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Cosmology in nonrelativistic general covariant theory of gravity: Horava and Melby-Thompson recently proposed a new version of the
Horava-Lifshitz theory of gravity, in which the spin-0 graviton is eliminated
by introducing a Newtonian pre-potential $\phi$ and a local U(1) gauge field
$A$. In this paper, we first derive the corresponding Hamiltonian,
super-momentum constraints, the dynamical equations, and the equations for
$\phi$ and $A$, in the presence of matter fields. Then, we apply the theory to
cosmology, and obtain the modified Friedmann equation and the conservation law
of energy, in addition to the equations for $\phi$ and $A$. When the spatial
curvature is different from zero, terms behaving like dark radiation and
stiff-fluid exist, from which, among other possibilities, bouncing universe can
be constructed. We also study linear perturbations of the FRW universe with any
given spatial curvature $k$, and derive the most general formulas for scalar
perturbations. The vector and tensor perturbations are the same as those
recently given by one of the present authors [A. Wang, Phys. Rev. D{\bf 82},
124063 (2010)] in the setup of Sotiriou, Visser and Weinfurtner. Applying these
formulas to the Minkowski background, we have shown explicitly that the scalar
and vector perturbations of the metric indeed vanish, and the only remaining
modes are the massless spin-2 gravitons. | Moduli Corrections to D-term Inflation: We present a D-term hybrid inflation model, embedded in supergravity with
moduli stabilisation. Its novel features allow us to overcome the serious
challenges of combining D-term inflation and moduli fields within the same
string-motivated theory. One salient point of the model is the positive
definite uplifting D-term arising from the moduli stabilisation sector. By
coupling this D-term to the inflationary sector, we generate an effective
Fayet-Iliopoulos term. Moduli corrections to the inflationary dynamics are also
obtained. Successful inflation is achieved for a limited range of parameter
values with spectral index compatible with the WMAP3 data. Cosmic D-term
strings are also formed at the end of inflation; these are no longer
Bogomol'nyi-Prasad-Sommerfeld (BPS) objects. The properties of the strings are
studied. |
Dyonic branes and linear dilaton background: We study dyonic solutions to the gravity-dilaton-antisymmetric form equations
with the goal of identifying new $p$-brane solutions on the fluxed linear
dilaton background. Starting with the generic solutions constructed by reducing
the system to decoupled Liouville equations for certain values of parameters,
we identify the most general solution whose singularities are hidden behind a
regular event horizon, and then explore the admissible asymptotic behaviors. In
addition to known asymptotically flat dyonic branes, we find two classes of
asymptotically non-flat solutions which can be interpreted as describing
magnetically charged branes on the electrically charged linear dilaton
background (and the $S$-dual configuration of electrically charged branes on
the magnetically charged background), and uncharged black branes on the
dyonically charged linear dilaton background. This interpretation is shown to
be consistent with the first law of thermodynamics for the new solutions. | Effective potential for quantum scalar fields on a de Sitter geometry: We study the quantum theory of an O(N) scalar field on de Sitter geometry at
leading order in a nonperturbative 1/N-expansion. This resums the infinite
series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric
solutions of the corresponding, properly renormalized, dynamical field
equations and compute the complete effective potential. Because of its
self-interactions, the field acquires a strictly positive square mass which
screens potential infrared divergences. Moreover, strongly enhanced
ultralong-wavelength fluctuations prevent the existence of a spontaneously
broken symmetry state in any dimension. |
The M-Theory Three-Form and Singular Geometries: While M- and F-theory compactifications describe a much larger class of vacua
than perturbative string compactifications, they typically need singularities
to generate non-abelian gauge fields and charged matter. The physical
explanation involves M2-branes wrapped on vanishing cycles. Here we seek an
alternative explanation that could address outstanding issues such as the
description of nilpotent branches, stability walls, frozen singularities and so
forth. To this end we use a model in which the three-form is related to the
Chern-Simons form of a bundle. The model has a one-form non-abelian gauge
symmetry which normally eliminates all the degrees of freedom associated to the
bundle. However by restricting the transformations to preserve the bundle along
the vanishing cycles, we may get new degrees of freedom associated to
singularities, without appealing to wrapped M2-branes. The analysis can be
simplified by gauge-fixing the one-form symmetry using higher-dimensional
instanton equations. We explain how this mechanism leads to the natural
emergence of phenomena such as enhanced ADE gauge symmetries, nilpotent
branches, charged matter fields and their holomorphic couplings. | New BPS solitons in N=4 gauged supergravity and black holes in
Einstein-Yang-Mills-dilaton theory: We start by revisiting the problem of finding BPS solutions in
$\mathcal{N}=4$ SU(2)$\times$SU(2) gauged supergravity. We report on a new
supersymmetric solution in the Abelian sector of the theory, which describes a
soliton that is regular everywhere. The solution is 1/4 BPS and can be obtained
from a double analytic continuation of a planar solution found by Klemm in
hep-th/9810090. Also in the Abelian sector, but now for a spherically symmetric
ansatz we find a new solution whose supersymmetric nature was overlooked in the
previous literature. Then, we move to the non-Abelian sector of the theory by
considering the meron ansatz for SU(2). We construct electric-meronic and
double-meron solutions and show that the latter also leads to 1/4 BPS
configurations that are singular and acquire an extra conformal Killing vector.
We then move beyond the supergravity embedding of this theory by modifying the
self-interaction of the scalar, but still within the same meron ansatz for a
single gauge field, which is dilatonically coupled with the scalar. We
construct exact black holes for two families of self-interactions that admit
topologically Lifshitz black holes, as well as other black holes with
interesting causal structures and asymptotic behavior. We analyze some thermal
properties of these spacetimes. |
M Theory, Type IIA Superstrings, and Elliptic Cohomology: The topological part of the M-theory partition function was shown by Witten
to be encoded in the index of an E8 bundle in eleven dimensions. This partition
function is, however, not automatically anomaly-free. We observe here that the
vanishing W_7=0 of the Diaconescu-Moore-Witten anomaly in IIA and compactified
M-theory partition function is equivalent to orientability of spacetime with
respect to (complex-oriented) elliptic cohomology. Motivated by this, we define
an elliptic cohomology correction to the IIA partition function, and propose
its relationship to interaction between 2-branes and 5-branes in the M-theory
limit. | Linear space of spinor monomials and realization of the Nambu-Goldstone
fermion in the Volkov-Akulov and Komargodski-Seiberg Lagrangians: The analytical algorithm previously proposed by the author for matching the
Volkov-Akulov (VA) and Komargodski-Seiberg (KS) actions describing the
Nambu-Goldstone (NG) fermion, is discussed. The essence of the algotithm is
explained, its consistency is proved and the recent results obtained with
computer assistance are reproduced, when the proper Fierz rearrangements for
Majorana bispinors are taken into account. We reveal a linear space of
composite spinorial monomials $\Delta_{m}$ which are the solutions of the
scalar constraint $(\partial^{m}\bar\psi\Delta_{m})=0$. This space is used to
clarify relations between the KS and VA realizations of the NG fermionic field
$\psi$. |
The Holographic Space-Time Model of Cosmology: This essay outlines the Holographic Space-time (HST) theory of cosmology and
its relation to conventional theories of inflation. The predictions of the
theory are compatible with observations, and one must hope for data on
primordial gravitational waves or non-Gaussian fluctuations to distinguish it
from conventional models. The model predicts an early era of structure
formation, prior to the Big Bang. Understanding the fate of those structures
requires complicated simulations that have not yet been done. The result of
those calculations might falsify the model, or might provide a very economical
framework for explaining dark matter and the generation of the baryon
asymmetry. | Phases of bosonic strings and two dimensional gauge theories: We suggest that the extrinsic curvature and torsion of a bosonic string can
be employed as variables in a two dimensional Landau-Ginzburg gauge field
theory. Their interpretation in terms of the abelian Higgs multiplet leads to
two different phases. In the phase with unbroken gauge symmetry the ground
state describes open strings while in the phase with broken gauge symmetry the
ground state involves closed strings. When we allow for an additional abelian
gauge structure along the string, we arrive at an interpretation in terms of
the two dimensional SU(2) Yang-Mills theory. |
The Low Energy Effective Equations of Motion for Multibrane World
Gravity: The three 3-brane system with both positive or negative tension is studied in
a low energy regime by using gradient expansion method. The effective equations
of motion on the brane is derived and in particular we examine, in the first
order, the radion effective lagrangian for this system. In this case, we show
the solution of the modified Friedmann equation with dark radiation on the
middle brane and the other 3-branes by direct elimination of the radion fields
and Weyl scaling of the metric on the branes. We also derived the scalar-tensor
gravity on the branes. | Fine Structure Constant in the Spacetime of a Cosmic String: We calculate the fine structure constant in the spacetime of a cosmic string.
In the presence of a cosmic string the value of the fine structure constant
reduces. We also discuss on numerical results. |
$D_n$ Dynkin quiver moduli spaces: We study $3d$ $\mathcal{N}=4$ quiver gauge theories with gauge nodes forming
a $D_n$ Dynkin diagram. The class of good $D_n$ Dynkin quivers is completely
characterised and the moduli space singularity structure fully determined for
all such theories. The class of good $D_n$ Dynkin quivers is denoted
$D_\nu^\mu(n)_p$ where $n \geq 2$ is an integer, $\nu$ and $\mu$ are integer
partitions and $p \in \{ \textrm{even}, \textrm{odd}\}$ denotes membership of
one of two broad subclasses. A full assessment of which $\mathfrak{so}_{2n}$
nilpotent varieties are realisable as $D_n$ Dynkin quiver moduli spaces is
provided. Quiver addition is introduced and is used to give large subclasses of
$D_n$ Dynkin quivers poset structure. The partial ordering is determined by
inclusion relations for the moduli space branches. The resulting Hasse diagrams
are used to both classify $D_n$ Dynkin quivers and determine the moduli space
singularity structure for an arbitrary good theory. The poset constructions and
local moduli space analyses are complemented throughout by explicit checks
utilising moduli space dimension matching. | Bounce beyond Horndeski with GR asymptotics and $γ$-crossing: It is known that beyond Horndeski theory admits healthy bouncing cosmological
solutions. However, the constructions proposed so far do not reduce to General
Relativity (GR) in either infinite past or infinite future or both. The
obstacle is so called $\gamma$-crossing, which off hand appears pathological.
By working in the unitary gauge, we confirm the recent observation by Ijjas
[arXiv:1710.05990] that $\gamma$-crossing is, in fact, healthy. On this basis
we construct a spatially flat, stable bouncing Universe solution whose
asymptotic past and future are described by GR with conventional massless
scalar field. |
Gauge-invariant fields and flow equations for Yang-Mills theories: We discuss the concept of gauge-invariant fields for non-abelian gauge
theories. Infinitesimal fluctuations around a given gauge field can be split
into physical and gauge fluctuations. Starting from some reference field the
gauge-invariant fields are constructed by consecutively adding physical
fluctuations. An arbitrary gauge field can be mapped to an associated gauge
invariant field. An effective action that depends on gauge-invariant fields
becomes a gauge-invariant functional of arbitrary gauge fields by associating
to every gauge field the corresponding gauge-invariant field. The
gauge-invariant effective action can be obtained from an implicit functional
integral with a suitable "physical gauge fixing". We generalize this concept to
the gauge-invariant effective average action or flowing action, which involves
an infrared cutoff. It obeys a gauge-invariant functional flow equation. We
demonstrate the use of this flow equation by a simple computation of the
running gauge coupling and propagator in pure $SU(N)$-Yang-Mills theory. | Comments on Brane Recombination, Finite Flux Vacua, and the Swampland: The Swampland program relies heavily on the conjecture that there can only be
a finite number of flux vacua (FFV conjecture). Stipulating this FFV conjecture
and applying it to some older work in flux vacua construction we show that
within a patch of the landscape the FFV conjecture makes predictions on the
non-existence of otherwise viable non-perturbative objects arising from brane
recombination. Future gains in direct non-perturbative analysis could therefore
not only test this prediction but also test portions of the Swampland program
itself. We also discuss implications of a weaker FFV conjecture on the counting
of flux vacua which predicts positivity of the brane central charge if the EFT
analysis is to be qualitatively trusted. |
Charged rotating Kaluza-Klein multi-black holes and multi-black strings
in five-dimensional Einstein-Maxwell theory: We construct exact solutions, which represent regular charged rotating
Kaluza-Klein multi-black holes in the five-dimensional pure Einstein-Maxwell
theory. Quantization conditions between the mass, the angular momentum, and
charges appear from the regularity condition of horizon. We also obtain
multi-black string solutions by taking some limits in the solutions. We extend
the black hole solutions to the five-dimensional Einstein-Maxwell-Chern-Simons
theory with an arbitrary Chern-Simons coupling constant. | Dirac-Born-Infeld-Volkov-Akulov and Deformation of Supersymmetry: We deform the action and the supersymmetry transformations of the d=10 and
d=4 Maxwell supermultiplets so that at each order of the deformation the theory
has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov
type non-linear supersymmetries. The result agrees with the expansion in the
string tension of the explicit action of the Dirac-Born-Infeld model and its
supersymmetries, extracted from D9 and D3 superbranes, respectively. The
half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed
supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new
class of d=6 vector branes related to chiral (2,0) supergravity, which we
denote as `Vp-branes'. We use a space-filling V5 superbrane for the d=6 model
and a V3 superbrane for the d=4 half-maximal Dirac-Born-Infeld (DBI) models. In
this way we present a completion to all orders of the deformation of the
Maxwell supermultiplets with maximal 16+16 supersymmetries in d=10 and 4, and
half-maximal 8+8 supersymmetries in d=6 and 4. |
The Third Way to Interacting $p$-form Theories: We construct a class of interacting $(d-2)$-form theories in $d$ dimensions
that are `third way' consistent. This refers to the fact that the interaction
terms in the $p$-form field equations of motion neither come from the variation
of an action nor are they off-shell conserved on their own. Nevertheless the
full equation is still on-shell consistent. Various generalizations, e.g.
coupling them to $(d-3)$-forms, where 3-algebras play a prominent role, are
also discussed. The method to construct these models also easily recovers the
modified 3$d$ Yang-Mills theory obtained earlier and straightforwardly allows
for higher derivative extensions. | On the Supersymmetric Extension of Gauss-Bonnet like Gravity: We explore the supersymmetry invariance of a supergravity theory in the
presence of a non-trivial boundary. The explicit construction of a bulk
Lagrangian based on an enlarged superalgebra, known as $AdS$-Lorentz, is
presented. Using a geometric approach we show that the supersymmetric extension
of a Gauss-Bonnet like gravity is required in order to restore the
supersymmetry invariance of the theory. |
Spontaneous symmetry breaking in N=2 supergravity: A model describing the $N=2$ supergravity interaction with vector and linear
multiplets is constructed. It admits the introduction of the spontaneous
breaking of supersymmetry with arbitrary scales, one of which may be equal to
zero, which corresponds to partial super-Higgs effect ($N=2 \rightarrow N=1$).
A cosmological term is automatically equal to zero. | Axion electrodynamics and nonrelativistic photons in nuclear and quark
matter: We argue that the effective theory for electromagnetic fields in spatially
varying meson condensations in dense nuclear and quark matter is given by the
axion electrodynamics. We show that one of the helicity states of photons there
has the nonrelativistic gapless dispersion relation $\omega \sim k^2$ at small
momentum, while the other is gapped. This "nonrelativistic photon" may also be
realized at the interface between topological and trivial insulators in
condensed matter systems. |
Supersymmetric completion of supersymmetric quantum mechanics: Via supersymmetry argument, we determine the effective action of the SU(2)
supersymmetric Yang-Mills quantum mechanics up to two constants, which results
from the full supersymmetric completion of the F^4 term. The effective action,
consisting of zero, two, four, six and eight fermion terms, agrees with the
known perturbative one-loop calculations from the type II string theory and the
matrix theory. Our derivation thus demonstrates its non-renormalization
properties, namely, the one-loop exactness of the aforementioned action and the
absence of the non-perturbative corrections. We briefly discuss generalizations
to other branes and the comparison to the DLCQ supergravity analysis. In
particular, our results show that the stringent constraints from the
supersymmetry are responsible for the agreement between the matrix theory and
supergravity with sixteen supercharges. | Notes on Integrable Boundary Interactions of Open $SU(4)$ Alternating
Spin Chains: In arXiv:1704.05807, it was shown that the planar flavored ABJM theory is
integrable in the scalar sector at two-loop order using coordinate Bethe
ansatz. A salient feature of this case is that the boundary reflection matrices
are anti-diagonal with respect to the chosen basis. In this paper, we relax the
coefficients of the boundary terms to be general constants in order to search
for integrable systems among this class. We found that at each end of the spin
chain, the only integrable boundary interaction, besides the one in
arXiv:1704.05807, is the one with vanishing boundary interactions leading to
diagonal reflection matrices. We also construct non-supersymmetric plannar
flavored ABJM theory which leads to trivial boundary interaction at both ends
of the open chain from two-loop anomalous dimension matrix in the scalar
sector. |
A systematic study of finite field dependent BRST-BV transformations in
$Sp(2)$ extended field-antifield formalism: In the framework of $Sp(2)$ extended Lagrangian field-antifield BV formalism
we study systematically the role of finite field-dependent BRST-BV
transformations. We have proved that the Jacobian of a finite BRST-BV
transformation is capable of generating arbitrary finite change of the
gauge-fixing function in the path integral. | Black and super p-branes in diverse dimensions: We present a generic Lagrangian, in arbitrary spacetime dimension $D$,
describing the interaction of a dilaton, a graviton and an antisymmetric tensor
of arbitrary rank $d$. For each $D$~and~$d$, we find ``solitonic'' black
$\tilde{p}$-brane solutions where $\tilde{p} = \tilde{d} - 1$~and~ $\tilde d =
D - d - 2$. These solutions display a spacetime singularity surrounded by an
event horizon, and are characterized by a mass per unit $\tilde p$-volume,
${\cal M}_{\tilde{d}}$, and topological ``magnetic'' charge $g_{\tilde{d}}$,
obeying $\kappa {\cal M}_{\tilde{d}} \geq g_{\tilde{d}}/ \sqrt{2}$. In the
extreme limit $\kappa {\cal M}_{\tilde{d}}=g_{\tilde{d}}/ \sqrt{2}$, the
singularity and event horizon coalesce. For specific values of $D$~and~$d$,
these extreme solutions also exhibit supersymmetry and may be identified with
previously classified heterotic, Type IIA and Type IIB super $\tilde p$-branes.
The theory also admits elementary $p$-brane solutions with ``electric'' Noether
charge $e_d$, obeying the Dirac quantization rule $e_d g_{\tilde{d}} = 2\pi n$,
$n =$~integer. We also present the Lagrangian describing the theory dual to the
original theory, whose antisymmetric tensor has rank $\tilde{d}$ and for which
the roles of topological and elementary solutions are interchanged. The super
$p$-branes and their duals are mutually non-singular. As special cases of our
general solution we recover the black $p$-branes of Horowitz and Strominger $(D
= 10)$, Guven $(D = 11)$ and Gibbons et al $(D = 4)$, the $N = 1$, $N =
2a$~and~$N = 2b$ super-$p$-branes of Dabholkar et al $(4 \leq D \leq 10)$, Duff
and Stelle $(D = 11)$, Duff and Lu $(D = 10)$ and Callan, Harvey and Strominger
$(D = 10)$, and the axionic instanton of Rey $(D = 4)$. In particular, the
electric/magnetic duality of Gibbons and Perry in $D = 4$ is seen to be a
consequence of particle/sixbrane duality in $D = 10$. Among the new solutions
is a self-dual superstring in $D = 6$. |
Dynamics of the Peccei Quinn Scale: Invoking the Peccei-Quinn (PQ) solution to the strong CP problem substitutes
the puzzle of why $\theta_{qcd}$ is so small with the puzzle of why the PQ
symmetry is of such high quality. Cosmological and astrophysical considerations
raise further puzzles. This paper explores this issues in several contexts:
string theory and field theory, and theories without and with low energy
supersymmetry. Among the questions studied are whether requiring axion dark
matter can account for the quality of the PQ symmetry, to which the answer is
sometimes yes. In non-supersymmetric theories, we find $f_a = 10^{12}$ GeV is
quite plausible. In gauge mediation, cosmological constraints on pseudomoduli
place $f_a$ in this range, and require that the gravitino mass be of order an
MeV. | Deformed Boost Transformations That Saturate at the Planck Scale: We derive finite boost transformations based on the Lorentz sector of the
bicross-product-basis $\kappa$-Poincare' Hopf albegra. We emphasize the role of
these boost transformations in a recently-proposed new relativistic theory. We
find that when the (dimensionful) deformation parameter is identified with the
Planck length, which together with the speed-of-light constant has the status
of observer-independent scale in the new relativistic theory, the deformed
boosts saturate at the value of momentum that corresponds to the inverse of the
Planck length. |
The Ising Model on Random Lattices in Arbitrary Dimensions: We study analytically the Ising model coupled to random lattices in dimension
three and higher. The family of random lattices we use is generated by the
large N limit of a colored tensor model generalizing the two-matrix model for
Ising spins on random surfaces. We show that, in the continuum limit, the spin
system does not exhibit a phase transition at finite temperature, in agreement
with numerical investigations. Furthermore we outline a general method to study
critical behavior in colored tensor models. | Mass gaps of a $\mathbb{Z}_3$ gauge theory with three fermion flavors in
1 + 1 dimensions: We consider a $\mathbb{Z}_3$ gauge theory coupled to three degenerate massive
flavors of fermions, which we term "QZD". The spectrum can be computed in $1+1$
dimensions using tensor networks. In weak coupling the spectrum is that of the
expected mesons and baryons, although the corrections in weak coupling are
nontrivial, analogous to those of non-relativistic QED in 1+1 dimensions. In
strong coupling, besides the usual baryon, the singlet meson is a baryon
anti-baryon state. For two special values of the coupling constant, the
lightest baryon is degenerate with the lightest octet meson, and the lightest
singlet meson, respectively. |
From Locality and Unitarity to Cosmological Correlators: In the standard approach to deriving inflationary predictions, we evolve a
vacuum state in time according to the rules of a given model. Since the only
observables are the future values of correlators and not their time evolution,
this brings about a large degeneracy: a vast number of different models are
mapped to the same minute number of observables. Furthermore, due to the lack
of time-translation invariance, even tree-level calculations require an
increasing number of nested integrals that quickly become intractable. Here we
ask how much of the final observables can be "bootstrapped" directly from
locality, unitarity and symmetries.
To this end, we introduce two new bootstrap tools to efficiently compute
cosmological correlators/wavefunctions. The first is a Manifestly Local Test
(MLT) that any $n$-point (wave)function of massless scalars or gravitons must
satisfy if it is to arise from a manifestly local theory. When combined with a
sub-set of the recently proposed Bootstrap Rules, this allows us to compute
explicitly all bispectra to all orders in derivatives for a single scalar.
Since we don't invoke soft theorems, this can also be extended to multi-field
inflation. The second is a partial energy recursion relation that allows us to
compute exchange correlators. Combining a bespoke complex shift of the partial
energies with Cauchy's integral theorem and the Cosmological Optical Theorem,
we fix exchange correlators up to a boundary term. The latter can be determined
up to contact interactions using unitarity and manifest locality. As an
illustration, we use these tools to bootstrap scalar inflationary trispectra
due to graviton exchange and inflaton self-interactions. | Multiscale Renormalization and Decoupling: The standard MS renormalization prescription is inadequate for dealing with
multiscale problems. To illustrate this, we consider the computation of the
effective potential in the Higgs-Yukawa model. It is argued that the most
natural way to deal with this problem is to introduce a 2-scale renormalization
group. We review various ways of implementing this idea and consider to what
extent they fit in with the notion of heavy particle decoupling. |
Regularized Casimir energy for an infinite dielectric cylinder subject
to light-velocity conservation: The Casimir energy of a dilute dielectric cylinder, with the same
light-velocity as in its surrounding medium, is evaluated exactly to first
order in $\xi^2$ and numerically to higher orders in $\xi^2$. The first part is
carried out using addition formulas for Bessel functions, and no Debye
expansions are required. | Modular properties of surface operators in N=2 SQCD: We study half-BPS surface operators in N=2 supersymmetric QCD in four
dimensions with gauge group SU(2) and four fundamental flavours. We compute the
twisted chiral superpotential that describes the effective theory on the
surface operator using equivariant localization as well as the Seiberg-Witten
data. We then use the constraints imposed by S-duality to resum the instanton
contributions to the twisted superpotential into elliptic functions and
(quasi-) modular forms. The resummed results match what one would obtain from
the description of surface operators as the insertion of a degenerate operator
in a spherical conformal block in Liouville CFT. |
Quantum vacuum effects in braneworlds on AdS bulk: We review the results of investigations for brane-induced effects on the
local properties of quantum vacuum in background of AdS spacetime. Two
geometries are considered: a brane parallel to the AdS boundary and a brane
intersecting the AdS boundary. For both these cases the contribution in the
vacuum expectation value (VEV) of the energy-momentum tensor is separated
explicitly and its behavior in various asymptotic regions of the parameters is
studied. It is shown that the influence of the gravitational field on the local
properties of the quantum vacuum is essential at distance from the brane larger
than the AdS curvature radius. In the geometry with a brane parallel to the AdS
boundary the VEV of the energy-momentum tensor is considered for scalar field
with the Robin boundary condition, for Dirac field with the bag boundary
condition and for the electromagnetic field. In the latter case two types of
boundary conditions are discussed. The first one is a generalization of the
perfect conductor boundary condition and the second one corresponds to the
confining boundary condition used in QCD for gluons. For the geometry of a
brane intersecting the AdS boundary, the case of a scalar field is considered.
The corresponding energy-momentum tensor, apart from the diagonal components,
has nonzero off-diagonal component. As a consequence of the latter, in addition
to the normal component, the Casimir force acquires a component parallel to the
brane. | Meson spectroscopy in a confining theory via AdS/CFT: Instanton effects may have implications for hadronization of quark-gluon
plasma as it cools. Here we study dispersion relations of mesons in a strongly
coupled plasma with an instanton background present. It will be shown that at
higher energies the instanton effect diminishes and some comments on the
limiting velocity of mesons in the plasma. the profile function of mesons on
the gravity side is considered also because of its relevance to energy loss of
quark in plasma. |
Asymptotic symmetries of Schrödinger spacetimes: We discuss the asymptotic symmetry algebra of the Schrodinger-invariant
metrics in d+3 dimensions and its realization on finite temperature solutions
of gravity coupled to matter fields. These solutions have been proposed as
gravity backgrounds dual to non-relativistic CFTs with critical exponent z in d
space dimensions. It is known that the Schrodinger algebra possesses an
infinite-dimensional extension, the Schrodinger-Virasoro algebra. However, we
show that the asymptotic symmetry algebra of Schrodinger spacetimes is only
isomorphic to the exact symmetry group of the background. It is possible to
construct from first principles finite and integrable charges that
infinite-dimensionally extend the Schrodinger algebra but these charges are not
correctly represented via a Dirac bracket. We briefly comment on the extension
of our analysis to spacetimes with Lifshitz symmetry. | Testing String Theory with CMB: Future detection/non-detection of tensor modes from inflation in CMB
observations presents a unique way to test certain features of string theory.
Current limit on the ratio of tensor to scalar perturbations, r=T/S, is r <
0.3, future detection may take place for r > 10^{-2}-10^{-3}. At present all
known string theory inflation models predict tensor modes well below the level
of detection. Therefore a possible experimental discovery of tensor modes may
present a challenge to string cosmology.
The strongest bound on r in string inflation follows from the observation
that in most of the models based on the KKLT construction, the value of the
Hubble constant H during inflation must be smaller than the gravitino mass. For
the gravitino mass in the usual range, m_{3/2} < O(1) TeV, this leads to an
extremely strong bound r < 10^{-24}. A discovery of tensor perturbations with r
> 10^{-3} would imply that the gravitinos in this class of models are
superheavy, m_{3/2} > 10^{13} GeV. This would have important implications for
particle phenomenology based on string theory. |
A Renormalization Group Approach to A Yang-Mills Two Matrix Model: A Yang-Mills type two matrix model with mass terms is studied by use of a
matrix renormalization group approach proposed by Brezin and Zinn-Justin. The
renormalization group method indicates that the model exhibits a critical
behavior similar to that of two dimensional Euclidean gravity. A massless limit
and the generation of quadratic terms along the renormalization group flow are
discussed. | Lattice effective potential of $(λΦ^4)_4$: nature of the phase
transition and bounds on the Higgs mass: We present a detailed discussion of Spontaneous Symmetry Breaking (SSB) in
$(\lambda\Phi^4)_4$. In the usual approach, inspired by perturbation theory,
one predicts a second-order phase transition, the Higgs mass $m_h$, related to
the value of the renormalized 4-point coupling, gets smaller when increasing
the ultraviolet cutoff and this leads to the generally quoted upper bounds
$m_h<$700-900 GeV. On the other hand, by exploring the structure of the
effective potential in those approximation consistent with `triviality', where
the Higgs mass does not represent a measure of any observable interaction, SSB
does not require an ultraviolet cutoff, the phase transition is first-order,
such that the massless `Coleman-Weinberg' regime lies in the broken phase, and
one gets only $m_h<$3 TeV from vacuum stability. To separate out the two
alternatives, we present a precise lattice computation of the slope of the
effective potential in the region of bare parameters indicated by the
Luscher~\&~Weisz and Brahm's analysis of the critical line. Our lattice data
strongly support the latter description of SSB. Indeed, our data cannot be
reproduced in perturbation theory, and then they confirm the existence on the
lattice of a remarkable phase of $(\lambda\Phi^4)_4$ where SSB is generated
through ``dimensional transmutation'', and show no evidence for residual
self-interaction effects of the shifted ``Higgs'' field
$h(x)=\Phi(x)-\langle\Phi\rangle$, in agreement with ``triviality''. |
Holographic Reconstruction of AdS Exchanges from Crossing Symmetry: Motivated by AdS/CFT, we address the following outstanding question in large
$N$ conformal field theory: given the appearance of a single-trace operator in
the ${\cal O}\times{\cal O}$ OPE of a scalar primary ${\cal O}$, what is its
total contribution to the vacuum four-point function $\langle {\cal O}{\cal
O}{\cal O}{\cal O}\rangle$ as dictated by crossing symmetry? We solve this
problem in 4d conformal field theories at leading order in $1/N$. Viewed
holographically, this provides a field theory reconstruction of
crossing-symmetric, four-point exchange amplitudes in AdS$_5$. Our solution
takes the form of a resummation of the large spin solution to the crossing
equations, supplemented by corrections at finite spin, required by crossing.
The method can be applied to the exchange of operators of arbitrary twist
$\tau$ and spin $s$, although it vastly simplifies for even-integer twist,
where we give explicit results. The output is the set of OPE data for the
exchange of all double-trace operators $[{\cal O}{\cal O}]_{n,\ell}$. We find
that the double-trace anomalous dimensions $\gamma_{n,\ell}$ are negative,
monotonic and convex functions of $\ell$, for all $n$ and all $\ell>s$. This
constitutes a holographic signature of bulk causality and classical dynamics of
even-spin fields. We also find that the "derivative relation" between
double-trace anomalous dimensions and OPE coefficients does not hold in
general, and derive the explicit form of the deviation in several cases.
Finally, we study large $n$ limits of $\gamma_{n,\ell}$, relevant for the Regge
and bulk-point regimes. | Polarization spin-tensors in two-spinor formalism and Behrends-Fronsdal
spin projection operator for $D$-dimensional case: In the work, the recurrent differential relations that connecting the
polarization spin-tensor of the wave function of a free massive particle of an
arbitrary spin for $D=4$ and new formula of the $D$-dimensional
Behrends-Fronsdal spin projection operator are found. |
Some Applications of String Field Theory: We study general properties of the classical solutions in non-polynomial
closed string field theory and their relationship with two dimensional
conformal field theories. In particular we discuss how different conformal
field theories which are related by marginal or nearly marginal deformations
can be regarded as different classical solutions of some underlying string
field theory. We also discuss construction of a classical solution labelled by
infinite number of parameters in string field theory in two dimensions. For a
specific set of values of the parameters the solution can be identified to the
black hole solution. | Chirality and fermion number in a knotted soliton background: We consider the coupling of a single Dirac fermion to the three component
unit vector field which appears as an order parameter in the Faddeev model.
Classically, the coupling is determined by requiring that it preserves a
certain local frame independence. But quantum mechanically the separate left
and right chiral fermion number currents suffer from a frame anomaly. We employ
this anomaly to compute the fermion number of a knotted soliton. The result
coincides with the self-linking number of the soliton. In particular, the
anomaly structure of the fermions relates directly to the inherent chiral
properties of the soliton. Our result suggests that interactions between
fermions and knotted solitons can lead to phenomena akin the Callan-Rubakov
effect. |
A short review on Noether's theorems, gauge symmetries and boundary
terms: This review is dedicated to some modern applications of the remarkable paper
written in 1918 by E. Noether. On a single paper, Noether discovered the
crucial relation between symmetries and conserved charges as well as the impact
of gauge symmetries on the equations of motion. Almost a century has gone since
the publication of this work and its applications have permeated modern
physics. Our focus will be on some examples that have appeared recently in the
literature. This review is aim at students, not researchers. The main three
topics discussed are (i) global symmetries and conserved charges (ii) local
symmetries and gauge structure of a theory (iii) boundary conditions and
algebra of asymptotic symmetries. All three topics are discussed through
examples. | Vector Effective Field Theories from Soft Limits: We present a bottom-up construction of vector effective field theories using
the infrared structure of scattering amplitudes. Our results employ two
distinct probes of soft kinematics: multiple soft limits and single soft limits
after dimensional reduction, applicable in four and general dimensions,
respectively. Both approaches uniquely specify the Born-Infeld (BI) model as
the only theory of vectors completely fixed by certain infrared conditions
which generalize the Adler zero for pions. These soft properties imply new
recursion relations for on-shell scattering amplitudes in BI theory and suggest
the existence of a wider class of vector effective field theories. |
Anomalous Hall conductivity of the holographic $\mathbb{Z}_2$ Dirac
semimetals: The anomalous spin Hall conductivity in the holographic model of Dirac
semimetals with two Dirac nodes protected by the crystal symmetry has been
elaborated. Such system besides the chiral anomaly possesses another anomaly
which is related to the $\mathbb{Z}_2$ topological charge of the system. The
holographic model of the system contains matter action with two $U(1)$-gauge
fields as well as the appropriate combination of the Chern-Simons gauge terms.
We also allow for the coupling of two gauge fields {\it via} the kinetic
mixing parametrised by the coupling $\alpha$. The holographic approach in the
probe limit enables us to obtain Hall conductivity. The aim of this work is to
describe the phase transitions in the $\mathbb{Z}_2$ Dirac semimetals between
the topologically trivial and non-trivial phases. Interestingly the anomalous
Hall conductivity plays a role of the order parameter of this phase transition.
The holographically found prefactor of the Hall conductivity in the
topologically non-trivial phase, depends on the coupling $\alpha$ and the Chern
- Simons couplings. | Integrability + Supersymmetry + Boundary: Life on the edge is not so
dull after all!: After a brief review of integrability, first in the absence and then in the
presence of a boundary, I outline the construction of actions for the N=1 and
N=2 boundary sine-Gordon models. The key point is to introduce Fermionic
boundary degrees of freedom in the boundary actions. |
String Theory on K3 Surfaces: The moduli space of N=(4,4) string theories with a K3 target space is
determined, establishing in particular that the discrete symmetry group is the
full integral orthogonal group of an even unimodular lattice of signature
(4,20). The method combines an analysis of the classical theory of K3 moduli
spaces with mirror symmetry. A description of the moduli space is also
presented from the viewpoint of quantum geometry, and consequences are drawn
concerning mirror symmetry for algebraic K3 surfaces. | Near-Extremal Spherically Symmetric Black Holes in an
Arbitrary-Dimensional Spacetime: In a recent paper (hep-th/0111091), the near-extremal thermodynamics of a
4-dimensional Reissner-Nordstrom black hole had been considered. In the current
letter, we extend this prior treatment to the more general case of a
spherically symmetric, charged black hole of arbitrary dimensionality. After
summarizing the earlier work, we demonstrate a duality that exists between the
near-extremal sector of spherically symmetric black holes and Jackiw-Teitelboim
theory. On the basis of this correspondence, we argue that back-reaction
effects prohibit any of these ``RN-like'' black holes from reaching extremality
and, moreover, from coming arbitrarily close to an extremal state. |
Discrete Spectra of Semirelativistic Hamiltonians: We review various attempts to localize the discrete spectra of
semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r)
(w.l.o.g. in three spatial dimensions) as entering, for instance, in the
spinless Salpeter equation. Every Hamiltonian in this class of operators
consists of the relativistic kinetic energy \beta \sqrt{m^2 + p^2} (where \beta
> 0 allows for the possibility of more than one particles of mass m) and a
spherically symmetric attractive potential V(r), r = |x|. In general, accurate
eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of
a numerical approximation procedure. Our main emphasis, however, is on the
derivation of rigorous semi-analytical expressions for both upper and lower
bounds to the energy levels of such operators. We compare the bounds obtained
within different approaches and present relationships existing between the
bounds. | Non-invertible Time-reversal Symmetry: In gauge theory, it is commonly stated that time-reversal symmetry only
exists at $\theta=0$ or $\pi$ for a $2\pi$-periodic $\theta$-angle. In this
paper, we point out that in both the free Maxwell theory and massive QED, there
is a non-invertible time-reversal symmetry at every rational $\theta$-angle,
i.e., $\theta= \pi p/N$. The non-invertible time-reversal symmetry is
implemented by a conserved, anti-linear operator without an inverse. It is a
composition of the naive time-reversal transformation and a fractional quantum
Hall state. We also find similar non-invertible time-reversal symmetries in
non-Abelian gauge theories, including the $\mathcal{N}=4$ $SU(2)$ super
Yang-Mills theory along the locus $|\tau|=1$ on the conformal manifold. |
Gravitational Waves as a Probe of the Extra Dimension: We consider the Einstein-Hilbert action without cosmological constant in
5-dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the
fifth direction on a circle of small but finite radius. For non-zero
compactification radius, the 4- dimensional spectrum contains massless and
massive KK modes. For the massive KK modes, we retain four KK tensor and one KK
scalar modes after a gauge fixing. We treat those massive KK modes as
stochastic sources of gravitational wave (GW) with characteristic dependences
of the frequencies on the size of the extra dimension. Using the observational
bounds on the size of the extra dimension and on the characteristic strain, we
make an order estimation on the frequencies and amplitudes of the massive KK
modes that can contribute to the GW. | Superspace Gauge Fixing in Yang-Mills Matter Coupled Conformal
Supergravity: In $D=4$, $\cal{N}=1$ conformal superspace, the Yang-Mills matter coupled
supergravity system is constructed where the Yang-Mills gauge interaction is
introduced by extending the superconformal group to include the K\"ahler
isometry group of chiral matter fields. There are two gauge-fixing procedures
to get to the component Poincar\'e supergravity: one via the superconformal
component formalism and the other via the Poincar\'e superspace formalism.
These two types of superconformal gauge-fixing conditions are analyzed in
detail and their correspondence is clarified. |
Graceful exit via polymerization of pre-big bang cosmology: We consider a phenomenological modification of the Pre Big Bang scenario
using ideas from the resolution of curvature singularities in Loop Quantum
Cosmology. We show that non-perturbative Loop modifications to the dynamics,
arising from the underlying polymer representation, can resolve the graceful
exit problem. The curvature and the dilaton energy stay finite at all times, in
both the string and Einstein frames. In the string frame, the dilaton tends to
a constant value at late times after the bounce. | CP-violating phases in the CKM matrix in orbifold compactifications: The picture of CP-violation in orbifold compactifications in which the
$T$-modulus is at a complex fixed point of the modular group is studied.
CP-violation in the neutral kaon system and in the neutron electric dipole
moment are both discussed. The situation where the $T$-modulus takes complex
values on the unit circle which are not at a fixed point is also discussed. |
Lee-Wald Charge and Asymptotic Behaviors of the Weyl-invariant
Topologically Massive Gravity: We apply the Lee-Wald covariant phase space method to the Weyl-invariant
Topologically Massive Gravity and compute the corresponding on-shell conserved
charges. By using appropriate decay conditions for the existing propagating
modes in the near-horizon of a stationary black hole, we obtain the charges
generating the asymptotic symmetries. We show that the charges are integrable
and the (modified) algebras among the asymptotic generators are closed for the
certain choice of central extensions. | Classical dynamics on Snyder spacetime: We study the classical dynamics of a particle in Snyder spacetime, adopting
the formalism of constrained Hamiltonian systems introduced by Dirac. We show
that the motion of a particle in a scalar potential is deformed with respect to
special relativity by terms of order \beta E^2. An important result is that in
the relativistic Snyder model a consistent choice of the time variable must
necessarily depend on the dynamics. |
Three Dimensional Gravity and Schramm-Loewner Evolution: The partition function of three dimensional gravity in the quantum level,
where the AdS radius $\ell$ is Planck scale, is dual to the Ising model when
the central charge $c=3\ell/2G$ is $1/2$. Mathematically, we show that the
three dimensional gravity can be described by Schramm-Loewner Evolution(SLE)
with certain $\kappa$. In fact, SLE depends on the parameter $\kappa$ which
controls the diffusion of the Brownian motion. Since every value of $c < 1$
corresponding to two values of $\kappa$, then it may hint that the three
dimensional gravity has two different phases at certain central charge c.
Moreover, phase transition is also discussed in Ads and Ising model. | Mapping pure gravity to strings in three-dimensional anti-de Sitter
geometry: Strings propagating in three-dimensional anti-de Sitter space with a
background antisymmetric tensor field are well understood, even at the quantum
level. Pure three-dimensional gravity with a negative cosmological constant is
potentially important because of the existence of black hole solutions and an
asymptotic conformal symmetry, but it is mysterious and surprisingly resistant
to analysis. In this letter, the two theories are related by a map on the
classical level. The map is obtained by gauge fixing the string completely,
like in a light cone gauge, and comparing the resulting constrained theory with
the boundary theory obtained from gravity by imposing the appropriate
asymptotic boundary conditions. The two theories are formally related as
different gauge fixings of the same gauge theory. |
Fermionic vacuum polarization by a flat boundary in cosmic string
spacetime: In this paper we investigate the fermionic condensate and the renormalized
vacuum expectation value (VEV) of the energy-momentum tensor for a massive
fermionic field induced by a flat boundary in the cosmic string spacetime. In
this analysis we assume that the field operator obeys MIT bag boundary
condition on the boundary. We explicitly decompose the VEVs into the
boundary-free and boundary-induced parts. General formulas are provided for
both parts which are valid for any value of the parameter associated with the
cosmic string. For a massless field, the boundary-free part in the fermionic
condensate and the boundary-induced part in the energy-momentum tensor vanish.
For a massive field the radial stress is equal to the energy density for both
boundary-free and boundary-induced parts. The boundary-induced part in the
stress along the axis of the cosmic string vanishes. The total energy density
is negative everywhere, whereas the effective pressure along the azimuthal
direction is positive near the boundary and negative near the cosmic string. We
show that for points away from the boundary, the boundary-induced parts in the
fermionic condensate and in the VEV of the energy-momentum tensor vanish on the
string. | Gerbes and Massive Type II Configurations: We find novel bound states of NS5, D6 and D8-branes in massive Type IIA
string theory. As the NS gauge transformations can change the Chern class of
the RR field these configurations should be thought of as nonlocal objects
called gerbes. We develop a global formalism for theories that involve massive
tensor fields in general, and apply it in massive Type IIA supergravity. We
check the results by investigating the T-dual NS5/D5-brane configurations in
Type IIB, and relate them to an F-theory compactification on a CY3. We comment
on the implications to consistency conditions for brane-wrapping and the
classification of D-brane charges in terms of K-theory classes. |
On K(E_9): We study the maximal compact subgroup K(E_9) of the affine Lie group E_9(9)
and its on-shell realization as an R symmetry of maximal N=16 supergravity in
two dimensions. We first give a rigorous definition of the group K(E_9), which
lives on the double cover of the spectral parameter plane, and show that the
infinitesimal action of K(E_9) on the chiral components of the bosons and the
fermions is determined in terms of an expansion of the Lie algebra of K(E_9)
about the two branch points of this cover; this implies in particular that the
fermions of N=16 supergravity transform in a spinor representation of K(E_9).
The fermionic equations of motion can be fitted into the lowest components of a
single K(E_9) covariant `Dirac equation', with the linear system of N=16
supergravity as the gauge connection. These results suggest the existence of an
`off-shell' realization of K(E_9) in terms of an infinite component spinor
representation. We conclude with some coments on `generalized holonomies' of M
theory. | Fluxes in M-theory on 7-manifolds and G structures: We consider warp compactifications of M-theory on 7-manifolds in the presence
of 4-form fluxes and investigate the constraints imposed by supersymmetry. As
long as the 7-manifold supports only one Killing spinor we infer from the
Killing spinor equations that non-trivial 4-form fluxes will necessarily curve
the external 4-dimensional space. On the other hand, if the 7-manifold has at
least two Killing spinors, there is a non-trivial Killing vector yielding a
reduction of the 7-manifold to a 6-manifold and we confirm that 4-form fluxes
can be incorporated if one includes non-trivial SU(3) structures. |
On the exact Foldy-Wouthuysen transformation for a Dirac spinor in
torsion and other CPT and Lorentz violating backgrounds: We discuss the possibility to perform and use the exact Foldy-Wouthuysen
transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz
violating terms. The classification of such terms is performed, selecting those
of them which admit EFWT. For the particular example of an axial vector field,
which can be associated with the completely antisymmetric torsion, we construct
an explicit EFWT in the case when only a timelike component of this axial
vector is present. In the cases when EFWT is not possible, one can still use
the corresponding technique for deriving the perturbative Foldy-Wouthuysen
transformation, as is illustrated in a particular example in the Appendix. | Effective action of type II superstring theories at order $α'^3$:
NS-NS couplings: Recently, it has been shown that the minimum number of gauge invariant
couplings for $B$-field, metric and dilaton at order $\alpha'^3$ is 872. These
couplings, in a particular scheme, appear in 55 different structures. In this
paper, up to an overall factor, we fix all parameters in type II supertirng
theories by requiring the reduction of the couplings on a circle to be
invariant under T-duality transformations. We find that there are 445 non-zero
couplings which appear in 15 different structures. The couplings are fully
consistent with the partial couplings that have been found in the literature by
the four-point S-matrix element and by the non-linear Sigma model methods. |
Orbifold Reduction and 2d (0,2) Gauge Theories: We introduce Orbifold Reduction, a new method for generating $2d$ $(0,2)$
gauge theories associated to D1-branes probing singular toric Calabi-Yau
4-folds starting from $4d$ $\mathcal{N}=1$ gauge theories on D3-branes probing
toric Calabi-Yau 3-folds. The new procedure generalizes dimensional reduction
and orbifolding. In terms of T-dual configurations, it generates brane brick
models starting from brane tilings. Orbifold reduction provides an agile
approach for generating $2d$ $(0,2)$ theories with a brane realization. We
present three practical applications of the new algorithm: the connection
between $4d$ Seiberg duality and $2d$ triality, a combinatorial method for
generating theories related by triality and a $2d$ $(0,2)$ generalization of
the Klebanov-Witten mass deformation. | Induced Gauge Theory on a Noncommutative Space: We discuss the calculation of the 1-loop effective action on four
dimensional, canonically deformed Euclidean space. The theory under
consideration is a scalar $\phi^4$ model with an additional oscillator
potential. This model is known to be re normalisable. Furthermore, we couple an
exterior gauge field to the scalar field and extract the dynamics for the gauge
field from the divergent terms of the 1-loop effective action using a matrix
basis. This results in proposing an action for noncommutative gauge theory,
which is a candidate for a renormalisable model. |
General Covariant Gauge Fixing for Massless Spin-Two Fields: The most general covariant gauge fixing Lagrangian is considered for a
spin-two gauge theory in the context of the Faddeev-Popov procedure. In
general, five parameters characterize this gauge fixing. Certain limiting
values for these parameters give rise to a spin-two propagator that is either
traceless or transverse, but for no values of these parameters is this
propagator simultaneously traceless and transverse. Having a
traceless-transverse (TT) propagator ensures that only the physical degrees of
freedom associated with the tensor field propagate, and hence it is analogous
to the Landau gauge in electrodynamics. To obtain such a traceless-transverse
propagator, a gauge fixing Lagrangian which is not quadratic must be employed;
this sort of gauge fixing Lagrangian is not encountered in the usual
Faddeev-Popov procedure. It is shown that when this non-quadratic gauge fixing
Lagrangian is used, two Fermionic and one Bosonic ghost arise. As a simple
application we discuss the energy-momentum tensor of the gravitational field at
finite temperature. | Brane inflation in background supergravity: We propose a model of inflation in the framework of brane cosmology driven by
background supergravity. Starting from bulk supergravity we construct the
inflaton potential on the brane and employ it to investigate for the
consequences to inflationary paradigm. To this end, we derive the expressions
for the important parameters in brane inflation, which are somewhat different
from their counterparts in standard cosmology, using the one loop radiative
corrected potential. We further estimate the observable parameters and find
them to fit well with recent observational data by confronting with WMAP7 using
CAMB. We also analyze the typical energy scale of brane inflation with our
model, which resonates well with present estimates from cosmology and standard
model of particle physics. |
Emergent unitarity, all-loop cuts and integrations from the ABJM
amplituhedron: We elaborate on aspects of a new positive geometry proposed recently, which
was conjectured to be the four-point amplituhedron for ABJM theory. We study
generalized unitarity cuts from the geometry, and in particular we prove that
(1) the four-point integrand satisfies perturbative unitarity (or optical
theorem) to all loops, which follows directly from the geometry, and (2)
vanishing cuts involving odd-point amplitudes follow from the ``bipartite"
nature of the associated ``negative geometries", which justifies their
appearance in ABJM theory. We also take a first step in integrating the forms
of these negative geometries and obtain an infrared-finite quantity up to two
loops, from which we extract the cusp anomalous dimension at leading order. | N=1,2 Super-NLS Hierarchies as Super-KP Coset Reductions: We define consistent finite-superfields reductions of the $N=1,2$ super-KP
hierarchies via the coset approach we already developped for reducing the
bosonic KP-hierarchy (generating e.g. the NLS hierarchy from the
$sl(2)/U(1)-{\cal KM}$ coset). We work in a manifestly supersymmetric framework
and illustrate our method by treating explicitly the $N=1,2$ super-NLS
hierarchies. W.r.t. the bosonic case the ordinary covariant derivative is now
replaced by a spinorial one containing a spin ${\textstyle {1\over 2}}$
superfield. Each coset reduction is associated to a rational super-$\cw$
algebra encoding a non-linear super-$\cw_\infty$ algebra structure. In the
$N=2$ case two conjugate sets of superLax operators, equations of motion and
infinite hamiltonians in involution are derived. Modified hierarchies are
obtained from the original ones via free-fields mappings (just as a m-NLS
equation arises by representing the $sl(2)-{\cal KM}$ algebra through the
classical Wakimoto free-fields). |
The Most Irrational Rational Theories: We propose a two-parameter family of modular invariant partition functions of
two-dimensional conformal field theories (CFTs) holographically dual to pure
three-dimensional gravity in anti de Sitter space. Our two parameters control
the central charge, and the representation of $SL(2,\mathbb{Z})$. At large
central charge, the partition function has a gap to the first nontrivial
primary state of $\frac{c}{24}$. As the $SL(2,\mathbb{Z})$ representation
dimension gets large, the partition function exhibits some of the qualitative
features of an irrational CFT. This, for instance, is captured in the behavior
of the spectral form factor. As part of these analyses, we find similar
behavior in the minimal model spectral form factor as $c$ approaches $1$. | Integrability of Schwinger-Dyson Equations in 2D Quantum Gravity and c <
1 Non-critical String Field Theory: We investigate the integrability of the Schwinger-Dyson equations in $c = 1 -
\frac{6}{m(m+1)}$ string field theory which were proposed by Ikehara et al as
the continuum limit of the Schwinger-Dyson equations of the matrix chain model.
We show the continuum Schwinger-Dyson equations generate a closed algebra. This
algebra contains Virasoro algebra but does not coincide with $W_{\infty}$
algebra. We include in the Schwinger-Dyson equations a new process of removing
from the loop boundaries the operator ${\cal H}(\sigma)$ which locally changes
the spin configuration. We also derive the string field Hamiltonian from the
continuum Schwinger-Dyson equations. Its form is universal for all $c = 1 -
\frac{6}{m(m+1)}$ string theories. |
CFT correlators, ${\cal W}$-algebras and Generalized Catalan Numbers: In two spacetime dimensions the Virasoro heavy-heavy-light-light (HHLL)
vacuum block in a certain limit is governed by the Catalan numbers. The
equation for their generating function can be generalized to a differential
equation which the logarithm of the block satisfies. We show that a similar
story holds for the HHLL ${\cal W}_N$ vacuum blocks, where a suitable
generalization of the Catalan numbers plays the main role. Moreover, the ${\cal
W}_N$ blocks have the same form as the stress tensor sector of HHLL near
lightcone conformal correlators in $2(N-1)$ spacetime dimensions. In the latter
case the Catalan numbers are generalized to the numbers of linear extensions of
certain partially ordered sets. | Low-energy effective theory for a Randall-Sundrum scenario with a moving
bulk brane: We derive the low-energy effective theory of gravity for a generalized
Randall-Sundrum scenario, allowing for a third self-gravitating brane to live
in the 5D bulk spacetime. At zero order the 5D spacetime is composed of two
slices of anti-de Sitter spacetime, each with a different curvature scale, and
the 5D Weyl tensor vanishes. Two boundary branes are at the fixed points of the
orbifold whereas the third brane is free to move in the bulk. At first order,
the third brane breaks the otherwise continuous evolution of the projection of
the Weyl tensor normal to the branes. We derive a junction condition for the
projected Weyl tensor across the bulk brane, and combining this constraint with
the junction condition for the extrinsic curvature tensor, allows us to derive
the first-order field equations on the middle brane. The effective theory is a
generalized Brans-Dicke theory with two scalar fields. This is conformally
equivalent to Einstein gravity and two scalar fields, minimally coupled to the
geometry, but nonminimally coupled to matter on the three branes. |
Path integrals for the relativistic particle: Some conceptual and
pedagogical comments: In my textbook on Quantum Field Theory \cite{tpqft} and in a recent paper
\cite{tpejc2018}, I advocated a lattice regularization procedure for defining
the path integral for the relativistic particle, using the non-quadratic action
containing a square root. I also provided an interpretation of this result in
terms of the Jacobi action principle. This note clarifies several conceptual
and pedagogical issues related to this approach and highlights some interesting
open questions which this result leads to. | Quantum scale symmetry: Quantum scale symmetry is the realization of scale invariance in a quantum
field theory. No parameters with dimension of length or mass are present in the
quantum effective action. Quantum scale symmetry is generated by quantum
fluctuations via the presence of fixed points for running couplings. As for any
global symmetry, the ground state or cosmological state may be scale invariant
or not. Spontaneous breaking of scale symmetry leads to massive particles and
predicts a massless Goldstone boson. A massless particle spectrum follows from
scale symmetry of the effective action only if the ground state is scale
symmetric. Approximate scale symmetry close to a fixed point leads to important
predictions for observations in various areas of fundamental physics.
We review consequences of scale symmetry for particle physics, quantum
gravity and cosmology. For particle physics, scale symmetry is closely linked
to the tiny ratio between the Fermi scale of weak interactions and the Planck
scale for gravity. For quantum gravity, scale symmetry is associated to the
ultraviolet fixed point which allows for a non-perturbatively renormalizable
quantum field theory for all known interactions. The interplay between gravity
and particle physics at this fixed point permits to predict couplings of the
standard model or other "effective low energy models" for momenta below the
Planck mass. In particular, quantum gravity determines the ratio of Higgs boson
mass and top quark mass. In cosmology, approximate scale symmetry explains the
almost scale-invariant primordial fluctuation spectrum which is at the origin
of all structures in the universe. The pseudo-Goldstone boson of spontaneously
broken approximate scale symmetry may be responsible for dynamical dark energy
and a solution of the cosmological constant problem. |
Deformations of the Almheiri-Polchinski model: We study deformations of the Almheiri-Polchinski (AP) model by employing the
Yang-Baxter deformation technique. The general deformed AdS$_2$ metric becomes
a solution of a deformed AP model. In particular, the dilaton potential is
deformed from a simple quadratic form to a hyperbolic function-type potential
similarly to integrable deformations. A specific solution is a deformed black
hole solution. Because the deformation makes the spacetime structure around the
boundary change drastically and a new naked singularity appears, the
holographic interpretation is far from trivial. The Hawking temperature is the
same as the undeformed case but the Bekenstein-Hawking entropy is modified due
to the deformation. This entropy can also be reproduced by evaluating the
renormalized stress tensor with an appropriate counter term on the regularized
screen close to the singularity. | A Spin Chain from String Theory: We study the semiclassical spectrum of bosonic string theory on AdS_3 x S^1
in the limit of large AdS angular momentum. At leading semiclassical order,
this is a subsector of the IIB superstring on AdS_5 x S^5. The theory includes
strings with K spikes which approach the boundary in this limit. We show that,
for all K, the spectrum of these strings exactly matches that of the
corresponding operators in the dual gauge theory up to a single universal
prefactor which can be identified with the cusp anomalous dimension. We propose
a precise map between the dynamics of the spikes and the classical SL(2,R) spin
chain which arises in the large-spin limit of N=4 Super Yang-Mills theory. |
Two-point closed string amplitudes in the BRST formalism: Two-point tree-level amplitudes in bosonic closed string theory are described
by a correlation function within the BRST formalism, which respects manifest
Lorentz and conformal invariance. In the derivation of the two-point
amplitudes, we use the mostly BRST exact operator, which has been introduced
for two-point open string amplitudes, and a closed string vertex with ghost
number three, which has been explored in our recent work, in addition to the
conventional one. | Higher Quantum Geometry and Non-Geometric String Theory: We present a concise overview of the physical and mathematical structures
underpinning the appearence of nonassociative deformations of geometry in
non-geometric string theory. Starting from a quick recap of the appearence of
noncommutative product and commutator deformations of geometry in open string
theory with $B$-fields, we argue on physical principles that closed strings
should instead probe triproduct and tribracket deformations in backgrounds of
locally non-geometric fluxes. After describing the toy model of electric
charges moving in fields of smooth distributions of magnetic charge as a
physical introduction to the notions of nonassociative geometry, we review the
description of non-geometric fluxes in generalized geometry and double field
theory, and the worldsheet calculations suggesting the appearence of
nonassociative deformations, together with their caveats. We discuss how
algebroids and their associated AKSZ sigma-models give a description of
non-geometric backgrounds in terms of higher geometry, and consider the
quantization of the membrane sigma-model which geometrizes closed strings with
$R$-flux. From this we derive an explicit nonassociative star product for the
quantum geometry of the closed string phase space, and apply it to derive the
triproducts that appear in conformal field theory correlation functions, to
describe a consistent treatment of nonassociative quantum mechanics, to
demonstrate quantitatively the coarse-graining of spacetime due to $R$-flux,
and to describe the quantization of Nambu brackets. We also briefly review how
these constructions lead to a nonassociative theory of gravity, their uplifts
to non-geometric M-theory, and the role played by $L_\infty$-algebras in these
developments. |
Longitudinal Rescaling of Quantum Chromodynamics: We examine the effect of quantum longitudinal rescaling of coordinates, on
the action of quantum chromodynamics (with quarks) to one loop. We use an
aspherical Wilsonian integration (previously applied to the pure Yang-Mills
theory and to quantum electrodynamics). Quantum fluctuations produce anomalous
powers of the rescaling parameter in the coefficients of the rescaled action.
Our results are valid for small rescalings only, because perturbation theory
breaks down for large rescalings. | On the Quantization of Massive Superparticles: We consider the action of the D=11 supermembrane wrapping a compactified
sector of the target space in such a way that a non trivial central charge in
the SUSY algebra is induced. We show that the dynamics of the center of mass
corresponds to a superparticle in D=9 with additional fermionic terms
associated to the central charges . We perform the covariant quantization of
this system following a direct approach which introduces an equivalent action
for the system which has only first class constraints allowing to obtain the
space of physical states in a covariant way. The resulting multiplet contains
$2^8$ states corresponding to a $KKB$ ultrashort multiplet. |
The holographic interpretation of $J \bar T$-deformed CFTs: Recently, a non-local yet possibly UV-complete quantum field theory has been
constructed by deforming a two-dimensional CFT by the composite operator $J
\bar T$, where $J$ is a chiral $U(1)$ current and $\bar T$ is a component of
the stress tensor. Assuming the original CFT was a holographic CFT, we work out
the holographic dual of its $J \bar T$ deformation. We find that the dual
spacetime is still AdS$_3$, but with modified boundary conditions that mix the
metric and the Chern-Simons gauge field dual to the $U(1)$ current. We show
that when the coefficient of the chiral anomaly for $J$ vanishes, the energy
and thermodynamics of black holes obeying these modified boundary conditions
precisely reproduce the previously derived field theory spectrum and
thermodynamics. Our proposed holographic dictionary can also reproduce the
field-theoretical spectrum in presence of the chiral anomaly, upon a certain
assumption that we justify. The asymptotic symmetry group associated to these
boundary conditions consists of two copies of the Virasoro and one copy of the
$U(1)$ Ka\v{c}-Moody algebra, just as before the deformation; the only effect
of the latter is to modify the spacetime dependence of the right-moving
Virasoro generators, whose action becomes state-dependent and effectively
non-local. | The operator form of the effective potential governing the time
evolution in n-dimensional subspace of states: This paper presents the operator form of the effective potential V governing
the time evolution in 2 and 3 and n dimensional subspace of states. The general
formula for the n dimensional case is considered the starting point for the
calculation of the explicit formulae for 2 and 3 dimensional degenerate and
non-degenerate cases. We relate the 2 and 3 dimensional cases to some physical
systems which are currently investigated. |
Chiral decomposition in the non-commutative Landau problem: The decomposition of the non-commutative Landau (NCL) system into two
uncoupled one-dimensional chiral components, advocated by Alvarez, Gomis,
Kamimura and Plyushchay [1], is generalized to nonvanishing electric fields.
This allows us to discuss the main properties of the NCL problem including its
exotic Newton-Hooke symmetry and its relation to the Hall effect. The "phase
transition" when the magnetic field crosses a critical value determined by the
non-commutative parameter is studied in detail. | Dual Form of the Paperclip Model: The ``paperclip model'' is 2D model of Quantum Field Theory with boundary
interaction defined through a special constraint imposed on the boundary values
of massless bosonic fields (hep-th/0312168). Here we argue that this model
admits equivalent ``dual'' description, where the boundary constraint is
replaced by special interaction of the boundary values of the bosonic fields
with an additional boundary degree of freedom. The dual form involves the
topological theta-angle in explicit way. |
Where is the Information Stored in Black Holes?: It is shown that many modes of the gravitational field exist only inside the
horizon of an extreme black hole in string theory. At least in certain cases,
the number of such modes is sufficient to account for the Bekenstein-Hawking
entropy. These modes are associated with sources which carry Ramond-Ramond
charge, and so may be viewed as the strong coupling limit of D-branes. Although
these sources naturally live at the singularity, they are well defined and
generate modes which extend out to the horizon. This suggests that the
information in an extreme black hole is not localized near the singularity or
the horizon, but extends between them. | The 1/N Expansion in Noncommutative Quantum Mechanics: We study the 1/N expansion in noncommutative quantum mechanics for the
anharmonic and Coulombian potentials. The expansion for the anharmonic
oscillator presented good convergence properties, but for the Coulombian
potential, we found a divergent large N expansion when using the usual
noncommutative generalization of the potential. We proposed a modified version
of the noncommutative Coulombian potential which provides a well-behaved 1/N
expansion. |
Magnetic Soft Charges, Dual Supertranslations and 't Hooft Line
Dressings: We construct the Faddeev-Kulish asymptotic states in a quantum field theory
of electric and magnetic charges. We find that there are two kind of dressings:
apart from the well known (electric) Wilson line dressing, there is a magnetic
counterpart which can be written as a 't Hooft line operator. The 't Hooft line
dressings are charged under the magnetic large gauge transformation (LGT), but
are neutral under electric LGT. This is in contrast to the Faddeev-Kulish
dressings of electrons, which can be written as a Wilson line operator and are
charged under electric LGT but neutral under magnetic LGT. With these dressings
and the corresponding construction of the coherent states, the infrared
finiteness of the theory of electric and magnetic charges is guaranteed. Even
in the absence of magnetic monopoles, the electric and magnetic soft modes
exhibit the electromagnetic duality of vacuum Maxwell theory. Using only the
asymptotic form of three-point interactions in a field theory of electric and
magnetic charges, we show that the leading magnetic dressings, like the leading
electric ones, are exact in the field theory of electric and magnetic charges,
in accordance with a conjecture of Strominger. We then extend the construction
to perturbative quantum gravity in asymptotically flat spacetime, and construct
gravitational 't Hooft line dressings that are charged under dual
supertranslations. The duality in the quantum theory between the electric and
magnetic soft charges and their dressings is thus made manifest. | 5d Field Theories and M Theory: 5-brane configurations describing 5d field theories are promoted to an M
theory description a la Witten in terms of polynomials in two complex
variables. The coefficients of the polynomials are the Coulomb branch. This
picture resolves apparent singularities at vertices and reveals exponentially
small corrections. These corrections ask to be compared to world line instanton
corrections. From a different perspective this procedure may be used to define
a diagrammatic representation of polynomials in two variables. |
Baryons as Vortexes on the $η^{\prime}$ Domain Wall: We show that the recent construction of $N_f=1$ baryons on the $\eta^\prime$
domain wall can be understood as vortexes of the principal effective theory --
the Chern-Simons-Higgs theory -- on a 2+1-dimensional sheet. This theory has a
series of vertex solutions, and the vortex with unit topological charge
naturally spins $N_c/2$, which coincides with the spin of the one-flavor baryon
in QCD. Since the $N_c$ scaling of the vortexes is the same as that of baryons,
baryons can be regarded as vortexes. By virtue of the particle-vortex symmetry,
the dual Zhang-Hansson-Kivelson theory indicates that the quark carries
topological charge $1/N_c$ and obeys fractional statistics. The generalization
to arbitrary $N_f$ is also discussed. | Motivations and Physical Aims of Algebraic QFT: We present illustrations which show the usefulness of algebraic QFT. In
particular in low-dimensional QFT, when Lagrangian quantization does not exist
or is useless (e.g. in chiral conformal theories), the algebraic method is
beginning to reveal its strength. |
Superconformal hypermultiplets in superspace: We use the manifestly N=2 supersymmetric, off-shell, harmonic (or twistor)
superspace approach to solve the constraints implied by four-dimensional N=2
superconformal symmetry on the N=2 non-linear sigma-model target space, known
as the special hyper-K"ahler geometry. Our general solution is formulated in
terms of a homogeneous (of degree two) function of unconstrained (analytic)
Fayet-Sohnius hypermultiplet superfields. We also derive the improved (N=2
superconformal) actions for the off-shell (constrained) N=2 projective
hypermultiplets, and relate them (via non-conformal deformations) to the
asymptotically locally-flat (ALF) A_k and D_k series of the gravitational
instantons. The same metrics describe Kaluza-Klein monopoles in M-theory, while
they also arise in the quantum moduli spaces of N=4 supersymmetric gauge field
theories with SU(2) gauge group and matter hypermultiplets in three spacetime
dimensions. We comment on rotational isometries versus translational isometries
in the context of N=2 NLSM in terms of projective hypermultiplets. | On a self-dual phase space for 3+1 lattice Yang-Mills theory: I propose a self-dual deformation of the classical phase space of lattice
Yang--Mills theory, in which both the electric and magnetic fluxes take value
in the gauge Lie group. A local construction of the deformed phase space
requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which
is here reviewed. The results is a full-fledged finite-dimensional and
gauge-invariant phase space, whose self-duality properties are largely enhanced
in (3+1) spacetime dimensions. This enhancement is due to a correspondence with
the moduli space of an auxiliary non-commutative flat connection living on a
Riemann surface defined from the lattice itself, which in turn equips the
duality between electric and magnetic fluxes with a neat geometrical
interpretation in terms of a Heegaard splitting of the space manifold. Finally,
I discuss the consequences of the proposed deformation on the quantization of
the phase space, its quantum gravitational interpretation, as well as its
relevance for the construction of (3+1) dimensional topological field theories
with defects. |
New Algorithm for Tensor Calculation in Field Theories: Tensor calculation of suffix-contraction is carried out by a C-program.
Tensors are represented graphically, and the algorithm makes use of the
topology of graphs. Classical and quantum gravity, in the weak-field
perturbative approach, is a special interest. Examples of the leading order
calculation of some general invariants such as $R_{\mn\ls}R^{\mn\ls}$ are
given. Application to Weyl anomaly calculation is commented. | Linearization of thick K-branes: We study the linearization of a class of thick K-branes, namely,
four-dimensional domain walls generated by a scalar field with particular
nonstandard kinetic terms. The master equations for linear perturbations are
derived from the point of view of both dynamical equations and quadratic
action. The spectra of the canonical normal modes are studied using
supersymmetric quantum mechanics. Our results indicate that the scalar
perturbation is nonlocalizable in general. Conditions for stable $K$-branes are
also found. |
Form factors, correlation functions and vertex operators in the
eight-vertex model at reflectionless points: The eight-vertex model at the reflectionless points is considered on the
basis of Smirnov's axiomatic approach. Integral formulae for form factors of
the eight-vertex model can be obtained in terms of those of the eight-vertex
SOS model, by using vertex-face transformation. The resulting formulae have
very simple forms at the reflectionless points, and suggests us the explicit
expressions of the type II vertex operators of the eight-vertex model. | A renormalization group improved computation of correlation functions in
theories with non-trivial phase diagram: We present a simple and consistent way to compute correlation functions in
interacting theories with non-trivial phase diagram. As an example we show how
to consistently compute the four-point function in three dimensional
$\mathbb{Z}_2$-scalar theories. The idea is to perform the path integral by
weighting the momentum modes that contribute to it according to their
renormalization group (RG) relevance, i.e. we weight each mode according to the
value of the running couplings at that scale. In this way, we are able encode
in a loop computation the information regarding the RG trajectory along which
we are integrating. We show that depending on the initial condition, or initial
point in the phase diagram, we obtain different behaviors of the four-point
function at the end point of the flow. |
Searching for a Connection Between Matroid Theory and String Theory: We make a number of observations about matter-ghost string phase, which may
eventually lead to a formal connection between matroid theory and string
theory. In particular, in order to take advantage of the already established
connection between matroid theory and Chern-Simons theory, we propose a
generalization of string theory in terms of some kind of Kahler metric. We show
that this generalization is closely related to the Kahler-Chern-Simons action
due to Nair and Schiff. In addition, we discuss matroid/string connection via
matroid bundles and a Schild type action, and we add new information about the
relationship between matroid theory, D=11 supergravity and Chern-Simons
formalism. | He-McKellar-Wilkens-type effect from the Lorentz symmetry breaking
effects: From the effects of the Lorentz symmetry violation in the CPT-even gauge
sector of Standard Model Extension, we establish a possible scenario where an
analogue of the He-McKellar-Wilkens effect can stem from. Besides, we build
quantum holonomies associated with the analogue of the He-McKellar-Wilkens
effect and discuss a possible analogy with the holonomic quantum computation
[P. Zanardi and M. Rasetti, Phys. Lett. A {\bf264}, 94 (1999)]. Finally, we
investigate the dependence of the energy levels on the He-McKellar-Wilkens
geometric phase induced by Lorentz symmetry breaking effects when the particle
is confined to a hard-wall confining potential. |
Casimir Energy of an irregular membrane: We compute the Casimir energy which arises in a bi-dimensional surface due to
the quantum fluctuations of a scalar field. We assume that the boundaries are
irregular and the field obeys Dirichlet condition. We re-parametrize the
problem to one which has flat boundary conditions and the irregularity is
treated as a perturbation in the Laplace-Beltrami operator which appears.
Later, to compute the Casimir energy, we use zeta function regularization. It
is compared the results coming from perturbation theory with the WKB method. | What Becomes of Semilocal non-Abelian Strings in ${\mathcal N}=1$
Supersymmetric QCD: We study non-Abelian vortex strings in ${\mathcal N}=2$ supersymmetric QCD
with the gauge group U$(N)$ deformed by the mass $\mu$ of the adjoint matter.
This deformation breaks ${\mathcal N}=2$ supersymmetry down to ${\mathcal N}=1$
and in the limit of large $\mu$ the theory flows to ${\mathcal N}=1$ QCD.
Non-Abelian strings in addition to translational zero modes have orientation
moduli. In the ${\mathcal N}=2$ limit of small $\mu$ the dynamics of
orientational moduli is described by the two dimensional $CP(N-1)$ model for
QCD with $N_f=N$ flavors of quark hypermultiplets. For the case of $N_f>N$ the
non-Abelian string becomes semilocal developing additional size moduli which
modify the effective two dimensional $\sigma$-model on the string making its
target space non-compact. In this paper we consider the $\mu$-deformed theory
with $N_f>N$ eventually making $\mu$ large. We show that size moduli develop a
potential that forces the string transverse size to shrink. Eventually in the
large $\mu$ limit size moduli decouple and the effective theory on the string
reduces to the $CP(N-1)$ model. We also comment on physics of confined
monopoles. |
Interquark Potential in Schrodinger Representation: Static charges are introduced in Yang-Mills theory via coupling to heavy
fermions. The states containing static color charges are constructed using
integration over gauge transformations. A functional representation for
interquark potential is obtained. This representation provides a simple
criterion for confinement. | Perturbative 4D conformal field theories and representation theory of
diagram algebras: The correlators of free four dimensional conformal field theories (CFT4) have
been shown to be given by amplitudes in two-dimensional $so(4,2)$ equivariant
topological field theories (TFT2), by using a vertex operator formalism for the
correlators. We show that this can be extended to perturbative interacting
conformal field theories, using two representation theoretic constructions. A
co-product deformation for the conformal algebra accommodates the equivariant
construction of composite operators in the presence of non-additive anomalous
dimensions. Explicit expressions for the co-product deformation are given
within a sector of $ \mathcal{N} =4 $ SYM and for the Wilson-Fischer fixed
point near four dimensions. The extension of conformal equivariance beyond
integer dimensions (relevant for the Wilson-Fischer fixed point) leads to the
definition of an associative diagram algebra $ {\bf U}_{*} $, abstracted from $
Uso(d)$ in the limit of large integer $d$, which admits extension of $ Uso(d)$
representation theory to general real (or complex) $d$. The algebra is related,
via oscillator realisations, to $so(d)$ equivariant maps and Brauer category
diagrams. Tensor representations are constructed where the diagram algebra acts
on tensor products of a fundamental diagram representation. A similar
diagrammatic algebra ${\bf U}_{\star ,2}$, related to a general $d$ extension
for $ Uso(d,2)$ is defined, and some of its lowest weight representations
relevant to the Wilson-Fischer fixed point are described. |
Quantum gravitational contributions to quantum electrodynamics: Quantum electrodynamics describes the interactions of electrons and photons.
Electric charge (the gauge coupling constant) is energy dependent, and there is
a previous claim that charge is affected by gravity (described by general
relativity) with the implication that the charge is reduced at high energies.
But that claim has been very controversial with the situation inconclusive.
Here I report an analysis (free from earlier controversies) demonstrating that
that quantum gravity corrections to quantum electrodynamics have a quadratic
energy dependence that result in the reduction of the electric charge at high
energies, a result known as asymptotic freedom. | One-point Functions in AdS/dCFT from Matrix Product States: One-point functions of certain non-protected scalar operators in the defect
CFT dual to the D3-D5 probe brane system with k units of world volume flux can
be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain
and a matrix product state. We present a closed expression of determinant form
for these one-point functions, valid for any value of k. The determinant
formula factorizes into the k=2 result times a k-dependent prefactor. Making
use of the transfer matrix of the Heisenberg spin chain we recursively relate
the matrix product state for higher even and odd k to the matrix product state
for k=2 and k=3 respectively. We furthermore find evidence that the matrix
product states for k=2 and k=3 are related via a ratio of Baxter's Q-operators.
The general k formula has an interesting thermodynamical limit involving a
non-trivial scaling of k, which indicates that the match between string and
field theory one-point functions found for chiral primaries might be tested for
non-protected operators as well. We revisit the string computation for chiral
primaries and discuss how it can be extended to non-protected operators. |
Holographic superconductor with nonlinear arcsin-electrodynamics: We investigate holographic s-wave superconductors with nonlinear
arcsin-electrodynamics in the background of Schwarzschild anti-de Sitter black
holes. The analytical Sturm-Liouville eigenvalue problem is explored and we
assume that the scalar and electromagnetic fields do not influence on the
background metric (the probe limit). The critical temperatures of phase
transitions depending on the parameter of the model is obtained. We show that
in our case the condensation formation becomes easier compared to Born-Infeld
nonlinear electrodynamics. The critical exponent near the critical temperature
is calculated which is 1/2. With the help of the matching method we derive
analytic expressions for the condensation value and the critical temperature.
The real and imaginary parts of the conductivity in our model, making use of an
analytical method, are computed. | Matrix Models of Induced Large-N QCD: I review recent works on the problem of inducing large-N QCD by matrix
fields. In the first part of the talk I describe the matrix models which induce
large-N QCD and present the results of studies of their phase structure by the
standard lattice technology (in particular, by the mean field method). The
second part is devoted to the exact solution of these models in the strong
coupling region by means of the loop equations. |
Analogue Aharonov-Bohm effect in neo-Newtonian theory: We address the issues of the scattering of massless planar scalar waves by an
acoustic black hole in neo-Newtonian hydrodynamics. We then compute the
differential cross section through the use of the partial wave approach in the
neo-Newtonian theory which is a modification of the usual Newtonian theory that
correctly incorporates the effects of pressure. We mainly show that the
scattering of planar waves leads to a modified analogue Aharonov-Bohm effect
due to a nontrivial response of the parameters defining the equation of state. | A Note on c=1 Virasoro Boundary States and Asymmetric Shift Orbifolds: We comment on the conformal boundary states of the c=1 free boson theory on a
circle which do not preserve the U(1) symmetry. We construct these Virasoro
boundary states at a generic radius by a simple asymmetric shift orbifold
acting on the fundamental boundary states at the self-dual radius. We further
calculate the boundary entropy and find that the Virasoro boundary states at
irrational radius have infinite boundary entropy. The corresponding open string
description of the asymmetric orbifold is given using the quotient algebra
construction. Moreover, we find that the quotient algebra associated with a
non-fundamental boundary state contains the noncommutative Weyl algebra. |
The Quantum Geometer's Universe: Particles, Interactions and Topology: With the two most profound conceptual revolutions of XXth century physics,
quantum mechanics and relativity, which have culminated into relativistic
spacetime geometry and quantum gauge field theory as the principles for gravity
and the three other known fundamental interactions, the physicist of the XXIst
century has inherited an unfinished symphony: the unification of the quantum
and the continuum. As an invitation to tomorrow's quantum geometers who must
design the new rulers by which to size up the Universe at those scales where
the smallest meets the largest, these lectures review the basic principles of
today's conceptual framework, and highlight by way of simple examples the
interplay that presently exists between the quantum world of particle
interactions and the classical world of geometry and topology. | N=4 Gauged Supergravity from Duality-Twist Compactifications of String
Theory: We investigate the lifting of half-maximal four-dimensional gauged
supergravities to compactifications of string theory. It is shown that a class
of such supergravities can arise from compactifications of IIA string theory on
manifolds of SU(2)-structure which may be thought of as K3 fibrations over T^2.
Examples of these SU(2)-structure backgrounds, as smooth K3 bundles and as
compactifications with H-flux, are given and we also find evidence for a class
of non-geometric, Mirror-fold backgrounds. By applying the duality between IIA
string theory on K3 and Heterotic string theory on T^4 fibrewise, we argue that
these SU(2)-structure backgrounds are dual to Heterotic compactifications on a
class T^4 fibrations over T^2. Examples of these fibrations as twisted tori,
H-flux and T-fold compactifications are given. We also construct a new set of
backgrounds, particular to Heterotic string theory, which includes a previously
unknown class of Heterotic T-folds. A sigma model description of these
backgrounds, from the Heterotic perspective, is presented in which we
generalize the Bosonic doubled formalism to Heterotic string theory. |
Lorentz invariance violation and simultaneous emission of
electromagnetic and gravitational waves: In this work, we compute some phenomenological bounds for the electromagnetic
and massive gravitational high-derivative extensions supposing that it is
possible to have an astrophysical process that generates simultaneously
gravitational and electromagnetic waves. We present Lorentz invariance
violating (LIV) higher-order derivative models, following the Myers-Pospelov
approach, to electrodynamics and massive gravitational waves. We compute the
corrected equation of motion of these models, their dispersion relations and
the velocities. The LIV parameters for the gravitational and electromagnetic
sectors, $\xi_{g}$ and $\xi_{\gamma}$, respectively, were also obtained for
three different approaches: luminal photons, time delay of flight and the
difference of graviton and photon velocities. These LIV parameters depend on
the mass scales where the LIV-terms become relevant, $M$ for the
electromagnetic sector and $M_{1}$ for the gravitational one. We obtain, using
the values for $M$ and $M_{1}$ found in the literature, that
$\xi_{g}\sim10^{-2}$, which is expected to be phenomenologically relevant and
$\xi_{\gamma}\sim10^{3}$, which cannot be suitable for an effective LIV theory.
However, we show that $\xi_{\gamma}$ can be interesting in a phenomenological
point of view if $M\gg M_{1}$. Finally the relation between the variation of
the velocities of the photon and the graviton in relation to the speed of light
was calculated and resulted in $\Delta v_{g}/\Delta
v_{\gamma}\lesssim1.82\times 10^{-3}$. | N=6 superconformal Chern-Simons-matter theories, M2-branes and their
gravity duals: We construct three dimensional Chern-Simons-matter theories with gauge groups
U(N)xU(N) and SU(N)xSU(N) which have explicit N=6 superconformal symmetry.
Using brane constructions we argue that the U(N)xU(N) theory at level k
describes the low energy limit of N M2-branes probing a C^4/Z_k singularity. At
large N the theory is then dual to M theory on AdS_4xS^7/Z_k. The theory also
has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type
IIA string theory on AdS_4xCP^3. For k=1 the theory is conjectured to describe
N M2-branes in flat space, although our construction realizes explicitly only
six of the eight supersymmetries. We give some evidence for this conjecture,
which is similar to the evidence for mirror symmetry in d=3 gauge theories.
When the gauge group is SU(2)xSU(2) our theory has extra symmetries and becomes
identical to the Bagger-Lambert theory. |
Emission of linearly polarized photons in a strongly coupled magnetized
plasma from the gauge/gravity correspondence: We use holographic methods to show that photons emitted by a strongly coupled
plasma subject to a magnetic field are linearly polarized regardless of their
four-momentum, except when they propagate along the field direction. The
gravitational dual is constructed using a 5D truncation of 10-dimensional type
IIB supergravity, and includes a scalar field in addition to the constant
magnetic one. In terms of the geometry of the collision experiment that we
model, our statement is that any photon produced there has to be in its only
polarization state parallel to the reaction plane. | Completing the Bootstrap Program for
$\mathrm{T}\bar{\mathrm{T}}$-Deformed Massive Integrable Quantum Field
Theories: In recent years a considerable amount of attention has been devoted to the
investigation of 2D quantum field theories perturbed by certain types of
irrelevant operators. These are the composite field
$\mathrm{T}\bar{\mathrm{T}}$ - constructed out of the components of the
stress-energy tensor - and its generalisations - built from higher-spin
conserved currents. The effect of such perturbations on the infrared and
ultraviolet properties of the theory has been extensively investigated. In the
context of integrable quantum field theories, a fruitful perspective is that of
factorised scattering theory. In fact, the above perturbations were shown to
preserve integrability. The resulting deformed scattering matrices -
extensively analysed with the thermodynamic Bethe ansatz - provide the first
step in the development of a complete bootstrap program. In this letter we
present a systematic approach to computing matrix elements of operators in
generalised $\mathrm{T}\bar{\mathrm{T}}$-perturbed models, based on employing
the standard form factor program. Our approach is very general and can be
applied to all theories with diagonal scattering. We show that the deformed
form factors, just as happens for the $S$-matrix, factorise into the product of
the undeformed ones and of a perturbation- and theory-dependent term. From
these solutions, correlation functions can be obtained and their asymptotic
properties studied. Our results set the foundations of a new research program
for massive integrable quantum field theory perturbed by irrelevant operators. |
Reflections on the Matter of 3d $\mathcal{N} = 1$ Vacua and Local
$Spin(7)$ Compactifications: We use Higgs bundles to study the 3d $\mathcal{N} = 1$ vacua obtained from
M-theory compactified on a local $Spin(7)$ space given as a four-manifold $M_4$
of ADE singularities with further generic enhancements in the singularity type
along one-dimensional subspaces. There can be strong quantum corrections to the
massless degrees of freedom in the low energy effective field theory, but
topologically robust quantities such as "parity" anomalies are still
calculable. We show how geometric reflections of the compactification space
descend to 3d reflections and discrete symmetries. The "parity" anomalies of
the effective field theory descend from topological data of the
compactification. The geometric perspective also allows us to track various
perturbative and non-perturbative corrections to the 3d effective field theory.
We also provide some explicit constructions of well-known 3d theories,
including those which arise as edge modes of 4d topological insulators, and 3d
$\mathcal{N} = 1$ analogs of grand unified theories. An additional result of
our analysis is that we are able to track the spectrum of extended objects and
their transformations under higher-form symmetries. | SU(N) monopoles with and without SUSY: These are expanded notes of lectures given at the Advanced Summer School on
Modern Mathematical Physics (JINR Dubna, July 2005) and at the 8th
International School-Seminar ``The actual problems of microworld physics 2005''
(Gomel-Dubna, August 2005). I review classical monopole solutions of the SU(N)
Yang-Mills-Higgs theory. The first part is a pedagogical introduction into to
the theory of non-Abelian SU(2) monopoles. In the second part I discuss a
particular case of SU(3) theories containing different limits of symmetry
breaking. It turns out that the multimonopole configurations are natural in a
model with the gauge group of higher rank. Here I discuss fundamental and
composite monopoles and consider the limiting situation of the massless states.
In the last part I briefly discuss construction of the $N = 2$ SU(2)
supersymmetric monopoles and some of the basic properties which are connected
with the field theoretical aspects of these classical solutions. |
D-branes et orientifolds dans des espaces courbes ou dependant du temps: In this thesis we study string theory with D-branes and possibly orientifolds
in curved or time-dependent spaces. Our study aims at understanding some
aspects of curved and time-dependent spaces, notably because of their
importance in cosmology.
The first chapter introduces some bases of string theory.
The second chapter studies non-oriented strings on compact groups SU(2) and
SO(3): after reviewing known results about D-branes in such spaces, we present
our results on the position of orientifolds and their interaction with open and
closed strings.
The third chapter studies D-branes in certain backgrounds of Ramond-Ramond
type, using S-duality, which links them with backgrounds of Neveu-Schwarz type,
where calculations can be done.
The last chapter considers strings on a D-brane embedded with a plane wave,
and introduces tools which allow to study interactions in such a background. | Topological and non-topological kink families in non-linear
$(\mathbb{S}^1\times \mathbb{S}^1)$-Sigma models: In this paper we construct a family of Hamilton-Jacobi separable non-linear
$\mathbb{S}^1\times\mathbb{S}^1$ Sigma models for which the kink variety can be
analytically identified and for which the linear stability of the emerging
kinks is ensured. Furthermore, a model with only one vacuum point is found,
where all kinks are forced to be non-topological. The non-simply connectedness
of the torus guarantees the global stability of all the non-topological kinks
in these models. |
Harmonic BRST Quantization of Systems with Irreducible Holomorphic Boson
and Fermion Constraints: We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing
bosonic systems with second-class constraints or first-class holomorphic
constraints extends to systems having both bosonic and fermionic second-class
or first-class holomorphic constraints. Using a limit argument, we show that
the harmonic BRST modified path integral reproduces the correct Senjanovic
measure. | The Linear Multiplet and Quantum 4-D String Effective Actions: In 4-D heterotic superstrings, the dilaton and antisymmetric tensor fields
belong to a linear N=1 supersymmetric multiplet L. We study the lagrangian
describing the coupling of one linear multiplet to chiral and gauge multiplets
in global and local supersymmetry, with particular emphasis on string
tree-level and loop-corrected effective actions. This theory is dual to an
equivalent one with chiral multiplets only. But the formulation with a linear
multiplet appears to have decisive advantages beyond string tree-level since,
in particular, <L> is the string loop-counting parameter and the duality
transformation is in general not exactly solvable beyond tree-level. This
formulation allows us to easily deduce some powerful non-renormalization
theorems in the effective theory and to obtain explicitly some loop corrections
to the string effective supergravity for simple compactifications. Finally, we
discuss the issue of supersymmetry breaking by gaugino condensation using this
formalism. |
Additional Symmetries of Supersymmetric KP Hierarchies: We investigate the additional symmetries of several supersymmetric KP
hierarchies: the SKP hierarchy of Manin and Radul, the $\hbox{SKP}_2$
hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the
algebra of symmetries is isomorphic to the algebra of superdifferential
operators, or equivalently $\SW_{1+\infty}$. These results seem to suggest that
despite their realization depending on the dynamics, the additional symmetries
are kinematical in nature. | Holographic dark energy with non-minimal coupling: We study a scalar field non-minimally coupled to the curvature, in the
framework of holographic dark energy. We obtain a relation between the coupling
of the scalar field and the holographic DE parameters. In the model without
potential we found the EOS parameter in different regions of the parameters,
giving rise to accelerated expansion. For some restrictions on the parameters,
the model presents quintom behavior. |
Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4
SYM: A non-trivial consequence of the super-correlator/super-amplitude duality is
that the integrand of the four-point correlation function of stress-tensor
multiplets in planar N=4 super Yang-Mills contains a certain combination of
n-point amplitude integrands for any n. This combination is the sum of products
of all helicity super-amplitudes with their corresponding helicity conjugates.
The four-point correlator itself is described by a single scalar function whose
loop level integrands possess a hidden permutation symmetry facilitating its
computation up to ten loops. We discover that assuming Yangian symmetry and an
appropriate basis of planar dual conformal integrands it is possible to
disentangle the contributions from the individual amplitudes from this
combination. We test this up to seven points and up to two loops. This suggests
that any scattering amplitude for any n, with any helicity structure and at any
loop order may be extractable from the four-point correlator. | On the backreaction issue for the black hole in de Sitter space-time: We consider quantum real massive scalar field in the de Sitter-Schwarzschild
space-time backround. To have an analytic head way we study in detail the
two-dimensional case, assuming that the situation in four dimensions will not
be much different conceptually. It is assumed, that quantum field is in a
thermal state i.e. described by the planckian distribution for the exact modes
in the geometry under consideration. We calculate approximately the expectation
value of stress-energy tensor near the cosmological and black hole horizons. It
is shown that for a generic temperature backreaction from quantum fields on the
geometry cannot be neglected. Thus, de Sitter-Schwarzschild space-time geometry
inevitably is strongly modified by the quantum fluctuations of the matter
fields. |
Dynamical Generation of the Primordial Magnetic Field by Ferromagnetic
Domain Walls: The spontaneous generation of uniform magnetic condensate in $QED_3$ gives
rise to ferromagnetic domain walls at the electroweak phase transition. These
ferromagnetic domain walls are caracterized by vanishing effective surface
energy density avoiding, thus, the domain wall problem. Moreover we find that
the domain walls generate a magnetic field $B \simeq 10^{24} Gauss$ at the
electroweak scale which account for the seed field in the so called dynamo
mechanism for the cosmological primordial magnetic field. We find that the
annihilation processes of walls with size $R \simeq 10^5 Km$ could release an
energy of order $10^{52} erg$ indicating the invisible ferromagnetic walls as
possible compact sources of Gamma Ray Bursts. | Reflected entropy for free scalars: We continue our study of reflected entropy, $R(A,B)$, for Gaussian systems.
In this paper we provide general formulas valid for free scalar fields in
arbitrary dimensions. Similarly to the fermionic case, the resulting
expressions are fully determined in terms of correlators of the fields, making
them amenable to lattice calculations. We apply this to the case of a
$(1+1)$-dimensional chiral scalar, whose reflected entropy we compute for two
intervals as a function of the cross-ratio, comparing it with previous
holographic and free-fermion results. For both types of free theories we find
that reflected entropy satisfies the conjectural monotonicity property $R(A,BC)
\geq R(A,B)$. Then, we move to $(2+1)$ dimensions and evaluate it for square
regions for free scalars, fermions and holography, determining the very-far and
very-close regimes and comparing them with their mutual information
counterparts. In all cases considered, both for $(1+1)$- and
$(2+1)$-dimensional theories, we verify that the general inequality relating
both quantities, $R(A,B)\geq I(A,B)$, is satisfied. Our results suggest that
for general regions characterized by length-scales $L_A\sim L_B\sim L$ and
separated a distance $\ell$, the reflected entropy in the large-separation
regime ($x\equiv L/\ell \ll 1$) behaves as $R(x) \sim - I(x) \log x$ for
general CFTs in arbitrary dimensions. |
Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity: Models of cosmological inflation resembling the Starobinsky R + R^2 model
emerge naturally among the effective potentials derived from no-scale
SU(N,1)/SU(N) x U(1) supergravity when N > 1. We display several examples in
the SU(2,1)/SU(2) x U(1) case, in which the inflaton may be identified with
either a modulus field or a matter field. We discuss how the modulus field may
be stabilized in models in which a matter field plays the role of the inflaton.
We also discuss models that generalize the Starobinsky model but display
different relations between the tilt in the spectrum of scalar density
perturbations, n_s, the tensor-to-scalar ratio, r, and the number of e-folds,
N_*. Finally, we discuss how such models can be probed by present and future
CMB experiments. | Twisted Weil Algebras for the String Lie 2-Algebra: In this article, we give a concise summary of $L_\infty$-algebras viewed in
terms of Chevalley-Eilenberg algebras, Weil algebras and invariant polynomials
and their use in defining connections in higher gauge theory. Using this, we
discuss the example of the string Lie 2-algebra in both the skeletal and the
loop model. In both cases, we show how to arrive at the twisted Weil algebras
which were used in arXiv:1705.02353 to construct a non-Abelian self-dual string
soliton, see also arXiv:1712.06623, arXiv:0801.3480, arXiv:0910.4001. |
Dual gravity and E11: We consider the equation of motion in the gravity sector that arises from the
non-linear realisation of the semi-direct product of E11 and its first
fundamental representation, denoted by l1, in four dimensions. This equation is
first order in derivatives and at low levels relates the usual field of gravity
to a dual gravity field. When the generalised space-time is restricted to be
the usual four dimensional space-time we show that this equation does correctly
describe Einstein's theory at the linearised level. We also comment on previous
discussions of dual gravity. | AdS$_4$ solutions of massive IIA from dyonic ISO(7) supergravity: Explicit formulae are given for the consistent truncation of massive type IIA
supergravity on the six-sphere to the SU(3)--invariant sector of $D=4$ ${\cal
N}=8$ supergravity with dyonic ISO(7) gauging. These formulae are then used to
construct AdS$_4$ solutions of massive type IIA via uplift on $S^6$ of the
critical points of the $D=4$ supergravity with at least SU(3) symmetry. We find
a new ${\cal N}=1$ solution with SU(3) symmetry, a new non-supersymmetric
solution with SO(6) symmetry, and recover previously known solutions. We
quantise the fluxes, calculate the gravitational free energies of the solutions
and discuss the stability of the non-supersymmetric ones. Among these, a
(previously known) G$_2$--invariant solution is found to be stable. |
Low-energy structure of six-dimensional open-string vacua: This dissertation reviews some properties of the low-energy effective actions
for six dimensional open-string models. The first chapter is a pedagogical
introduction about supergravity theories. In the second chapter closed strings
are analyzed, with particular emphasis on type IIB, whose orientifold
projection, in order to build type-I models, is the subject of the third
chapter. Original results are reported in chapters 4 and 5. In chapter 4 we
describe the complete coupling of (1,0) six-dimensional supergravity to tensor,
vector and hypermultiplets. The generalized Green-Schwarz mechanism implies
that the resulting theory embodies factorized gauge and supersymmetry
anomalies, to be disposed of by fermion loops. Consequently, the low-energy
theory is determined by the Wess-Zumino consistency conditions, rather than by
the requirement of supersymmetry, and this procedure does not fix a quartic
coupling for the gauginos. In chapter 5 we describe the low-energy effective
actions for type-I models with brane supersymmetry breaking, resulting form the
simultaneous presence of supersymmetric bulks, with one or more gravitinos, and
non-supersymmetric combinations of BPS branes.The consistency of the resulting
gravitino couplings implies that local supersymmetry is non-linearly realized
on some branes. We analyze in detail the ten-dimensional $USp(32)$ model and
the six-dimensional (1,0) models. | Poisson gauge theory: The Poisson gauge algebra is a semi-classical limit of complete
non-commutative gauge algebra. In the present work we formulate the Poisson
gauge theory which is a dynamical field theoretical model having the Poisson
gauge algebra as a corresponding algebra of gauge symmetries. The proposed
model is designed to investigate the semi-classical features of the full
non-commutative gauge theory with coordinate dependent non-commutativity
$\Theta^{ab}(x)$, especially whose with a non-constant rank. We derive the
expression for the covariant derivative of matter field. The commutator
relation for the covariant derivatives defines the Poisson field strength which
is covariant under the Poisson gauge transformations and reproduces the
standard $U(1)$ field strength in the commutative limit. We derive the
corresponding Bianchi identities. The field equations for the gauge and the
matter fields are obtained from the gauge invariant action. We consider
different examples of linear in coordinates Poisson structures
$\Theta^{ab}(x)$, as well as non-linear ones, and obtain explicit expressions
for all proposed constructions. Our model is unique up to invertible field
redefinitions and coordinate transformations. |
Linking Past and Future Null Infinity in Three Dimensions: We provide a mapping between past null and future null infinity in
three-dimensional flat space, using symmetry considerations. From this we
derive a mapping between the corresponding asymptotic symmetry groups. By
studying the metric at asymptotic regions, we find that the mapping is energy
preserving and yields an infinite number of conservation laws. | Lax pair formulation in the simultaneous presence of boundaries and
defects: Inspired by recent results on the effect of integrable boundary conditions on
the bulk behavior of an integrable system, and in particular on the behavior of
an existing defect we systematically formulate the Lax pairs in the
simultaneous presence of integrable boundaries and defects. The respective
sewing conditions as well as the relevant equations of motion on the defect
point are accordingly extracted. We consider a specific prototype i.e. the
vector non-linear Schr\"{o}dinger (NLS) model to exemplify our construction.
This model displays a highly non-trivial behavior and allows the existence of
two distinct types of boundary conditions based on the reflection algebra or
the twisted Yangian. |
Mathieu moonshine in four dimensional $\mathcal{N}=1$ theories: We show that the recently discovered Mathieu moonshine plays a role for
certain four dimensional theories with $\mathcal{N}=1$ supersymmetry. These
theories are obtained from the $E_8 \times E_8$ heterotic string theory by
compactifying on toroidal orbifolds. We find that a universal contribution to
the holomorphic gauge kinetic function can be expanded in such a way that the
expansion coefficients are the dimensions of representations of the Mathieu
group M$_{24}$. | Non-geodesic motion in $f({\mathcal G})$ gravity with non-minimal
coupling: The dynamics of test particles in $f(\mathcal G)$ modified Gauss-Bonnet
gravity is investigated. It is shown that in $f({\mathcal G})$ gravity models
with non-minimal coupling to matter, particles experience an extra force normal
to their four-velocities and as a result move along non- geodesic world-lines.
The explicit form of the extra force depends on the function of the
Gauss-Bonnet term included in coupling term. The effects of this force on the
relative accelerations of particles are studied. |
Deriving particle physics from quantum gravity: a plan: I give a short review of the holographic approach to quantum gravity, with
emphasis on its application to deriving the properties of elementary particles. | On Higher Derivative Couplings in Theories with Sixteen Supersymmetries: We give simple arguments for new non-renormalization theorems on higher
derivative couplings of gauge theories to supergravity, with sixteen
supersymmetries, by considerations of brane-bulk superamplitudes. This leads to
some exact results on the effective coupling of D3-branes in type IIB string
theory. We also derive exact results on higher dimensional operators in the
torus compactification of the six dimensional (0, 2) superconformal theory. |
Perturbative Confinement: A Procedure is outlined that may be used as a starting point for a
perturbative treatment of theories with permanent confinement. By using a
counter term in the Lagrangian that renormalizes the infrared divergence in the
Coulomb potential, it is achieved that the perturbation expansion at a finite
value of the strong coupling constant may yield reasonably accurate properties
of hadrons, and an expression for the string constant as a function of the QCD
Lambda parameter. | On the trees of quantum fields: The solution of some equations involving functional derivatives is given as a
series indexed by planar binary trees. The terms of the series are given by an
explicit recursive formula. Some algebraic properties of these series are
investigated. Several examples are treated in the case of quantum
electrodynamics: the complete fermion and photon propagators, the two-body
Green function, and the one-body Green function in the presence of an external
source, the complete vacuum polarization, electron self-energy and irreducible
vertex. |
BMS Symmetry of Celestial OPE: In this paper we study the BMS symmetry of the celestial OPE of two positive
helicity gravitons in Einstein theory in four dimensions. The celestial OPE is
obtained by Mellin transforming the scattering amplitude in the (holomorphic)
collinear limit. The collinear limit at leading order gives the singular term
of the celestial OPE. We compute the first subleading correction to the OPE by
analysing the four graviton scattering amplitude directly in Mellin space. The
subleading term can be written as a linear combination of BMS descendants with
the OPE coefficients determined by BMS algebra and the coefficient of the
leading term in the OPE. This can be done by defining a suitable BMS primary
state. We find that among the descendants, which appear at the first subleading
order, there is one which is created by holomorphic supertranslation with
simple pole on the celestial sphere. | Stability of spin-0 graviton and strong coupling in Horava-Lifshitz
theory of gravity: In this paper, we consider two different issues, stability and strong
coupling, raised lately in the newly-proposed Horava-Lifshitz (HL) theory of
quantum gravity with projectability condition. We find that all the scalar
modes are stable in the de Sitter background, due to two different kinds of
effects, one from high-order derivatives of the spacetime curvature, and the
other from the exponential expansion of the de Sitter space. Combining these
effects properly, one can make the instability found in the Minkowski
background never appear even for small-scale modes, provided that the IR limit
is sufficiently closed to the relativistic fixed point. At the fixed point, all
the modes become stabilized. We also show that the instability of Minkowski
spacetime can be cured by introducing mass to the spin-0 graviton. The strong
coupling problem is investigated following the effective field theory approach,
and found that it cannot be cured by the Blas-Pujolas-Sibiryakov mechanism,
initially designed for the case without projectability condition, but might be
circumvented by the Vainshtein mechanism, due to the non-linear effects. In
fact, we construct a class of exact solutions, and show explicitly that it
reduces smoothly to the de Sitter spacetime in the relativistic limit. |
Discrete gauge theories of charge conjugation: We define gauge theories whose gauge group includes charge conjugation as
well as standard $\mathrm{SU}(N)$ transformations. When combined, these
transformations form a novel type of group with a semidirect product structure.
For $N$ even, we show that there are exactly two possible such groups which we
dub $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$. We construct the
transformation rules for the fundamental and adjoint representations, allowing
us to explicitly build four-dimensional $\mathcal{N}=2$ supersymmetric gauge
theories based on $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$ and understand
from first principles their global symmetry. We compute the Haar measure on the
groups, which allows us to quantitatively study the operator content in
protected sectors by means of the superconformal index. In particular, we find
that both types of $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$ groups lead to
non-freely generated Coulomb branches. | Couplings in Asymmetric Orbifolds and Grand Unified String Models: Using the bosonic supercurrent (or covariant lattice) formalism, we review
how to compute scattering amplitudes in asymmetric orbifold string models. This
method is particularly useful for calculating scattering of multiple
asymmetrically twisted string states, where the twisted states are rewritten as
ordinary momentum states. We show how to reconstruct some of the 3-family grand
unified string models in this formalism, and identify the quantum numbers of
the massless states in their spectra. The discrete symmetries of these models
are rather intricate. The superpotentials for the 3-family E_6 model and a
closely related SO(10) model are discussed in some detail. The forms of the
superpotentials of the two 3-family SU(6) models (with asymptotically-free
hidden sectors SU(3) and SU(2) \otimes SU(2)) are also presented. |
Black Hole State Dependence as a Single Parameter: It has previously been proposed that the black hole interior of typical state
large black holes in AdS can be described using state-dependent operators. We
investigate the possibility that the interior can be described by explicit time
dependence, which reduces the state-dependence of the interior operators to a
single parameter. We also propose to use the natural cone, obtained from
Tomita-Takesaki theory, as a candidate construction for the interior operators. | QED Effective Action in Magnetic Field Backgrounds and Electromagnetic
Duality: In the in-out formalism we advance a method of the inverse scattering matrix
for calculating effective actions in pure magnetic field backgrounds. The
one-loop effective actions are found in a localized magnetic field of Sauter
type and approximately in a general magnetic field by applying the uniform
semiclassical approximation. The effective actions exhibit the electromagnetic
duality between a constant electric field and a constant magnetic field and
between $E(x) = E sech^2 (x/L)$ and $B(x) = B sech^2 (x/L)$. |
No hair theorem in quasi-dilaton massive gravity: We investigate the static, spherically symmetric black hole solutions in the
quasi-dilaton model and its generalizations, which are scalar extended dRGT
massive gravity with a shift symmetry. We show that, unlike generic scalar
extended massive gravity models, these theories do not admit static,
spherically symmetric black hole solutions until the theory parameters in the
dRGT potential is fine-tuned. When fine-tuned, the geometry of the static,
spherically symmetric black hole is necessarily that of general relativity and
the quasi-dilaton field is constant across the spacetime. The fine-tuning and
the no hair theorem apply to black holes with flat, anti-de Sitter or de Sitter
asymptotics. | Amalgamated Codazzi Raychaudhuri identity for foliation: It is shown how a pure background tensor formalism provides a concise but
explicit and highly flexible machinery for the generalised curvature analysis
of individual embedded surfaces and foliations such as arise in the theory of
topological defects in cosmological and other physical contexts. The unified
treatment provided here shows how the relevant extension of the Raychaudhuri
identity is related to the correspondingly extended Codazzi identity. |
Coadjoint orbit action of Virasoro group and two-dimensional quantum
gravity dual to SYK/tensor models: The Nambu-Goldstone (NG) bosons of the SYK model are described by a coset
space Diff/$\mathbb{SL}(2,\mathbb{R})$, where Diff, or Virasoro group, is the
group of diffeomorphisms of the time coordinate valued on the real line or a
circle. It is known that the coadjoint orbit action of Diff naturally turns out
to be the two-dimensional quantum gravity action of Polyakov without
cosmological constant, in a certain gauge, in an asymptotically flat spacetime.
Motivated by this observation, we explore Polyakov action with cosmological
constant and boundary terms, and study the possibility of such a
two-dimensional quantum gravity model being the AdS dual to the low energy (NG)
sector of the SYK model. We find strong evidences for this duality: (a) the
bulk action admits an exact family of asymptotically AdS$_2$ spacetimes,
parameterized by Diff/$\mathbb{SL}(2,\mathbb{R})$, in addition to a fixed
conformal factor of a simple functional form; (b) the bulk path integral
reduces to a path integral over Diff/$\mathbb{SL}(2,\mathbb{R})$ with a
Schwarzian action; (c) the low temperature free energy qualitatively agrees
with that of the SYK model. We show, up to quadratic order, how to couple an
infinite series of bulk scalars to the Polyakov model and show that it
reproduces the coupling of the higher modes of the SYK model with the NG
bosons. | Fourth order spatial derivative gravity: In this work we study a modified theory of gravity that contains up to fourth
order spatial derivatives as a model for the Horava-Lifshitz gravity. The
propagator is evaluated and, as a result, it is obtained one extra pole
corresponding to a spin two nonrelativistic massless particle, an extra term
which jeopardizes renormalizability, besides the unexpected general relativity
unmodified propagator. Then, unitarity is proved at the tree-level, where the
general relativity pole has shown to have no dynamics, remaining only the two
degrees of freedom of the new pole. Next, the nonrelativistic effective
potential is determined from a scattering process of two identical massive
gravitationally interacting bosons. In this limit, Newton's potential is
obtained, together with a Darwin-like term that comes from the extra non-pole
term in the propagator. Regarding renormalizability, this extra term may be
harmful, by power counting, but it can be eliminated by adjusting the free
parameters of the model. This adjustment is in accord with the detailed balance
condition suggested in the literature and shows that the way in which extra
spatial derivative terms are added is of fundamental importance. |
Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points: We investigate spectral functions of matter-gauge theories that are
asymptotically free in the ultraviolet and display a Banks-Zaks conformal fixed
point in the infrared. Using perturbation theory, Callan-Symanzik resummations,
and UV-IR connecting renormalisation group trajectories, we analytically
determine the gluon, quark, and ghost propagators in the entire complex
momentum plane. At weak coupling, we find that a K\"all\'en-Lehmann spectral
representation of propagators is achieved for all fields, and determine
suitable ranges for gauge-fixing parameters. At strong coupling, a
proliferation of complex conjugated branch cuts renders a causal representation
impossible. We also derive relations for scaling exponents that determine the
presence or absence of propagator non-analyticities. Further results include
spectral functions for all fields up to five loop order, bounds on the
conformal window, and an algorithm to find running gauge coupling analytically
at higher loops. Implications of our findings and extensions to other theories
are discussed. | Brane Resolution and Gravitational Chern-Simons terms: We show that gravitational Chern-Simons corrections, associated with the
sigma-model anomaly on the M5-brane world-volume, can resolve the singularity
of the M2-brane solution with Ricci-flat, special holonomy transverse space. We
explicitly find smooth solutions in the cases when the transverse space is a
manifold of Spin(7) holonomy and SU(4) holonomy. We comment on the consequences
of these results for the holographically related three-dimensional theories
living on the world volume of a stack of such resolved M2-branes. |
Effects of heavy modes on vacuum stability in supersymmetric theories: We study the effects induced by heavy fields on the masses of light fields in
supersymmetric theories, under the assumption that the heavy mass scale is much
higher than the supersymmetry breaking scale. We show that the square-masses of
light scalar fields can get two different types of significant corrections when
a heavy multiplet is integrated out. The first is an indirect level-repulsion
effect, which may arise from heavy chiral multiplets and is always negative.
The second is a direct coupling contribution, which may arise from heavy vector
multiplets and can have any sign. We then apply these results to the sGoldstino
mass and study the implications for the vacuum metastability condition. We find
that the correction from heavy chiral multiplets is always negative and tends
to compromise vacuum metastability, whereas the contribution from heavy vector
multiplets is always positive and tends on the contrary to reinforce it. These
two effects are controlled respectively by Yukawa couplings and gauge charges,
which mix one heavy and two light fields respectively in the superpotential and
the Kahler potential. Finally we also comment on similar effects induced in
soft scalar masses when the heavy multiplets couple both to the visible and the
hidden sector. | On AdS$_7$ stability: AdS$_7$ supersymmetric solutions in type IIA have been classified, and they
are infinitely many. Moreover, every such solution has a non-supersymmetric
sister. In this paper, we study the perturbative and non-perturbative stability
of these non-supersymmetric solutions, focusing on cases without orientifolds.
Perturbatively, we first look at the KK spectrum of spin-2 excitations. This
does not exhibit instabilities, but it does show that there is no separation of
scales for either the BPS and the non-BPS case, thus proving for supersymmetric
AdS$_7$ a well-known recent conjecture. We then use 7d gauged supergravity and
a brane polarization computation to access part of the spectrum of KK scalars.
The result signals an instability for all non-supersymmetric solutions except
those that have a single D8 on each side. We finally look at non-perturbative
instabilities, and find that NS5 bubbles make these remaining solutions decay. |
Heterotic Stringy Corrections to Metrics of Toroidal Orbifolds and Their
Resolutions: We explicitly analyse $O(\alpha')$ corrections to heterotic supergravity on
toroidal orbifolds and their resolutions, which play important roles in string
phenomenology as well as moduli stabilisation. Using a conformal factor ansatz
that is valid only for four dimensional geometries, we obtain a closed
expression for the $O(\alpha')$ metric corrections in the case of several
orbifold limits of K3, namely $T^4/\mathbb{Z}_n$ where $n=2,3,4,6$. However, we
find that non-standard embedding requires the inclusion of five-branes on such
orbifolds. We also numerically investigate the behaviour around orbifold fixed
points by considering the metric correction on the resolution of a
$\mathbb{C}^2/\mathbb{Z}_2$ singularity. In this case, a non-trivial conformal
factor can be obtained in non-standard embedding even without five-branes. In
the same manner, we generalise our analysis to study metric corrections on
$T^6/\mathbb{Z}_3$ and its resolution described by a complex line bundle over
$\mathbb{CP}^2$. Further prospects of utilising these $O(\alpha')$ corrected
metrics as a novel approach in obtaining realistic or semi-realistic Yukawa
couplings are discussed. | Large Field Distances from EFT strings: In any consistent effective field theory of quantum gravity limits of
infinite field distance are expected to lead to the EFT breakdown due to the
appearance of an infinite tower of light states, as predicted by the Distance
Conjecture. We review the Distant Axionic String Conjecture, which proposes
that any 4d EFT infinite-field-distance limit can be realized as an RG flow of
a fundamental axionic string. The RG flow can be understood in terms of the 4d
backreaction of such a string, and implies that it becomes tensionless towards
the said limit. This property is understood as a shielding mechanism towards
realizing an exact axionic symmetry, and it implies the breakdown of the EFT in
a way that reproduces the Distance Conjecture. Motivated by string theory data
we further propose the Integral Scaling Conjecture, which provides a specific
relation between the string tension and the EFT maximal cut-off set by the
infinite tower of states. |
Exploring a Tractable Lagrangian for Arbitrary Spin: A simple Lagrangian is proposed that by the choice of the representation of
SU(2), gives rise to field equations for arbitrary spin. In explicit examples
it is shown, how the Klein-Gordon, the Dirac, and the Proca equation can be
obtained from this Lagrangian. On the same footing, field equations for
arbitrary spin are given. Finally, symmetries are discussed, the fields are
quantized, their statistics is deduced, and Feynman rules are derived. | Infrared Modification of Gravity: In this lecture I address the issue of possible large distance modification
of gravity and its observational consequences. Although, for the illustrative
purposes we focus on a particular simple generally-covariant example, our
conclusions are rather general and apply to large class of theories in which,
already at the Newtonian level, gravity changes the regime at a certain very
large crossover distance $r_c$. In such theories the cosmological evolution
gets dramatically modified at the crossover scale, usually exhibiting a
"self-accelerated" expansion, which can be differentiated from more
conventional "dark energy" scenarios by precision cosmology. However, unlike
the latter scenarios, theories of modified-gravity are extremely constrained
(and potentially testable) by the precision gravitational measurements at much
shorter scales. Despite the presence of extra polarizations of graviton, the
theory is compatible with observations, since the naive perturbative expansion
in Newton's constant breaks down at a certain intermediate scale. This happens
because the extra polarizations have couplings singular in $1/r_c$. However,
the correctly resummed non-linear solutions are regular and exhibit continuous
Einsteinian limit. Contrary to the naive expectation, explicit examples
indicate that the resummed solutions remain valid after the ultraviolet
completion of the theory, with the loop corrections taken into account. |
S-duality as a beta-deformed Fourier transform: An attempt is made to formulate Gaiotto's S-duality relations in an explicit
quantitative form. Formally the problem is that of evaluation of the Racah
coefficients for the Virasoro algebra, and we approach it with the help of the
matrix model representation of the AGT-related conformal blocks and Nekrasov
functions. In the Seiberg-Witten limit, this S-duality reduces to the Legendre
transformation. In the simplest case, its lifting to the level of Nekrasov
functions is just the Fourier transform, while corrections are related to the
beta-deformation. We calculate them with the help of the matrix model approach
and observe that they vanish for beta=1. Explicit evaluation of the same
corrections from the U_q(sl(2)) infinite-dimensional representation formulas
due to B.Ponsot and J.Teshner remains an open problem. | On the Evolution of Jet Energy and Opening Angle in Strongly Coupled
Plasma: We calculate how the energy and the opening angle of jets in ${\cal N}=4$ SYM
theory evolve as they propagate through the strongly coupled plasma of that
theory. We define the rate of energy loss $dE_{\rm jet}/dx$ and the jet opening
angle in a straightforward fashion directly in the gauge theory before
calculating both holographically, in the dual gravitational description. In
this way, we rederive the previously known result for $dE_{\rm jet}/dx$ without
the need to introduce a finite slab of plasma. We obtain a striking
relationship between the initial opening angle of the jet, which is to say the
opening angle that it would have had if it had found itself in vacuum instead
of in plasma, and the thermalization distance of the jet. Via this
relationship, we show that ${\cal N}=4$ SYM jets with any initial energy that
have the same initial opening angle and the same trajectory through the plasma
experience the same fractional energy loss. We also provide an expansion that
describes how the opening angle of the ${\cal N}=4$ SYM jets increases slowly
as they lose energy, over the fraction of their lifetime when their fractional
energy loss is not yet large. We close by looking ahead toward potential
qualitative lessons from our results for QCD jets produced in heavy collisions
and propagating through quark-gluon plasma. |
Orientifolds, Brane Coordinates and Special Geometry: We report on the gauged supergravity analysis of Type IIB vacua on K3x T2/Z2
orientifold in the presence of D3-D7-branes and fluxes. We discuss
supersymmetric critical points correspond to Minkowski vacua and the related
fixing of moduli, finding agreement with previous analysis. An important role
is played by the choice of the symplectic holomorphic sections of special
geometry which enter the computation of the scalar potential. The related
period matrix N is explicitly given. The relation between the special geometry
and the Born--Infeld action for the brane moduli is elucidated. | Scale invariance and constants of motion: Scale invariance in the theory of classical mechanics can be induced from the
scale invariance of background fields. In this paper we consider the relation
between the scale invariance and the constants of particle motion in a
self-similar spacetime, only in which the symmetry is well-defined and is
generated by a homothetic vector. Relaxing the usual conservation condition by
the Hamiltonian constraint in a particle system, we obtain a conservation law
holding only on the constraint surface in the phase space. By the conservation
law, we characterize constants of motion associated with the scale invariance
not only for massless particles but for massive particles and classify the
condition for the existence of the constants of motion. Furthermore, we find
the explicit form of the constants of motion by solving the conservation
equations. |
Gravitational Properties of the Proca Field: We study various properties of a Proca field coupled to gravity through
minimal and quadrupole interactions, described by a two-parameter family of
Lagrangians. St\"uckelberg decomposition of the effective theory spells out its
model-dependent ultraviolet cutoff, parametrically larger than the Proca mass.
We present pp-wave solutions that the model admits, consider linear
fluctuations on such backgrounds, and thereby constrain the parameter space of
the theory by requiring null-energy condition and the absence of negative time
delays in high-energy scattering. We briefly discuss the positivity
constraints$-$derived from unitarity and analyticity of scattering
amplitudes$-$that become ineffective in this regard. | Diagrammar and metamorphosis of coset symmetries in dimensionally
reduced type IIB supergravity: Studying the reduction of type IIB supergravity from ten to three space-time
dimensions we describe the metamorphosis of Dynkin diagram for gravity line
"caterpillar" into a type IIB supergravity "dragonfly" that is triggered by
inclusion of scalars and antisymmetric tensor fields. The final diagram
corresponds to type IIB string theory E8 global symmetry group which is the
subgroup of the conjectured E11 hidden symmetry group. Application of the
results for getting the type IIA/IIB T-duality rules and for searching for type
IIB vacua solutions is considered. |
Generalized Scaling Function at Strong Coupling: We considered folded spinning string in AdS_5 x S^5 background dual to the
Tr(D^S Phi^J) operators of N=4 SYM theory. In the limit S,J-> \infty and l=pi
J/\sqrt\lambda\log S fixed we compute the string energy with the 2-loop
accuracy in the worldsheet coupling \sqrt\lambda from the asymptotical Bethe
ansatz. In the limit l-> 0 the result is finite due to the massive cancelations
with terms coming from the conjectured dressing phase. We also managed to
compute all leading logarithm terms l^{2m}\log^n l/\lambda^n/2 to an arbitrary
order in perturbation theory. In particular for m=1 we reproduced results of
Alday and Maldacena computed from a sigma model. The method developed in this
paper could be used for a systematic expansion in 1/\sqrt\lambda and also at
weak coupling. | Noncommutative nonsingular black holes: Adopting noncommutative spacetime coordinates, we determined a new solution
of Einstein equations for a static, spherically symmetric matter source. The
limitations of the conventional Schwarzschild solution, due to curvature
singularities, are overcome. As a result, the line element is endowed of a
regular DeSitter core at the origin and of two horizons even in the considered
case of electrically neutral, nonrotating matter. Regarding the Hawking
evaporation process, the intriguing new feature is that the black hole is
allowed to reach only a finite maximum temperature, before cooling down to an
absolute zero extremal state. As a consequence the quantum back reaction is
negligible. |
Duality Cascade in Brane Inflation: We show that brane inflation is very sensitive to tiny sharp features in
extra dimensions, including those in the potential and in the warp factor. This
can show up as observational signatures in the power spectrum and/or
non-Gaussianities of the cosmic microwave background radiation (CMBR). One
general example of such sharp features is a succession of small steps in a
warped throat, caused by Seiberg duality cascade using gauge/gravity duality.
We study the cosmological observational consequences of these steps in brane
inflation. Since the steps come in a series, the prediction of other steps and
their properties can be tested by future data and analysis. It is also possible
that the steps are too close to be resolved in the power spectrum, in which
case they may show up only in the non-Gaussianity of the CMB temperature
fluctuations and/or EE polarization. We study two cases. In the slow-roll
scenario where steps appear in the inflaton potential, the sensitivity of brane
inflation to the height and width of the steps is increased by several orders
of magnitude comparing to that in previously studied large field models. In the
IR DBI scenario where steps appear in the warp factor, we find that the
glitches in the power spectrum caused by these sharp features are generally
small or even unobservable, but associated distinctive non-Gaussianity can be
large. Together with its large negative running of the power spectrum index,
this scenario clearly illustrates how rich and different a brane inflationary
scenario can be when compared to generic slow-roll inflation. Such distinctive
stringy features may provide a powerful probe of superstring theory. | Graviton mediated polarisation-polarisation entanglement of photons by
means of the Schwinger Keldysh and Kadanoff Baym formalisms and Quantum
Boltzmann equations: In order to show that the graviton is a quantum entity an experiment is
proposed that can show that quantum entanglement is produced by means of an
exchange of gravitons. For this to be possible, one has to be able to witness
the entanglement between the two objects considered in the experiment and to be
able to eliminate other sources of entanglement like the exchange of virtual
photons. Graviton mediated polarisation-polarisation photon entanglement is
being analysed by methods originating from the Schwinger Keldysh and the
Kadanoff Baym formalisms in conjunction with quantum Boltzmann type equations.
Applications in the context of cosmology are discussed. |
Backreaction in spinor QED and decoherence functional: Using the Schwinger-Keldysh (closed time path or CTP) and Feynman-Vernon
influence functional formalisms we obtain an expression for the influence
functional in terms of Bogoliubov coefficients for the case of spinor quantum
electrodynamics. Then we derive a CTP effective action in semiclassical
approximation and its cumulant expansion. Using it we obtain a equation for the
description of the charged particle creation in electric field and of
backreaction of charged quantum fields and their fluctuations on time evolution
of this electric field. Also an intimate connection between CTP effective
action and decoherence functional will allow us to analyze how macroscopic
electromagnetic fields are ``measured'' through interaction with charges and
thereby rendered classical. | The Secret Chern-Simons Action for the Hot Gluon Plasma: We show that the generating functional for hard thermal loops with external
gluons in QCD is essentially given by the eikonal for a Chern-Simons gauge
theory. This action, determined essentially by gauge invariance arguments, also
gives an efficient way of obtaining the hard thermal loop contributions without
the more involved calculation of Feynman diagrams. |
Non-Perturbative Gravity and the Spin of the Lattice Graviton: The lattice formulation of quantum gravity provides a natural framework in
which non-perturbative properties of the ground state can be studied in detail.
In this paper we investigate how the lattice results relate to the continuum
semiclassical expansion about smooth manifolds. As an example we give an
explicit form for the lattice ground state wave functional for semiclassical
geometries. We then do a detailed comparison between the more recent
predictions from the lattice regularized theory, and results obtained in the
continuum for the non-trivial ultraviolet fixed point of quantum gravity found
using weak field and non-perturbative methods. In particular we focus on the
derivative of the beta function at the fixed point and the related universal
critical exponent $\nu$ for gravitation. Based on recently available lattice
and continuum results we assess the evidence for the presence of a massless
spin two particle in the continuum limit of the strongly coupled lattice
theory. Finally we compare the lattice prediction for the vacuum-polarization
induced weak scale dependence of the gravitational coupling with recent
calculations in the continuum, finding similar effects. | Marginal deformations of heterotic interpolating models and exponential
suppression of the cosmological constant: Following our previous work of 1905.10745 [hep-th], 2003.11217 [hep-th], we
study heterotic interpolating models $D$ dimensionally compactified with
constant background fields that include the full set of Wilson lines and radii.
Focusing on the phenomenoloically viable supersymmetry restoring parameter
region, we analyze the pattern of gauge symmetry enhancement and the
representation of massless fermions. We obtain the set of cases with the
exponentially small cosmological constant. Our analysis does not depend on
non-supersymmetric endpoint models of interpolations. A part of the moduli
space of interpolating models is in one-to-one correspondence with the
counterpart of toroidal compactification of heterotic superstrings. |
Generalized G-inflation: Inflation with the most general second-order
field equations: We study generalized Galileons as a framework to develop the most general
single-field inflation models ever, Generalized G-inflation, containing yet
further generalization of G-inflation, as well as previous examples such as
k-inflation, extended inflation, and new Higgs inflation as special cases. We
investigate the background and perturbation evolution in this model,
calculating the most general quadratic actions for tensor and scalar
cosmological perturbations to give the stability criteria and the power spectra
of primordial fluctuations. It is pointed out in the Appendix that the
Horndeski theory and the generalized Galileons are equivalent. In particular,
even the non-minimal coupling to the Gauss-Bonnet term is included in the
generalized Galileons in a non-trivial manner. | Quantum-mechanical tunnelling and the renormalization group: We explore the applicability of the exact renormalization group to the study
of tunnelling phenomena. We investigate quantum-mechanical systems whose energy
eigenstates are affected significantly by tunnelling through a barrier in the
potential. Within the approximation of the derivative expansion, we find that
the exact renormalization group predicts the correct qualitative behaviour for
the lowest energy eigenvalues. However, quantitative accuracy is achieved only
for potentials with small barriers. For large barriers, the use of alternative
methods, such as saddle-point expansions, can provide quantitative accuracy. |
Gauge-Invariant Energy Functional in Relativistic Schroedinger Theory: The non-invariant energy functional of the preceding paper is improved in
order to obtain its gauge-invariant form by strictly taking into account the
non-Abelian character of Relativistic Schroedinger Theory (RST). As an
application of the results, the dichotomy of positronium with respect to
singlet and triplet states is discussed (ortho- and para-positronium). The
degeneracy of the ortho- and para-states occurs in RST if (i) the magnetic
interactions are neglected (as in the conventional theory) and (ii) the
anisotropy of the electric interaction potential is disregarded. In view of
such a very crude approximation procedure, the non-relativistic positronium
spectrum in RST agrees amazingly well with the conventional predictions. | Generalizations of Lunin-Maldacena transformation on the $AdS sub 5 x S
sup 5$ background: In this paper we consider a simple generalization of the method of Lunin and
Maldacena for generating new string backgrounds based on TsT-transformations.
We study multi-shift $Ts... sT$ transformations applied to backgrounds with at
least two U(1) isometries. We prove that the string currents in any two
backgrounds related by Ts...sT-transformations are equal. Applying this
procedure to the $AdS_{5}\times S^{5}$, we find a new background and study some
properties of the semiclassical strings. |
Note on refined topological vertex, Jack polynomials and instanton
counting: In this article, we calculated the refined topological vertex for the one
parameter case using the Jack symmetric functions. Also, we obtain the
partition function for elliptic N=2 models, the results coincide with those of
Nekrasov instanton counting partition functions for the $N=2^{\ast}$ theories. | Holographic scalar and vector exchange in OTOCs and pole-skipping
phenomena: We study scalar and vector exchange terms in out-of-time-order correlators
(OTOCs) holographically. By applying a computational method in graviton
exchange, we analyze exponential behaviors in scalar and vector exchange terms
at late times. We show that their exponential behaviors in simple holographic
models are related to pole-skipping points obtained from the near-horizon
equations of motion of scalar and vector fields. Our results are
generalizations of the relation between the graviton exchange effect in OTOCs
and the pole-skipping phenomena of the dual operator, to scalar and vector
fields. |
Quantized equations of motion in non-commutative theories: Quantum field theories based on interactions which contain the Moyal star
product suffer, in the general case when time does not commute with space, from
several diseases: quantum equation of motions contain unusual terms, conserved
currents can not be defined and the residual spacetime symmetry is not
maintained. All these problems have the same origin: time ordering does not
commute with taking the star product. Here we show that these difficulties can
be circumvented by a new definition of time ordering: namely with respect to a
light-cone variable. In particular the original spacetime symmetries SO(1,1) x
SO(2) and translation invariance turn out to be respected. Unitarity is
guaranteed as well. | Off-shell N=(4,4) supersymmetry for new (2,2) vector multiplets: We discuss the conditions for extra supersymmetry of the N=(2,2)
supersymmetric vector multiplets described in arXiv:0705.3201 [hep-th] and in
arXiv:0808.1535 [hep-th]. We find (4,4) supersymmetry for the semichiral vector
multiplet but not for the Large Vector Multiplet. |
Current Algebra on the Conformal Boundary and the Variables of Quantum
Gravity: I argue that scattering theory for massless particles in Minkowski space
should be reformulated as a mapping between past and future representations of
an algebra of densities on the conformal boundary. These densities are best
thought of as living on the momentum space light cone dual to null infinity,
which describes the simultaneous eigenstates of the BMS generators. The
currents describe the flow of other quantum numbers through the holographic
screen at infinity. They are operator valued measures on the momentum light
cone, with non-zero support at $P = 0$, which is necessary to describe finite
flows of total momentum, with zero energy-momentum density, on the asymptotic
holographic screen. Jet states, the closest approximation to the conventional
notion of asymptotic particle state, have finite momentum flowing out through
spherical caps of finite opening angle, with the zero momentum currents
vanishing in annuli surrounding these caps. Although these notions are valid
both in field theory and quantum gravity, I'll argue that they form the basis
for understanding the holographic/covariant entropy principle in the latter
framework, where the densities form a complete set of operators. The variables
on a finite area holographic screen are restrictions of those at infinity. The
restriction is implemented by a cutoff on the Euclidean Dirac spectrum on the
screen, which is a generalized UV/IR correspondence. | Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy
and Full Counting Statistics: We consider the symmetry-resolved R\'{e}nyi and entanglement entropies for
two-dimensional conformal field theories on a circle at nonzero temperature. We
assume a unique ground state with a nonzero mass gap induced by the system's
finite size and then calculate the leading corrections to the contributions of
individual charge sectors in a low-temperature expansion. Besides the size of
the mass gap and the degeneracy of the first excited state, these universal
corrections depend only on the four-point correlation function of the primary
fields. We also obtain thermal corrections to the full counting statistics of
the ground state and define the \textit{probability fluctuations} function. It
scales as $e^{-2 \pi \Delta_{\psi} \beta /L}$, where $\Delta_{\psi}$ is the
scaling dimension of the lowest weight states. As an example, we explicitly
evaluate the thermal corrections to the symmetry-resolved entanglement entropy
and FCS for the spinless fermions. |
A connection between $\mathcal{R}$-invariants and Yang-Baxter
$R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory: The BCFW recursion relation in $\mathcal{N}=4$ super-Yang-Mills theory is
solved using Yang-Baxter $R$-operators in the NMHV sector. Explicit expressions
for $\mathcal{R}$-invariants are obtained in terms of the chains of
$R$-operators acting on an appropriate basic state. | Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes: We consider solutions of massive IIA supergravity corresponding to the
half-BPS intersection of D8/D4-branes with fundamental strings. The
$1+1$-dimensional intersection preserves the symmetry $D(2,1;\gamma;1) \times
SO(4)$. We give a reduction and partial integration of the BPS equations for
this symmetry group. We then specialize to the cases of enhanced supersymmetry
corresponding to $\gamma = -1/2,-2$ or $\gamma = 1$. In the first case, we show
that the only solution with enhanced symmetry is given by the $AdS_6$ geometry
describing the near horizon geometry of D8/D4-branes in the presence of an
O8-plane. In the second case, we identify novel solutions corresponding to
fundamental strings ending on D8-branes and a second set of novel solutions
corresponding to fundamental strings ending on an O8-plane. In both cases, the
fundamental string geometry contains an asymptotically flat region where the
string coupling goes to zero. We also show that there are no solutions
corresponding to $1+0$-dimensional CFTs, which one may have hoped to construct
by suspending fundamental strings between D8-branes. |
Line operators on S^1xR^3 and quantization of the Hitchin moduli space: We perform an exact localization calculation for the expectation values of
Wilson-'t Hooft line operators in N=2 gauge theories on S^1xR^3. The
expectation values are naturally expressed in terms of the complexified
Fenchel-Nielsen coordinates, and form a quantum mechanically deformed algebra
of functions on the associated Hitchin moduli space by Moyal multiplication. We
propose that these expectation values are the Weyl transform of the Verlinde
operators, which act on Liouville/Toda conformal blocks as difference
operators. We demonstrate our proposal explicitly in SU(N) examples. | Singular perturbation theory for the thermodynamic properties of
holographic QCD: We explore the thermodynamics of a black-hole solution in improved
holographic QCD with a simple dilaton potential having two parameters. By
applying techniques of singular perturbation theory, we get uniform
approximations for the metric and the dilaton field in the two regimes of big
and small black-holes. These techniques lead to a resummation of the naive
expansion at high temperatures, providing an important theoretical improvement
with respect to previous results in the literature. By using this technique, it
is shown how a quadratic dependence at low enough temperatures can naturally
appear in the free energy. A comparison with lattice data of gluodynamics is
performed. It is provided as well an estimate of the value of the gluon
condensate at zero temperature which turns out to be in quite good agreement
with the accepted values in the literature from phenomenological studies of
QCD. |
Linearly resummed hydrodynamics in a weakly curved spacetime: We extend our study of all-order linearly resummed hydrodynamics in a flat
space~\cite{1406.7222,1409.3095} to fluids in weakly curved spaces. The
underlying microscopic theory is a finite temperature $\mathcal{N}=4$
super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates
black brane solutions of the Einstein gravity in asymptotically \emph{locally}
$\textrm{AdS}_5$ geometry to relativistic conformal fluids in a weakly curved
4D background. To linear order in the amplitude of hydrodynamic variables and
metric perturbations, the fluid's energy-momentum tensor is computed with
derivatives of both the fluid velocity and background metric resummed to all
orders. We extensively discuss the meaning of all order hydrodynamics by
expressing it in terms of the memory function formalism, which is also suitable
for practical simulations. In addition to two viscosity functions discussed at
length in refs.~\cite{1406.7222,1409.3095}, we find four curvature induced
structures coupled to the fluid via new transport coefficient functions. In
ref.~\cite{0905.4069}, the latter were referred to as gravitational
susceptibilities of the fluid. We analytically compute these coefficients in
the hydrodynamic limit, and then numerically up to large values of momenta. | Novel color superconducting phases of $\cal{N}$ = 4 super Yang-Mills at
strong coupling: We revisit the large-$N_c$ phase diagram of $\cal{N}$ = 4 super Yang-Mills
theory at finite $R$-charge density and strong coupling, by means of the
AdS/CFT correspondence. We conjecture new phases that result from a black hole
shedding some of its charge through the nucleation of probe color D3-branes
that remain at a finite distance from the black hole when the dual field theory
lives on a sphere. In the corresponding ground states the color group is
partially Higgsed, so these phases can be identified as having a type of color
superconductivity. The new phases would appear at intermediate values of the
$R$-charge chemical potential and we expect them to be metastable but
long-lived in the large-$N_c$ limit. |
$f(R, R_{μν}^2)$ at one loop: We compute the one-loop divergences in a theory of gravity with Lagrangian of
the general form $f(R,R_{\mu\nu}R^{\mu\nu})$, on an Einstein background. We
also establish that the one-loop effective action is invariant under a duality
that consists of changing certain parameters in the relation between the metric
and the quantum fluctuation field. Finally, we discuss the unimodular version
of such a theory and establish its equivalence at one-loop order with the
general case. | From Boundary Data to Bound States II: Scattering Angle to Dynamical
Invariants (with Twist): We recently introduced in [1910.03008] a "boundary-to-bound" dictionary
between gravitational scattering data and observables for bound states of
non-spinning bodies. In this paper, we elaborate further on this (holographic)
map. We start by deriving the following -- remarkably simple -- formula
relating the periastron advance to the scattering angle: $\Delta \Phi(J,{\cal
E}) =\chi(J,{\cal E}) + \chi (-J,{\cal E})$, via analytic continuation in
angular momentum and binding energy. Using explicit expressions from
[1910.03008], we confirm its validity to all orders in the Post-Minkowskian
(PM) expansion. Furthermore, we reconstruct the radial action for the bound
state directly from the knowledge of the scattering angle. The radial action
enables us to write compact expressions for dynamical invariants in terms of
the deflection angle to all PM orders, which can also be written as a function
of the PM-expanded amplitude. As an example, we reproduce our result in
[1910.03008] for the periastron advance, and compute the radial and azimuthal
frequencies and redshift variable to two-loops. Agreement is found in the
overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we
initiate the study of our dictionary including spin. We demonstrate that the
same relation between deflection angle and periastron advance applies for
aligned-spin contributions, with $J$ the (canonical) total angular momentum.
Explicit checks are performed to display perfect agreement using
state-of-the-art PN results in the literature. Using the map between test- and
two-body dynamics, we also compute the periastron advance up to quadratic order
in the spin, to one-loop and to all orders in velocity. We conclude with a
discussion on the generalized "impetus formula" for spinning bodies and black
holes as "elementary particles". |
Beyond Amplitudes' Positivity and the Fate of Massive Gravity: We constrain effective field theories by going beyond the familiar positivity
bounds that follow from unitarity, analyticity, and crossing symmetry of the
scattering amplitudes. As interesting examples, we discuss the implications of
the bounds for the Galileon and ghost-free massive gravity. The combination of
our theoretical bounds with the experimental constraints on the graviton mass
implies that the latter is either ruled out or unable to describe gravitational
phenomena, let alone to consistently implement the Vainshtein mechanism, down
to the relevant scales of fifth-force experiments, where general relativity has
been successfully tested. We also show that the Galileon theory must contain
symmetry-breaking terms that are at most one-loop suppressed compared to the
symmetry-preserving ones. We comment as well on other interesting applications
of our bounds. | Hawking temperature in the eternal BTZ black hole: an example of
Holography in AdS spacetime: We review the relation between AdS spacetime in 1+2 dimensions and the BTZ
black hole. Later we show that a ground state in AdS spacetime becomes a
thermal state in the BTZ black hole. We show that this is true in the bulk and
in the boundary of AdS spacetime. The existence of this thermal state is
tantamount to say that the Unruh effect exists in AdS spacetime and becomes the
Hawking effect for an eternal BTZ black hole. In order to make this we use the
correspondence introduced in Algebraic Holography between algebras of
quasi-local observables associated to wedges and doble cones regions in the
bulk of AdS spacetime and its conformal boundary respectively. Also we give the
real scalar quantum field as a concrete heuristic realization of this
formalism. |
Einstein equations for an asymmetric brane-world: We consider a brane-world of co-dimension one without the reflection symmetry
that is commonly imposed between the two sides of the brane. Using the
coordinate-free formalism of the Gauss-Codacci equations, we derive the
effective Einstein equations by relating the local curvature to the matter on
the brane in the case when its bare tension is much larger than the localized
matter, and hence show that Einstein gravity is a natural consequence of such
models in the weak field limit. We find agreement with the recently derived
cosmological case, which can be solved exactly, and point out that such models
can be realized naturally in the case where there is a minimally coupled form
field in the bulk. | Open-closed superstring amplitudes using vertex operators in
$\mathrm{AdS}_5 \times \mathrm{S}^5$: Using the pure spinor formalism, a particular superstring scattering
amplitude involving one closed string and $N$ open string vertex operators in
$\mathrm{AdS}{}_5 \times \mathrm{S}^5$ is studied. It is shown that the
tree-level amplitude containing one supergravity state and $N$ super-Yang-Mills
states located on D3-branes near the AdS${}_5$ boundary can be expressed as a
$d=4$ ${\cal N}=4$ harmonic superspace integral in terms of the supergravity
and super-Yang-Mills superfields. |
Quantum correlation in quark-gluon medium: We study thermodynamics and quantum correlations of the string cloud geometry
whose field theory dual is the quark-gluon medium. We found the novel
universality of the entanglement entropy first law in the high quark density
limit. We also showed that a correlation function generally decreases as the
entanglement entropy of the background medium increases due to the screening
effect of the background. We study the UV and IR effects of the medium on phase
transition behaviour observed in the holographic mutual information using both
perturbative and numerical computations. Moreover, by numerical computation, we
show that in the IR region the critical length obtained from the mutual
information behaves similar to the correlation length of the two-point
function. | A correspondence between standard model fermions and degrees of freedom
of polycrystalline materials: We identify natural degrees of freedom of polycrystalline materials -- affine
transformations of grains -- with those of a three-dimensional lattice theory
for $(T\otimes\Omega)(\mathbb{R}^3)$. We define a lattice Dirac operator on
this space and identify its continuous limit with the free field limit of the
whole fermionic sector of the standard model. Fermion doubling is used here as
a tool to obtain the necessary number of steps of freedom. The correspondence
extends to important structural properties (families, colors, flavor pairs,
electromagnetic charge). We find a lattice version of chiral symmetry similar
to the Ginsparg-Wilson approach.
This correspondence suggests to propose a ``polycrystalline ether''. Combined
with GLET, a general Lorentz ether theory of gravity with GR limit, this
becomes a concept for a theory of everything. The extension to gauge fields is
the major open problem and requires new concepts. |
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