plates perpendicular to the $z$-axis can be either attractive or
repulsive, dependent on the gradient of $\theta$. We call this repulsive
component in the Casimir force induced by inhomogeneous $\theta$ the anomalous
Casimir effect. |
Konishi operator at intermediate coupling: TBA equations for two-particle states from the sl(2) sector proposed by
Arutyunov, Suzuki and the author are solved numerically for the Konishi
operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained
is used to analyze the properties of Y-functions and address the issue of the
existence of the critical values of the coupling. In addition we find a new
integral representation for the BES dressing phase which substantially reduces
the computational time. | A Note on Supersymmetries in AdS_5/CFT_4: The N=4 superconformal algebra is derived from the symmetry transformations
of fields in the N=4 SYM action in D=4. We use a Majorana-Weyl spinor in D=10
instead of four Weyl spinors in D=4. This makes it transparent to relate
generators of the N=4 superconformal algebra to those of the super-AdS_5XS^5
algebra. Especially, we obtain the concrete map from the supersymmetries Q and
conformal supersymmetries S in N=4 SYM to the supersymmetries (Q_1, Q_2) in the
AdS_5XS^5 background. |
Higher Derivative Quantum Gravity with Gauss-Bonnet Term: Higher derivative theory is one of the important models of quantum gravity,
renormalizable and asymptotically free within the standard perturbative
approach. We consider the $4-\epsilon$ renormalization group for this theory,
an approach which proved fruitful in $2-\epsilon$ models. A consistent
formulation in dimension $n=4-\epsilon$ requires taking quantum effects of the
topological term into account, hence we perform calculation which is more
general than the ones done before. In the special $n=4$ case we confirm a known
result by Fradkin-Tseytlin and Avramidi-Barvinsky, while contributions from
topological term do cancel. In the more general case of $4-\epsilon$
renormalization group equations there is an extensive ambiguity related to
gauge-fixing dependence. As a result, physical interpretation of these
equations is not universal unlike we treat $\epsilon$ as a small parameter. In
the sector of essential couplings one can find a number of new fixed points,
some of them have no analogs in the $n=4$ case. | Fermionic Quasi-Particle Representations for Characters of ${(G^{(1)})_1
\times (G^{(1)})_1 ø(G^{(1)})_2}$: We present fermionic quasi-particle sum representations for some of the
characters (or branching functions) of ~${(G^{(1)})_1 \times (G^{(1)})_1 \o
(G^{(1)})_2}$ ~for all simply-laced Lie algebras $G$. For given $G$ the
characters are written as the partition function of a set of rank~$G$ types of
massless quasi-particles in certain charge sectors, with nontrivial lower
bounds on the one-particle momenta. We discuss the non-uniqueness of the
representations for the identity character of the critical Ising model, which
arises in both the $A_1$ and $E_8$ cases. |
Higher-Spin Gauge Interactions for Matter Fields in Two Dimensions: We formulate a new model which describes higher-spin gauge interactions for
matter fields in two dimensions. This model is a higher-spin generalization of
d2 gravity and turns out to be integrable. No vanishing higher-spin current
conditions are imposed on the matter fields. | A Geometric Interpretation of the Open String Tachyon: Unstable, non-BPS D-branes in weakly coupled ten dimensional string theory
have many mysterious properties. Among other things, it is not clear what sets
their tension, what is their relation to the better understood BPS D-branes,
and why the open string tachyon on them is described by an effective Lagrangian
which suggests that the tachyon corresponds to an extra spatial dimension
transverse to the branes. We point out that the dynamics of D-branes in the
presence of Neveu-Schwarz fivebranes on a transverse R^3 times S^1 provides a
useful toy model for studying these issues. From the point of view of a 5+1
dimensional observer living on the fivebranes, BPS D-branes in ten dimensions
give rise to two kinds of D-branes, which are BPS or non-BPS depending on
whether they do or do not wrap the S^1. Their tensions are related, since from
a higher dimensional perspective, they are the same objects. D-branes localized
on the S^1 have a tachyon corresponding to their position on the circle. This
field is described by the same Lagrangian as that of a tachyon on a non-BPS
D-brane in ten dimensions. Its geometrical interpretation is useful for
clarifying the properties of non-BPS branes in six dimensions. If the lessons
from the six dimensional system can be applied in ten dimensions, the existence
of non-BPS D-branes seems to suggest the presence of at least one extra
dimension in critical type II string theory. |
S-Wave Scattering of Fermion Revisited: A model where a Dirac fermion is coupled to background dilaton field is
considered to study s-wave scattering of fermion by a back ground dilaton black
hole. It is found that an uncomfortable situation towards information loss
scenario arises when one loop correction gets involved during bosonization. | Chiral perturbation theory for GR: We describe a new perturbation theory for General Relativity, with the chiral
first-order Einstein-Cartan action as the starting point. Our main result is a
new gauge-fixing procedure that eliminates the connection-to-connection
propagator. All other known first-order formalisms have this propagator
non-zero, which significantly increases the combinatorial complexity of any
perturbative calculation. In contrast, in the absence of the
connection-to-connection propagator, our formalism leads to an effective
description in which only the metric (or tetrad) propagates, there are only
cubic and quartic vertices, but some vertex legs are special in that they
cannot be connected by the propagator. The new formalism is the gravity analog
of the well-known and powerful chiral description of Yang-Mills theory. |
Quantum Gravity induced Lorentz invariance violation in the Standard
Model:hadrons: The most important problem of fundamental Physics is the quantization of the
gravitational field. A main difficulty is the lack of available experimental
tests that discriminate among the theories proposed to quantize gravity.
Recently we showed that the Standard Model(SM) itself contains tiny Lorentz
invariance violation(LIV) terms coming from QG. All terms depend on one
arbitrary parameter $\alpha$ that set the scale of QG effects. In this paper we
obtain the LIV for mesons and nucleons and apply it to study several effects,
including the GZK anomaly. | Non-linear stability of $α'$-corrected Friedmann equations: We study the non-linear stability of fixed-point solutions to the
$\alpha'$-exact equations from O$(d,d)$ invariant cosmology, with and without
matter perturbations. Previous non-linear analysis in the literature is
revisited, and its compatibility with known linear perturbation results is
shown. Some formal aspects of cosmological perturbations in duality invariant
cosmology are discussed, and we show the existence of time-reparameterization
invariant variables for perturbations. |
Inflation on an Open Racetrack: We present a variant of warped D-brane inflation by incorporating multiple
sets of holomorphically-embedded D7-branes involved in moduli stabilization
with extent into a warped throat. The resultant D3-brane motion depends on the
D7-brane configuration and the relative position of the D3-brane in these
backgrounds. The non-perturbative moduli stabilization superpotential takes the
racetrack form, but the additional D3-brane open string moduli dependence
provides more flexibilities in model building. For concreteness, we consider
D3-brane motion in the warped deformed conifold with the presence of multiple
D7-branes, and derive the scalar potential valid for the entire throat. By
explicit tuning of the microphysical parameters, we obtain inflationary
trajectories near an inflection point for various D7-brane configurations.
Moreover, the open racetrack potential admits approximate Minkowski vacua
before uplifting. We demonstrate with a concrete D-brane inflation model where
the Hubble scale during inflation can exceed the gravitino mass. Finally, the
multiple sets of D7-branes present in this open racetrack setup also provides a
mechanism to stabilize the D3-brane to metastable vacua in the intermediate
region of the warped throat. | Induced gravity with complex metric field: The possible existence of a complex metric tensor field is studied. We show
that an effective scalar field is induced by an overall phase component of the
complex metric tensor. The corresponding gauge field is shown to be a tachyon.
Possible implications of this scalar field to the no hair theorem in a
spherically symmetric space is also analyzed. We also study its impact on the
evolution of the early universe. |
Spacelike localization of long-range fields in a model of asymptotic
electrodynamics: A previously proposed algebra of asymptotic fields in quantum electrodynamics
is formulated as a net of algebras localized in regions which in general have
unbounded spacelike extension. Electromagnetic fields may be localized in
`symmetrical spacelike cones', but there are strong indications this is not
possible in the present model for charged fields, which have tails extending in
all space directions. Nevertheless, products of appropriately `dressed' fermion
fields (with compensating charges) yield bi-localized observables. | Inverse magnetic catalysis in holographic models of QCD: We study the effect of magnetic field $B$ on the critical temperature $T_{c}$
of the confinement-deconfinement phase transition in hard-wall AdS/QCD, and
holographic duals of flavored and unflavored $\mathcal{N}=4$ super-Yang Mills
theories on $\mathbb{R}^3\times \rm S^1$. For all of the holographic models, we
find that $T_{c}(B)$ decreases with increasing magnetic field $B\ll T^2$,
consistent with the inverse magnetic catalysis recently observed in lattice QCD
for $B\lesssim 1~GeV^2$. We also predict that, for large magnetic field $B\gg
T^2$, the critical temperature $T_{c}(B)$, eventually, starts to increase with
increasing magnetic field $B\gg T^2$ and asymptotes to a constant value. |
Three-point functions at strong coupling in the BMN limit: We consider structure constants of single-trace operators at strong coupling
in planar $\mathcal{N}=4$ SYM theory using the hexagon formalism. We
concentrate on heavy-heavy-light correlators where the heavy operators are BMN
operators, with large R-charges and finite anomalous dimensions, and the light
one is a finite-charge chiral primary operator. They describe the couplings
between two highly boosted strings and a supergravity mode in the bulk dual. In
the hexagon framework, two sums over virtual magnons are needed to bind the
hexagons together around the light operator. We evaluate these sums explicitly
at strong coupling, for a certain choice of BMN operators, and show that they
factorise into a ratio of Gamma functions and a simple stringy prefactor. The
former originates from giant mirror magnons scanning the AdS geometry while the
latter stems from small fluctuations around the BMN vacuum. The resulting
structure constants have poles at positions where an enhanced mixing with
double-trace operators is expected and zeros whenever the process is forbidden
by supersymmetry. We also discuss the transition to the classical regime, when
the length of the light operator scales like the string tension, where we
observe similitudes with the Neumann coefficients of the pp-wave String Field
Theory vertex. | Hamiltonian Formulation of the W-Infinity Minimal Models: The W-infinity minimal models are conformal field theories which can describe
the edge excitations of the hierarchical plateaus in the quantum Hall effect.
In this paper, these models are described in very explicit terms by using a
bosonic Fock space with constraints, or, equivalently, with a non-trivial
Hamiltonian. The Fock space is that of the multi-component Abelian conformal
theories, which provide another possible description of the hierarchical
plateaus; in this space, the minimal models are shown to correspond to the
sub-set of states which satisfy the constraints. This reduction of degrees of
freedom can also be implemented by adding a relevant interaction to the
Hamiltonian, leading to a renormalization-group flow between the two theories.
Next, a physical interpretation of the constraints is obtained by representing
the quantum incompressible Hall fluids as generalized Fermi seas. Finally, the
non-Abelian statistics of the quasi-particles in the W-infinity minimal models
is described by computing their correlation functions in the Coulomb Gas
approach. |
A note on the Hamiltonian of the real scalar field: We address the question of ambiguity in defining a Hamiltonian for a scalar
field. We point out that the Hamiltonian for a real Klein-Gordon scalar field
must be consistent with the energy density obtained from the Schrodinger
equation in the non-relativistic regime. To achieve this we had to add some
surface terms (total divergencies) to the standard Hamiltonian, which in
general will not change the equations of motion, but will redefine energy. As
an additional requirement, a Hamiltonian must be able to reproduce the
equations of motion directly from Hamilton's equations defined by the principle
of the least action. We find that the standard Hamiltonian does not always do
so and that the proposed Hamiltonian provides a good non-relativistic limit.
This is a hint that something as simple as the Hamiltonian of the real
Klein-Gordon scalar field has to be treated carefully. We had illustrated our
discussion with an explicit example of the kink solution. | Rigidity and stability of cold dark solid universe model: Observational evidence suggests that the large scale dynamics of the universe
is presently dominated by dark energy, meaning a non-luminous cosmological
constituent with a negative value of the pressure to density ratio $w=P/\rho$,
which would be unstable if purely fluid, but could be stable if effectively
solid with sufficient rigidity. It was suggested by Bucher and Spergel that
such a solid constituent might be constituted by an effectively cold (meaning
approximately static) distribution of cosmic strings with $w=-1/3$, or
membranes with the observationally more favoured value $w=-2/3$, but it was not
established whether the rigidity in such models actually would be sufficient
for stabilisation. The present article provides an explicit evaluation of the
rigidity to density ratio, which is shown to be given in both string and
membrane cases by $\mu/\rho=4/15$, and it is confirmed that this is indeed
sufficient for stabilisation. |
Zero-point energy of massless scalar fields in the presence of soft and
semihard boundaries in D dimensions: The renormalized energy density of a massless scalar field defined in a
D-dimensional flat spacetime is computed in the presence of "soft" and
"semihard" boundaries, modeled by some smoothly increasing potential functions.
The sign of the renormalized energy densities for these different confining
situations is investigated. The dependence of this energy on $D$ for the cases
of "hard" and "soft/semihard" boundaries are compared. | Stability in Einstein-Scalar Gravity with a Logarithmic Branch: We investigate the non-perturbative stability of asymptotically anti-de
Sitter gravity coupled to tachyonic scalar fields with mass saturating the
Breitenlohner-Freedman bound. Such "designer gravity" theories admit a large
class of boundary conditions at asymptotic infinity. At this mass, the
asymptotic behavior of the scalar field develops a logarithmic branch, and
previous attempts at proving a minimum energy theorem failed due to a large
radius divergence in the spinor charge. In this paper, we finally resolve this
issue and derive a lower bound on the conserved energy. Just as for masses
slightly above the BF bound, a given scalar potential can admit two possible
branches of the corresponding superpotential, one analytic and one
non-analytic. The key point again is that existence of the non-analytic branch
is necessary for the energy bound to hold. We discuss several AdS/CFT
applications of this result, including the use of double-trace deformations to
induce spontaneous symmetry breaking. |
Matrix Models and 2D Critical String Theory --2D Black Hole by c=1
Matrix Model--: (Lecture at the workshop "Basic Problems in String Theory", Yukawa Institute
for Theoretical Physics, Kyoto, October 19-21) In this talk, we first review
the possibility of matrix models toward a nonperturbative (critical) string
theory. We then discuss whether the $c=1$ matrix model can describe the black
hole solution of 2D critical string theory. We show that there exists a class
of integral transformations which send the Virasoro condition for the tachyon
field around the 2D black hole to that around the linear dilaton vacuum. In
particular, we construct an explicit integral formula wihich describes a
continuous deformation of the linear dilaton vacuum to the black hole
background. | Butterfly Velocities for Holographic Theories of General Spacetimes: The butterfly velocity characterizes the spread of correlations in a quantum
system. Recent work has provided a method of calculating the butterfly velocity
of a class of boundary operators using holographic duality. Utilizing this and
a presumed extension of the canonical holographic correspondence of AdS/CFT, we
investigate the butterfly velocities of operators with bulk duals living in
general spacetimes. We analyze some ubiquitous issues in calculating butterfly
velocities using the bulk effective theory, and then extend the previously
proposed method to include operators in entanglement shadows. We explicitly
compute butterfly velocities for bulk local operators in the holographic theory
of flat Friedmann-Robertson-Walker spacetimes and find a universal scaling
behavior for the spread of operators in the boundary theory, independent of
dimension and fluid components. This result may suggest that a Lifshitz field
theory with z = 4 is the appropriate holographic dual for these spacetimes. |
A note on backreacting flavors from calibrated geometry: One of the main problems in the search for string duals with backreacting,
smeared flavors is the construction of a suitable source density. We review how
this issue may be addressed using generalized calibrated geometry. | Mirror Symmetry, Mirror Map and Applications to Complete Intersection
Calabi-Yau Spaces: We extend the discussion of mirror symmetry, Picard-Fuchs equations,
instanton-corrected Yukawa couplings, and the topological one-loop partition
function to the case of complete intersections with higher-dimensional moduli
spaces. We will develop a new method of obtaining the instanton-corrected
Yukawa couplings through a close study of the solutions of the Picard-Fuchs
equations. This leads to closed formulas for the prepotential for the K\"ahler
moduli fields induced from the ambient space for all complete intersections in
non singular weighted projective spaces. As examples we treat part of the
moduli space of the phenomenologically interesting three-generation models that
are found in this class. We also apply our method to solve the simplest model
in which a topology change was observed and discuss examples of complete
intersections in singular ambient spaces. |
Prepotentials of N=2 SU(2) Yang-Mills theories coupled with massive
matter multiplets: We discuss N=2 SU(2) Yang-Mills gauge theories coupled with N_f (=2,3)
massive hypermultiplets in the weak coupling limit. We determine the exact
massive prepotentials and the monodromy matrices around the weak coupling
limit. We also study that the double scaling limit of these massive theories
and find that the massive N_f -1 theory can be obtained from the massive N_f
theory. New formulae for the massive prepotentials and the monodromy matrices
are proposed. In these formulae, N_f dependences are clarified. | Asymmetric Orbifold Models of Non-supersymmetric Heterotic Strings: We investigate asymmetric orbifold models constructed from non-supersymmetric
heterotic strings. We systematically classify the asymmetric orbifold models
with standard embeddings and present a list of asymmetric orbifolds which are
geometrically interpreted as toroidal compactifications of non-supersymmetric
heterotic strings. By studying non-standard embedding models, we also construct
examples of the {\em supersymmetric} asymmetric orbifold models based on
non-supersymmetric heterotic strings. |
On the boundary conditions in deformed quantum mechanics with minimal
length uncertainty: We find the coordinate space wave functions, maximal localization states, and
quasiposition wave functions in a GUP framework that implies a minimal length
uncertainty using a formally self-adjoint representation. We show that how the
boundary conditions in quasiposition space can be exactly determined from the
boundary conditions in coordinate space. | Planck Scale from Broken Local Conformal Invariance in Weyl Geometry: It is shown that in the quadratic gravity based on Weyl's conformal geometry,
the Planck mass scale can be generated from quantum effects of the
gravitational field and the Weyl gauge field via the Coleman-Weinberg mechanism
where a local scale symmetry, that is, conformal symmetry, is broken. At the
same time, the Weyl gauge field acquires mass less than the Planck mass by
absorbing the dilaton. The shape of the effective potential is almost flat
owing to a gravitational character and high symmetries, so our model would
provide an attractive model for the inflationary universe. We also present a
toy model showing spontaneous symmetry breakdown of a scale symmetry by moving
from the Jordan frame to the Einstein one, and point out its problem. |
Localised and nonuniform thermal states of super-Yang-Mills on a circle: At low energies or temperatures, maximally supersymmetric Yang-Mills theory
on $\mathbb R^{(t)}\times S^1$ with large $N$ gauge group $SU(N)$ and strong
t'Hooft coupling is conjectured to be dual to the low energy dynamics of a
collection of D0-branes on a circle. We construct thermal states in the
gravitational side of the correspondence where we find a first-order phase
transition between states that are uniform on the $S^1$ and states that are
localised on it. When compared with lattice computations that are now
available, these critical values provide the first instance where a first-order
phase transition is tested on both sides of gauge/gravity duality. | Exact solutions for some N=2 supersymmetric SO(N) gauge theories with
vectors and spinors: We find exact solutions for N=2 supersymmetric SO(N), N=7,9,10,11,12 gauge
theories with matter in the fundamental and spinor representation. These
theories, with specific numbers of vectors and spinors, arise naturally in the
compactification of type IIA string theory on suitably chosen Calabi-Yau
threefolds. Exact solutions are obtained by using mirror symmetry to find the
corresponding type IIB compactification. We propose generalizations of these
results to cases with arbitrary numbers of massive vectors and spinors. |
Spontaneous breaking of conformal invariance, solitons and gravitational
waves in theories of conformally invariant gravitation: We study conformal gravity as an alternative theory of gravitation. For
conformal gravity to be phenomenologically viable requires that the conformal
symmetry is not manifest at the energy scales of the other known physical
forces. Hence we require a mechanism for the spontaneous breaking of conformal
invariance. In this paper we study the possibility that conformal invariance is
spontaneously broken due to interactions with conformally coupled matter
fields. The vacuum of the theory admits conformally non-invariant solutions
corresponding to maximally symmetric space-times and variants thereof. These
are either de Sitter space-time or anti-de Sitter space-time in the full four
space-time dimensions or in a lower dimensional sub-space. We consider in
particular normalizable, linearized gravitational perturbations around the
anti-de Sitter background. Exploiting the conformal flatness of this
space-time, we show to second order, that these gravitational fluctuations,
that are taken to be fourier decomposable, carry zero energy-momentum. This
squares well with the theorem that asymptotically flat space-times conformal
gravity contain zero energy and momentum \cite{bhs}. We also show the
possibility of domain wall solitons interpolating between the ground states of
spontaneously broken conformal symmetry that we have found. These solitons
necessarily require the vanishing of the scalar field, repudiating the recent
suggestion \cite{f} that the conformal symmetry could be quarantined to a
sterile sector of the theory by choosing an appropriate field redefinition. | Comparing strings in AdS(5)xS(5) to planar diagrams: an example: The correlator of a Wilson loop with a local operator in N=4 SYM theory can
be represented by a string amplitude in AdS(5)xS(5). This amplitude describes
an overlap of the boundary state, which is associated with the loop, with the
string mode, which is dual to the local operator. For chiral primary operators
with a large R charge, the amplitude can be calculated by semiclassical
techniques. We compare the semiclassical string amplitude to the SYM
perturbation theory and find an exact agrement to the first two non-vanishing
orders. |
D=11 SUGRA as the Low Energy Effective Action of Matrix Theory: Three
Form Scattering: We employ the LSZ reduction formula for Matrix Theory introduced in our
earlier work to compute the t-pole S-matrix for three form-three form
scattering. The result agrees completely with tree level D=11 SUGRA. Taken
together with previous results on graviton-graviton scattering this shows that
Matrix Theory indeed reproduces the bosonic sector of the D=11 SUGRA action
including the Chern-Simons term. Furthermore we provide a detailed account of
our framework along with the technology to compute any Matrix Theory one-loop
t-pole scattering amplitude at vanishing p^- exchange. | The structure of invariants in conformal mechanics: We investigate the integrals of motion of general conformal mechanical
systems with and without confining harmonic potential as well as of the related
angular subsystems, by employing the SL(2,R) algebra and its representations.
In particular, via the tensor product of two representations we construct new
integrals of motion from old ones. Furthermore, the temporally periodic
observables (including the integrals) of the angular subsystem are explicitly
related to those of the full system in a confining harmonic potential. The
techniques are illustrated for the rational Calogero models and their angular
subsystems, where they generalize known methods for obtaining conserved charges
beyond the Liouville ones. |
Classical A_n--W-Geometry: This is a detailed development for the $A_n$ case, of our previous article
entitled "W-Geometries" to be published in Phys. Lett. It is shown that the
$A_n$--W-geometry corresponds to chiral surfaces in $CP^n$. This is comes out
by discussing 1) the extrinsic geometries of chiral surfaces (Frenet-Serret and
Gauss-Codazzi equations) 2) the KP coordinates (W-parametrizations) of the
target-manifold, and their fermionic (tau-function) description, 3) the
intrinsic geometries of the associated chiral surfaces in the Grassmannians,
and the associated higher instanton- numbers of W-surfaces. For regular points,
the Frenet-Serret equations for $CP^n$--W-surfaces are shown to give the
geometrical meaning of the $A_n$-Toda Lax pair, and of the conformally-reduced
WZNW models, and Drinfeld-Sokolov equations. KP coordinates are used to show
that W-transformations may be extended as particular diffeomorphisms of the
target-space. This leads to higher-dimensional generalizations of the WZNW and
DS equations. These are related with the Zakharov- Shabat equations. For
singular points, global Pl\"ucker formulae are derived by combining the
$A_n$-Toda equations with the Gauss-Bonnet theorem written for each of the
associated surfaces. | An operator approach to BRST invariant transition amplitudes: The transition amplitudes for the free spinless and spinning relativistic
particles are obtained by applying an operator method developed long ago by
Dirac and Schwinger to the BFV form of the BRST theory for constrained systems. |
From Linear SUSY to Constrained Superfields: We present a new formalism for finding the low-energy effective Lagrangian of
Goldstinos and other fields. This Lagrangian is written using standard
superspace and the superfields are constrained to include only the light
degrees of freedom. The Goldstino resides in a (constrained) chiral superfield
X which is naturally identified at short distances. This allows us to exactly
compute the IR behavior of some correlation functions even in strongly coupled
theories with SUSY breaking. The Goldstino couplings above the scale of the
matter superpartners are determined by identifying X with the standard spurion.
At energies below the superpartners' scale, fermions, scalars (including
Goldstone bosons) and gauge fields are also described by constrained
superfields. Our framework makes it easy to find the leading order terms in the
Lagrangian and to control their corrections. It simplifies the derivation of
many known results and leads to new ones. | 4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher
Gauge Theory Methods in the BV-BFV Formalism: We study the behavior of Donaldson's invariants of 4-manifolds based on the
moduli space of anti self-dual connections (instantons) in the perturbative
field theory setting where the underlying source manifold has boundary. It is
well-known that these invariants take values in the instanton Floer homology
groups of the boundary 3-manifold. Gluing formulae for these constructions lead
to a functorial topological field theory description according to a system of
axioms developed by Atiyah, which can be also regarded in the setting of
perturbative quantum field theory, as it was shown by Witten, using a version
of supersymmetric Yang-Mills theory, known today as Donaldson-Witten theory.
One can actually formulate an AKSZ model which recovers this theory for a
certain gauge-fixing. We consider these constructions in a perturbative quantum
gauge formalism for manifolds with boundary that is compatible with cutting and
gluing, called the BV-BFV formalism, which was recently developed by Cattaneo,
Mnev and Reshetikhin. We prove that this theory satisfies a modified Quantum
Master Equation and extend the result to a global picture when perturbing
around constant background fields. Additionally, we relate these constructions
to Nekrasov's partition function by treating an equivariant version of
Donaldson-Witten theory in the BV formalism. Moreover, we discuss the
extension, as well as the relation, to higher gauge theory and enumerative
geometry methods, such as Gromov-Witten and Donaldson-Thomas theory and recall
their correspondence conjecture for general Calabi-Yau 3-folds. In particular,
we discuss the corresponding (relative) partition functions, defined as the
generating function for the given invariants, and gluing phenomena. |
The Page Curve for Reflected Entropy: We study the reflected entropy $S_R$ in the West Coast Model, a toy model of
black hole evaporation consisting of JT gravity coupled to end-of-the-world
branes. We demonstrate the validity of the holographic duality relating it to
the entanglement wedge cross section away from phase transitions. Further, we
analyze the important non-perturbative effects that smooth out the
discontinuity in the $S_R$ phase transition. By performing the gravitational
path integral, we obtain the reflected entanglement spectrum analytically. The
spectrum takes a simple form consisting of superselection sectors, which we
interpret as a direct sum of geometries, a disconnected one and a connected one
involving a closed universe. We find that area fluctuations of $O(\sqrt{G_N})$
spread out the $S_R$ phase transition in the canonical ensemble, analogous to
the entanglement entropy phase transition. We also consider a Renyi
generalization of the reflected entropy and show that the location of the phase
transition varies as a function of the Renyi parameter. | Mirage Torsion: Z_NxZ_M orbifold models admit the introduction of a discrete torsion phase.
We find that models with discrete torsion have an alternative description in
terms of torsionless models. More specifically, discrete torsion can be 'gauged
away' by changing the shifts by lattice vectors. Similarly, a large class of
the so-called generalized discrete torsion phases can be traded for changing
the background fields (Wilson lines) by lattice vectors. We further observe
that certain models with generalized discrete torsion are equivalent to
torsionless models with the same gauge embedding but based on different
compactification lattices. We also present a method of classifying heterotic
Z_NxZ_M orbifolds. |
Off-shell $N=2\to N=1$ reduction in 4D conformal supergravity: We discuss $N=2\to N=1$ reduction in four dimensional conformal supergravity.
In particular, we keep the off-shell structure of supermultiplets (except
hypermultiplets). As we will show, starting with (almost) off-shell conformal
supergravity makes the procedure simpler than that from $N=2$ Poincar\'e
supergravity, which makes it easier to show the correspondence to the standard
$N=1$ conformal supergravity. We find that the $N=1$ superconformal symmetry is
simply realized by truncating the gravitino multiplet. We also discuss the
consistency with the original $N=2$ system and show the reduced $N=1$ conformal
supergravity action. | The emergence of flagpole and flag-dipole fermions in fluid/gravity
correspondence: The emergence of flagpole and flag-dipole singular spinor fields is explored,
in the context of fermionic sectors of fluid/gravity correspondence, arising
from the duality between the gravitino, in supergravity, and the phonino, in
supersymmetric hydrodynamics. Generalized black branes, whose particular case
consists of the AdS--Schwarzschild black brane, are regarded. The
correspondence between hydrodynamic transport coefficients, and the universal
absorption cross sections of the generalized black branes, is extended to
fermionic sectors, including supersound diffusion constants. A free parameter,
in the generalized black brane solution, is shown to control the flipping
between regular and singular fermionic solutions of the equations of motion for
the gravitino. |
Nonrelativistic Chern-Simons Vortices on the Torus: A classification of all periodic self-dual static vortex solutions of the
Jackiw-Pi model is given. Physically acceptable solutions of the Liouville
equation are related to a class of functions which we term
Omega-quasi-elliptic. This class includes, in particular, the elliptic
functions and also contains a function previously investigated by Olesen. Some
examples of solutions are studied numerically and we point out a peculiar
phenomenon of lost vortex charge in the limit where the period lengths tend to
infinity, that is, in the planar limit. | The giant graviton on AdS_{4} x CP^{3} - another step towards the
emergence of geometry: We construct the giant graviton on AdS_{4} x CP^{3} out of a four-brane
embedded in and moving on the complex projective space. This configuration is
dual to the totally anti-symmetric Schur polynomial operator
\chi_{R}(A_{1}B_{1}) in the 2+1-dimensional, N = 6 super Chern-Simons ABJM
theory. We demonstrate that this BPS solution of the D4-brane action is
energetically degenerate with the point graviton solution and initiate a study
of its spectrum of small fluctuations. Although the full computation of this
spectrum proves to be analytically intractable, by perturbing around a "small'"
giant graviton, we find good evidence for a dependence of the spectrum on the
size, \alpha_{0}, of the giant. This is a direct result of the changing shape
of the worldvolume as it grows in size. |
A new symmetry of the colored Alexander polynomial: We present a new conjectural symmetry of the colored Alexander polynomial,
that is the specialization of the quantum $\mathfrak{sl}_N$ invariant widely
known as the colored HOMFLY-PT polynomial. We provide arguments in support of
the existence of the symmetry by studying the loop expansion and the character
expansion of the colored HOMFLY-PT polynomial. We study the constraints this
symmetry imposes on the group theoretic structure of the loop expansion and
provide solutions to those constraints. The symmetry is a powerful tool for
research on polynomial knot invariants and in the end we suggest several
possible applications of the symmetry. | String Bits and Gluing of Metastring Strips: In this essay, we review the meta-string formulation proposed by Freidel,
Leigh, Minic in a recent paper. Our work focuses on the construction of a
closed-string world-sheet from gluing of Nakamura strips. We review the
symplectic current formulation for determining the gluing condition for a
single strip. We then study the two-strip scenario in a new notation to
rigorously derive the boundary equations of motion and finally generalize our
result to N -strips. We find the conjugate momenta to the strip separation
variable and relate it to the midpoint velocity of a strip. We see the natural
evolution of meta-D-branes in meta- string theory from the strip picture.
Finally, we motivate and show the connection of the strip picture to the
string-bit picture put forward by Klebanov and Susskind and conjecture the
relation to the Chan-Paton factors. |
Exact Equation for Wilson Loops in 2-Dimentional Euclidean Space: We derive an exact equation for simple self non-intersecting Wilson loops in
non-abelian gauge theories with gauge fields interacting with fermions in
2-dimensional Euclidean space. | The limits of the strong $CP$ problem: While $CP$ violation has never been observed in the strong interactions, the
QCD Lagrangian admits a $CP$-odd topological interaction proportional to the so
called $\theta$ angle, which weighs the contributions to the partition function
from different topological sectors. The observational bounds are usually
interpreted as demanding a severe tuning of $\theta$ against the phases of the
quark masses, which constitutes the strong $CP$ problem. Here we report on
recent challenges to this view based on a careful treatment of boundary
conditions in the path integral and of the limit of infinite spacetime volume,
which leads to $\theta$ dropping out of fermion correlation functions and
becoming unobservable, implying that $CP$ is preserved in QCD. |
Chern-Simons action for zero-mode supporting gauge fields in three
dimensions: Recent results on zero modes of the Abelian Dirac operator in three
dimensions support to some degree the conjecture that the Chern-Simons action
admits only certain quantized values for gauge fields that lead to zero modes
of the corresponding Dirac operator. Here we show that this conjecture is wrong
by constructing an explicit counter-example. | Convergent WKB Series: A set of simple exactly solvable potentials are shown to have convergent WKB
series. The resulting all-orders quantisation conditions provide a unified
description of all known cases where an exact WKB quantisation condition has
been obtained by modifying the potential with Langer-style terms, together with
several new examples. |
Dark Energy, $H_0$ and Weak Gravity Conjecture: We point out that the physics at the extreme IR---cosmology---might provide
tests of the physics of the extreme UV---the Weak Gravity Conjecture. The
current discrepancies in the determination of $H_0$ may hint at a modification
of $\Lambda$CDM. An extension which may fit better comprises of an early
contribution to dark energy which `decays' into relativistic matter. On the
other hand the discourse on WGC to date suggests that fields which support
cosmic acceleration may produce relativistic matter after they traverse a
$\sim$ Planckian distance in field space. We explain how this offers a simple
realization of the requisite cosmic phenomenology. Thus if the resolution of
$H_0$ discrepancies is really early dark energy that ends with a shower of
relativistic matter and the current ideas on WGC are indicative, this may be a
rare opportunity to link the two extreme limits of quantum field theory. | Towards a four-loop form factor: The four-loop, two-point form factor contains the first non-planar correction
to the lightlike cusp anomalous dimension. This anomalous dimension is a
universal function which appears in many applications. Its planar part in N = 4
SYM is known, in principle, exactly from AdS/CFT and integrability while its
non-planar part has been conjectured to vanish. The integrand of the form
factor of the stress-tensor multiplet in N = 4 SYM including the non-planar
part was obtained in previous work. We parametrise the difficulty of
integrating this integrand. We have obtained a basis of master integrals for
all integrals in the four-loop, two-point class in two ways. First, we computed
an IBP reduction of the integrand of the N = 4 form factor using massive
computer algebra (Reduze). Second, we computed a list of master integrals based
on methods of the Mint package, suitably extended using Macaulay2 / Singular.
The master integrals obtained in both ways are consistent with some minor
exceptions. The second method indicates that the master integrals apply beyond
N = 4 SYM, in particular to QCD. The numerical integration of several of the
master integrals will be reported and remaining obstacles will be outlined |
N=2 SUSY gauge theories on S^4: We review exact results in N=2 supersymmetric gauge theories defined on S^4
and its deformation. We first summarize the construction of rigid SUSY theories
on curved backgrounds based on off-shell supergravity, then explain how to
apply localization principle to supersymmetric path integrals. Closed formulae
for partition function as well as expectation values of non-local BPS
observables are presented. | Mass gap for a monopole interacting with a nonlinear spinor field: Within SU(2) Yang-Mills theory with a source of the non-Abelian gauge field
in the form of a classical spinor field, we study the dependence of the mass
gap on the coupling constant between the gauge and nonlinear spinor fields. It
is shown that the total dimensionless energy of the monopole interacting with
the nonlinear spinor fields depends only on the dimensionless coupling
constant. |
Center Vortices, Nexuses, and the Georgi-Glashow Model: In a gauge theory with no Higgs fields the mechanism for confinement is by
center vortices, but in theories with adjoint Higgs fields and generic symmetry
breaking, such as the Georgi-Glashow model, Polyakov showed that in d=3
confinement arises via a condensate of 't Hooft-Polyakov monopoles. We study
the connection in d=3 between pure-gauge theory and the theory with adjoint
Higgs by varying the Higgs VEV v. As one lowers v from the Polyakov semi-
classical regime v>>g (g is the gauge coupling) toward zero, where the unbroken
theory lies, one encounters effects associated with the unbroken theory at a
finite value v\sim g, where dynamical mass generation of a gauge-symmetric
gauge- boson mass m\sim g^2 takes place, in addition to the Higgs-generated
non-symmetric mass M\sim vg. This dynamical mass generation is forced by the
infrared instability (in both 3 and 4 dimensions) of the pure-gauge theory. We
construct solitonic configurations of the theory with both m,M non-zero which
are generically closed loops consisting of nexuses (a class of soliton recently
studied for the pure-gauge theory), each paired with an antinexus, sitting like
beads on a string of center vortices with vortex fields always pointing into
(out of) a nexus (antinexus); the vortex magnetic fields extend a transverse
distance 1/m. An isolated nexus with vortices is continuously deformable from
the 't Hooft-Polyakov (m=0) monopole to the pure-gauge nexus-vortex complex
(M=0). In the pure-gauge M=0 limit the homotopy $\Pi_2(SU(2)/U(1))=Z_2$ (or its
analog for SU(N)) of the 't Hooft monopoles is no longer applicable, and is
replaced by the center-vortex homotopy $\Pi_1(SU)N)/Z_N)=Z_N$. | Chiral Algebra, Localization, Modularity, Surface defects, And All That: We study the 2D vertex operator algebra (VOA) construction in 4D
$\mathcal{N}=2$ superconformal field theories (SCFT) on $S^3 \times S^1$,
focusing both on old puzzles as well as new observations. The VOA lives on a
two-torus $\mathbb{T}^2\subset S^3\times S^1$, it is
$\frac12\mathbb{Z}$-graded, and this torus is equipped with the natural choice
of spin structure (1,0) for the $\mathbb{Z} +\frac12$-graded operators,
corresponding to the NS sector vacuum character. By analyzing the possible
refinements of the Schur index that preserve the VOA, we find that it admits
discrete deformations, which allow access to the remaining spin structures
(1,1), (0,1) and (0,0), of which the latter two involve the inclusion of a
particular surface defect. For Lagrangian theories, we perform the detailed
analysis: we describe the natural supersymmetric background, perform
localization, and derive the gauged symplectic boson action on a torus in any
spin structure. In the absence of flavor fugacities, the 2D and 4D path
integrals precisely match, including the Casimir factors. We further analyze
the 2D theory: we identify its integration cycle, the two-point functions, and
interpret flavor holonomies as screening charges in the VOA. Next, we make some
observations about modularity; the $T$-transformation acts on our four
partition functions and lifts to a large diffeomorphism on $S^3\times S^1$.
More interestingly, we generalize the four partition functions on the torus to
an infinite family labeled both by the spin structure and the integration cycle
inside the complexified maximal torus of the gauge group. Members of this
family transform into one another under the full modular group, and we confirm
the recent observation that the $S$-transform of the Schur index in Lagrangian
theories exhibits logarithmic behavior. Finally, we comment on how locally our
background reproduces the $\Omega$-background. |
Use of Physical Variables in the Chern-Simons Theories: The use of the physical variables in the fashion of Dirac in the
three-dimensional Chern-Simons theories is presented. Our previous results are
reinterpreted in a new aspect. | Ladder Operators in Repulsive Harmonic Oscillator with Application to
the Schwinger Effect: The ladder operators in harmonic oscillator are a well-known strong tool for
various problems in physics. In the same sense, it is sometimes expected to
handle the problems of repulsive harmonic oscillator in a similar way to the
ladder operators in harmonic oscillators, though their analytic solutions are
well known. In this paper, we discuss a simple algebraic way to introduce the
ladder operators of the repulsive harmonic oscillators, which can reproduce
well-known analytic solutions. Applying this formalism, we discuss the charged
particles in a constant electric field in relation to the Schwinger effect; the
discussion is also made on a supersymmetric extension of this formalism. |
Quantum Vacuum Energy of Self-Similar Configurations: We offer in this review a description of the vacuum energy of self-similar
systems. We describe two views of setting self-similar structures and point out
the main differences. A review of the authors' work on the subject is
presented, where they treat the self-similar system as a many-object problem
embedded in a regular smooth manifold. Focused on Dirichlet boundary
conditions, we report a systematic way of calculating the Casimir energy of
self-similar bodies where the knowledge of the quantum vacuum energy of the
single building block element is assumed and in fact already known. A
fundamental property that allows us to proceed with our method is the
dependence of the energy on a geometrical parameter that makes it possible to
establish the scaling property of self-similar systems. Several examples are
given. We also describe the situation, shown by other authors, where the
embedded space is a fractal space itself, having fractal dimension. A fractal
space does not hold properties that are rather common in regular spaces like
the tangent space. We refer to other authors who explain how some self-similar
configurations "do not have any smooth structures and one cannot define
differential operators on them directly". This gives rise to important
differences in the behavior of the vacuum. | Duality and asymptotic geometries: We consider a series of duality transformations that leads to a constant
shift in the harmonic functions appearing in the description of a configuration
of branes. This way, for several intersections of branes, we can relate the
original brane configuration which is asymptotically flat to a geometry of the
type $adS_k \xx E^l \xx S^m$. The implications of our results for supersymmetry
enhancement, M(atrix) theory at finite N, and for supergravity theories in
diverse dimensions are discussed. |
A minimal BV action for Vasiliev's four-dimensional higher spin gravity: The action principle for Vasiliev's four-dimensional higher-spin gravity
proposed recently by two of the authors, is converted into a minimal BV master
action using the AKSZ procedure, which amounts to replacing the classical
differential forms by vectorial superfields of fixed total degree given by the
sum of form degree and ghost number. The nilpotency of the BRST operator is
achieved by imposing boundary conditions and choosing appropriate gauge
transitions between charts leading to a globally-defined formulation based on a
principal bundle. | Nonperturbative Field Correlators in the Abelian Higgs Model: By making use of the duality transformation, gauge field correlators of the
Abelian Higgs Model are studied in the London limit. The obtained results are
in a good agreement with the dual Meissner scenario of confinement and with the
Stochastic Model of QCD vacuum. The nontrivial contribution to the quartic
correlator arising due to accounting for the finiteness of the coupling
constant is discussed. |
Boundary stress tensors for spherically symmetric conformal Rindler
observers: The boundary energy - momentum tensors for a static observer in the
conformally flat Rindler geometry are considered. We found the surface energy
is positive far form the Planck world but the transversal pressures are
negative. The kinematical parameters associated to a nongeodesic congruence of
static observers are computed. The entropy $S$ corresponding to the degrees of
freedom on the two surface of constant $\rho$ and $t$ equals the horizon
entropy of a black hole with a time dependent mass and the Padmanabhan
expression $E = 2 S T$ is obeyed. The two surface shear tensor is vanishing but
the coefficient of the bulk viscosity $\zeta$ is $1/16 \pi$ and therefore the
negative pressure due to it acts as a surface tension. | Critical Super F-theories: We present F-theories that reduce to 10D Type II Green-Schwarz superstrings.
They vary in manifest U-duality according to division between spacetime and
"internal" coordinates. They are defined by selfdual current superalgebras in
higher worldvolume dimensions with manifest $\mathrm G\times \mathrm G'$
symmetry where the spacetime symmetry $\mathrm G=\mathrm E_{n(n)}$ ranges over
the (split form of the) exceptional groups with ranks $n=\mathrm D+1 \leq 7$
and the internal symmetry $\mathrm {G'= GL(10-D)}$. |
Defects in conformal field theory: We discuss consequences of the breaking of conformal symmetry by a flat or
spherical extended operator. We adapt the embedding formalism to the study of
correlation functions of symmetric traceless tensors in the presence of the
defect. Two-point functions of a bulk and a defect primary are fixed by
conformal invariance up to a set of OPE coefficients, and we identify the
allowed tensor structures. A correlator of two bulk primaries depends on two
cross-ratios, and we study its conformal block decomposition in the case of
external scalars. The Casimir equation in the defect channel reduces to a
hypergeometric equation, while the bulk channel blocks are recursively
determined in the light-cone limit. In the special case of a defect of
codimension two, we map the Casimir equation in the bulk channel to the one of
a four-point function without defect. Finally, we analyze the contact terms of
the stress-tensor with the extended operator, and we deduce constraints on the
CFT data. In two dimensions, we relate the displacement operator, which appears
among the contact terms, to the reflection coefficient of a conformal
interface, and we find unitarity bounds for the latter. | On the Stress Tensor of Kerr/CFT: The recently-conjectured Kerr/CFT correspondence posits a field theory dual
to dynamics in the near-horizon region of an extreme Kerr black hole with
certain boundary conditions. We construct a boundary stress tensor for this
theory via covariant phase space techniques. The structure of the stress tensor
indicates that any dual theory is a discrete light cone quantum theory, in
agreement with recent arguments by Balasubramanian et al. The key technical
step in our construction is the addition of an appropriate counter-term to the
symplectic structure, which is necessary to make the theory fully covariant and
to resolve a subtle problem involving the integrability of charges. |
Gauge field localization on Abelian vortices in six dimensions: The vector and tensor fluctuations of vortices localizing gravity in the
context of the six-dimensional Abelian Higgs model are studied. These
string-like solutions break spontaneously six-dimensional Poincar\'e invariance
leading to a finite four-dimensional Planck mass and to a regular geometry both
in the bulk and on the core of the vortex. While the tensor modes of the metric
are decoupled and exhibit a normalizable zero mode, the vector fluctuations,
present in the gauge sector of the theory, are naturally coupled to the
graviphoton fields associated with the vector perturbations of the warped
geometry. Using the invariance under infinitesimal diffeomorphisms, it is found
that the zero modes of the graviphoton fields are never localized. On the
contrary,the fluctuations of the Abelian gauge field itself admit a
normalizable zero mode. | Supergravity and a Bogomol'nyi Bound in Three Dimensions: We discuss the $2+1$ dimensional Abelian Higgs model coupled to $N=2$
supergravity. We construct the supercharge algebra and, from it, we show that
the mass of classical static solutions is bounded from below by the topological
charge. As it happens in the global case, half of the supersymmetry is broken
when the bound is attained and Bogomol'nyi equations, resulting from the
unbroken supersymmetry, hold. These equations, which correspond to gravitating
vortices, include a first order self-duality equation whose integrability
condition reproduces the Einstein equation. |
The spectrum of anomalous magnetohydrodynamics: The equations of anomalous magnetohydrodynamics describe an Abelian plasma
where conduction and chiral currents are simultaneously present and constrained
by the second law of thermodynamics. At high frequencies the magnetic currents
play the leading role and the spectrum is dominated by two-fluid effects. The
system behaves instead as a single fluid in the low-frequency regime where the
vortical currents induce potentially large hypermagnetic fields. After deriving
the physical solutions of the generalized Appleton-Hartree equation, the
corresponding dispersion relations are scrutinized and compared with the
results valid for cold plasmas. Hypermagnetic knots and fluid vortices can be
concurrently present at very low frequencies and suggest a qualitatively
different dynamics of the hydromagnetic nonlinearities. | Axial current in QED and semi-naive dimensional renormalization: We renormalize at two loops the axial current and $F \tilde{F}$ in massless
QED, using the recently proposed semi-naive dimensional renormalization scheme.
We show that the results are in agreement with those in the
Breitenlohner-Maison-'t Hooft-Veltman scheme, previously obtained indirectly by
making a three-loop computation. |
The virial relation for the Q-balls in the thermal logarithmic potential
revisited analytically: We study the properties of Q-balls dominated by the thermal logarithmic
potential analytically instead of estimating the characters with only some
specific values of model variables numerically. In particular the analytical
expressions for radius and energy of this kind of Q-ball are obtained.
According to these explicit expressions we demonstrate strictly that the large
Q-balls enlarge and the small ones become smaller in the background with lower
temperature. The energy per unit charge will not be divergent if the charge is
enormous. We find that the lower temperature will lead the energy per unit
charge of Q-ball smaller. We also prove rigorously the necessary conditions
that the model parameters should satisfy to keep the stability of the Q-balls.
When one of model parameters of Q-balls $K$ is positive, the Q-balls will not
form or survive unless the temperature is high enough. In the case of negative
$K$, the Q-balls are stable no matter the temperature is high or low. | Integrability in Fluid Dynamics: 3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria
for exact integrability, i.e. having an infinite set of independent, conserved
quantities in involution, with the Hamiltonian being one of them. With (density
dependent) interaction present, distinct infinite serieses of conserved
quantities in involution are discovered. Clebsch parametrization of the
velocity field is used in the the latter analysis. Relativistic generalization
of the free system is also shown to be integrable. |
Hyperbolic three-string vertex: We begin developing tools to compute off-shell string amplitudes with the
recently proposed hyperbolic string vertices of Costello and Zwiebach.
Exploiting the relation between a boundary value problem for Liouville's
equation and a monodromy problem for a Fuchsian equation, we construct the
local coordinates around the punctures for the generalized hyperbolic
three-string vertex and investigate their various limits. This vertex
corresponds to the general pants diagram with three boundary geodesics of
unequal lengths. We derive the conservation laws associated with such vertex
and perform sample computations. We note the relevance of our construction to
the calculations of the higher-order string vertices using the pants
decomposition of hyperbolic Riemann surfaces. | BRST Invariance and Renormalisability of the SU(2)$\times$U(1)
Electroweak Theory with Massive W Z Bosons: Since the SU(n) gauge theory with massive gauge bosons has been proven to be
renormalisable we reinvestigate the renormalisability of the
SU$_L$(2) $\times$ U$_Y$(1) electroweak theory with massive W Z bosons. We
expound that with the constraint conditions caused by the W Z mass term and the
additional condition chosen by us we can performed the quantization and
construct the ghost action in a way similar to that used for the massive SU(n)
theory. We also show that when the $\delta-$ functions appearing in the path
integral of the Green functions and representing the constraint conditions are
rewritten as Fourier integrals with Lagrange multipliers $\lambda_a$ and
$\lambda_y$, the BRST invariance is kept in the total effective action
consisting of the Lagrange multipliers, ghost fields and the original fields.
Furthermore, by comparing with the massless theory and with the massive SU(n)
theory we find the general form of the divergent part of the generating
functional for the regular vertex functions and prove the renormalisability of
the theory. It is also clarified that the renormalisability of the theory with
the W Z mass term is ensured by that of the massless theory and the massive
SU(n) theory. |
BRS Cohomology in Topological String Theory and Integrable Systems: In cohomological field theory we can obtain topological invariants as
correlation functions of BRS cohomology classes. A proper understanding of BRS
cohomology which gives non-trivial results requires the equivariant cohomology
theory. Both topological Yang-Mills theory and topological string theory are
typical examples of this fact. After reviewing the role of the equivariant
cohomology in topological Yang-Mills theory, we show in purely algebraic
framework how the $U(1)$ equivariant cohomology in topological string theory
gives the gravitational descendants. The free energy gives a generating
function of topological correlation functions and leads us to consider a
deformation family of cohomological field theories. In topological strings such
a family is controlled by the theory of integrable system. This is most easily
seen in the Landau-Ginzburg approach by looking at the contact term
interactions between topological observables. | On the renormalization of periodic potentials: The renormalization of the periodic potential is investigated in the
framework of the Euclidean one-component scalar field theory by means of the
differential RG approach. Some known results about the sine-Gordon model are
recovered in an extremely simple manner. There are two phases, an ordered one
with asymptotical freedom and a disordered one where the model is
non-renormalizable and trivial. The order parameter of the periodicity, the
winding number, indicates spontaneous symmetry breaking in the ordered phase
where the fundamental group symmetry is broken and the solitons acquire
dynamical stability. It is argued that the periodicity and the convexity are so
strong constraints on the effective potential that it always becomes flat. This
flattening is reproduced by integrating out the RG equation. |
Reaction-Diffusion Processes as Physical Realizations of Hecke Algebras: We show that the master equation governing the dynamics of simple diffusion
and certain chemical reaction processes in one dimension give time evolution
operators (Hamiltonians) which are realizations of Hecke algebras. In the case
of simple diffusion one obtains, after similarity transformations, reducible
hermitian representations while in the other cases they are non-hermitian and
correspond to supersymmetric quotients of Hecke algebras. | Second Law of Black Hole Mechanics for all 2d Dilaton Theories: It is shown that all generalized two--dimensional dilaton theories with
arbitrary matter content (with a curvature independent coupling to gravity) do
not only obey a first law of black hole mechanics (which follows from Wald's
general considerations, if the entropy S is defined appropriately), but also a
second law: \delta S \ge 0 provided only that the null energy condition holds
and that, loosely speaking, for late times a stationary state is assumed. Also
any two-dimensional f(R)--theory is covered. This generalizes a previous proof
of Frolov [1] to a much wider class of theories. |
Fermion transfer in the $φ^4$ model with a half-BPS preserving
impurity: We study a fermion field coupled to a scalar via a Yukawa term. The scalar
field is the $\phi^4$ model with an impurity that preserves half of the BPS
property. We analyze the spectrum of the defects of the model and collisions
between them both close to the BPS regime and not. As the fermion binds to
these defects, it may be transferred from one to the other, which we quantify
via overlaps, known as Bogoliubov coefficients. BPS collisions are less likely
to transfer the fermion between defects and can be adiabatic for
non-relativistic velocities, especially for small coupling constants. Moreover,
closer to the BPS limit only a small fraction of the fermion number is radiated
away. In contrast, non-BPS collisions lead to more radiation in the fermion
field and excitation of the fermion to higher bound states, and the result is
more sensitive to the parameters. | Entanglement entropy in FRW backgrounds: We use holography in order to study the entanglement entropy for a spherical
entangling surface in a FRW background with an arbitrary time dependence of the
scale factor. The calculation is done in various dimensions, allowing for
nonzero spatial curvature. The entanglement entropy of a CFT at nonzero
temperature in this background is also considered. Our approach is based on
coordinate transformations that relate the extremization problem to the one for
a static background, with a careful determination of the UV cutoff. We
demonstrate the agreement with the expected form of the entanglement entropy
and with various known results in specific cases. In four dimensions, apart
from the cutoff-dependent terms, we compute and discuss the finite term related
to the expansion rate. |
Pfaffian Diagrams for Gluon Tree Amplitudes: Pfaffian diagrams are formulated to represent gluon amplitudes computed from
the Cachazo-He-Yuan (CHY) formula. They may be regarded as a systematic
regrouping of Feynman diagrams after internal momenta are expanded and products
of vertex factors are evaluated. This reprocessing enables gluon amplitudes
expressed in Pfaffian diagrams to contain less terms. For example, there are 19
terms for the four-point amplitude in Pfaffian diagrams, and 35 terms in
Feynman diagrams. Gauge invariance is simpler and more explicit in Pfaffian
diagrams, in that subset of diagrams with the same root configuration are
already gauge invariant in all lines but two. In getting to these results,
several technical difficulties must be overcome. Double poles must be converted
to simple poles, integrations must be carried out directly and formulated into
simple rules, and the three \M constant lines must be suitably chosen to
minimize the number of terms present. | Heisenberg-Euler Effective Lagrangians : Basics and Extensions: I present a pedagogical review of Heisenberg-Euler effective Lagrangians,
beginning with the original work of Heisenberg and Euler, and Weisskopf, for
the one loop effective action of quantum electrodynamics in a constant
electromagnetic background field, and then summarizing some of the important
applications and generalizations to inhomogeneous background fields, nonabelian
backgrounds, and higher loop effective Lagrangians. |
A pedagogical review on solvable irrelevant deformations of 2d quantum
field theory: This is a pedagogical review on $\mathrm{T}\overline{\mathrm{T}}$ deformation
of two dimensional quantum field theories. It is based on three lectures which
the author gave at ITP-CAS in December 2018. This review consists of four
parts. The first part is a general introduction to
$\mathrm{T}\overline{\mathrm{T}}$ deformation. Special emphasises are put on
the deformed classical Lagrangian and the exact solvability of the spectrum.
The second part focuses on the torus partition sum of the
$\mathrm{T}\overline{{\mathrm{T}}}$/$\mathrm{J}\overline{\mathrm{T}}$ deformed
conformal field theories and modular invariance/covariance. In the third part,
different perspectives of $\mathrm{T}\overline{\mathrm{T}}$ deformation are
presented, including its relation to random geometry, 2d topological gravity
and holography. We summarize more recent developments until January 2021 in the
last part. | String Backgrounds of the Yang-Baxter Deformed
$AdS_4\times\mathbb{CP}^3$ Superstring: We build string backgrounds for Yang-Baxter deformations of the
$AdS_4\times\mathbb{CP}^3$ superstring generated by $r$-matrices satisfying the
classical Yang-Baxter equation. We obtain the metric and the NS-NS two-form of
the gravity dual corresponding to noncommutative and dipole deformations of
ABJM theory, as well as a deformed background with Schr\"odinger symmetry. The
first two backgrounds may also be found by TsT transformations while for the
last background we get a new family of non-relativistic ABJM theories with
Schr\"odinger symmetry. |
More on vacua of exotic massive 3D gravity: In a recent paper [arXiv:1806.06254], we explored the space of solutions of
the exotic massive 3D gravity theory proposed in [arXiv:1806.04179]. We showed
that the theory admits a rich space of vacua, including asymptotically Anti
de-Sitter (AdS) geometries obeying different types of boundary conditions. The
examples include black holes dressed with low decaying gravitons. Based on what
happens in other theories of massive gravity, we conjectured that such
geometries appear on a curve of the parameter space (chiral curve) where the
exotic massive gravity on AdS with sufficiently strong boundary conditions
results dual to a 2D chiral conformal field theory. Here, we show that this
expectation is consistent with the conserved charges and thermodynamical
properties of the black holes of the theory, which have recently been computed
[arXiv:1812.09525]. When the boundary conditions are relaxed relative to the
standard Brown-Henneaux boundary conditions, the theory exhibits solutions
consistent with the definition of the so-called Log-gravity. The asymptotic
behavior of these solutions presents a logarithmic term in the Fefferman-Graham
expansion that, nonetheless, is compatible with the AdS asymptotic symmetries.
This long range interaction is due to a mode of the massive gravity that
becomes massless precisely on the chiral curve. We construct exact solutions
exhibiting this behavior, which admit to be interpreted as fully backreacting
gravitational waves propagating on an extremal black hole, and carrying
non-vanishing gravitational energy. We also discuss other vacua of the theory,
such as Warped-AdS$_3$ black holes, gravitational waves on such backgrounds,
AdS$_2\times S^1$ spaces, and black holes in dS$_3$ space. | Bose-Fermi Degeneracy and Duality in Non-Supersymmetric Strings: Following Kachru, Kumar and Silverstein, we construct a set of
non-supersymmetric Type II string models which have equal numbers of bosons and
fermions at each mass level. The models are asymmetric {\bf Z}_2 \otimes {\bf
Z}_2^{\prime} orbifolds. We demonstrate that this bose-fermi degeneracy feature
implies that both the one-loop and the two-loop contributions to the
cosmological constant vanish. We conjecture that the cosmological constant
actually vanishes to all loops. We construct a strong-weak dual pair of models,
both of which have bose-fermi degeneracy. This implies that at least some of
the non-perturbative corrections to the cosmological constant are absent. |
Stable Monopole-Antimonopole String Background in SU(2) QCD: Motivated by the instability of the Savvidy-Nielsen-Olesen vacuum we make a
systematic search for a stable magnetic background in pure SU(2) QCD. It is
shown that a pair of axially symmetric monopole and antimonopole strings is
stable, provided that the distance between the two strings is less than a
critical value. The existence of a stable monopole-antimonopole string
background strongly supports that a magnetic condensation of
monopole-antimonopole pairs can generate a dynamical symmetry breaking, and
thus the magnetic confinement of color in QCD. | Running with the Radius in RS1: We derive a renormalization group formalism for the Randall-Sundrum scenario,
where the renormalization scale is set by a floating compactification radius.
While inspired by the AdS/CFT conjecture, our results are derived concretely
within higher-dimensional effective field theory. Matching theories with
different radii leads to running hidden brane couplings. The hidden brane
Lagrangian consists of four-dimensional local operators constructed from the
induced value of the bulk fields on the brane. We find hidden Lagrangians which
are non-trivial fixed points of the RG flow. Calculations in RS1 can be greatly
simplified by ``running down'' the effective theory to a small radius. We
demonstrate these simplifications by studying the Goldberger-Wise stabilization
mechanism. In this paper, we focus on the classical and tree-level quantum
field theory of bulk scalar fields, which demonstrates the essential features
of the RG in the simplest context. |
Static skyrmions in (2+1)-dimensions: In the spirit of previous papers, but using more general field
configurations, the non-linear O(3) model in (2+1)-D, modified by the addition
of both a potential-like term and a Skyrme-like term, is considered. The
instanton solutions are numerically evolved in time and some of their stability
properties studied. They are found to be stable, and a repulsive force is seen
to exist among them. These results, which are restricted to the case of zero
speed systems, confirm those obtained in previous investigations, in which a
similar problem was studied for a different choice of the potential-like term. | Lorentz violation and higher-derivative gravity: In this work, we analyze a gravity model with higher derivatives including a
CPT-even Lorentz-violating term. In principle, the model could be a low-energy
limit of a Lorentz-invariant theory presenting the violation of Lorentz
symmetry as a consequence of a spontaneous symmetry-breaking mechanism if a
decoupling between the metric and the Nambu-Goldstone modes is assumed. We have
set up a convenient operator basis for the expansion of wave operators for
symmetric second-rank tensors in the presence of a background vector. By using
this set of operators, the particle content is obtained, and its consistency,
regarding the conditions for stability and unitarity, is discussed. We conclude
that this extra Lorentz noninvariant contribution is unable to address the
problems of stability and unitarity of higher-derivative gravity models. |
Quantum Corrections to Scattering Amplitude in Conical Space-time: It is known that the vacuum polarization of zero-point field arises around a
conical singularity generated by an infinite, straight cosmic string. In this
paper we study quantum electromagnetic corrections to the gravitational
Aharonov-Bohm effect around a cosmic string. We find the scattering amplitude
from a conical defect for charged Klein-Gordon field. | Fock Space Representation of Differential Calculus on the Noncommutative
Quantum Space: A complete Fock space representation of the covariant differential calculus
on quantum space is constructed. The consistency criteria for the ensuing
algebraic structure, mapping to the canonical fermions and bosons and the
consequences of the new algebra for the statistics of quanta are analyzed and
discussed. The concept of statistical transmutation between bosons and fermions
is introduced. |
3-point functions of universal scalars in maximal SCFTs at large N: We compute all 3-point functions of the ``universal'' scalar operators
contained in the interacting, maximally supersymmetric CFTs at large N by using
the AdS/CFT correspondence. These SCFTs are related to the low energy
description of M5, M2 and D3 branes, and the common set of universal scalars
corresponds through the AdS/CFT relation to the fluctuations of the metric and
the magnetic potential along the internal manifold. For the interacting (0,2)
SCFT_6 at large N, which is related to M5 branes, this set of scalars is
complete, while additional non-universal scalar operators are present in the
d=4, N=4 super Yang-Mills theory and in the N=8 SCFT_3, related to D3 and M2
branes, respectively. | Wilson Lines and a Canonical Basis of SU(4) Heterotic Standard Models: The spontaneous breaking of SU(4) heterotic standard models by Z_3 x Z_3
Wilson lines to the MSSM with three right-handed neutrino supermultiplets and
gauge group SU(3)_C x SU(2)_L x U(1) x U(1) is explored. The two-dimensional
subspace of the Spin(10) Lie algebra that commutes with su(3)_C + su(2)_L is
analyzed. It is shown that there is a unique basis for which the initial soft
supersymmetry breaking parameters are uncorrelated and for which the U(1) x
U(1) field strengths have no kinetic mixing at any scale. If the Wilson lines
"turn on" at different scales, there is an intermediate regime with either a
left-right or a Pati-Salam type model. We compute their spectra directly from
string theory, and adjust the associated mass parameter so that all gauge
parameters exactly unify. A detailed analysis of the running gauge couplings
and soft gaugino masses is presented. |
Noncommutative Perturbative Dynamics: We study the perturbative dynamics of noncommutative field theories on R^d,
and find an intriguing mixing of the UV and the IR. High energies of virtual
particles in loops produce non-analyticity at low momentum. Consequently, the
low energy effective action is singular at zero momentum even when the original
noncommutative field theory is massive. Some of the nonplanar diagrams of these
theories are divergent, but we interpret these divergences as IR divergences
and deal with them accordingly. We explain how this UV/IR mixing arises from
the underlying noncommutativity. This phenomenon is reminiscent of the channel
duality of the double twist diagram in open string theory. | Coadjoint orbits of the Virasoro algebra and the global Liouville
equation: The classification of the coadjoint orbits of the Virasoro algebra is
reviewed and is then applied to analyze the so-called global Liouville
equation. The review is self-contained, elementary and is tailor-made for the
application. It is well-known that the Liouville equation for a smooth, real
field $\phi$ under periodic boundary condition is a reduction of the SL(2,R)
WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to
be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction
yields, for the field $Q=\kappa g_{22}$ where $\kappa\neq 0$ is a constant,
what we call the global Liouville equation. Corresponding to the winding number
of the SL(2,R) WZNW model there is a topological invariant in the reduced
theory, given by the number of zeros of Q over a period. By the substitution
$Q=\pm\exp(- \phi/2)$, the Liouville theory for a smooth $\phi$ is recovered in
the trivial topological sector. The nontrivial topological sectors can be
viewed as singular sectors of the Liouville theory that contain blowing-up
solutions in terms of $\phi$. Since the global Liouville equation is
conformally invariant, its solutions can be described by explicitly listing
those solutions for which the stress-energy tensor belongs to a set of
representatives of the Virasoro coadjoint orbits chosen by convention. This
direct method permits to study the `coadjoint orbit content' of the topological
sectors as well as the behaviour of the energy in the sectors. The analysis
confirms that the trivial topological sector contains special orbits with
hyperbolic monodromy and shows that the energy is bounded from below in this
sector only. |
Ground-state wave-functional in (2+1)-dimensional Yang-Mills theory:
Abelian limit, spectrum and robustness: We compute the glueball spectrum in (2+1)-dimensional Yang-Mills theory by
analyzing correlators of the Leigh-Minic-Yelnikov ground-state wave-functional
in the Abelian limit. The contribution of the WZW measure is treated by a
controlled approximation and the resulting spectrum is shown to reduce to that
obtained by Leigh et al., at large momentum. | Emergent electrodynamics from the Nambu model for spontaneous Lorentz
symmetry breaking: After imposing the Gauss law constraint as an initial condition upon the
Hilbert space of the Nambu model, in all its generic realizations, we recover
QED in the corresponding non-linear gauge A_{\mu}A^{\mu}=n^{2}M^{2}. Our result
is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to
the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz
symmetry breaking dynamically generates gauge invariance, provided the Gauss
law is imposed as an initial condition. In this way electrodynamics is
recovered, with the photon being realized as the Nambu-Goldstone modes of the
spontaneously broken symmetry, which finally turns out to be non-observable |
Single-step de Sitter vacua from non-perturbative effects with matter: A scenario of moduli stabilisation based on the interplay between closed and
open string sectors is explored in a bottom-up approach. We study N=1 effective
supergravities inspired by type IIB orientifold constructions that include
background fluxes and non-perturbative effects. The former generate the
standard flux superpotential for the axiodilaton and complex structure moduli.
The latter can be induced by gaugino condensation in a non-Abelian sector of
D7-branes and involve the overall Kaehler modulus of the compactification as
well as matter fields. We analyse the dynamics of this coupled system and show
that it is compatible with single-step moduli stabilisation in a metastable de
Sitter vacuum. A novelty of the scenario is that the F-term potential suffices
to generate a positive cosmological constant and to stabilise all moduli,
except for a flat direction that can be either lifted by a mass term or eaten
up by an anomalous U(1). | The N=4 Quantum Conformal Algebra: We determine the spectrum of currents generated by the operator product
expansion of the energy-momentum tensor in N=4 super-symmetric Yang-Mills
theory. Up to the regular terms and in addition to the multiplet of the stress
tensor, three current multiplets appear, Sigma, Xi and Upsilon, starting with
spin 0, 2 and 4, respectively. The OPE's of these new currents generate an
infinite tower of current multiplets, one for each even spin, which exhibit a
universal structure, of length 4 in spin units, identified by a two-parameter
rational family. Using higher spin techniques developed recently for conformal
field theories, we compute the critical exponents of Sigma, Xi and Upsilon in
the TT OPE and prove that the essential structure of the algebra holds at
arbitrary coupling. We argue that the algebra closes in the strongly coupled
large-$N_c$ limit. Our results determine the quantum conformal algebra of the
theory and answer several questions that previously remained open. |
Identification of perturbation modes and controversies in ekpyrotic
perturbations: If the linear perturbation theory is valid through the bounce, the surviving
fluctuations from the ekpyrotic scenario (cyclic one as well) should have very
blue spectra with suppressed amplitude for the scalar-type structure. We derive
the same (and consistent) result using the curvature perturbation in the
uniform-field (comoving) gauge and in the zero-shear gauge. Previously, Khoury
et al. interpreted results from the latter gauge condition incorrectly and
claimed the scale-invariant spectrum, thus generating controversy in the
literature. We also correct similar errors in the literature based on wrong
mode identification and joining condition. No joining condition is needed for
the derivation. | Holographic Complexity Bounds: We study the action growth rate in the Wheeler-DeWitt (WDW) patch for a
variety of $D\ge 4$ black holes in Einstein gravity that are asymptotic to the
anti-de Sitter spacetime, with spherical, toric and hyperbolic horizons,
corresponding to the topological parameter $k=1,0,-1$ respectively. We find a
lower bound inequality $\frac{1}{T} \frac{\partial \dot I_{\rm WDW}}{\partial
S}|_{Q,P_{\rm th}}> C$ for $k=0,1$, where $C$ is some order-one numerical
constant. The lowest number in our examples is $C=(D-3)/(D-2)$. We also find
that the quantity $(\dot I_{\rm WDW}-2P_{\rm th}\, \Delta V_{\rm th})$ is
greater than, equal to, or less than zero, for $k=1,0,-1$ respectively. For
black holes with two horizons, $\Delta V_{\rm th}=V_{\rm th}^+-V_{\rm th}^-$,
i.e. the difference between the thermodynamical volumes of the outer and inner
horizons. For black holes with only one horizon, we introduce a new concept of
the volume $V_{\rm th}^0$ of the black hole singularity, and define $\Delta
V_{\rm th}=V_{\rm th}^+-V_{\rm th}^0$. The volume $V_{\rm th}^0$ vanishes for
the Schwarzschild black hole, but in general it can be positive, negative or
even divergent. For black holes with single horizon, we find a relation between
$\dot I_{\rm WDW}$ and $V_{\rm th}^0$, which implies that the holographic
complexity preserves the Lloyd's bound for positive or vanishing $V_{\rm
th}^0$, but the bound is violated when $V_{\rm th}^0$ becomes negative. We also
find explicit black hole examples where $V_{\rm th}^0$ and hence $\dot I_{\rm
WDW}$ are divergent. |
Localization in Quantum Field Theory for inertial and accelerated
observers: We study the problem of localization in Quantum Field Theory (QFT) from the
point of view of inertial and accelerated experimenters. We consider the
Newton-Wigner, the Algebraic Quantum Field Theory (AQFT) and the modal
localization schemes, which are, respectively, based on the orthogonality
condition for states localized in disjoint regions of space, on the algebraic
approach to QFT and on the representation of single particles as positive
frequency solution of the field equation. We show that only the AQFT scheme
obeys causality and physical invariance under diffeomorphisms.
Then, we consider the nonrelativistic limit of quantum fields in the Rindler
frame. We demonstrate the convergence between the AQFT and the modal scheme and
we show the emergence of the Born notion of localization of states and
observables. Also, we study the scenario in which an experimenter prepares
states over a background vacuum by means of nonrelativistic local operators and
another experimenter carries out nonrelativistic local measurements in a
different region. We find that the independence between preparation of states
and measurements is not guaranteed when both experimenters are accelerated and
the background state is different from Rindler vacuum, or when one of the two
experimenters is inertial. | Higher Symmetries of Toda Equations: The symmetries of the simplest non-abelian Toda equations are discussed. The
set of characteristic integrals whose Hamiltonian counterparts form a
W-algebra, is presented. |
Kinetic Field Theory: Higher-Order Perturbation Theory: We give a detailed exposition of the formalism of Kinetic Field Theory (KFT)
with emphasis on the perturbative determination of observables. KFT is a
statistical non-equilibrium classical field theory based on the path integral
formulation of classical mechanics, employing the powerful techniques developed
in the context of quantum field theory to describe classical systems. Unlike
previous work on KFT, we perform the integration over the probability
distribution of initial conditions in the very last step. This significantly
improves the clarity of the perturbative treatment and allows for physical
interpretation of intermediate results. We give an introduction to the general
framework, but focus on the application to interacting $N$-body systems.
Specializing the results to cosmic structure formation, we reproduce the linear
growth of the cosmic density fluctuation power spectrum on all scales from
microscopic, Newtonian particle dynamics alone. | Effective Action and Schwinger Pair Production in Strong QED: Some field theoretical aspects, such as the effective action and Schwinger
pair production, are critically reviewed in strong QED. The difference of the
boundary conditions on the solutions of the field equation is discussed to
result in the effective action both in the Coulomb and time-dependent gauge.
Finally, the apparent spin-statistics inversion is also discussed, where the
WKB action for bosons (fermions) works well for fermion (boson) pair-production
rate. |
Generalized metric formulation of double field theory: The generalized metric is a T-duality covariant symmetric matrix constructed
from the metric and two-form gauge field and arises in generalized geometry. We
view it here as a metric on the doubled spacetime and use it to give a simple
formulation with manifest T-duality of the double field theory that describes
the massless sector of closed strings. The gauge transformations are written in
terms of a generalized Lie derivative whose commutator algebra is defined by a
double field theory extension of the Courant bracket. | The exceptional story of massive IIA supergravity: The framework of exceptional field theory is extended by introducing
consistent deformations of its generalised Lie derivative. For the first time,
massive type IIA supergravity is reproduced geometrically as a solution of the
section constraint. This provides a unified description of all ten- and
eleven-dimensional maximal supergravities. The action of the E7 deformed theory
is constructed, and reduces to those of exceptional field theory and gauged
maximal supergravity in respective limits. The relation of this new framework
to other approaches for generating the Romans mass non-geometrically is
discussed. |
Dynamical Supersymmetry Breaking versus Run-away behavior in
Supersymmetric Gauge Theories: We consider Dynamical Supersymmetry Breaking (DSB) in models with classical
flat directions. We analyze a number of examples, and develop a systematic
approach to determine if classical flat directions are stabilized in the full
quantum theory, or lead to run-away behavior. In some cases pseudo-flat
directions remain even at the quantum level before taking into account
corrections to the K\"ahler potential. We show that in certain limits these
corrections are calculable. In particular, we find that in the
Intriligator-Thomas $SU(2)$ and its generalizations, a potential for moduli is
generated. Moreover, there is a region of the parameter space where K\"ahler
potential corrections lead to calculable (local) minima at large but finite
distance from the origin. | Comments on Good's Proposal for New Rules of Quantization: In a recent paper \cite{[Good1]} Good postulated new rules of quantization,
one of the major features of which is that the quantum evolution of the wave
function is always given by ordinary differential equations. In this paper we
analyse the proposal in some detail and discuss its viability and its
relationship with the standard quantum theory. As a byproduct, a simple
derivation of the `mass spectrum' for the Klein-Gordon field is presented, but
it is also shown that there is a complete additional spectrum of negative
`masses'. Finally, two major reasons are presented against the viability of
this alternative proposal: a) It does not lead to the correct energy spectrum
for the hydrogen atom. b) For field models, the standard quantum theory cannot
be recovered from this alternative description. |
BRST extension of the Faddeev model: The Faddeev model is a second class constrained system. Here we construct its
nilpotent BRST operator and derive the ensuing manifestly BRST invariant
Lagrangian. Our construction employs the structure of Stuckelberg fields in a
nontrivial fashion. | Conformal Yang-Mills field in arbitrary dimensions: Lagrangian of a classical conformal Yang-Mills field in the flat space of
even dimension greater than or equal to six involves higher derivatives. We
study Lagrangian formulation of the classical conformal Yang-Mills field by
using ordinary-derivative (second-derivative) approach. In the framework of the
ordinary-derivative approach, a field content, in addition to generic
Yang-Mills field, consists of auxiliary vector fields and Stueckelberg scalar
fields. For such field content, we obtain a gauge invariant Lagrangian with the
conventional second-derivative kinetic terms and the corresponding gauge
transformations. The Lagrangian is built in terms of non-abelian field
strengths. Structure of a gauge algebra entering gauge symmetries of the
conformal Yang-Mills field is described. FFF-vertex of the conformal Yang-Mills
field which involves three derivatives is also obtained. For six, eight, and
ten dimensions, eliminating the auxiliary vector fields and gauging away the
Stueckelberg scalar fields, we obtain a higher-derivative Lagrangian of the
conformal Yang-Mills field. For arbitrary dimensions, we demonstrate that all
auxiliary fields can be integrated out at non-linear level leading just to a
local higher-derivative action which is expressed only in terms of the generic
Yang-Mills field. |
Chiral limit of the two-dimensional fermionic determinant in a general
magnetic field: We consider the effective action for massive two-dimensional QED in flat
Euclidean space-time in the background of a general square-integrable magnetic
field with finite range. It is shown that its small mass limit is controlled by
the chiral anomaly. New results for the low-energy scattering of electrons in
2+1 dimensions in static, inhomogenous magnetic fields are also presented. | Brane polarization is no cure for tachyons: Anti-M2 and anti-D3 branes placed in regions with charges dissolved in fluxes
have a tachyon in their near-horizon region, which causes these branes to repel
each other. If the branes are on the Coulomb branch this tachyon gives rise to
a runaway behavior, but when the branes are polarized into five-branes this
tachyon only appears to lower the energy of the polarized branes, without
affecting its stability. We analyze brane polarization in the presence of a
brane-brane-repelling tachyon and show that when the branes are polarized along
the direction of the tachyon the polarized shell is unstable. This implies that
tachyons cannot be cured by brane polarization and indicates that, at least in
a certain regime of parameters, anti-D3 branes polarized into NS5 branes at the
bottom of the Klebanov-Strassler solution have an instability. |
On the Rotating and Oscillating strings in $(AdS_3\times
S^3)_{\varkappa}$: We study rigidly rotating strings in the $\varkappa$-deformed $AdS_3 \times
S^3$ background. We find out two classes of solutions corresponding to the
giant magnon and single spike solutions of the string rotating in two
$S^2_{\varkappa}$ subspace of rotations reduced along two different isometries.
We verify that the dispersion relations reduce to the well known relation in
the $\varkappa\rightarrow 0$ limit. We further study some oscillating string
solutions in the $S^3_{\varkappa}$ subspace. | Quantization of Chern-Simons Coefficient: The relation between the Dirac quantization condition of magnetic charge and
the quantization of the Chern-Simons coefficient is obtained. It implies that
in a (2+1)-dimensional QED with the Chern-Simons topological mass term and the
existence of a magnetic monopole with magnetic charge $g$, the Chern-Simons
coefficient must be also quantized, just as in the non-Abelian case. |
Thermodynamic Bethe Ansatz for Fishnet CFT: We present the TBA equations and the Y-system for the exact spectrum of
general multi-magnon local operators in the $D$-dimensional anisotropic version
of the bi-scalar fishnet CFT. The mixing matrix of such operators is given in
terms of fishnet planar graphs of multi-wheel and multi-spiral type. These
graphs probe the two main building blocks of the TBA approach that are the
magnon dispersion relation and the magnon scattering matrix and which we both
obtain by diagonalising suitable graph-building operators. We also obtain the
dual version of the TBA equations, which relates, in the continuum limit,
$D$-dimensional graphs to two dimensional sigma models in $AdS_{D+1}$. It
allows us to verify a general formula obtained by A.~Zamolodchikov for the
critical coupling. | General relativistic analog solutions for Yang-Mills theory: Finding solutions to non-linear field theories, such as Yang-Mills theories
or general relativity, is usually difficult. The field equations of Yang-Mills
theories and general relativity are known to share some mathematical
similarities, and this connection can be used to find solutions to one theory
using known solutions of the other theory. For example, the Schwarzschild
solutions of general relativity can be shown to have a mathematically similar
counterpart in Yang-Mills theory. In this article we will discuss several
solutions to the Yang-Mills equations which can be found using this connection
between general relativity and Yang-Mills theory. Some comments about the
possible physical meaning of these solutions will be discussed. In particular
it will be argued that some of these analog solutions of Yang-Mills theory may
have some connection with the confinement phenomenon. To this end we will
briefly look at the motion of test particles moving in the background potential
of the Schwarzschild analog solution. |
Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity: The fate of the Nambu-Goldstone modes arising from spontaneous Lorentz
violation is investigated. Using the vierbein formalism, it is shown that up to
10 Lorentz and diffeomorphism Nambu-Goldstone modes can appear and that they
are contained within the 10 modes of the vierbein associated with gauge degrees
of freedom in a Lorentz-invariant theory. A general treatment of spontaneous
local Lorentz and diffeomorphism violation is given for various spacetimes, and
the fate of the Nambu-Goldstone modes is shown to depend on both the spacetime
geometry and the dynamics of the tensor field triggering the spontaneous
Lorentz violation. The results are illustrated within the general class of
bumblebee models involving vacuum values for a vector field. In Minkowski and
Riemann spacetimes, the bumblebee model provides a dynamical theory generating
a photon as a Nambu-Goldstone boson for spontaneous Lorentz violation. The
Maxwell and Einstein-Maxwell actions are automatically recovered in axial
gauge. Associated effects of potential experimental relevance include
Lorentz-violating couplings in the matter and gravitational sectors of the
Standard-Model Extension and unconventional Lorentz-invariant couplings. In
Riemann-Cartan spacetime, the possibility also exists of a Higgs mechanism for
the spin connection, leading to the absorption of the propagating
Nambu-Goldstone modes into the torsion component of the gravitational field. | Velocity of signal in attractive potential and propagation of light in
gravitational field: The propagation of a massless field in attractive and repulsive potentials is
considered. It is shown that though the group velocity in such potentials can
be larger than one, the wave front propagates with the speed of light. A
larger-than-one group velocity leads only to a strong deformation of the wave
packet. The results obtained are applied to the light propagation in a
gravitational field. An erroneous assertion concerning the last problem,
recently made in the literature, is refuted. |
Canonical Coherent States for the Relativistic Harmonic Oscillator: In this paper we construct manifestly covariant relativistic coherent states
on the entire complex plane which reproduce others previously introduced on a
given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow
z_D \in $ unit disk is performed. We also introduce higher-order, relativistic
creation and annihilation operators, $\C,\Cc$, with canonical commutation
relation $[\C,\Cc]=1$ rather than the covariant one $[\Z,\Zc]\approx$ Energy
and naturally associated with the $SL(2,R)$ group. The canonical (relativistic)
coherent states are then defined as eigenstates of $\C$. Finally, we construct
a canonical, minimal representation in configuration space by mean of
eigenstates of a canonical position operator. | A study of spacetime distortion around a scattered recoiling D-particle
and possible astrophysical consequences: We study a four-dimensional spacetime induced by the recoil of a
D(irichlet)-particle, embeded in it, due to scattering by a moving string. The
induced spacetime has curvature only up to a radius that depends on the energy
of the incident string. Outside that region (`bubble') the spacetime is matched
with the Minkowski spacetime. The interior of the bubble is consistent with the
effective field theory obtained from strings, with non-trivial tachyon-like and
antisymmetric tensor fields (in four dimensions the latter gives rise to an
axion pseudoscalar field). The tachyonic mode, however, does not represent the
standard flat-spacetime string tachyon, but merely expresses the instability of
the distorted spacetime. Due to the non-trivial matter content of the interior
of the bubble, there is entropy production, which expresses the fact that
information is carried away by the recoil degrees of freedom. We also
demonstrate that a particle can be captured by the bubble, depending on the
particle's impact parameter. This will result in information loss for an
external asymptotic observer, corresponding to production of entropy
propotional to the area of the bubble. For the validity of our approach it is
essential that the string length is a few orders of magnitude larger than the
Planck length, which is a typical situation encountered in many D-brane-world
models. A very interesting feature of our model is the emission of high-energy
photons from the unstable bubble, which might be related to the observed
apparent ``violations'' of the GZK cutoff. |
First-order phase boundaries of the massive 1+1 dimensional
Nambu--Jona-Lasinio model with isospin: The massive two-dimensional Nambu--Jona-Lasinio model with isospin (isoNJL)
is reconsidered in the large $N_c$ limit. We continue the exploration of its
phase diagram by constructing missing first-order phase boundaries. At zero
temperature, a phase boundary in the plane of baryon and isospin chemical
potentials separates the vacuum from a crystal phase. We derive it from the
baryon spectrum of the isoNJL model which, in turn, is obtained via a numerical
Hartree-Fock (HF) calculation. At finite temperature, a first-order phase
boundary sheet is found using a thermal HF calculation. It interpolates
smoothly between the zero temperature phase boundary and the perturbative
sheet. The calculations remain tractable owing to the assumption that the
charged pion condensate vanishes. In that case, most of the calculations can be
done with methods developed in the past for solving the massive one-flavor NJL
model. | Regge Behaviour from an Environmentally Friendly Renormalization Group: The asymptotic behaviour of cubic field theories is investigated in the Regge
limit using the techniques of environmentally friendly renormalization,
environmentally friendly in the present context meaning asymmetric in its
momentum dependence. In particular we consider the crossover between large and
small energies at fixed momentum transfer for a model scalar theory of the type
phi^2 psi. The asymptotic forms of the crossover scaling functions are
exhibited for all two particle scattering processes in this channel to one loop
in a renormalization group improved perturbation theory. |
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