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Abelian Chern-Simons field theory and anyon equation on a cylinder: We present the anyon equation on a cylinder and in an infinite potential wall
from the abelian Chern-Simons theory coupled to non-relativistic matter field
by obtaining the effective hamiltonian through the canonical transformation
method used for the theory on a plane and on a torus. We also give the periodic
property of the theory on the cylinder. | hep-th |
DeWitt-Virasoro construction in tensor representations: We generalize the DeWitt-Virasoro (DWV) construction of arXiv:0912.3987
[hep-th] to tensor representations of higher ranks. A rank-$n$ tensor state,
which is by itself coordinate invariant, is expanded in terms of position
eigenstates that transform as tensors of the same rank. The representation of
the momentum operator in these basis states is then obtained by generalizing
DeWitt's argument in Phys.Rev.85:653-661,1952. Such a representation is written
in terms of certain bi-vector of parallel displacement and its covariant
derivatives. With this machinery at hand we find tensor representations of the
DWV generators defined in the previous work. The results differ from those in
spin-zero representation by additional terms involving the spin connection.
However, we show that the DWV algebra found earlier as a scalar expectation
value remains the same, as required by consistency, as all the additional
contributions conspire to cancel in various ways. In particular, vanishing of
the anomaly term requires the same condition of Ricci-flatness for the
background. | hep-th |
A Note About Localized Photons on the Brane: A first order formulation for the Maxwell field in five dimensions is
dimensionally reduced using the Randall-Sundrum mechanism. We will see that
massive photons can not be localized on the brane. | hep-th |
Quantum Field, Thermodynamics and Black Hole on Coherent State
Representation of Fuzzy Space: We first use the coherent state formalism of fuzzy space to show that the
fuzziness will eliminate point-like structure of a particle in favor of smeared
object, which is an exponential decay function in contrast to the Gaussian type
in the Moyal noncommutative space. The exponential decay function implies that,
in the UV region, the fuzziness provides an extra power-decay factor in the
Feynman propagator, contrasts to the exponential-decay factor in the Moyal
space. We also calculate the particle heat capacity and see that it approaches
to zero at high temperature. Next, we use the found smeared source to study the
Schwarzschild-like geometry and see that the black hole can reach a finite
maximum temperature before cooling down to absolute zero and leave a stable
remnant, as that in the noncommutative case. The properties of fuzzy 3D BTZ and
the fuzzy Kaluza-Klein black holes are also discussed. Finally, we present a
criterion for existence a regular black hole with a general smeared source
function. | hep-th |
Conformal Anomaly and Off-Shell Extensions of Gravity: The gauge dependence of the conformal anomaly for spin 3/2 and spin 2 fields
in non-conformal supergravities has been a long standing puzzle. In this Letter
we argue that the `correct' gauge choice is the one that follows from requiring
all terms that would imply a violation of the Wess-Zumino consistency condition
to be absent in the counterterm, because otherwise the usual link between the
anomaly and the one-loop divergence becomes invalid. Remarkably, the `good'
choice of gauge is the one that confirms our previous result that a complete
cancellation of conformal anomalies in D=4 can only be achieved for N-extended
(Poincar\'e) supergravities with $N\geq 5$. | hep-th |
Non-Hermitian Lagrangian for quasi-relativistic fermions: We present a Lorentz-symmetry violating Lagrangian for free fermions, which
is local but not Hermitian, whereas the corresponding Hamiltonian is Hermitian
but not local. A specific feature of the model is that the dispersion relation
is relativistic in both the IR and in the UV, but not in an intermediate
regime, set by a given mass scale. The consistency of the model is shown by the
study of properties expected in analogy with the Dirac Lagrangian. | hep-th |
Wedge-Local Quantum Fields and Noncommutative Minkowski Space: Within the setting of a recently proposed model of quantum fields on
noncommutative Minkowski spacetime, the consequences of the consistent
application of the proper, untwisted Poincare group as the symmetry group are
investigated. The emergent model contains an infinite family of fields which
are labelled by different noncommutativity parameters, and related to each
other by Lorentz transformations. The relative localization properties of these
fields are investigated, and it is shown that to each field one can assign a
wedge-shaped localization region of Minkowski space. This assignment is
consistent with the principles of covariance and locality, i.e. fields
localized in spacelike separated wedges commute.
Regarding the model as a non-local, but wedge-local, quantum field theory on
ordinary (commutative) Minkowski spacetime, it is possible to determine
two-particle S-matrix elements, which turn out to be non-trivial. Some partial
negative results concerning the existence of observables with sharper
localization properties are also obtained. | hep-th |
Large N and double scaling limits in two dimensions: Recently, the author has constructed a series of four dimensional
non-critical string theories with eight supercharges, dual to theories of light
electric and magnetic charges, for which exact formulas for the central charge
of the space-time supersymmetry algebra as a function of the world-sheet
couplings were obtained. The basic idea was to generalize the old matrix model
approach, replacing the simple matrix integrals by the four dimensional matrix
path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov
critical points by the Argyres-Douglas critical points. In the present paper,
we study qualitatively similar toy path integrals corresponding to the two
dimensional N=2 supersymmetric non-linear sigma model with target space CP^n
and twisted mass terms. This theory has some very strong similarities with N=2
super Yang-Mills, including the presence of critical points in the vicinity of
which the large n expansion is IR divergent. The model being exactly solvable
at large n, we can study non-BPS observables and give full proofs that double
scaling limits exist and correspond to universal continuum limits. A complete
characterization of the double scaled theories is given. We find evidence for
dimensional transmutation of the string coupling in some non-critical string
theories. We also identify en passant some non-BPS particles that become
massless at the singularities in addition to the usual BPS states. | hep-th |
The Algebra of Chern-Simons Classes and the Poisson Bracket on it: Developing ideas based on combinatorial formulas for characteristic classes
we introduce the algebra modeling secondary characteristic classes associated
to $N$ connections. Certain elements of the algebra correspond to the ordinary
and secondary characteristic classes.That construction allows us to give easily
the explicit formulas for some known secondary classes and to construct the new
ones. We write how $i$-th differential and $i$-th homotopy operator in the
algebra are connected with the Poisson bracket defined in this algebra. There
is an analogy between this algebra and the noncommutative symplectic geometry
of Kontsevich. We consider then an algebraic model of the action of the gauge
group. We describe how elements in the algebra corresponding to the secondary
characteristic classes change under this action. | hep-th |
Non supersymmetric femion boson symmetry: In this work we present symmetry transformations relating bosons to fermions
which cannot be represented as a supersymmetric algebra. We present a symmetry
transformation relating a complex scalar and a fermion in four dimensions and
construct a theory defined by an action that respects the symmetry quantum
mechanically. We next invoke gauge symmetry by adding a gauge field and a
corresponding fermion and construct two different symmetry transformations with
corresponding actions such that the corresponding theories respect the fermion
boson symmetry transformations quantum mechanically. Unlike in a supersymmetric
theory, the vacuum energy in the above theories could be negative.
Phenomenological implications of the theories are open to research. | hep-th |
Noncommutative hamiltonian formalism for noncommutative gravity: We present a covariant canonical formalism for noncommutative gravity, and in
general for noncommutative geometric theories defined via a twisted
$\star$-wedge product between forms. Noether theorems are generalized to the
noncommutative setting, and gauge generators are constructed in a twisted phase
space with $\star$-deformed Poisson bracket. This formalism is applied to
noncommutative $d=4$ vierbein gravity, and allows to find the canonical
generators of the tangent space $\star$-gauge group. | hep-th |
Curiosities on Free Fock Spaces: We consider some curious aspects of single-species free Fock spaces, such as
novel bosonization and fermionization formulae and relations to various
physical properties of bosonic particles. We comment on generalizations of
these properties to physically more interesting many-species free Fock spaces. | hep-th |
One-loop analysis with nonlocal boundary conditions: In the eighties, Schroder studied a quantum mechanical model where the
stationary states of Schrodinger's equation obey nonlocal boundary conditions
on a circle in the plane. For such a problem, we perform a detailed one-loop
calculation for three choices of the kernel characterizing the nonlocal
boundary conditions. In such cases, the zeta(0) value is found to coincide with
the one resulting from Robin boundary conditions. The detailed technique here
developed may be useful for studying one-loop properties of quantum field
theory and quantum gravity if nonlocal boundary conditions are imposed. | hep-th |
Massless Thirring fermion fields in the boson field representation: We show that the boson field representation of the massless fermion fields,
suggested by Morchio, Pierotti and Strocchi in J. Math. Phys. 33, 777 (1992)
for the operator solution of the massless Thirring model, agrees completely
with the existence of the chirally broken phase in the massless Thirring model
revealed in EPJC 20, 723 (2001) and hep-th/0112183, when the free massless
boson fields are described by the quantum field theory, free of infrared
divergences in 1+1-dimensional space-time, formulated in hep-th/0112184 and
hep-th/0204237. | hep-th |
Supergravity EFTs and swampland constraints: In these proceedings, we review recent progress in analyzing the behavior of
lower-dimensional supergravity theories when combined with swampland
conjectures. We show that within supergravity the effectiveness and usefulness
of swampland conjectures gets amplified, existing criteria can be intertwined
and also new ones can be uncovered. Furthermore, we elaborate on some
previously unpublished work. This includes evidence for the possible existence
of a novel conjecture on Yukawa couplings and an argument to constrain large
classes of D-term inflationary models using known conjectures. | hep-th |
The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM: We give an explicit recursive formula for the all L-loop integrand for
scattering amplitudes in N=4 SYM in the planar limit, manifesting the full
Yangian symmetry of the theory. This generalizes the BCFW recursion relation
for tree amplitudes to all loop orders, and extends the Grassmannian duality
for leading singularities to the full amplitude. It also provides a new
physical picture for the meaning of loops, associated with canonical operations
for removing particles in a Yangian-invariant way. Loop amplitudes arise from
the "entangled" removal of pairs of particles, and are naturally presented as
an integral over lines in momentum-twistor space. As expected from manifest
Yangian-invariance, the integrand is given as a sum over non-local terms,
rather than the familiar decomposition in terms of local scalar integrals with
rational coefficients. Knowing the integrands explicitly, it is straightforward
to express them in local forms if desired; this turns out to be done most
naturally using a novel basis of chiral, tensor integrals written in
momentum-twistor space, each of which has unit leading singularities. As simple
illustrative examples, we present a number of new multi-loop results written in
local form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise
expressions are presented for all 2-loop MHV amplitudes, as well as the 5-point
3-loop MHV amplitude. The structure of the loop integrand strongly suggests
that the integrals yielding the physical amplitudes are "simple", and
determined by IR-anomalies. We briefly comment on extending these ideas to more
general planar theories. | hep-th |
The Quantum Effective Action, Wave Functions and Yang-Mills (2+1): We explore the relationship between the quantum effective action and the
ground state (and excited state) wave functions of a field theory. Applied to
the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the
effective action from the ground state wave function previously obtained in the
Hamiltonian formalism by solving the Schrodinger equation. | hep-th |
A modification of the 10d superparticle action inspired by the
Gupta-Bleuler quantization scheme method: We reconsider the issue of the existence of a complex structure in the
Gupta-Bleuler quantization scheme. We prove an existence theorem for the
complex structure associated with the $d=10$ Casalbuoni-Brink-Schwarz
superparticle, based on an explicitly constructed Lagrangian that allows a
holomorphic-antiholomorphic splitting of the fermionic constraints consistent
with the vanishing of all first class constraints on the physical states. | hep-th |
An analytic study on the excited states of holographic superconductors: Based on the Sturm-Liouville eigenvalue problem, we develop a general
analytic technique to investigate the excited states of the holographic
superconductors. By including more higher order terms in the expansion of the
trial function, we observe that the analytic results agree well with the
numeric data, which indicates that the Sturm-Liouville method is very powerful
to study the holographic superconductors even if we consider the excited
states. For both the holographic s-wave and p-wave models, we find that the
excited state has a lower critical temperature than the corresponding ground
state and the difference of the dimensionless critical chemical potential
between the consecutive states is around 5. Moreover, we analytically confirm
that the holographic superconductor phase transition with the excited states
belongs to the second order, which can be used to back up the numerical
findings for both s-wave and p-wave superconductors. | hep-th |
Including four-gluon interactions into Landau and maximally-Abelian
gauge Dyson-Schwinger studies: In Dyson-Schwinger studies of the Yang-Mills propagators the four-gluon
interaction has been usually neglected due to the related technical
difficulties with the associated two-loop terms and especially their
renormalization. A possible scenario to renormalize these fully-dressed
two-loop terms is presented. Preliminary results for the Landau gauge gluon
propagator are shown. Implications for the gluon propagators in maximally
Abelian gauge are discussed. | hep-th |
String solutions in Chern-Simons-Higgs model coupled to an axion: We study a d=2+1 dimensional Chern-Simons gauge theory coupled to a Higgs
scalar and an axion field, finding the form of the potential that allows the
existence of selfdual equations and the corresponding Bogomolny bound for the
energy of static configurations. We show that the same conditions allow for the
N=2 supersymmetric extension of the model, reobtaining the BPS equations from
the supersymmetry requirement. Explicit electrically charged vortex-like
solutions to these equations are presented. | hep-th |
The B-field soft theorem and its unification with the graviton and
dilaton: In theories of Einstein gravity coupled with a dilaton and a two-form, a soft
theorem for the two-form, known as the Kalb-Ramond B-field, has so far been
missing. In this work we fill the gap, and in turn formulate a unified soft
theorem valid for gravitons, dilatons and B-fields in any tree-level scattering
amplitude involving the three massless states. The new soft theorem is fixed by
means of on-shell gauge invariance and enters at the subleading order of the
graviton's soft theorem. In contrast to the subsubleading soft behavior of
gravitons and dilatons, we show that the soft behavior of B-fields at this
order cannot be fully fixed by gauge invariance. Nevertheless, we show that it
is possible to establish a gauge invariant decomposition of the amplitudes to
any order in the soft expansion. We check explicitly the new soft theorem in
the bosonic string and in Type II superstring theories, and furthermore
demonstrate that, at the next order in the soft expansion, totally gauge
invariant terms appear in both string theories which cannot be factorized into
a soft theorem. | hep-th |
Particle astrophysics in nonlinear supersymmetric general relativity: An explanation of relations between the large scale structure of the universe
and the tiny scale structure of the particle physics, e.g. the observed
mysterious relation between the (dark) energy density and the dark matter of
the universe and the neutrino mass and the SUSY breaking mass scale of the
particle physics may be given by the nonlinear supersymmmetric general
relativity (NLSUSY GR). NLSUSY GR shows that studying the physics before/of the
Big Bang of the universe may be significant and may give new insight to
unsolved problems of the low energy particle physics, cosmology and their
relations. | hep-th |
Infinite statistics, symmetry breaking and combinatorial hierarchy: The physics of symmetry breaking in theories with strongly interacting quanta
obeying infinite (quantum Boltzmann) statistics known as quons is discussed.
The picture of Bose/Fermi particles as low energy excitations over nontrivial
quon condensate is advocated. Using induced gravity arguments it is
demonstrated that the Planck mass in such low energy effective theory can be
factorially (in number of degrees of freedom) larger than its true ultraviolet
cutoff. Thus, the assumption that statistics of relevant high energy
excitations is neither Bose nor Fermi but infinite can remove the hierarchy
problem without necessity to introduce any artificially large numbers. Quantum
mechanical model illustrating this scenario is presented. | hep-th |
Quantization of Fayet-Iliopoulos Parameters in Supergravity: In this short note we discuss quantization of the Fayet-Iliopoulos parameter
in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos
parameter determines a lift of the group action to a line bundle, and such
lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted
in terms of moment maps and symplectic reductions, we argue that in
supergravity the quantization of the Fayet-Iliopoulos parameter has a natural
understanding in terms of linearizations in geometric invariant theory (GIT)
quotients, the algebro-geometric version of symplectic quotients. | hep-th |
The Casimir effect for pistons with transmittal boundary conditions: This work focuses on the analysis of the Casimir effect for pistons subject
to transmittal boundary conditions. In particular we consider, as piston
configuration, a direct product manifold of the type $I\times N$ where $I$ is a
closed interval of the real line and $N$ is a smooth compact Riemannian
manifold. By utilizing the spectral zeta function regularization technique, we
compute the Casimir energy of the system and the Casimir force acting on the
piston. Explicit results for the force are provided when the manifold $N$ is a
$d$-dimensional ball. | hep-th |
High Temperature Effects on Compactlike Structures: In this work we investigate the transition from kinks to compactons at high
temperatures. We deal with a family of models, described by a real scalar field
with standard kinematics, controlled by a single parameter, real and positive.
The family of models supports kinklike solutions, and the solutions tend to
become compact when the parameter increases to larger and larger values. We
study the one-loop corrections at finite temperature, to see how the thermal
effects add to the effective potential. The results suggest that the symmetry
is restored at very high temperatures. | hep-th |
Arbitrary Superspin Massive Superparticles: We propose the action for a massive $N$-extended superparticle with a pure
(half)integer superspin $Y,~Y = 0, 1/2, 1, 3/2, \ldots$. Regardless of the
superspin value, the configuration space is ${\Bbb R}^{4|4N} \times S^2$, where
$S^2$ corresponds to spinning degrees of freedom. Being explicitly
super-Poincar\'e invariant, the model possesses two gauge symmetries implying
strong conservation of the squared momentum and superspin. Hamilton constrained
dynamics is developed and canonical quantization is studied. For $N$ = 1 we
show that the physical super wave-functions are to be on-shell massive chiral
superfields. Central-charges generalizations of the model are given. | hep-th |
Supersymmetric Yang-Mills Theories in $D\ge 12$: We present supersymmetric Yang-Mills theories in arbitrary even dimensions
with the signature (9+m,1+m) where $m=0,1,2,...$ beyond ten-dimensions up to
infinity. This formulation utilizes null-vectors and is a generalization of our
previous work in 10+2 dimensions to arbitrary even dimensions with the above
signature. We have overcome the previously-observed obstruction beyond 11+3
dimensions, by the aid of projection operators. Both component and superspace
formulations are presented. This also suggests the possibility of consistent
supergravity theories in any even dimensions beyond 10+1 dimensions. | hep-th |
Charged Open Membrane Solutions On A Manifold With Boundary: Explicit open single and multi-membrane solutions of the low energy limit of
M-theory on the orbifold $R^{10}\times S^1/Z_2$ are presented. This low energy
action is described by an 11-dimensional supergravity action coupled to two
$E_8$ super Yang-Mills fields, which propagate only on the 10-dimensional
boundaries of the target space. The membrane solutions we construct preserve
half the supersymmetries. They carry electric charge and current with respect
to the gauge fields, whose generators are in the Cartan subalgebra of the two
$E_8$ gauge groups present at the boundaries. | hep-th |
Quantum gravity on a torus: Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach
to quantum gravity where one assumes space-time foliation into spatial
hyper-surfaces of fixed topology. Most of the CDT results were obtained for the
spatial topology of the 3-sphere. It was shown that CDT has rich phase
structure, including the semiclassical phase consistent with Einstein's general
relativity. Some of the phase transitions were found to be second (or higher)
order which makes a possibility of taking continuum limit viable. Here we
present new results of changing the spatial topology to that of the 3-torus. We
argue that the topology change does not change the phase structure nor the
order of the phase transitions. Therefore CDT results seem to be universal
independent of the topology chosen. | hep-th |
Non-geometric heterotic backgrounds and 6D SCFTs/LSTs: We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of
non-geometric backgrounds of the $E_8\times E_8$ and the
$\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be
analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau
threefolds. The majority of the resulting dual threefolds turn out to contain
singularities which do not admit a crepant resolution. When the singularities
can be resolved crepantly, the theories living on the defect are explicitly
determined and reveal a form of duality in which distinct defects are described
by the same IR fixed point. In particular, a subclass of non-geometric defects
corresponds to SCFTs/LSTs arising from small heterotic instantons on ADE
singularities. | hep-th |
Dyson's Classification And Real Division Superalgebras: It is well-known that unitary irreducible representations of groups can be
usefully classified in a 3-fold classification scheme: Real, Complex,
Quaternionic. In 1962 Freeman Dyson pointed out that there is an analogous
10-fold classification of irreducible representations of groups involving both
unitary and antiunitary operators. More recently it was realized that there is
also a 10-fold classification scheme involving superdivision algebras. Here we
give a careful proof of the equivalence of these two 10-fold ways. | hep-th |
Exact conditions for Quasi-normal modes of extremal M5-branes and Exact
WKB analysis: We study the quasi-normal modes (QNMs) of a massless scalar perturbation to
the extremal M5-branes metric by using the exact WKB analysis. The exact WKB
analysis provides two exact QNMs conditions depending on the argument of the
complex frequency of the perturbation. The exact conditions show that the
discontinuity of the perturbative part of the QNMs leads the non-perturbative
part of themselves. We also find a new example of the Seiberg-Witten/gravity
correspondence, which helps us to compute the QNMs from our conditions. | hep-th |
On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli
Black Holes and Their Holographic Pictures: In this paper, the curvature structure of a (2+1)-dimensional black hole in
the massive-charged-Born-Infeld gravity is investigated. The metric that we
consider is characterized by four degrees of freedom which are the mass and
electric charge of the black hole, the mass of the graviton field, and a
cosmological constant. For the charged and neutral cases separately, we present
various constraints among scalar polynomial curvature invariants which could
invariantly characterize our desired spacetimes. Specially, an appropriate
scalar polynomial curvature invariant and a Cartan curvature invariant which
together could detect the black hole horizon would be explicitly constructed.
Using algorithms related to the focusing properties of a bundle of light rays
on the horizon which are accounted for by the Raychaudhuri equation, a
procedure for isolating the black hole parameters, as the algebraic
combinations involving the curvature invariants, would be presented. It will be
shown that this technique could specially be applied for black holes with zero
electric charge, contrary to the cases of solutions of lower-dimensional
non-massive gravity. In addition, for the case of massive (2+1)-dimensional
black hole, the irreducible mass, which quantifies the maximum amount of energy
which could be extracted from a black hole would be derived. Therefore, we show
that the Hawking temperatures of these black holes could be reduced to the pure
curvature properties of the spacetimes. Finally, we comment on the relationship
between our analysis and the novel roles it could play in numerical quark-gluon
plasma simulations and other QCD models and also black hole information paradox
where the holographic correspondence could be exploited. | hep-th |
Standard Model Vacua in Heterotic M-Theory: We present a class of N=1 supersymmetric ``standard'' models of particle
physics, derived directly from heterotic M-theory, that contain three families
of chiral quarks and leptons coupled to the gauge group SU(3)_C X SU(2)_L X
U(1)_Y. These models are a fundamental form of ``brane world'' theories, with
an observable and hidden sector each confined, after compactification on a
Calabi--Yau threefold, to a BPS three-brane separated by a higher dimensional
bulk space with size of the order of the intermediate scale. The requirement of
three families, coupled to the fundamental conditions of anomaly freedom and
supersymmetry, constrains these models to contain additional five-branes
located in the bulk space and wrapped around holomorphic curves in the
Calabi--Yau threefold. | hep-th |
Dynamical supersymmetry analysis of conformal invariance for
superstrings in type IIB R-R plane-wave: In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet
conformal invariance for superstrings in type IIB R-R plane-wave in
semi-light-cone gauge. Here we give further justification to the results found
in that work through alternative arguments using dynamical supersymmetries. We
show that by using the susy algebra the same quantum definition of the
energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi
identities we indirectly compute the Virasoro anomaly terms by calculating
second order susy variation of the EM tensor. Certain integrated form of all
such terms are shown to vanish. In order to deal with various divergences that
appear in such computations we take a point-split definition of the same EM
tensor. The final results are shown not to suffer from the ordering ambiguity
as noticed in the previous work provided the coincidence limit is taken before
sending the regularization parameter to zero at the end of the computation. | hep-th |
The Bubble of Nothing under T-duality: The bubble of nothing is a solution to Einstein's equations where a circle
shrinks and pinches off smoothly. As such, it is one of the simplest examples
of a dynamical cobordism to nothing. We take a first step in studying how this
solution transforms under T-duality in bosonic string theory. Applying
Buscher's rules reveals that the dual solution features a singular, strongly
coupled core, with a circle blowing-up rather than pinching off. This naive
approach to T-duality solely accounts for the zero-modes of the fields after
dimensional reduction on the circle. For this reason, we argue that this is not
the full picture that the T-dual solution should depend non-trivially on the
dual circle. We point out evidence to this effect both in the gravity
description and on the worldsheet. A more complete description of the T-dual
object would require a full-fledged sigma model for the bubble of nothing.
Nevertheless, inspired by similar examples in the literature, we detail one
possible scenario where the stringy bubble of nothing is mediated by closed
string tachyon condensation and we discuss its T-duality. | hep-th |
Continuous Spin Representations of the Poincaré and Super-Poincaré
Groups: We construct Wigner's continuous spin representations of the Poincar\'e
algebra for massless particles in higher dimensions. The states are labeled
both by the length of a space-like translation vector and the Dynkin indices of
the {\it short little group} $SO(d-3)$, where $d$ is the space-time dimension.
Continuous spin representations are in one-to-one correspondence with
representations of the short little group. We also demonstrate how combinations
of the bosonic and fermionic representations form supermultiplets of the
super-Poincar\'e algebra. If the light-cone translations are nilpotent, these
representations become finite dimensional, but contain zero or negative norm
states, and their supersymmetry algebra contains a central charge in four
dimensions. | hep-th |
Closed String Tachyon Condensation in Supercritical Strings and RG Flows: We show an explicit relation between an RG flow of a two-dimensional gravity
and an on-shell tachyon condensation in the corresponding string theory, in the
case when the string theory is supercritical. The shape of the tachyon
potential in this case can, in principle, be obtained by examining various RG
flows. We also argue that the shape of tachyon potential for a (sub)critical
string can be obtained by analyzing a supercritical string which is obtained
from the (sub)critical string. | hep-th |
Kinklike structures in models of the Dirac-Born-Infeld type: The present work investigates several models of a single real scalar field,
engendering kinetic term of the Dirac-Born-Infeld type. Such theories introduce
nonlinearities to the kinetic part of the Lagrangian, which presents a square
root restricting the field evolution and including additional powers in
derivatives of the scalar field, controlled by a real parameter. In order to
obtain topological solutions analytically, we propose a first-order framework
that simplifies the equation of motion ensuring solutions that are linearly
stable. This is implemented using the deformation method, and we introduce
examples presenting two categories of potentials, one having polynomial
interactions and the other with nonpolynomial interactions. We also explore how
the Dirac-Born-Infeld kinetic term affects the properties of the solutions. In
particular, we note that the kinklike solutions are similar to the ones
obtained through models with standard kinetic term and canonical potential, but
their energy densities and stability potentials vary according to the parameter
introduced to control the new models. | hep-th |
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole: We apply the technique of Hamiltonian reduction for the construction of
three-dimensional ${\cal N}=4$ supersymmetric mechanics specified by the
presence of a Dirac monopole. For this purpose we take the conventional ${\cal
N}=4$ supersymmetric mechanics on the four-dimensional conformally-flat spaces
and perform its Hamiltonian reduction to three-dimensional system. We formulate
the final system in the canonical coordinates, and present, in these terms, the
explicit expressions of the Hamiltonian and supercharges. We show that, besides
a magnetic monopole field, the resulting system is specified by the presence of
a spin-orbit coupling term. A comparison with previous work is also carried
out. | hep-th |
A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds: We explore a ``fertile patch'' of the heterotic landscape based on a Z_6-II
orbifold with SO(10) and E_6 local GUT structures. We search for models
allowing for the exact MSSM spectrum. Our result is that of order 100 out of a
total 3\times 10^4 inequivalent models satisfy this requirement. | hep-th |
Quantum group gauge theory on quantum spaces: We construct quantum group-valued canonical connections on quantum
homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere
of Podles quantum differential coming from the 3-D calculus of Woronowicz on
$SU_q(2)$ . The construction is presented within the setting of a general
theory of quantum principal bundles with quantum group (Hopf algebra) fiber,
associated quantum vector bundles and connection one-forms. Both the base space
(spacetime) and the total space are non-commutative algebras (quantum spaces). | hep-th |
Lagrange Brackets and U(1) fields: The idea of a companion Lagrangian associated with $p$-Branes is extended to
include the presence of U(1) fields. The Brane Lagrangians are constructed with
$F_{ij}$ represented in terms of Lagrange Brackets, which make manifest the
reparametrisation invariance of the theory; these are replaced by Poisson
Brackets in the companion Lagrangian, which is now covariant under field
redefinition. The ensuing Lagrangians possess a similar formal structure to
those in the absence of an anti-symmetric field tensor. | hep-th |
Quantum Einstein Gravity as a Topological Field Theory: General covariance in quantum gravity is seen once one integrates over all
possible metrics. In recent years topological field theories have given us a
different route to general covariance without integrating over all possible
metrics. Here we argue that Einstein quantum gravity may be viewed as a
topological field theory provided a certain constrant from the path integral
measure is satisfied. | hep-th |
Critical exponents of the Gross-Neveu model from the effective average
action: The phase transition of the Gross-Neveu model with N fermions is investigated
by means of a non-perturbative evolution equation for the scale dependence of
the effective average action. The critical exponents and scaling amplitudes are
calculated for various values of N in d=3. It is also explicitely verified that
the Neveu-Yukawa model belongs to the same universality class as the
Gross-Neveu model. | hep-th |
Super Gluon Five-Point Amplitudes in AdS Space: We present the tree-level five-point amplitude of the lowest KK mode of SYM
on AdS$_5$$\times$S$^3$, dual to the correlator of the flavor current multiplet
in the dual 4d ${\cal N}=2$ SCFT. Its color and kinematical structure is
particularly simple and resembles that of the flat-space gluon amplitude. | hep-th |
Comparing Double String Theory Actions: Aimed to a deeper comprehension of a manifestly T-dual invariant formulation
of string theory, in this paper a detailed comparison between the non-covariant
action proposed by Tseytlin and the covariant one proposed by Hull is done.
These are obtained by making both the string coordinates and their duals
explicitly appear, on the same foot, in the world-sheet action, so "doubling"
the string coordinates along the compact dimensions. After a discussion of the
nature of the constraints in both the models and the relative quantization, it
results that the string coordinates and their duals behave like "non-commuting"
phase space type coordinates but their expressions in terms of Fourier modes
generate the oscillator algebra of the standard bosonic string formulation. A
proof of the equivalence of the two formulations is given. Furthermore,
open-string solutions are also discussed. | hep-th |
Superpotential de-sequestering in string models: Non-perturbative superpotential cross-couplings between visible sector matter
and K\"ahler moduli can lead to significant flavour-changing neutral currents
in compactifications of type IIB string theory. Here, we compute corrections to
Yukawa couplings in orbifold models with chiral matter localised on D3-branes
and non-perturbative effects on distant D7-branes. By evaluating a threshold
correction to the D7-brane gauge coupling, we determine conditions under which
the non-perturbative corrections to the Yukawa couplings appear. The flavour
structure of the induced Yukawa coupling generically fails to be aligned with
the tree-flavour structure. We check our results by also evaluating a
correlation function of two D7-brane gauginos and a D3-brane Yukawa coupling.
Finally, by calculating a string amplitude between n hidden scalars and visible
matter we show how non-vanishing vacuum expectation values of distant D7-brane
scalars, if present, may correct visible Yukawa couplings with a flavour
structure that differs from the tree-level flavour structure. | hep-th |
On General BCJ Relation at One-loop Level in Yang-Mills Theory: BCJ relation reveals a dual between color structures and kinematic structure
and can be used to reduce the number of independent color-ordered amplitudes at
tree level. Refer to the loop-level in Yang-Mills theory, we investigate the
similar BCJ relation in this paper. Four-point 1-loop example in N = 4 SYM can
hint about the relation of integrands. Five-point example implies that the
general formula can be proven by unitary- cut method. We will then prove a
'general' BCJ relation for 1-loop integrands by D-dimension unitary cut, which
can be regarded as a non-trivial generalization of the (fundamental)BCJ
relation given by Boels and Isermann in [arXiv:1109.5888 [hep-th]] and
[arXiv:1110.4462 [hep-th]]. | hep-th |
Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on
Confining Strings: Recently we observed a crossover transition (in the Fayet-Iliopoulos
parameter) from weak to strong coupling in N=2 supersymmetric QCD with the U(N)
gauge group and N_f > N quark flavors. At strong coupling this theory can be
described by a dual non-Abelian weakly coupled SQCD with the dual gauge group
U(N_f-N) and N_f light dyon flavors. Both theories support non-Abelian strings.
We continue the study of confinement dynamics in these theories, in particular,
metamorphoses of excitation spectra, from a different side. A number of results
obtained previously are explained, enhanced and supplemented by analyzing the
world-sheet dynamics on the non-Abelian confining strings. The world-sheet
theory is the two-dimensional N=(2,2) supersymmetric weighted CP(N_f-1) model.
We explore the vacuum structure and kinks on the world sheet, corresponding to
confined monopoles in the bulk theory. We show that (in the equal quark mass
limit) these kinks fall into the fundamental representation of the unbroken
global SU(N)\times SU(N_f-N)\timesU(1) group. This result confirms the presence
of "extra" stringy meson states in the adjoint representation of the global
group in the bulk theory. The non-Abelian bulk duality is in one-to-one
correspondence with a duality taking place in the N=(2,2) supersymmetric
weighted CP(N_f-1) model. | hep-th |
String theory and the 4D/3D reduction of Seiberg duality. A Review: We review the reduction of four-dimensional N=1 Seiberg duality to three
dimensions focusing on the D brane engineering approach. We start with an
overview of four-dimensional Seiberg duality for theories with various types of
gauge groups and matter content both from a field-theoretic and a brane
engineering point of view. Then we describe two families of N=2
three-dimensional dualities, namely Giveon-Kutasov-like and Aharony-like
dualities. The last part of our discussion is devoted to the 4D/3D reduction of
the dualities studied above. We discuss both the analysis at finite radius,
crucial for preserving the duality in the dimensional reduction, and the
zero-size limit that must be supported by a real mass flow and a Higgsing,
which can differ case by case. We show that this mechanism is reproduced in the
brane description by T-duality, supplying a unified picture for all the
different cases. As a bonus we show that this analysis provides a brane
description for Aharony-like dualities. | hep-th |
Combinatorial $B_n$-analogues of Schubert polynomials: Combinatorial $B_n$-analogues of Schubert polynomials and corresponding
symmetric functions are constructed from an exponential solution of the
$B_n$-Yang-Baxter equation that involves the nilCoxeter algebra of the
hyperoctahedral group. | hep-th |
Singularity-free model of electric charge in physical vacuum: Non-zero
spatial extent and mass generation: We propose a model of a spinless electrical charge as a self-consistent field
configuration of the electromagnetic (EM) field interacting with a physical
vacuum effectively described by the logarithmic quantum Bose liquid. We show
that, in contrast to the EM field propagating in a trivial vacuum, a regular
solution does exist, and both its mass and spatial extent emerge naturally from
dynamics. It is demonstrated that the charge and energy density distribution
acquire Gaussian-like form. The solution in the logarithmic model is stable and
energetically favourable, unlike that obtained in a model with a quartic
(Higgs-like) potential. | hep-th |
Entanglement Entropy at Finite Density from Extremal Black Holes: I compute the entanglement entropy of a strongly coupled 2+1d quantum field
theory containing fermions at finite density using gauge/gravity duality. The
dual geometry is an extremal black hole in 3+1d Einstein-Maxwell theory. This
system was recently shown to exhibit non-Fermi liquid behavior, but the leading
geometrical contribution to the entanglement entropy does not produce an
expected violation of the boundary law. I discuss this negative result in the
context of attempts to find highly entangled states of quantum matter. | hep-th |
Forces from Connes' geometry: We try to give a pedagogical introduction to Connes' derivation of the
standard model of electro-magnetic, weak and strong forces from gravity. | hep-th |
Quantum Null Energy Condition and its (non)saturation in 2d CFTs: We consider the Quantum Null Energy Condition (QNEC) for holographic
conformal field theories in two spacetime dimensions (CFT$_2$). We show that
QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein
gravity, including systems that are far from thermal equilibrium. If the
Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be
saturated, whereby we give both analytical and numerical examples. In
particular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries
we find a curious half-saturation of QNEC for large entangling regions. We also
address order one corrections from quantum backreactions of a scalar field in
AdS$_3$ dual to a primary operator of dimension $h$ in a large central charge
expansion and explicitly compute both, the backreacted Ryu--Takayanagi surface
part and the bulk entanglement contribution to EE and QNEC. At leading order
for small entangling regions the contribution from bulk EE exactly cancels the
contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders
in the size of the region the contributions are almost equal while QNEC is not
saturated. For a half-space entangling region we find that QNEC is gapped by
$h/4$ in the large $h$ expansion. | hep-th |
Einstein gravity from the ${\N=4}$ spinning particle: We obtain a manifestly background independent BRST quantization of the $\N=4$
supersymmetric spinning particle. We show that nilpotency of the BRST charge
$Q$ implies the Einstein equations admitting a cosmological constant of
indefinite sign. The physical graviton states are given by the vertex operator,
obtained by an infinitesimal variation of $Q$, acting on diffeomorphism ghost
states. In addition, the tree-point graviton scattering vertex is correctly
reproduced by the worldline computation with these vertex operators. | hep-th |
Natural inflation with multiple sub-Planckian axions: We extend the Kim-Nilles-Peloso (KNP) alignment mechanism for natural
inflation to models with $N>2$ axions, which obtains a super-Planckian
effective axion decay constant $f_{\textrm{eff}}\gg M_{Pl}$ through an
alignment of the anomaly coefficients of multiple axions having sub-Planckian
fundamental decay constants $f_0\ll M_{Pl}$. The original version of the KNP
mechanism realized with two axions requires that some of the anomaly
coefficients should be of the order of $f_{\textrm{eff}}/f_0$, which would be
uncomfortably large if $f_{\rm eff}/f_0 \gtrsim {\cal O}(100)$ as suggested by
the recent BICEP2 results. We note that the KNP mechanism can be realized with
the anomaly coefficients of $\mathcal{O}(1)$ if the number of axions $N$ is
large as $N\ln N\gtrsim 2\ln (f_{\textrm{eff}}/f_0)$, in which case the
effective decay constant can be enhanced as $f_{\rm eff}/f_0 \sim \sqrt{N
!}\,n^{N-1}$ for $n$ denoting the typical size of the integer-valued anomaly
coefficients. Comparing to the other multiple axion scenario, the N-flation
scenario which requires $N \sim f_{\textrm{eff}}^2/f_0^2$, the KNP mechanism
has a virtue of not invoking to a too large number of axions, although it
requires a specific alignment of the anomaly coefficients, which can be
achieved with a probability of ${\cal O}(f_0/f_{\rm eff})$ under a random
choice of the anomaly coefficients. We also present a simple model realizing a
multiple axion monodromy along the inflaton direction. | hep-th |
Closed Universe in Mirage Cosmology: We study the cosmological evolution of the closed universe on a spherical
probe brane moving in the AdS$_m\times S^n$ background and the near-horizon
background of the dilatonic D-branes. The Friedmann equations describing the
evolution of the brane universe, and the effective energy density and pressure
simulated on the probe brane due to its motion in the curved background
spacetime are obtained and analyzed. We also comment on the relevance of the
spherical probe brane to the giant graviton for the special value of the probe
energy. | hep-th |
Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions: The task of calculating operator dimensions in the planar limit of N=4 super
Yang-Mills theory can be vastly simplified by mapping the dilatation generator
to the Hamiltonian of an integrable spin chain. The Bethe ansatz has been used
in this context to compute the spectra of spin chains associated with various
sectors of the theory which are known to decouple in the planar (large-N_c)
limit. These techniques are powerful at leading order in perturbation theory
but become increasingly complicated beyond one loop in the 't Hooft parameter
lambda=g_YM^2 N_c, where spin chains typically acquire long-range
(non-nearest-neighbor) interactions. In certain sectors of the theory,
moreover, higher-loop Bethe ansaetze do not even exist. We develop a virial
expansion of the spin chain Hamiltonian as an alternative to the Bethe ansatz
methodology, a method which simplifies the computation of dimensions of
multi-impurity operators at higher loops in lambda. We use these methods to
extract previously reported numerical gauge theory predictions near the BMN
limit for comparison with corresponding results on the string theory side of
the AdS/CFT correspondence. For completeness, we compare our virial results
with predictions that can be derived from current Bethe ansatz technology. | hep-th |
The $L_{\infty}$ structure of gauge theories with matter: In this work we present an algebraic approach to the dynamics and
perturbation theory at tree-level for gauge theories coupled to matter. The
field theories we will consider are: Chern-Simons-Matter, Quantum
Chromodynamics, and scalar Quantum Chromodynamics. Starting with the
construction of the master action in the classical Batalin-Vilkovisky
formalism, we will extract the $L_{\infty}$-algebra that allow us to
recursively calculate the perturbiner expansion from its minimal model. The
Maurer-Cartan action obtained in this procedure will then motivate a generating
function for all the tree-level scattering amplitudes. There are two
interesting outcomes of this construction: a generator for fully-flavoured
amplitudes via a localisation on Dyck words; and closed expressions for fermion
and scalar lines attached to $n$-gluons with arbitrary polarisations. | hep-th |
Quenched mesonic spectrum at large N: We compute the masses of the $\pi$ and of the $\rho$ mesons in the quenched
approximation on a lattice with fixed lattice spacing $a \simeq 0.145 \
\mathrm{fm}$ for SU($N$) gauge theory with $N = 2,3,4,6$. We find that a simple
linear expression in $1/N^2$ correctly captures the features of the
lowest-lying meson states at those values of $N$. This enables us to
extrapolate to $N = \infty$ the behaviour of $m_{\pi}$ as a function of the
quark mass and of $m_{\rho}$ as a function of $m_{\pi}$. Our results for the
latter agree within 5% with recent predictions obtained in the AdS/CFT
framework. | hep-th |
Hamiltonian formalism for Bose excitations in a plasma with a
non-Abelian interaction I: plasmon -- hard particle scattering: The Hamiltonian theory for the collective longitudinally polarized gluon
excitations (plasmons) coupling with classical high-energy test color-charged
particle propagating through a high-temperature gluon plasma is developed. A
generalization of the Lie-Poisson bracket to the case of a continuous medium
involving bosonic normal field variable
$a^{\phantom{\ast}\!\!a}_{\hspace{0.03cm}{\bf k}}$ and a non-Abelian color
charge $Q^{\hspace{0.03cm}a}$ is performed and the corresponding Hamilton
equations are presented. The canonical transformations including simultaneously
both bosonic degrees of freedom of the soft collective excitations and degree
of freedom of hard test particle connecting with its color charge in the hot
gluon plasma are written out. A complete system of the canonicity conditions
for these transformations is derived. The notion of the plasmon number density
${\mathcal N}^{a\hspace{0.03cm}a^{\prime}_{\phantom{1}}\!}_{{\bf k}}$, which is
a nontrivial matrix in the color space, is introduced. An explicit form of the
effective fourth-order Hamiltonian describing elastic scattering of plasmon off
a hard color particle is found and the self-consistent system of Boltzmann type
kinetic equations taking into account the time evolution of the mean value of
the color charge of the hard particle is obtained. On the basis of these
equations, a model problem of interaction of two infinitly narrow wave packets
is considered. A system of nonlinear first-order ordinary differential
equations defining the dynamics of the interaction of the colorless $N^{l}_{\bf
k}$ and color $W^{l}_{\bf k}$ components of the plasmon number density is
derived. The problem of determining the third- and fourth-order coefficient
functions entering into the canonical transformations of the original bosonic
variable $a^{\phantom{\ast}\!\!a}_{{\bf k}}$ and color charge
$Q^{\hspace{0.03cm}a}$ is discussed. | hep-th |
Comment on ``On spin-1 massive particles coupled to a Chern-Simons
field'': In this comment we discuss some serious inconsistencies presented by Gomes,
Malacarne and da Silva in their paper, Phys.Rev. D60 (1999) 125016
(hep-th/9908181). | hep-th |
The Monodromic Axion-Photon Coupling: We consider the general form of the axion coupling to photons in the
axion-Maxwell theory. On general grounds this coupling takes the form of a
monodromic function of the axion, which we call $g(a)$, multiplying the
Chern-Pontryagin density $F \widetilde{F}$ of the photon. We show that the
non-linearity of $g(a)$ is a spurion for the shift symmetry of the axion. In
this context, when $g(a) \neq \mathbb{Z}a$, the linearized coupling of the
axion $g'(a)$ is not quantized and there is a correlated mass term for the
axion. Singularities in $g(a)$ due to the fast rearrangement of degrees of
freedom are shown to have corresponding cusps and singularities in the axion
potential. We derive the general form of $g(a)$ for the QCD axion, axions with
perturbatively broken shift symmetries and axions descending from extra
dimensions. In all cases, we show that there is a uniform general form of the
monodromic function $g(a)$ and it is connected to the axion potential. | hep-th |
Application of the canonical quantization of systems with curved phase
space to the EMDA theory: The canonical quantization of dynamical systems with curved phase space
introduced by I.A. Batalin, E.S. Fradkin and T.E. Fradkina is applied to the
four-dimensional Einstein-Maxwell Dilaton-Axion theory. The spherically
symmetric case with radial fields is considered. The Lagrangian density of the
theory in the Einstein frame is written as an expression with first order in
time derivatives of the fields. The phase space is curved due to the nontrivial
interaction of the dilaton with the axion and the electromagnetic fields. | hep-th |
Generalized Uncertainty Principle: Implications for Black Hole
Complementarity: At the heart of the black hole information loss paradox and the firewall
controversy lies the conflict between quantum mechanics and general relativity.
Much has been said about quantum corrections to general relativity, but much
less in the opposite direction. It is therefore crucial to examine possible
corrections to quantum mechanics due to gravity. Indeed, the Heisenberg
Uncertainty Principle is one profound feature of quantum mechanics, which
nevertheless may receive correction when gravitational effects become
important. Such generalized uncertainty principle [GUP] has been motivated from
not only quite general considerations of quantum mechanics and gravity, but
also string theoretic arguments. We examine the role of GUP in the context of
black hole complementarity. We find that while complementarity can be violated
by large N rescaling if one assumes only the Heisenberg's Uncertainty
Principle, the application of GUP may save complementarity, but only if certain
N-dependence is also assumed. This raises two important questions beyond the
scope of this work, i.e., whether GUP really has the proposed form of
N-dependence, and whether black hole complementarity is indeed correct. | hep-th |
The Number Operator for Generalized Quons: We construct the number operator for particles obeying infinite statistics,
defined by a generalized q-deformation of the Heisenberg algebra, and prove the
positivity of the norm of linearly independent state vectors. | hep-th |
Curiosities above c = 24: Two-dimensional rational CFT are characterised by an integer $\ell$, related
to the number of zeroes of the Wronskian of the characters. For two-character
RCFT's with $\ell<6$ there is a finite number of theories and most of these are
classified. Recently it has been shown that for $\ell \ge 6$ there are
infinitely many admissible characters that could potentially describe CFT's. In
this note we examine the $\ell=6$ case, whose central charges lie between 24
and 32, and propose a classification method based on cosets of meromorphic
CFT's. We illustrate the method using theories on Kervaire lattices with
complete root systems. In the process we construct the first known
two-character RCFT's beyond $\ell=2$. | hep-th |
Coupled Inflation and Brane Gases: We study an effective four-dimensional theory with an action with two scalar
fields minimally coupled to gravity, and with a matter action which couples to
the two scalar fields via an overall field-dependent coefficient in the action.
Such a theory could arise from a dimensional reduction of supergravity coupled
to a gas of branes winding the compactified dimensions. We show the existence
of solutions corresponding to power-law inflation. The graceful exit from
inflation can be obtained by postulating the decay of the branes, as would
occur if the branes are unstable in the vacuum and stabilized at high densities
by plasma effects. This construction provides an avenue for connecting string
gas cosmology and the late-time universe. | hep-th |
Remarks on a $B \wedge F$ model with topological mass from gauging spin: Aspects of screening and confinement are reassessed for a $B \wedge F$ model
with topological mass with the gauging of spin. Our discussion is carried out
using the gauge-invariant, but path-dependent, variables formalism. We
explicitly show that the static potential profile is the sum of a Yukawa and a
linear potential, leading to the confinement of static external charges.
Interestingly enough, similar results are obtained in a theory of antisymmetric
tensor fields that results from the condensation of topological defects as a
consequence of the Julia-Toulouse mechanism. | hep-th |
Practicalities of renormalizing quantum field theories: We review the techniques used to renormalize quantum field theories at
several loop orders. This includes the techniques to systematically extract the
infinities in a Feynman integral and the implementation of the algorithm within
computer algebra. To illustrate the method we discuss the renormalization of
phi^4 theory and QCD including the application of the critical point large $N$
technique as a check on the anomalous dimensions. The renormalization of
non-local operators in QCD is also discussed including the derivation of the
two loop correction to the Gribov mass gap equation in the Landau gauge. | hep-th |
On the Two-Point Correlation Function in Dynamical Scaling and
SCHRÖdinger Invariance: The extension of dynamical scaling to local, space-time dependent rescaling
factors is investigated. For a dynamical exponent $z=2$, the corresponding
invariance group is the Schr\"odinger group. Schr\"odinger invariance is shown
to determine completely the two-point correlation function. The result is
checked in two exactly solvable models. | hep-th |
The large Nc limit of N=2 super Yang-Mills, fractional instantons and
infrared divergences: We investigate the large Nc limit of pure N=2 supersymmetric gauge theory
with gauge group SU(Nc) by using the exact low energy effective action. Typical
one-complex dimensional sections of the moduli space parametrized by a global
complex mass scale v display three qualitatively different regions depending on
the ratio between |v| and the dynamically generated scale Lambda. At large
|v|/Lambda, instantons are exponentially suppressed as N goes to infinity. When
|v| is of order Lambda, singularities due to massless dyons occur. They are
densely distributed in rings of calculable thicknesses in the v-plane. At small
|v|/Lambda, instantons disintegrate into fractional instantons of charge
1/(2N). These fractional instantons give non-trivial contributions to all
orders of 1/N, unlike a planar diagrams expansion which generates a series in
1/N^2, implying the presence of open strings. We have explicitly calculated the
fractional instantons series in two representative examples, including the 1/N
and 1/N^2 corrections. Our most interesting finding is that the 1/N expansion
breaks down at singularities on the moduli space due to severe infrared
divergencies, a fact that has remarkable consequences. | hep-th |
Mobility edge and Black Hole Horizon: We conjecture that the mobility edge in the 4D Euclidean Dirac operator
spectrum in QCD in the deconfined phase found in the lattice studies
corresponds to the near black hole (BH) horizon region in the holographic dual.
We present some evidences both from the field theory side and from the
worldsheet theory of long open string. | hep-th |
Universal Bounds in Even-Spin CFTs: We prove using invariance under the modular $S$- and $ST$-transformations
that every unitary two-dimensional conformal field theory (CFT) of only
even-spin operators (with no extended chiral algebra and with central charges
$c,\tilde{c}>1$) contains a primary operator with dimension $\Delta_1$
satisfying $0 < \Delta_1 < (c+\tilde{c})/24 + 0.09280...$ After deriving both
analytical and numerical bounds, we discuss how to extend our methods to bound
higher conformal dimensions before deriving lower and upper bounds on the
number of primary operators in a given energy range. Using the AdS$_3$/CFT$_2$
dictionary, the bound on $\Delta_1$ proves the lightest massive excitation in
appropriate theories of 3D matter and gravity with cosmological constant
$\Lambda < 0$ can be no heavier than $1/(8G_N)+O(\sqrt{-\Lambda})$; the bounds
on the number operators are related via AdS/CFT to the entropy of states in the
dual gravitational theory. In the flat-space approximation, the limiting mass
is exactly that of the lightest BTZ black hole. | hep-th |
Thermal Operator Representation of Finite Temperature Graphs II: Using the mixed space representation, we extend our earlier analysis to the
case of Dirac and gauge fields and show that in the absence of a chemical
potential, the finite temperature Feynman diagrams can be related to the
corresponding zero temperature graphs through a thermal operator. At non-zero
chemical potential we show explicitly in the case of the fermion self-energy
that such a factorization is violated because of the presence of a singular
contact term. Such a temperature dependent term which arises only at finite
density and has a quadratic mass singularity cannot be related, through a
regular thermal operator, to the fermion self-energy at zero temperature which
is infrared finite. Furthermore, we show that the thermal radiative corrections
at finite density have a screening effect for the chemical potential leading to
a finite renormalization of the potential. | hep-th |
Tachyonic Instability and Darboux Transformation: Using Darboux transformation one can construct infinite family of potentials
which lead to the flat spectrum of scalar field fluctuations with arbitrary
multiple precision, and, at the same time, with "essentially blue" spectrum of
perturbations of metric. Besides, we describe reconstruction problem: find
classical potential V(phi) starting from the known "one-loop potential" u(t) =
d^2V(phi(t))/d phi(t)^2. | hep-th |
Fusion Algebras Induced by Representations of the Modular Group: Using the representation theory of the subgroups SL_2(Z_p) of the modular
group we investigate the induced fusion algebras in some simple examples. Only
some of these representations lead to 'good' fusion algebras. Furthermore, the
conformal dimensions and the central charge of the corresponding rational
conformal field theories are calculated. Two series of representations which
can be realized by unitary theories are presented. We show that most of the
fusion algebras induced by admissible representations are realized in well
known rational models. | hep-th |
BPS Supermultiplets in Five Dimensions: BPS representations of 5-dimensional supersymmetry algebras are classified.
For BPS states preserving 1/2 the supersymmetry, there are two distinct classes
of multiplets for N=4 supersymmetry and three classes for N=8 supersymmetry.
For N=4 matter theories, the two 1/2 supersymmetric BPS multiplets are the
massive vector multiplet and the massive self-dual 2-form multiplet. Some
applications to super-Yang-Mills, supergravity and little string theories are
considered. | hep-th |
Quantization and the Issue of Time for Various Two-Dimensional Models of
Gravity: It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and
$R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of
2D NonEinsteinian Gravity. Different approaches to the formulation of a
quantum theory for the above systems are then presented: The Dirac constraints
can be solved exactly in the momentum representation, the path integral can be
integrated out, and the constraint algebra can be {\em explicitely} canonically
abelianized, thus allowing also for a (superficial) reduced phase space
quantization. Non--trivial dynamics are obtained by means of time dependent
gauges. All of these approaches lead to the {\em same} finite dimensional
quantum mechanical system. | hep-th |
Criticality and Transport in Magnetized Holographic Systems: In this master's thesis the Einstein-Maxwell-Dilaton theory is used to model
the dynamics of 2+1-dimensional, strongly coupled, large-$N$ quantum field
theories with intrinsic T-violation, at finite density and temperature, in the
presence of a magnetic field. We include axion fields in order to introduce
momentum relaxation. We find analytic expressions for the DC conductivity and
present numerical results for the AC conductivity. We also classify the
IR-asymptotic hyperscaling violating solutions of the theory. | hep-th |
Quantum Black Hole Formation in the BFSS Matrix Model: We study the various head-on collisions of two bunches of D0-branes and their
real-time evolution in the BFSS matrix model in classical limit. For a various
matrix size N respecting the 't Hooft scaling, we find quantitative evidence
for the formation of a single bound state of D0-branes at late time, which is
matrix model thermalization and dual to the formation of a larger black hole. | hep-th |
Metal or Insulator? Dirac operator spectrum in holographic QCD: The lattice studies in QCD demonstrate the nontrivial localization behavior
of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian
of $4+1$ dimensional disordered system. We use the holographic viewpoint to
provide the conjectural explanation of these properties. The delocalization of
all modes in the confined phase is related to the $\theta=\pi$ - like phenomena
when the domain walls between degenerated vacua are possible. It is conjectured
that the localized modes separated by mobility edge from the rest of the
spectrum in deconfined QCD correspond to the near-horizon region in the
holographic dual. | hep-th |
Gauss-Bonnet black holes supported by a nonlinear electromagnetic field: We study $D$-dimensional charged static spherically symmetric black hole
solutions in Gauss-Bonnet theory coupled to nonlinear electrodynamics defined
as arbitrary functions of the field invariant and constrained by several
physical conditions. These solutions are characterized in terms of the mass
parameter $m$, the electromagnetic energy $\varepsilon$ and the Gauss-Bonnet
parameter $l_{\alpha}^2$. We find that a general feature of these solutions is
that the metric behaves in a different way in $D=5$ and $D>5$ space-time
dimensions. Moreover, such solutions split into two classes, according to
whether they are defined everywhere or show branch singularities, depending on
($m, \varepsilon, l_{\alpha}^2$). We describe qualitatively the structures
comprised within this scenario, which largely extends the results obtained in
the literature for several particular families of nonlinear electrodynamics. An
explicit new example, illustrative of our results, is introduced. Finally we
allow non-vanishing values of the cosmological constant length $l_{\Lambda}^2$,
and study the existence of new structures, in both asymptotically Anti-de
Sitter and de Sitter spaces. | hep-th |
Microscopics of Extremal Kerr from Spinning M5 Branes: We show that the spinning magnetic one-brane in minimal five-dimensional
supergravity admits a decoupling limit that interpolates smoothly between a
self-dual null orbifold of AdS_3 \times S^2 and the near-horizon limit of the
extremal Kerr black hole times a circle. We use this interpolating solution to
understand the field theory dual to spinning M5 branes as a deformation of the
Discrete Light Cone Quantized (DLCQ) Maldacena-Stominger-Witten (MSW) CFT. In
particular, the conformal weights of the operators dual to the deformation
around AdS_3 \times S^2 are calculated. We present pieces of evidence showing
that a CFT dual to the four-dimensional extremal Kerr can be obtained from the
deformed MSW CFT. | hep-th |
Why Comparable? A Multiverse Explanation of the Dark Matter-Baryon
Coincidence: The densities of dark and baryonic matter are comparable: \zeta = \rho_D /
\rho_B ~ O(1). This is surprising because they are controlled by different
combinations of low-energy physics parameters. Here we consider the probability
distribution over \zeta in the landscape. We argue that the Why Comparable
problem can be solved without detailed anthropic assumptions, and independently
of the nature of dark matter. Overproduction of dark matter suppresses the
probability like 1/(1+\zeta), if the causal patch is used to regulate
infinities. This suppression can counteract a prior distribution favoring large
\zeta, selecting \zeta ~ O(1).
This effect not only explains the Why Comparable coincidence but also renders
otherwise implausible models of dark matter viable. For the special case of
axion dark matter, Wilczek and independently Freivogel have already noted that
a 1/(1+\zeta) suppression prevents overproduction of a GUT-scale QCD axion. If
the dark matter is the LSP, the effect can explain the moderate fine-tuning of
the weak scale in simple supersymmetric models. | hep-th |
DBI Galileon inflation in background SUGRA: We introduce a model of potential driven DBI Galileon inflation in background
N=1,D=4 SUGRA. Starting from D4-$\bar{D4}$ brane-antibrane in the bulk N=2,D=5
SUGRA including quadratic Gauss-Bonnet corrections, we derive an effective
N=1,D=4 SUGRA by dimensional reduction, that results in a Coleman-Weinberg type
Galileon potential. We employ this potential in modeling inflation and in
subsequent study of primordial quantum fluctuations for scalar and tensor
modes. Further, we estimate the major observable parameters in both de Sitter
(DS) and beyond de Sitter (BDS) limits and confront them with recent
observational data from WMAP7 by using the publicly available code CAMB. | hep-th |
PT symmetric fermionic field theories with axions: Renormalization and
dynamical mass generation: We consider the renormalisation properties of non-Hermitian Yukawa theories
involving a pseudoscalar (axion) field at or near $4$ dimensions. The
non-Hermiticity is \cPT-symmetric where $\mathcal P$ is a linear idempotent
operator (such as parity) and $\mathcal T$ is an anti-linear idempotent
operator (such as time-reversal). The coupling constants of the Yukawa and
quartic scalar coupling terms reflect this non-Hermiticity. The path integral
representing the field theory is used to discuss the Feynman rules associated
with the field theory. The fixed point structure associated with the
renormalisation group has \cPT- symmetric and Hermitian fixed points. At two
loops in the massless theory, we demonstrate the flow from Hermitian to
non-Hermitian fixed points. From the one-loop renormalisation of a massive
Yukawa theory, a self-consistent Nambu-Jona Lasinio gap equation is established
and its real solutions are discussed. | hep-th |
Clarifying perturbations in the ekpyrotic universe: In this note I try to clarify the problem of perturbations in the ekpyrotic
universe. I write down the most general matching conditions and specify the
choices taken by the two debating sides. I also bring up the problem of surface
stresses which always have to be present when a transition from a collapsing to
an expanding phase is made. | hep-th |
Dualities in the classical supergravity limits: Duality symmetries of supergravity theories are powerful tools to restrict
the number of possible actions, to link different dimensions and number of
supersymmetries and might help to control quantisation.
(Hodge-Dirac-)Dualisation of gauge potentials exchanges Noether and topological
charges, equations of motion and Bianchi identities, internal rigid symmetries
and gauge symmetries, local transformations with nonlocal ones and most
exciting particles and waves. We compare the actions of maximally dualised
supergravities (ie with gauge potential forms of lowest possible degree) to the
non-dualised actions coming from 11 (or 10) dimensions by plain dimensional
reduction as well as to other theories with partial dualisations. The effect on
the rigid duality group is a kind of contraction resulting from the elimination
of the unfaithful generators associated to the (inversely) dualised scalar
fields. New gauge symmetries are introduced by these (un)dualisations and it is
clear that a complete picture of duality (F(ull)-duality) should include all
gauge symmetries at the same time as the rigid symmetries and the spacetime
symmetries. We may read off some properties of F-duality on the internal rigid
Dynkin diagram: field content, possible dualisations, increase of the rank
according to the decrease of space dimension... Some recent results are
included to suggest the way towards unification via a universal twisted
self-duality (TS) structure. The analysis of this structure had revealed
several profound differences according to the parity mod 4 of the dimension of
spacetime (to be contrasted with the (Bott) period 8 of spinor properties). | hep-th |
Thick Domain Walls and Charged Dilaton Black Holes: We study a black hole domain wall system in dilaton gravity which is the
low-energy limit of the superstring theory. We solve numerically equations of
motion for real self-interacting scalar field and justify the existence of
static axisymmetric field configuration representing the thick domain wall in
the background of a charged dilaton black hole. It was also confirmed that the
extreme dilaton black hole always expelled the domain wall. | hep-th |
Supergravity p-branes revisited: extra parameters, uniqueness, and
topological censorship: We perform a complete integration of the Einstein-dilaton-antisymmetric form
action describing black p-branes in arbitrary dimensions assuming the
transverse space to be homogeneous and possessing spherical, toroidal or
hyperbolic topology. The generic solution contains eight parameters satisfying
one constraint. Asymptotically flat solutions form a five-parametric subspace,
while conditions of regularity of the non-degenerate event horizon further
restrict this number to three, which can be related to the mass and the charge
densities and the asymptotic value of the dilaton. In the case of a degenerate
horizon, this number is reduced by one. Our derivation constitutes a
constructive proof of the uniqueness theorem for $p$-branes with the
homogeneous transverse space. No asymptotically flat solutions with toroidal or
hyperbolic transverse space within the considered class are shown to exist,
which result can be viewed as a demonstration of the topological censorship for
p-branes. From our considerations it follows, in particular, that some
previously discussed p-brane-like solutions with extra parameters do not
satisfy the standard conditions of asymptotic flatness and absence of naked
singularities. We also explore the same system in presence of a cosmological
constant, and derive a complete analytic solution for higher-dimensional
charged topological black holes, thus proving their uniqueness. | hep-th |
An Alternative to Compactification: Conventional wisdom states that Newton's force law implies only four
non-compact dimensions. We demonstrate that this is not necessarily true in the
presence of a non-factorizable background geometry. The specific example we
study is a single 3-brane embedded in five dimensions. We show that even
without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and
general relativistic gravity is reproduced to more than adequate precision. | hep-th |
Born-Infeld Black-Body Radiation: The problem of black-body radiation is considered in the Born-Infeld theory
of electrodynamics. In particular, at 2-loop order the deviation from the
Planck expression due to the self-interaction of photons is calculated. It is
seen that the system of interacting photons of the theory, opposed to its
non-Abelian counterpart, has higher internal energy at this order of
perturbation. Possible implications of the result on the evolution of very
hight temperature systems, including various stellar media and the early
universe, are briefly discussed. | hep-th |
Gravitational lensing and shadow of charged black holes in the
low-energy limit of string theory: In this work, we investigate the shadow cast and strong field gravitational
lensing of a new class of black hole solutions in dilaton gravity where dilaton
field is coupled with nonlinear Maxwell invariant [Younesizadeh et al. in Int J
Mod Phys A 34(35):1950239]. The space-time is a stationary axisymmetric
geometry. The key part in our investigations is finding the effect of dilaton
parameter N on the size of shadows and the energy emission rate. As the N
parameter increases, the size of black hole shadow increases. Also, the energy
emission rate increases with increase in the dilaton parameter N. By supposing
the gravitational field of the supermassive object at the heart of Milky Way
galaxy described by this metric, we estimated the numerical values of the
observables for gravitational lensing in the strong field limit. | hep-th |
Scaling Behaviors of Branched Polymers: We study the thermodynamic behavior of branched polymers. We first study
random walks in order to clarify the thermodynamic relation between the
canonical ensemble and the grand canonical ensemble. We then show that
correlation functions for branched polymers are given by those for $\phi^3$
theory with a single mass insertion, not those for the $\phi^3$ theory
themselves. In particular, the two-point function behaves as $1/p^4$, not as
$1/p^2$, in the scaling region. This behavior is consistent with the fact that
the Hausdorff dimension of the branched polymer is four. | hep-th |
T-Duality Group for Open String Theory: We study T-duality for open strings on tori $\T^d$. The general boundary
conditions for the open strings are constructed, and it is shown that T-duality
group, which preserves the mass spectrum of closed strings, preserves also the
mass spectrum of the open strings. The open strings are transformed to those
with different boundary conditions by T-duality. We also discuss the T-duality
for D-brane mass spectrum, and show that the D-branes and the open strings with
both ends on them are transformed together consistently. | hep-th |
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