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Universal behaviour of interfaces in 2d and dimensional reduction of
Nambu-Goto strings: We propose a simple effective model for the description of interfaces in 2d
statistical models, based on the first-order treatment of an action
corresponding to the length of the interface. The universal prediction of this
model for the interface free energy agrees with the result of an exact
calculation in the case of the 2d Ising model. This model appears as a
dimensional reduction of the Nambu-Goto stringy description of interfaces in
3d, i.e., of the capillary wave model. | Emergent SUSY Theories: QED, SM & GUT: It might be expected that only global symmetries are fundamental symmetries
of Nature, whereas local symmetries and associated massless gauge fields could
solely emerge due to spontaneous breaking of underlying spacetime symmetries
involved, such as relativistic invariance and supersymmetry. This breaking,
taken in the form of the nonlinear sigma-model type pattern for vector fields
or superfields, puts essential restrictions on geometrical degrees of freedom
of a physical field system that makes it to adjust itself in such a way that
its global internal symmetry G turns into the local symmetry G_{loc}.
Remarkably, this emergence process may naturally be triggered by spontaneously
broken supersymmetry, as is illustrated in detail by an example of a general
supersymmetric QED model which is then extended to electroweak models and grand
unified theories. Among others, the U(1)xSU(2) symmetrical Standard Model and
flipped SU(5) GUT appear preferable to emerge at high energies. |
A noncommutative anomaly through Seiberg-Witten map and non-locally
regularized BV quantization: Anomalies are one essential concept for the renormalization of noncommutative
(NC) gauge theories. A NC space can be visualized as a deformation of the usual
spacetime with the $\star$-product and can be constructed after the
quantization of a given space with its symplectic structure. The Seiberg-Witten
(SW) map connects NC fields, transformations parameters and gauge potential to
their commutative analogs. In this work we used the SW map to calculate the NC
version of the anomaly of the BV quantized chiral Schwinger model with nonlocal
regularization. | Blobbed topological recursion for the quartic melonic tensor model: Random tensor models are generalizations of random matrix models which admit
$1/N$ expansions. In this article we show that the topological recursion, a
modern approach to matrix models which solves the loop equations at all orders,
is also satisfied in some tensor models. While it is obvious in some tensor
models which are matrix models in disguise, it is far from clear that it can be
applied to others. Here we focus on melonic interactions for which the models
are best understood, and further restrict to the quartic case. Then
Hubbard-Stratonovich transformation maps the tensor model to a multi-matrix
model with multi-trace interactions. We study this matrix model and show that
after substracting the leading order, it satisfies the blobbed topological
recursion. It is a new extension of the topological recursion, recently
introduced by Borot and further studied by Borot and Shadrin. Here it applies
straightforwardly, yet with a novelty as our model displays a disconnected
spectral curve, which is the union of several spectral curves of the Gaussian
Unitary Ensemble. Finally, we propose a way to evaluate expectations of
tensorial observables using the correlation functions computed from the blobbed
topological recursion. |
Fast scrambling in holographic Einstein-Podolsky-Rosen pair: We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair
exhibits fast scrambling. Strongly entangled quark and antiquark in
$\mathcal{N}=4$ super Yang-Mills theory are considered. Their gravity dual is a
fundamental string whose endpoints are uniformly accelerated in opposite
direction. We slightly increase the acceleration of the endpoint and show that
it quickly destroys the correlation between the quark and antiquark. The proper
time scale of the destruction is $\tau_\ast\sim \beta \ln S$ where $\beta$ is
the inverse Unruh temperature and $S$ is the entropy of the accelerating quark.
We also evaluate the Lyapunov exponent from correlation function as
$\lambda_L=2\pi/\beta$, which saturates the Lyapunov bound. Our results suggest
that the fast scrambling or saturation of the Lyapunov bound do not directly
imply the existence of an Einstein dual. When we slightly decrease the
acceleration, the quark and antiquark are causally connected and an "one-way
traversable wormhole" is created on the worldsheet. It causes the divergence of
the correlation function between the quark and antiquark. | Free Fermions and Thermal AdS/CFT: The dynamics of finite temperature U(N) gauge theories on $S^3$ can be
described, at weak coupling, by an effective unitary matrix model. Here we
present an exact solution to these models, for any value of $N$, in terms of a
sum over representations. Taking the large $N$ limit of this solution provides
a new perspective on the deconfinement transition which is supposed to be dual
to the Hawking-Page transition. The large $N$ phase transition manifests itself
here in a manner similar to the Douglas-Kazakov phase transition in 2d
Yang-Mills theory. We carry out a complete analysis of the saddle
representation in the simplest case involving only the order parameter ${\rm
Tr}U$. We find that the saddle points corresponding to thermal $AdS$, the small
black hole and the large black hole can all be described in terms of free
fermions. They all admit a simple phase space description {\it a la} the BPS
geometries of Lin, Lunin and Maldacena. |
Modular Curves and the Refined Distance Conjecture: We test the refined distance conjecture in the vector multiplet moduli space
of 4D $\mathcal{N}=2$ compactifications of the type IIA string that admit a
dual heterotic description. In the weakly coupled regime of the heterotic
string, the moduli space geometry is governed by the perturbative heterotic
dualities, which allows for exact computations. This is reflected in the type
IIA frame through the existence of a K3 fibration. We identify the degree
$d=2N$ of the K3 fiber as a parameter that could potentially lead to large
distances, which is substantiated by studying several explicit models. The
moduli space geometry degenerates into the modular curve for the congruence
subgroup $\Gamma_0(N)^+$. In order to probe the large $N$ regime, we initiate
the study of Calabi-Yau threefolds fibered by general degree $d>8$ K3 surfaces
by suggesting a construction as complete intersections in Grassmann bundles. | Induced gravity and entanglement entropy of 2D black holes: Using the fact that 2D Newton constant is wholly induced by a conformal field
theory, we derive a formula for the entanglement entropy of the anti-de Sitter
black hole in two spacetime dimensions. The leading term in the large black
hole mass expansion of our formula reproduces exactly the Bekenstein-Hawking
entropy S_{BH}, whereas the subleading term behaves as ln S_{BH}. This
subleading term has the universal form typical for the entanglement entropy of
physical systems described by effective conformal fields theories (e.g.
one-dimensional statistical models at the critical point). |
Roles of Z_2-odd N=1 multiplets in off-shell dimensional reduction of 5D
supergravity: We discuss the dimensional reduction of five-dimensional supergravity
compactified on S^1/Z_2 keeping the N=1 off-shell structure. Especially we
clarify the roles of the Z_2-odd N=1 multiplets in such an off-shell
dimensional reduction. Their equations of motion provide constraints on the
Z_2-even multiplets and extract the zero modes from the latter. The procedure
can be applied to wide range of models and performed in a
background-independent way. We demonstrate it in some specific models. | Anomalies, boundaries and the in-in formalism: In the context of quantum field theory, an anomaly exists when a theory has a
classical symmetry which is not a symmetry of the quantum theory. This short
exposition aims at introducing a new point of view, which is that the proper
setting for anomaly calculations is the `in-in', or closed-time path
formulation of quantum field theory. There are also some new results for
anomalies in the context of boundary value problems, and a new correction to
the $a_5$ heat-kernel coefficient. |
Horizon Fluffs: In the Context of Generalized Minimal Massive Gravity: We consider a metric which describes Ba$\tilde{\text{n}}$ados geometries and
show that the considered metric is a solution of generalized minimal massive
gravity (GMMG) model. We consider the Killing vector field which preserves the
form of considered metric. Using the off-shell quasi-local approach we obtain
the asymptotic conserved charges of given solution. Similar to the Einstein
gravity in the presence of negative cosmological constant, for the GMMG model
also, we show that the algebra among the asymptotic conserved charges is
isomorphic to two copies of the Virasoro algebra. Eventually, we find relation
between the algebra of the near horizon and the asymptotic conserved charges.
This relation show that the main part of the horizon fluffs proposal of
Refs.\cite{140,14} appear for generic black holes in the class of
Ba$\tilde{\text{n}}$ados geometries in the context of GMMG model. | Near-extremal black hole entropy and fluctuating 3-branes: We discuss the known microscopic interpretations of the Bekenstein-Hawking
entropy for configurations of intersecting M-branes. In some cases the entropy
scales as that of a massless field theory on the intersection. A different
situation, found for configurations which reduce to 1-charge D=5 black holes or
2-charge D=4 black holes, is explained by a gas of non-critical strings at
their Hagedorn temperature. We further suggest that the entropy of
configurations reducing to 1-charge D=4 black holes is due to 3-branes moving
within 5-branes. |
The Quantum Theory of Chern-Simons Supergravity: We consider $AdS_3$ $N$-extended Chern-Simons supergravity (\`a la
Achucarro-Tonswend) and we study its gauge symmetries. We promote those gauge
symmetries to a BRST symmetry and we perform its quantization by choosing
suitable gauge-fixings. The resulting quantum theories have different features
which we discuss in the present work. In particular, we show that a special
choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez,
Valenzuela and Zanelli for the graphene fermion. | $q$-Virasoro Operators from $q$-Noether Currents: We discuss the $q$-Virasoro algebra based on the arguments of the Noether
currents in a two-dimensional massless fermion theory as well as in a
three-dimensional nonrelativistic one. Some notes on the $q$-differential
operator realization and the central extension are also included. |
Non-supersymmetric asymptotically AdS_5 x S^5 smooth geometries: We find soliton solutions in five-dimensional gauged supergravity, where a
circle degenerates smoothly in the core of the geometry. In the family of
solutions we consider, we find no completely smooth supersymmetric solutions,
but we find discrete families of non-supersymmetric solitons. We discuss the
relation to previous studies of the asymptotically flat case. We also consider
gauged supergravities in four and seven dimensions, but fail to find any smooth
solutions. | Energy-momentum balance in particle - domain wall perforating collision: We investigate the energy-momentum balance in the perforating collision of a
point particle with an infinitely thin planar domain wall within the linearized
gravity in arbitrary dimensions. Since the metric of the wall increases with
distance, the wall and the particle are never free, and their energy-momentum
balance involves not only the instantaneous kinetic momenta, but also the
non-local contribution of gravitational stresses. However, careful analysis
shows that the stresses can be unambiguously divided between the colliding
objects leading to definition of the gravitationally dressed momenta. These
take into account for gravity in the same way as the potential energy does in
the non-relativistic theory, but our treatment is fully relativistic. Another
unusual feature of our problem is the non-vanishing flux of the total
energy-momentum tensor through the lateral surface of the world tube. In this
case the zero divergence of the energy-momentum tensor does not imply
conservation of the total momentum defined as the integral over the space-like
section of the tube. But one can still define the conservation low
infinitesimally, passing to time derivatives of the momenta. Using this
definition we establish the momentum balance in terms of the dressed particle
and wall momenta. |
Exact Analysis of Scaling and Dominant Attractors Beyond the Exponential
Potential: By considering the potential parameter $\Gamma$ as a function of another
potential parameter $\lambda$[47], We successfully extend the analysis of
two-dimensional autonomous dynamical system of quintessence scalar field model
to the analysis of three-dimension, which makes us be able to research the
critical points of a large number of potentials beyond the exponential
potential exactly. We find that there are ten critical points in all, three
points $P_{3, 5, 6}$} are general points which are possessed by all
quintessence models regardless of the form of potentials and the rest points
are closely connected to the concrete potentials. It is quite surprising that,
apart from the exponential potential, there are a large number of potentials
which can give the scaling solution when the function
$f(\lambda)(=\Gamma(\lambda)-1)$ equals zero for one or some values of
$\lambda_{*}$ and if the parameter $\lambda_{*}$ also satisfies the condition
Eq.(16) or Eq.(17) at the same time. We give the differential equations to
derive these potentials $V(\phi)$ from $f(\lambda)$. We also find that, if some
conditions are satisfied, the de-Sitter-like dominant point $P_4$ and the
scaling solution point $P_9$(or $P_{10}$) can be stable simultaneously but
$P_9$ and $P_{10}$ can not be stable simultaneity. Although we survey scaling
solutions beyond the exponential potential for ordinary quintessence models in
standard general relativity, this method can be applied to other extensively
scaling solution models studied in literature[46] including coupled
quintessence, (coupled-)phantom scalar field, k-essence and even beyond the
general relativity case $H^2 \propto\rho_T^n$. we also discuss the disadvantage
of our approach. | On the Chaos Bound in Rotating Black Holes: We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes
using two different approaches: the elastic eikonal gravity approximation, and
the Chern-Simons formulations of 3-dimensional gravity. Within both methods the
OTOC is given as a sum of two contributions, corresponding to left and right
moving modes. The contributions have different Lyapunov exponents,
$\lambda_L^{\pm}=\frac{2\pi}{\beta}\frac{1}{1\mp \ell \Omega}$, where $\Omega$
is the angular velocity and $\ell$ is the AdS radius. Since $\lambda_L^{-} \leq
\frac{2\pi}{\beta} \leq \lambda_L^{+}$, there is an apparent contradiction with
the chaos bound. We discuss how the result can be made consistent with the
chaos bound if one views $\beta_{\pm}=\beta(1\mp \ell \Omega)$ as the effective
inverse temperatures of the left and right moving modes. |
Dirac fermions in strong gravitational fields: We discuss the dynamics of the Dirac fermions in the general strong
gravitational and electromagnetic fields. We derive the general Hermitian Dirac
Hamiltonian and transform it to the Foldy-Wouthuysen representation for the
spatially isotropic metric. The quantum operator equations of motion are
obtained and the semiclassical limit is analyzed. The comparison of the quantum
mechanical and classical equations shows their complete agreement. The helicity
dynamics in strong fields is discussed. Squaring the covariant Dirac equation
explicitly shows a similarity of the interactions of electromagnetic and
gravitational fields with a charged and spinning particle. | Magnetic Deformation of Super-Maxwell Theory in Supergravity: A necessary condition for partial breaking of N=2 global supersymmetry is the
presence of nonlinear deformations of the field transformations which cannot be
generated by background values of auxiliary fields. This work studies the
simplest of these deformations which already occurs in N=1 global
supersymmetry, and its coupling to supergravity. It can be viewed as an
imaginary constant shift of the D-auxiliary real field of an abelian gauge
multiplet. We show how this deformation describes the magnetic dual of a
Fayet-Iliopoulos term, a result that remains valid in supergravity, using its
new-minimal formulation. Local supersymmetry and the deformation induce a
positive cosmological constant. Moreover, the deformed U(1) Maxwell theory
coupled to supergravity describes upon elimination of the auxiliary fields the
gauging of R-symmetry, realised by the Freedman model of 1976. To this end, we
construct the chiral spinor multiplet in superconformal tensor calculus by
working out explicitly its transformation rules and use it for an alternative
description of the new-minimal supergravity coupled to a U(1) multiplet. We
also discuss the deformed Maxwell theory in curved superspace. |
Toward the construction of N=2 supersymmetric integrable hierarchies: We formulate a conjecture for the three different Lax operators that describe
the bosonic sectors of the three possible $N=2$ supersymmetric integrable
hierarchies with $N=2$ super $W_n$ second hamiltonian structure. We check this
conjecture in the simplest cases, then we verify it in general in one of the
three possible supersymmetric extensions. To this end we construct the $N=2$
supersymmetric extensions of the Generalized Non-Linear Schr\"{o}dinger
hierarchy by exhibiting the corresponding super Lax operator. To find the
correct hamiltonians we are led to a new definition of super-residues for
degenerate N=2 supersymmetric pseudodifferential operators. We have found a new
non-polinomial Miura-like realization for $N=2$ superconformal algebra in terms
of two bosonic chiral--anti--chiral free superfields. | AdS_5 and the 4D Cosmological Constant: The hypothesis is discussed that our universe is really 5--dimensional with a
nonzero cosmological constant that produces a large negative curvature. In this
scenario, the observable flat 4--dimensional universe is identified with the
holographic projection of the 5--dimensional world onto its own boundary. |
Causality & holographic entanglement entropy: We identify conditions for the entanglement entropy as a function of spatial
region to be compatible with causality in an arbitrary relativistic quantum
field theory. We then prove that the covariant holographic entanglement entropy
prescription (which relates entanglement entropy of a given spatial region on
the boundary to the area of a certain extremal surface in the bulk) obeys these
conditions, as long as the bulk obeys the null energy condition. While
necessary for the validity of the prescription, this consistency requirement is
quite nontrivial from the bulk standpoint, and therefore provides important
additional evidence for the prescription. In the process, we introduce a
codimension-zero bulk region, named the entanglement wedge, naturally
associated with the given boundary spatial region. We propose that the
entanglement wedge is the most natural bulk region corresponding to the
boundary reduced density matrix. | Exact Bosonic and Supersymmetric String Black Hole Solutions: We show that Witten's two-dimensional string black hole metric is exactly
conformally invariant in the supersymmetric case. We also demonstrate that this
metric, together with a recently proposed exact metric for the bosonic case,
are respectively consistent with the supersymmetric and bosonic $\sigma$-model
conformal invariance conditions up to four-loop order. |
Constraints on Axion Inflation from the Weak Gravity Conjecture: We derive constraints facing models of axion inflation based on decay
constant alignment from a string-theoretic and quantum gravitational
perspective. In particular, we investigate the prospects for alignment and
`anti-alignment' of $C_4$ axion decay constants in type IIB string theory,
deriving a strict no-go result in the latter case. We discuss the relationship
of axion decay constants to the weak gravity conjecture and demonstrate
agreement between our string-theoretic constraints and those coming from the
`generalized' weak gravity conjecture. Finally, we consider a particular model
of decay constant alignment in which the potential of $C_4$ axions in type IIB
compactifications on a Calabi-Yau three-fold is dominated by contributions from
$D7$-branes, pointing out that this model evades some of the challenges derived
earlier in our paper but is highly constrained by other geometric
considerations. | Thermodynamic Bethe Ansatz with Haldane Statistics: We derive the thermodynamic Bethe ansatz equation for the situation inwhich
the statistical interaction of a multi-particle system is governed by Haldane
statistics. We formulate a macroscopical equivalence principle for such
systems. Particular CDD-ambiguities play a distinguished role in compensating
the ambiguity in the exclusion statistics. We derive Y-systems related to
generalized statistics. We discuss several fermionic, bosonic and anyonic
versions of affine Toda field theories and Calogero-Sutherland type models in
the context of generalized statistics. |
Anomaly resolution via decomposition: In this paper we apply decomposition to orbifolds with quantum symmetries to
resolve anomalies. Briefly, it has been argued by e.g. Wang-Wen-Witten,
Tachikawa that an anomalous orbifold can sometimes be resolved by enlarging the
orbifold group so that the pullback of the anomaly to the larger group is
trivial. For this procedure to resolve the anomaly, one must specify a set of
phases in the larger orbifold, whose form is implicit in the extension
construction. There are multiple choices of consistent phases, which give rise
to physically distinct resolutions. We apply decomposition, and find that
theories with enlarged orbifold groups are equivalent to (disjoint unions of
copies of) orbifolds by nonanomalous subgroups of the original orbifold group.
In effect, decomposition implies that enlarging the orbifold group is
equivalent to making it smaller. We provide a general conjecture for such
descriptions, which we check in a number of examples. | Mass-Gaps and Spin Chains for (Super) Membranes: We present a method for computing the non-perturbative mass-gap in the theory
of Bosonic membranes in flat background spacetimes with or without background
fluxes. The computation of mass-gaps is carried out using a matrix
regularization of the membrane Hamiltonians. The mass gap is shown to be
naturally organized as an expansion in a 'hidden' parameter, which turns out to
be $\frac{1}{d}$: d being the related to the dimensionality of the background
space. We then proceed to develop a large $N$ perturbation theory for the
membrane/matrix-model Hamiltonians around the quantum/mass corrected effective
potential. The same parameter that controls the perturbation theory for the
mass gap is also shown to control the Hamiltonian perturbation theory around
the effective potential. The large $N$ perturbation theory is then translated
into the language of quantum spin chains and the one loop spectra of various
Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop
effective Hamiltonians for membranes in flat space times. Apart from membranes
in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for
non-critical membranes in plane wave type spacetimes are also analyzed within
the paradigm of quantum spin chains and the Bosonic sectors of all the models
proposed in (hep-th/0607005) are diagonalized at the one-loop level. |
Cosmology of the closed string tachyon: The spacetime physics of bulk closed string tachyon condensation is studied
at the level of a two-derivative effective action. We derive the unique
perturbative tachyon potential consistent with a full class of linearized
tachyonic deformations of supercritical string theory. The solutions of
interest deform a general linear dilaton background by the insertion of purely
exponential tachyon vertex operators. In spacetime, the evolution of the
tachyon drives an accelerated contraction of the universe and, absent
higher-order corrections, the theory collapses to a cosmological singularity in
finite time, at arbitrarily weak string coupling. When the tachyon exhibits a
null symmetry, the worldsheet dynamics are known to be exact and well-defined
at tree level. We prove that if the two-derivative effective action is free of
non-gravitational singularities, higher-order corrections always resolve the
spacetime curvature singularity of the null tachyon. The resulting theory
provides an explicit mechanism by which tachyon condensation can generate or
terminate the flow of cosmological time in string theory. Additional particular
solutions can resolve an initial singularity with a tachyonic phase at weak
coupling, or yield solitonic configurations that localize the universe along
spatial directions. | Quantization of $gl(1,{\bf R})$ Generalized Chern-Simons Theory in 1+1
Dimensions: We present a quantization of previously proposed generalized Chern-Simons
theory with $gl(1,{\bf R})$ algebra in 1+1 dimensions. This simplest model
shares the common features of generalized CS theories: on-shell reducibility
and violations of regularity. On-shell reducibility of the theory requires us
to use the Lagrangian Batalin-Vilkovisky and/or Hamiltonian
Batalin-Fradkin-Vilkovisky formulation. Since the regularity condition is
violated, their quantization is not straightforward. In the present case we can
show that both formulations give an equivalent result. It leads to an
interpretation that a physical degree of freedom which does not exist at the
classical level appears at the quantum level. |
Aspects of the Gribov-Zwanziger framework: The existence of gauge (Gribov) copies disturbs the usual Faddeev-Popov
quantization procedure in the Landau gauge. It is a very hard job to treat
these in the continuum, even in a partial manner. A decent way to do so was
worked out by Gribov, and later on by Zwanziger. The final point was a
renormalizable action (the Gribov-Zwanziger action), implementing the
restriction of the path integration to the so-called Gribov region, which is
free of a subset of gauge copies, but not of all copies. Till recently,
everybody agreed upon the fact that the restriction to the Gribov region
implied a infrared enhanced ghost, and vanishing zero momentum gluon
propagator. We discuss how the Gribov-Zwanziger action naturally leads to the
existence of vacuum condensates of dimension two. As it is very common, such
condensates can seriously alter the dynamics. In particular, the
Gribov-Zwanziger condensates give rise to a gluon propagator with a finite but
nonvanishing zero momentum limit, and reconstitute a nonenhanced ghost. We call
this the refined Gribov-Zwanziger framework. The predictions are in qualitative
agreement with most recent lattice simulations, and certain solutions of the
Schwinger-Dyson equations. A crucial feature of the Gribov-Zwanziger framework
is the soft (controllable) breaking of the BRST symmetry. We also point out
that imposing the Kugo-Ojima confinement criterion on the Faddeev-Popov theory
as a boundary condition from the beginning leads to the same partition function
as of Gribov-Zwanziger, with associated BRST symmetry breaking. This clouds the
interpretation of the Kugo-Ojima criterion in se. | Self-gravitating non-abelian kinks as brane worlds: We address the properties of self-gravitating domain walls arising from the
breaking of an SU(N) x Z_2- symmetric theory. In the particular case of N=5, we
find that the two classes of stable non-abelian kinks possible in flat space
have an analogue in the gravitational case, and construct the analytical
solutions. Localization of fermion fields in different representations of the
gauge group in these branes is investigated. It is also shown that non-abelian
gauge fields localization cannot be achieved through interactions with the
brane, but that in one of the two classes of kinks this localization can be
implemented via the Dvali-Shifman mechanism. |
Can we implement the holographic principle in asymptotically flat
spacetimes?: We discuss some recent results in the quest to implement the holographic
principle in asymptotically flat spacetimes. In particular we introduce the key
ingredients of the candidate dual theory which lives at null infinity and it is
invariant under the asymptotic symmetry group of this class of spacetimes. | Holographic Equilibration under External Dynamical Electric Field: The holographic equilibration of a far-from-equilibrium strongly coupled
gauge theory is investigated. The dynamics of a probe D7-brane in an AdS-Vaidya
background is studied in the presence of an external time-dependent electric
field. Defining the equilibration times $t_{eq}^c$ and $t_{eq}^j$, at which
condensation and current relax to their final equilibrated values, receptively,
the smallness of transition time $k_M$ or $k_E$ is enough to observe a
universal behaviour for re-scaled equilibration times $k_M k_E (t_{eq}^c)^{-2}$
and $k_M k_E (t_{eq}^j)^{-2}$. Moreover, regardless of the values for $k_M$ and
$k_E$, $t_{eq}^c/t_{eq}^j$ also behaves universally for large enough value of
the ratio of the final electric field to final temperature. Then a simple
discussion of the static case reveals that $t_{eq}^c \leq t_{eq}^j$. For an
out-of-equilibrium process, our numerical results show that, apart from the
cases for which $k_E$ is small, the static time ordering persists. |
Holographic Metal-Insulator Transition in Higher Derivative Gravity: We introduce a Weyl term into the Einstein-Maxwell-Axion theory in four
dimensional spacetime. Up to the first order of the Weyl coupling parameter
$\gamma$, we construct charged black brane solutions without translational
invariance in a perturbative manner. Among all the holographic frameworks
involving higher derivative gravity, we are the first to obtain metal-insulator
transitions (MIT) when varying the system parameters at zero temperature.
Furthermore, we study the holographic entanglement entropy (HEE) of strip
geometry in this model and find that the second order derivative of HEE with
respect to the axion parameter exhibits maximization behavior near quantum
critical points (QCPs) of MIT. It testifies the conjecture in 1502.03661 and
1604.04857 that HEE itself or its derivatives can be used to diagnose quantum
phase transition (QPT). | String and M-Theory Cosmological Solutions with Ramond Forms: A general framework for studying a large class of cosmological solutions of
the low-energy limit of type II string theory and of M-theory, with non-trivial
Ramond form fields excited, is presented. The framework is applicable to
spacetimes decomposable into a set of flat or, more generally, maximally
symmetric spatial subspaces, with multiple non-trivial form fields spanning one
or more of the subspaces. It is shown that the corresponding low-energy
equations of motion are equivalent to those describing a particle moving in a
moduli space consisting of the scale factors of the subspaces together with the
dilaton. The choice of which form fields are excited controls the potential
term in the particle equations. Two classes of exact solutions are given, those
corresponding to exciting only a single form and those with multiple forms
excited which correspond to Toda theories. Although typically these solutions
begin or end in a curvature singularity, there is a subclass with positive
spatial curvature which appears to be singularity free. Elements of this class
are directly related to certain black p-brane solutions. |
Non-Abelian Duality and Canonical Transformations: We construct explicit canonical transformations producing non-abelian duals
in principal chiral models with arbitrary group G. Some comments concerning the
extension to more general $\sigma$-models, like WZW models, are given. | Hirota equation as an example of integrable symplectic map: The hamiltonian formalism is developed for the sine-Gordon model on the
space-time light-like lattice, first introduced by Hirota. The evolution
operator is explicitely constructed in the quantum variant of the model, the
integrability of the corresponding classical finite-dimensional system is
established. |
The Casimir effect for parallel plates at finite temperature in the
presence of one fractal extra compactified dimension: We discuss the Casimir effect for massless scalar fields subject to the
Dirichlet boundary conditions on the parallel plates at finite temperature in
the presence of one fractal extra compactified dimension. We obtain the Casimir
energy density with the help of the regularization of multiple zeta function
with one arbitrary exponent and further the renormalized Casimir energy density
involving the thermal corrections. It is found that when the temperature is
sufficiently high, the sign of the Casimir energy remains negative no matter
how great the scale dimension $\delta$ is within its allowed region. We derive
and calculate the Casimir force between the parallel plates affected by the
fractal additional compactified dimension and surrounding temperature. The
stronger thermal influence leads the force to be stronger. The nature of the
Casimir force keeps attractive. | Two-dimensional Black Holes in a Higher Derivative Gravity and Matrix
Model: We construct perturbatively a class of charged black hole solutions in type
0A string theory with higher derivative terms. They have extremal limit, where
the solution interpolates smoothly between near horizon AdS_2 geometry and the
asymptotic linear dilaton geometry. We compute the free energy and the entropy
of those solution using various methods. In particular, we show that there is
no correction in the leading term of the free energy in the large charge limit.
This supports the duality of the type 0A strings on the extremal black hole and
the 0A matrix model in which the tree level free energy is exact without any
alpha' corrections. |
Covariant realizations of kappa-deformed space: We study a Lie algebra type $\kappa$-deformed space with undeformed rotation
algebra and commutative vector-like Dirac derivatives in a covariant way. Space
deformation depends on an arbitrary vector. Infinitely many covariant
realizations in terms of commuting coordinates of undeformed space and their
derivatives are constructed. The corresponding coproducts and star products are
found and related in a new way. All covariant realizations are physically
equivalent. Specially, a few simple realizations are found and discussed. The
scalar fields, invariants and the notion of invariant integration is discussed
in the natural realization. | The two-loop superstring five-point amplitude and S-duality: The low-energy limit of the massless two-loop five-point amplitudes for both
type IIA and type IIB superstrings is computed with the pure spinor formalism
and its overall coefficient determined from first principles. For the type IIB
theory, the five-graviton amplitude is found to be proportional to its
tree-level counterpart at the corresponding order in $\alpha'$. Their ratio
ties in with expectations based on S-duality since it matches the same modular
function $E_{5/2}$ which relates the two-loop and tree-level four-graviton
amplitudes. For R-symmetry violating states, the ratio between tree-level and
two-loop amplitudes at the same $\alpha'$-order carries an additional factor of
$-3/5$. Its S-duality origin can be traced back to a modular form derived from
$E_{5/2}$. |
Twin conformal field theories: Supersymmetric theories with the same bosonic content but different fermions,
aka \emph{twins}, were thought to exist only for supergravity. Here we show
that pairs of super conformal field theories, for example exotic
$\mathcal{N}=3$ and $\mathcal{N}=1$ theories in $D=4$ spacetime dimensions, can
also be twin. We provide evidence from three different perspectives: (i) a twin
S-fold construction, (ii) a double-copy argument and (iii) by identifying
candidate twin holographically dual gauged supergravity theories. Furthermore,
twin W-supergravity theories then follow by applying the double-copy
prescription to exotic super conformal field theories. | Time warps: I reconsider asymmetrically warped compactifications, in which time and space
have different warp factors. I call such compactifications time warps if the
bulk geometry has neither entropy nor temperature. I provide an example
starting from an asymptotically AdS_5 spacetime where the speed of light,
measured in a fixed coordinate system, is larger near the boundary than it is
deep in the interior. This example follows the general plan of earlier work on
superconducting black holes. To obtain a normalizable, four-dimensional
graviton, one can introduce a Planck brane whose action includes a wrong-sign
Einstein-Hilbert term. The equation of state of the Planck brane has w < -1,
which is a violation of the null energy condition. I show, in an almost
dimension-independent fashion, that such a violation must occur in a static
time warp geometry. Time warps of the type I describe provide an
extra-dimensional description of boost invariance as an emergent symmetry in
the infrared. High-energy violations of Lorentz symmetry, if confined to a
strongly coupled unparticle sector dual to the time warp geometry, might
manifest themselves through unusual kinematic constraints. As an example, I
explain how modifications of unparticle phase space would affect the decay of a
heavy particle into a light visible sector particle plus unparticle stuff. |
Update on the quantum properties of the Supermembrane: In this note we summarize some of the quantum properties found since the
early 80's until nowdays that characterize at quantum level the spectrum of the
supermembrane. In particular we will focus on a topological sector of the 11D
supermembrane that, contrary to the general case, has a purely discrete
spectrum at supersymmetric level. This construction has been consistently
implemented in different types of backgrounds: toroidal and orbifold-type with
G2 structure able to lead to a true G2 compactification manifold. This theory
has N=1 supersymmetries in 4D. comment on the relevant points of this
construction as well as on its spectral characteristics. We will also make some
comments on the quantum properties of some effective formulation of multiple
M2's theories recently found. | Matrix elements of the operator T\bar{T} in integrable quantum field
theory: Recently A. Zamolodchikov obtained a series of identities for the expectation
values of the composite operator T\bar{T} constructed from the components of
the energy-momentum tensor in two-dimensional quantum field theory. We show
that if the theory is integrable the addition of a requirement of factorization
at high energies can lead to the exact determination of the generic matrix
element of this operator on the asymptotic states. The construction is
performed explicitly in the Lee-Yang model. |
Scalar Perturbation and Stability of Ricci Dark Energy: The Ricci dark energy (RDE) proposed to explain the accelerating expansion of
the universe requires its parameter $\alpha < 1$, whose value will determine
the behavior of RDE. In this Letter, we study the scalar perturbation of RDE
with and without matter in the universe, and we find that in both cases, the
perturbation is stable if $\alpha> 1/3$, which gives a lower bound for $\alpha$
theoretically. | A next-to-leading Luescher formula: We propose a next-to-leading Luescher-like formula for the finite-size
corrections of the excited states energies in integrable theories. We
conjecture the expressions of the corrections for both the energy and the
particles' rapidities by interpreting the excited states as momenta-dependent
defects. We check the resulting formulas in some simple relativistic model and
conjecture those for the AdS5/CFT4 case. |
Lorentz invariance and confined noncommutativity: There have been comments on this paper which point out unclear motivation and
definitions on noncommutative momentum introduced. Therefore, this paper is
withdrawn by the author for more clear presentation. | The Near-Horizon Limit of the Extreme Rotating d=5 Black Hole as a
Homogenous Spacetime: We show that the spacetime of the near-horizon limit of the extreme rotating
d=5 black hole, which is maximally supersymmetric in N=2,d=5 supergravity for
any value of the rotation parameter j in [-1,1], is locally isomorphic to a
homogeneous non-symmetric spacetime corresponding to an element of the
1-parameter family of coset spaces SO(2,1)x SO(3)/SO(2)_j in which the subgroup
SO(2)_j is a combination of the two SO(2) subgroups of SO(2,1) and SO(3). |
Superradiant (In)stability, Greybody Radiation, and Quasinormal Modes of
Rotating Black Holes in non-linear Maxwell f (R) Gravity: The research of superradiant instability in the realm of quantum gravity is a
well-known topic, with many physicists and astronomers studying the potential
impact it can have on gravitational waves, the structure of the universe, and
spacetime itself. In this work, we investigate the superradiant (in)stability
of a rotating black hole obtained from the nonlinear Maxwell $f(R)$ gravity
theory. In this study, the evaluation of stability/instability is going to be
based on non-existence and existence of magnetic field, when the magnetic field
constant becomes $c_{4}=0$ and $c_{4}\neq 0$, respectively. The analyzes of
greybody factor (GF) and quasinormal modes (QNMs) are investigated in the
stationary black hole spacetime both in the absence and presence of the
magnetic field parameter. To this end, we first consider the Klein-Gordon
equation for the complex scalar field in the geometry of that rotating black
hole. In the sequel, the obtained radial equation is reduced to a
one-dimensional Schr\"{o}dinger-like wave equation with an effective potential
energy. The effects of the nonlinear Maxwell $f(R)$ gravity theory parameters
($q$, $c$, and $c_{4}$) on the effective potential, GFs, and QNMs are
thoroughly investigated. The obtained results show that even though the factors
$q$, $c$, and $c_{4}$ all affect the effective potential, this phenomena,
surprisingly, is not valid for the GFs and QNMs. With the proper graphics and
tables, all outputs are depicted, tabulated, and interpreted. | Open String Gravity?: We present a new application of Boundary String Field Theory: calculating the
induced-gravity action on a D-brane. Using a simple quadratic tachyon potential
to model a D-brane fluctuating in the flat target space we derive the effective
action in terms of the extrinsic curvature to all orders in alpha'. We identify
both the Born-Infeld structure as well as the Einstein-Hilbert term at order
alpha'. This corroborates the conjectured existence of the latter term in the
brane-world scenarios. The higher order terms in Ricci scalar and extrinsic
curvature suggest a pattern which calls for an explanation. |
Half-maximal supergravity in three dimensions: supergeometry,
differential forms and algebraic structure: The half-maximal supergravity theories in three dimensions, which have local
$SO(8)\xz SO(n)$ and rigid SO(8,n) symmetries, are discussed in a superspace
setting starting from the superconformal theory. The on-shell theory is
obtained by imposing further constraints; it is essentially a non-linear sigma
model that induces a Poincar\'e supergeometry. The deformations of the geometry
due to gauging are briefly discussed. The possible $p$-form field strengths are
studied using supersymmetry and SO(8,n) symmetry. The set of such forms obeying
consistent Bianchi identities constitutes a Lie super co-algebra while the
demand that these identities admit solutions places a further constraint on the
possible representations of SO(8,n) that the forms transform under which can be
easily understood using superspace cohomology. The dual Lie superalgebra can
then be identified as the positive sector of a Borcherds superalgebra that
extends the Lie algebra of the duality group. In addition to the known
$p=2,3,4$ forms, which we construct explicitly, there are five-forms that can
be non-zero in supergravity, while all forms with $p>5$ vanish. It is shown
that some six-forms can have non-trivial contributions at order $\a'$. | Construction of a Gauge-Invariant Action for Type II Superstring Field
Theory: We construct a gauge-invariant action for covariant type II string field
theory in the NS-NS sector. Our construction is based on the large Hilbert
space description and Zwiebach's string products are used. First, we rewrite
the action for bosonic string field theory into a new form where a state in the
kernel of the generator of the gauge transformation appears explicitly. Then we
use the same strategy and write down our type II action, where a projector onto
the small Hilbert space plays an important role. We present lower-order terms
up to quartic order and show that three-point amplitudes are reproduced
correctly. |
Disorder in AdS$_3$/CFT$_2$: We perturbatively study marginally relevant quenched disorder in
AdS$_3$/CFT$_2$ to second order in the disorder strength. Using the
Chern-Simons formulation of AdS$_3$ gravity for the Poincar\'e patch, we
introduce disorder via the chemical potentials. We discuss the bulk and
boundary properties resulting from the disorder averaged metric. The disorder
generates a small mass and angular momentum. In the bulk and the boundary, we
find unphysical features due to the disorder average. Motivated by these
features, we propose a Poincar\'e-Lindstedt-inspired resummation method. We
discuss how this method enables us to remove all of the unphysical features and
compare with other approaches to averaging. | Flow Equation of N=1 Supersymmetric O(N) Nonlinear Sigma Model in Two
Dimensions: We study the flow equation for the $\mathcal{N}=1$ supersymmetric $O(N)$
nonlinear sigma model in two dimensions, which cannot be given by the gradient
of the action, as evident from dimensional analysis. Imposing the condition on
the flow equation that it respects both the supersymmetry and the $O(N)$
symmetry, we show that the flow equation has a specific form, which however
contains an undetermined function of the supersymmetric derivatives $D$ and
$\bar D$. Taking the most simple choice, we propose a flow equation for this
model. As an application of the flow equation, we give the solution of the
equation at the leading order in the large $N$ expansion. The result shows that
the flow of the superfield in the model is dominated by the scalar term, since
the supersymmetry is unbroken in the original model. It is also shown that the
two point function of the superfield is finite at the leading order of the
large $N$ expansion. |
Classical r-matrices and construction of quantum groups: A problem of constructing quantum groups from classical r-matrices is
discussed. | Hawking radiation for scalar fields by Einstein-Gauss-Bonnet-de Sitter
black holes: We study the greybody factor and power spectra of Hawking radiation for the
minimally or nonminimally coupled scalar field with exact numerical method in
spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole spacetime. The
effects of scalar coupling constant, angular momentum number of scalar,
spacetime dimension, cosmological constant and Gauss-Bonnet coupling constant
on the Hawking radiation are studied in detail. Specifically, the Gauss-Bonnet
coupling constant always increases the greybody factor in the entire energy
regime. Different from the case of Schwarzschild-de Sitter black hole, the
effects of the scalar coupling constant on the greybody factor are not
monotonic but relevant to the values of Gauss-Bonnet coupling constant.
Moreover, both these two coupling constants always suppress the power spectra
of Hawking radiation in the whole energy regime. |
Strong Wilson polygons from the lodge of free and bound mesons: Previously predicted by the $S$-matrix bootstrap of the excitations over the
GKP quantum vacuum, the appearance of a new particle at strong coupling --
formed by one fermion and one anti-fermion -- is here confirmed: this
two-dimensional meson shows up, along with its infinite tower of bound states,
while analysing the fermionic contributions to the Operator Product Expansion
(collinear regime) of the Wilson null polygon loop. Moreover, its existence,
free \footnote{This term is used here as opposite to bound, thus as {\it
unbound}.} and bound, turns out to be a powerful idea in re-summing all the
contributions (at large coupling) for a general $n$-gon ($n\geq 6$) to a
Thermodynamic Bethe Ansatz, which is proven to be equivalent to the known one
and suggests new structures for a special $Y$-system. | Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations: New homotopy approach to the analysis of nonlinear higher-spin equations is
developed. It is shown to directly reproduce the previously obtained local
vertices. Simplest cubic (quartic in Lagrangian nomenclature) higher-spin
interaction vertices in four dimensional theory are examined from locality
perspective by the new approach and shown to be local. The results are obtained
in a background independent fashion. |
Transport coefficients, membrane couplings and universality at
extremality: We present an efficient method for computing the zero frequency limit of
transport coefficients in strongly coupled field theories described
holographically by higher derivative gravity theories. Hydrodynamic parameters
such as shear viscosity and conductivity can be obtained by computing residues
of poles of the off-shell lagrangian density. We clarify in which sense these
coefficients can be thought of as effective couplings at the horizon, and
present analytic, Wald-like formulae for the shear viscosity and conductivity
in a large class of general higher derivative lagrangians. We show how to apply
our methods to systems at zero temperature but finite chemical potential. Our
results imply that such theories satisfy $\eta/s=1/4\pi$ universally in the
Einstein-Maxwell sector. Likewise, the zero frequency limit of the real part of
the conductivity for such systems is shown to be universally zero, and we
conjecture that higher derivative corrections in this sector do not modify this
result to all orders in perturbation theory. | Canonical form of Euler-Lagrange equations and gauge symmetries: The structure of the Euler-Lagrange equations for a general Lagrangian theory
is studied. For these equations we present a reduction procedure to the
so-called canonical form. In the canonical form the equations are solved with
respect to highest-order derivatives of nongauge coordinates, whereas gauge
coordinates and their derivatives enter in the right hand sides of the
equations as arbitrary functions of time. The reduction procedure reveals
constraints in the Lagrangian formulation of singular systems and, in that
respect, is similar to the Dirac procedure in the Hamiltonian formulation.
Moreover, the reduction procedure allows one to reveal the gauge identities
between the Euler-Lagrange equations. Thus, a constructive way of finding all
the gauge generators within the Lagrangian formulation is presented. At the
same time, it is proven that for local theories all the gauge generators are
local in time operators. |
Lattice BRST without Neuberger 0/0 problem: We illustrate in a simple toy model how the methods of SUSY quantum mechanics
and topological quantum field theory can be used for covariant gauge-fixing
with unbroken BRST symmetry on a finite lattice. | More on integrable structures of superstrings in AdS(4) x CP(3) and
AdS(2) x S(2) x T(6) superbackgrounds: In this paper we continue the study, initiated in arXiv:1009.3498 and
arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings
in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum
contains non-supercoset worldsheet degrees of freedom corresponding to broken
supersymmetries in the bulk. We derive an explicit expression, to all orders in
the coset fermions and to second order in the non-coset fermions, which extends
the supercoset Lax connection in these backgrounds with terms depending on the
non-coset fermions. An important property of the obtained form of the Lax
connection is that it is invariant under Z_4-transformations of the
superisometry generators and the spectral parameter. This demonstrates that the
contribution of the non-coset fermions does not spoil the Z_4-symmetry of the
super-coset Lax connection which is of crucial importance for the application
of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and
AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a
very similar form. This is because their amount of target-space supersymmetries
complement each other to 32=24+8, the maximal number of 10d type II
supersymmetries. As a byproduct, this similarity has allowed us to obtain the
form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace
to all orders in the coset fermions and to the second order in the non-coset
ones. |
Hamiltonian Analysis of SL(2,R) Symmetry in Liouville Theory: We consider a Hamiltonian analysis of the Liouville theory and construction
of symmetry generators using Castellani's method. We then discuss the
light-cone gauge fixed theory. In particular, we clarify the difference between
Hamiltonian approaches based on different choices of time, $\xi^0$ and $\xi^+$.
Our main result is the construction of SL(2,R) symmetry generators in both
cases. ( Lectures presented at the Danube Workshop '93,
June 1993, Belgrade, Yugoslavia.) | Spinning Particles, Braid Groups and Solitons: We develop general techniques for computing the fundamental group of the
configuration space of $n$ identical particles, possessing a generic internal
structure, moving on a manifold $M$. This group generalizes the $n$-string
braid group of $M$ which is the relevant object for structureless particles. In
particular, we compute these generalized braid groups for particles with an
internal spin degree of freedom on an arbitrary $M$. A study of their unitary
representations allows us to determine the available spectrum of spin and
statistics on $M$ in a certain class of quantum theories. One interesting
result is that half-integral spin quantizations are obtained on certain
manifolds having an obstruction to an ordinary spin structure. We also compare
our results to corresponding ones for topological solitons in
$O(d+1)$-invariant nonlinear sigma models in $(d+1)$-dimensions, generalizing
recent studies in two spatial dimensions. Finally, we prove that there exists a
general scalar quantum theory yielding half-integral spin for particles (or
$O(d+1)$ solitons) on a closed, orientable manifold $M$ if and only if $M$
possesses a ${\rm spin}_c$ structure. |
Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces: We demonstrate how non-simply-laced gauge and flavor symmetries arise in
F-theory on spaces with non-isolated singularities. The breaking from a
simply-laced symmetry to one that is non-simply-laced is induced by Calabi-Yau
complex structure deformation. In all examples the deformation maintains
non-isolated singularities but is accompanied by a splitting of an I1
seven-brane that opens new loops in the geometry near a non-abelian
seven-brane. The splitting also arises in the moduli space of a probe D3-brane,
which upon traversing the new loop experiences a monodromy that acts on 3-7
string junctions on the singular space. The monodromy reduces the symmetry
algebra, which is the flavor symmetry of the D3-brane and the gauge symmetry of
the seven-brane, to one that is non-simply-laced. A collision of the D3-brane
with the seven-brane gives rise to a 4d N = 1 SCFT with a non-simply-laced
flavor symmetry. | Taking the Temperature of a Black Hole: We use the global embedding of a black hole spacetime into a higher
dimensional flat spacetime to define a local temperature for observers in free
fall outside a static black hole. The local free-fall temperature remains
finite at the event horizon and in asymptotically flat spacetime it approaches
the Hawking temperature at spatial infinity. Freely falling observers outside
an AdS black hole do not see any high-temperature thermal radiation even if the
Hawking temperature of such black holes can be arbitrarily high. |
NS Three-form Flux Deformation for the Critical Non-Abelian Vortex
String: It has been shown that non-Abelian solitonic vortex string supported in
four-dimensional (4D) N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group
and $N_f = 4$ quark flavors becomes a critical superstring. This string
propagates in the ten-dimensional space formed by a product of the flat 4D
space and an internal space given by a Calabi-Yau noncompact threefold, namely,
the conifold. The spectrum of low lying closed string states in the associated
type IIA string theory was found and interpreted as a spectrum of hadrons in 4D
N = 2 SQCD. In particular, the lowest string state appears to be a massless BPS
baryon associated with the deformation of the complex structure modulus $b$ of
the conifold. In the previous work the deformation of the 10-dimensional
background with nonzero Neveu-Schwarz 3-form flux was considered and
interpreted as a switching on a particular choice of quark masses in 4D SQCD.
This deformation was studied to the leading order at small 3-form flux. In this
paper we study the back reaction of the nonzero 3-form flux on the metric and
the dilaton introducing ansatz with several warp factors and solving gravity
equations of motion. We show that 3-form flux produces a potential for the
conifold complex structure modulus $b$, which leads to the runaway vacuum. At
the runaway vacuum warp factors disappear, while the conifold degenerates. In
4D SQCD we relate this to the flow to the U(1) gauge theory upon switching on
quark masses and decoupling of two flavors. | Is it Physically Sound to Add a Topologically Massive Term to
Three-Dimensional Massive Electromagnetic or Gravitational Models ?: The addition of a topologically massive term to an admittedly non-unitary
three-dimensional massive model, be it an electromagnetic system or a
gravitational one, does not cure its non-unitarity. What about the enlargement
of avowedly unitary massive models by way of a topologically massive term? The
electromagnetic models remain unitary after the topological augmentation but,
surprisingly enough, the gravitational ones have their unitarity spoiled. Here
we analyze these issues and present the explanation why unitary massive
gravitational models, unlike unitary massive electromagnetic ones, cannot
coexist from the viewpoint of unitarity with topologically massive terms. We
also discuss the novel features of the three-term effective field models that
are gauge-invariant. |
Reconstructing cosmic acceleration from modified and non-minimal
gravity: The Yang-Mills case: A variant of the accelerating cosmology reconstruction program is developed
for $f(R)$ gravity and for a modified Yang-Mills/Maxwell theory. Reconstruction
schemes in terms of e-foldings and by using an auxiliary scalar field are
developed and carefully compared, for the case of $f(R)$ gravity. An example of
a model with a transient phantom behavior without real matter is explicitly
discussed in both schemes. Further, the two reconstruction schemes are applied
to the more physically interesting case of a Yang-Mills/Maxwell theory, again
with explicit examples. Detailed comparison of the two schemes of
reconstruction is presented also for this theory. It seems to support, as well,
physical non-equivalence of the two frames. | Gauge/Gravity Duality and Some Applications: We discuss the AdS/CFT correspondence in which space-time emerges from an
interacting theory of D-branes and open strings. These ideas have a historical
continuity with QCD which is an interacting theory of quarks and gluons. In
particular we review the classic case of D3 branes and the non-conformal D1
brane system. We outline by some illustrative examples the calculations that
are enabled in a strongly coupled gauge theory by correspondence with dynamical
horizons in semi-classical gravity in one higher dimension. We also discuss
implications of the gauge-fluid/gravity correspondence for the information
paradox of black hole physics. |
Zero Modes of Massive Fermions Delocalize from Axion Strings: Massless chiral excitations can arise from the interactions between a fermion
and an axion string, propagating along the string and allowing it to
superconduct. The properties of these excitations, or zero modes, dictate how
the string interacts with light and can thus have important phenomenological
consequences. In this paper, we add a nowhere-vanishing Dirac mass for the
fermion in the usual model of axion electrodynamics. We find that the zero
modes exhibit an interesting phase structure in which they delocalize from the
string's core as the mass increases, up until a critical value past which they
disappear. We study this structure from an analytic perspective, with explicit
numerical solutions, and via anomaly inflow arguments. Finally, we derive the
two-dimensional effective theory of the zero mode and its interactions with the
four-dimensional gauge field and show how this effective theory breaks down as
the zero modes delocalize. | Dual Supergravity in D=10, N=1 Superspace with Tree-Level Superstring
Corrections: The dual version of the D=10 N=1 supergravity (SUGRA) is considered in the
superspace approach. The superstring (anomaly compensating) corrections are
described by the 3-form superfield $A_{abc}$ . The complete set of dynamical
equations for the $A$-field and for physical fields of the theory are
presented. The solution of the $A$-field equations as a finite order polynomial
in terms of curvature and graviphoton superfields is given. It makes possible
to incorporate some of the superstring corrections in the dual supergravity in
the explicit, supersymmetric and closed form. |
Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts
Quantum Spin Chain: We study the excitation spectrum and the correlation functions of the Z_3-
chiral Potts model in the massive high-temperature phase using perturbation
expansions and numerical diagonalization. We are mainly interested in results
for general chiral angles but we consider also the superintegrable case. For
the parameter values considered, we find that the band structure of the low-
lying part of the excitation spectrum has the form expected from a
quasiparticle picture with two fundamental particles. Studying the N-dependence
of the spectrum, we confirm the stability of the second fundamental particle in
a limited range of the momentum, even when its energy becomes so high that it
lies very high up among the multiparticle scattering states. This is not a
phenomenon restricted to the superintegrable line. Calculating a
non-translationally invariant correlation function, we give evidence that it is
oscillating. Within our numerical accuracy we find a relation between the
oscillation length and the dip position of the momentum dispersion of the
lightest particle which seems to be quite independent of the chiral angles. | Highest states in light-cone $AdS_5\times S^5$ superstring: We study the highest states in the compact rank-1 sectors of the AdS5 X S5
superstring in the framework of the recently proposed light cone Bethe Ansatz
equations. In the su(1|1) sector we present strong coupling expansions in the
two limits L,lambda -> OO (expanding in power of lambda^{-1/4} with fixed large
L) and lambda, L -> OO (expanding in power of 1/L with fixed large lambda)
where lambda is the 't Hooft coupling and L is the number of Bethe momenta. The
two limits do not commute apart from the leading term which reproduces the
result obtained with the Arutyunov-Frolov-Staudacher phase in the lambda, L ->
OO limit. In the su(2) sector we perform the strong coupling expansions in the
L->OO limit up to O(lambda^{-1/4}), and our result is in agreement with
previuos String Bethe Ansatz analysis. |
Two Stringy Systems of the Kerr Spinning Particle: A classical spinning particle based on the Kerr-Newman black hole (BH)
solution is considered. For parameters of spinning particles $|a|>>m$, the BH
horizons disappear and BH image is drastically changed. We show that it turns
into a skeleton formed by two coupled stringy systems. One of them is the Kerr
singular ring which can be considered as a circular D-string with an
orientifold world-sheet.
Analyzing the aligned to the Kerr congruence electromagnetic excitations of
this string, we obtain the second stringy system which consists of two axial
half-infinite chiral D-strings. These axial strings are similar to the Dirac
monopole strings but carry the induced chiral traveling pp-waves. Their field
structure can be described by the field model suggested by Witten for the
cosmic superconducting strings.
We discuss a relation of this stringy system to the Dirac equation and argue
that this stringy system can play a role of a classical carrier of the wave
function. | An Approach to SU_q(2)p Gauge Theory: In the usual approach to q-deformed gauge theories, the gauge fields are
required to be non-local or non-commutative one's. If we introduce, however, an
extended product, which we call `` $\star$-product\rq\rq, among the generators
of a q-deformed Lie group, the deformed group can be reduced to a ordinary Lie
group under the $\star$-product. According to this line of approach, we try to
construct a $[SU_q(2)\times U(1)]_\star$, a $SU(2)\times U(1)$ analogue under
the $\star$-product, gauge theory. In this gauge theory with the
$\star$-product, the U(1) symmetry is naturally incorporated into the SU(2)
symmetry. We also study the symmetry breaking by the Higgs mechanism associated
with $J=1/2$ and J=1 representations of $SU_q(2)$ algebra, and show that the
mixing angle between the SU(2) and U(1) gauge fields is determined uniquely in
a tree level. |
Two-Point Functions of Chiral Fields at One Loop in Type II: We compute the two-point functions for chiral matter states in toroidal
intersecting D6-brane models. In particular, we provide the techniques to
calculate Moebius strip diagrams including the worldsheet instanton
contribution. | Born-Infeld Dynamics in Uniform Electric Field: We investigate various properties of classical configurations of the
Born-Infeld theory in a uniform electric field. This system is involved with
dynamics of (F,Dp) bound states, which are bound states of fundamental strings
and Dp-branes. The uniform electric field can be treated as a constraint on the
asymptotic behavior of the fields on the brane. BPS configurations in this
theory correspond to fundamental strings attached to the (F,Dp) bound state,
and are found to be stable due to force balance. Fluctuations around these
stable configurations are subject to appropriate Dirichlet and Neumann boundary
conditions which are identical with the ones deduced from the ordinary
worldsheet description of the attached string. Additionally, non-BPS solutions
are studied and related physics are discussed. |
Time ordered perturbation theory for non-local interactions;
applications to NCQFT: In the past decades, time ordered perturbation theory was very successful in
describing relativistic scattering processes. It was developed for local
quantum field theories. However, there are field theories which are governed by
non-local interactions, for example non-commutative quantum field theory
(NCQFT). Filk (Phys. Lett. B 376 (1996) 53) first studied NCQFT perturbatively
obtaining the usual Feynman propagator and additional phase factors as the
basic elements of perturbation theory. However, this treatment is only
applicable for cases, where the deformation of space-time does not involve
time. Thus, we generalize Filk's approach in two ways: First, we study
non-local interactions of a very general type able to embed NCQFT. And second,
we also include the case, where non-locality involves time. A few applications
of the obtained formalism will also be discussed. | The influence of a conducting surface on the conductivity of graphene: In the present paper, using Pseudo-Quantum Electrodynamics to describe the
interaction between electrons in graphene, we investigate the longitudinal and
optical conductivities of a neutral graphene sheet near a grounded perfectly
conducting surface, with calculations up to 2-loop perturbation order. We show
that the longitudinal conductivity increases as we bring the conducting surface
closer to the graphene sheet. On the other hand, although the optical
conductivity initially increases with the proximity of the plate, it reaches a
maximum value, tending, afterwards, to the minimal conductivity in the ideal
limit of no separation between graphene and the conducting surface. We recover
the correspondent results in the literature when the distance to the plate
tends to infinity. Our results may be useful as an alternative way to control
the longitudinal and optical conductivities of graphene. |
Arithmetic of Calabi-Yau Varieties and Rational Conformal Field Theory: It is proposed that certain techniques from arithmetic algebraic geometry
provide a framework which is useful to formulate a direct and intrinsic link
between the geometry of Calabi-Yau manifolds and the underlying conformal field
theory. Specifically it is pointed out how the algebraic number field
determined by the fusion rules of the conformal field theory can be derived
from the number theoretic structure of the cohomological Hasse-Weil L-function
determined by Artin's congruent zeta function of the algebraic variety. In this
context a natural number theoretic characterization arises for the quantum
dimensions in this geometrically determined algebraic number field. | Yoga Dark Energy: Natural Relaxation and Other Dark Implications of a
Supersymmetric Gravity Sector: We construct a class of 4D `yoga' (naturally relaxed) models for which the
gravitational response of heavy-particle vacuum energies is strongly
suppressed. The models contain three ingredients: (i) a relaxation mechanism,
(ii) a very supersymmetric gravity sector coupled to matter for which
supersymmetry is non-linearly realised, and (iii) an accidental approximate
scale invariance expressed through the presence of a low-energy dilaton
supermultiplet. All three are common in higher-dimensional and string
constructions and although none suffices on its own, taken together they can
dramatically suppress the net vacuum-energy density. The dilaton's {\it
vev}~$\tau$ determines the weak scale $M_W \sim M_p/\sqrt\tau$. We compute the
potential for $\tau$ and find it can be stabilized in a local de Sitter minimum
at sufficiently large field values to explain the electroweak hierarchy, doing
so using input parameters no larger than $O(60)$ because the relevant potential
arises as a rational function of $\ln\tau$. The de Sitter vacuum energy at the
minimum is order $c\, M_W^8 \propto 1/\tau^4$, with $c \ll O(M_W^{-4})$. We
discuss how to achieve $c \sim 1/M_p^4$ as required by observations. Scale
invariance implies the dilaton couples to matter like a Brans-Dicke scalar with
dangerously large coupling yet because it comes paired with an axion it can
evade bounds through the novel screening mechanism described in {\tt
ArXiV:2110.10352}. Cosmological axio-dilaton evolution predicts a natural
quintessence model for Dark Energy, whose evolution can realize recent
proposals to resolve the Hubble tension, and whose axion contributes to Dark
Matter. We summarize inflationary implications and some remaining challenges,
including the unusual supersymmetry breaking regime used and the potential for
UV completions of our approach. |
Multi-Regge Limit of the n-Gluon Bubble Ansatz: We investigate n-gluon scattering amplitudes in the multi-Regge region of N=4
supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis
of the thermodynamic bubble ansatz (TBA) for surfaces in AdS5 with n-g(lu)on
boundary conditions we demonstrate that the multi-Regge limit probes the large
volume regime of the TBA. In reaching the multi-Regge regime we encounter
wall-crossing in the TBA for all n>6. Our results imply that there exists an
auxiliary system of algebraic Bethe ansatz equations which encode valuable
information on the analytical structure of amplitudes at strong coupling. | Potential energy of Yang-Mills vortices in three and four dimensions: We calculate the energy of a Yang-Mills vortex as function of its magnetic
flux or, else, of the Wilson loop surrounding the vortex center. The
calculation is performed in the 1-loop approximation. A parallel with a
potential as function of the Polyakov line at nonzero temperatures is drawn. We
find that quantized Z(2) vortices are dynamically preferred though vortices
with arbitrary fluxes cannot be ruled out. |
Global strings in five-dimensional supergravity: We show the existence of solitonic solutions of five-dimensional
supergravity, which can be interpreted as global cosmic strings in our
universe. They possess the same mathematical structure as the stringy cosmic
strings studied by Greene, Shapere, Vafa and Yau, while the size of the extra
space and the value of the extra-space component of the gauge field vary from
place to place around the string in our model. We also show that supersymmetry
is partially broken in the presence of the global strings. | Instantons and Berry's connections on quantum graph: In this paper, we study non-Abelian Berry's connections in the parameter
space of boundary conditions for Dirac zero modes on quantum graphs. We apply
the ADHM construction, which is the method for constructing Yang-Mills
instanton solutions, to the Berry's connections. Then we find that the
instanton configurations appear as the Berry's connections. |
Supersymmetry and Euler Multiplets: Some massless supermultiplets appear as the trivial solution of Kostant's
equation, a Dirac-like equation over special cosets. We study two examples; one
over the coset SU(3)/SU(2) times U(1) contains the N=2 hypermultiplet in (3+1)
dimensions with U(1) as helicity; the other over the coset F_4/SO(9) describes
the N=1 supermultiplet in eleven dimensions, where SO(9) is the light-cone
little group. We present the general solutions to Kostant's equation for both
cases; they describe massless physical states of arbitrary spins which display
the same relations as the fields in the supermultiplets. They come in sets of
three representations called Euler triplets, but do not display supersymmetry
although the number of bosons and fermions is the same when spin-statistics is
satisfied. We build the free light-cone Lagrangian for both cases. | Maximal Subgroups of the Coxeter Group $W(H_4)$ and Quaternions: The largest finite subgroup of O(4) is the noncrystallographic Coxeter group
$W(H_{4})$ of order 14400. Its derived subgroup is the largest finite subgroup
$W(H_{4})/Z_{2}$ of SO(4) of order 7200. Moreover, up to conjugacy, it has five
non-normal maximal subgroups of orders 144, two 240, 400 and 576. Two groups $[
W(H_{2})\times W(H_{2})] \times Z_{4}$ and $W(H_{3})\times Z_{2}$ possess
noncrystallographic structures with orders 400 and 240 respectively. The groups
of orders 144, 240 and 576 are the extensions of the Weyl groups of the root
systems of $SU(3)\times SU(3)$%, SU(5) and SO(8) respectively. We represent the
maximal subgroups of $% W(H_{4})$ with sets of quaternion pairs acting on the
quaternionic root systems. |
Is there supersymmetric Lee-Yang fixed point in three dimensions?: The supersymmetric Lee-Yang model is arguably the simplest interacting
supersymmetric field theory in two dimensions, albeit non-unitary. A natural
question is if there is an analogue of supersymmetric Lee-Yang fixed point in
higher dimensions. The absence of any $\mathbb{Z}_2$ symmetry (except for
fermion numbers) makes it impossible to approach it by using perturbative
$\epsilon$ expansions. We find that the truncated conformal bootstrap suggests
that candidate fixed points obtained by the dimensional continuation from two
dimensions annihilate below three dimensions, implying that there is no
supersymmetric Lee-Yang fixed point in three dimensions. We conjecture that the
corresponding phase transition, if any, will be the first order transition. | Extremal Black Brane Attractors on The Elliptic Curve: Reconsidering the analysis of the moduli space of N=2 eight dimensional
supergravity coupled to seven scalars, we propose a new scalar manifold
factorization given by \frac{\textsc {SO(2,2)}}{{\textsc{SO(2)}}\times
{\textsc{SO(2)}}}\times \frac{\textsc{SO(2,1)}}{\textsc{SO(2)}}\times \textsc
{SO(1,1)}. This factorization is supported by the appearance of three solutions
of Type IIA extremal black p-branes (p=0,1,2) with AdS_{p+2}\times S^{6-p}
near-horizon geometries in eight dimensions. We analyze the corresponding
attractor mechanism. In particular, we give an interplay between the scalar
manifold factors and the extremal black p-brane charges. Then we show that the
dilaton can be stabilized by the dyonic black 2-brane charges. |
Scalarization-like mechanism through spacetime anisotropic scaling
symmetry: We present a new family of exact black hole configurations, which is a
solution to a generalized Einstein-Maxwell-Dilaton setup in arbitrary
dimension. These solutions are asymptotically Lifshitz for any dynamical
critical exponent $z\geq 1$. It turns out that the existence of a nontrivial
scalar field is a direct consequence of breaking the spacetime isotropic
scaling symmetry. This black hole family accepts various interesting limits
that link it to well-known solutions in both the isotropic and anisotropic
cases. We study the thermodynamics of these field configurations showing that
the first law is satisfied and providing the corresponding Smarr formula, both
of these relations account for an electric contribution. Furthermore, we show
that for a certain parameter region, the anisotropic field configuration with a
nonzero scalar field is thermodynamically preferred. This observation, together
with a direct verification of the so-called scalarization conditions, suggest
that the emergence of the dilaton field is due to a mechanism similar to
spontaneous scalarization. | Interaction energy of Chern-Simons vortices in the gauged O(3) sigma
model: The purpose of this Letter is to present a computation of the interaction
energy of gauged O(3) Chern-Simons vortices which are infinitely separated. The
results will show the behaviour of the interaction energy as a function of the
constant coupling the potential, which measures the relative strength of the
matter self-coupling and the electromagnetic coupling. We find that vortices
attract each other for $\lambda > 1 $ and repel when $\lambda < 1 $. When
$\lambda =1 $ there is a topological lower bound on the energy. It is possible
to saturate the bound if the fields satisfy a set of first order partial
differential equations. |
Noncommutative correction to the entropy of BTZ black hole with GUP: We investigate the effect of noncommutativity and quantum corrections to the
temperature and entropy of a BTZ black hole based on a Lorentzian distribution
with the generalized uncertainty principle (GUP). To determine the Hawking
radiation in the tunneling formalism we apply the Hamilton-Jacobi method by
using the Wentzel-Kramers-Brillouin (WKB) approach. In the present study we
have obtained logarithmic corrections to entropy due to the effect of
noncommutativity and GUP. We also address the issue concerning stability of the
non-commutative BTZ black hole by investigating its modified specific heat
capacity. | Towards higher-N superextensions of Born-Infeld theory: We give a brief account of supersymmetric Born-Infeld theories with extended
supersymmetry, including those with partially broken supersymmetry. Some latest
developments in this area are presented. One of them is N=3 supersymmetric
Born-Infeld theory which admits a natural off-shell formulation in N=3 harmonic
superspace. |
An approach to BPS black hole microstate counting in an N=2 STU model: We consider four-dimensional dyonic single-center BPS black holes in the
$N=2$ STU model of Sen and Vafa. By working in a region of moduli space where
the real part of two of the three complex scalars $S, T, U$ are taken to be
large, we evaluate the quantum entropy function for these BPS black holes. In
this regime, the subleading corrections point to a microstate counting formula
partly based on a Siegel modular form of weight two. This is supplemented by
another modular object that takes into account the dependence on $Y^0$, a
complex scalar field belonging to one of the four off-shell vector multiplets
of the underlying supergravity theory. We also observe interesting connections
to the rational Calogero model and to formal deformation of a Poisson algebra,
and suggest a string web picture of our counting proposal. | From static to Vaidya solutions in scalar tensor theories: We consider some classes of Horndeski theories in four dimensions for which a
certain combination of the Einstein equations within a spherical ansatz splits
into two distinct branches. Recently, for these theories, some integrability
and compatibility conditions have been established which have made it possible
to obtain black hole solutions depending on a single integration constant
identified as the mass. Here, we will show that these compatibility conditions
can be generalized to accommodate a time dependence by promoting the constant
mass to an arbitrary function of the retarded (advanced) time. As a direct
consequence, we prove that all the static black hole solutions can be naturally
promoted to non static Vaidya-like solutions. We extend this study in arbitrary
higher dimensions where the pure gravity part is now described by the Lovelock
theory and, where the scalar field action enjoyed the conformal invariance. For
these theories, the splitting in two branches is also effective, and we show
that their known static black hole solutions can as well be promoted to
Vaidya-like solutions. |
Singularity-free model of electrically charged fermionic particles and
gauged Q-balls: We propose a model of an electrically charged fermion as a regular localized
solution of electromagnetic and spinor fields interacting with a physical
vacuum, which is phenomenologically described as a logarithmic superfluid. We
analytically study the asymptotic behavior of the solution, while obtaining its
form by numerical methods. The solution has physically plausible properties,
such as finite size, self-energy, total charge and mass. In the case of
spherical symmetry, its electric field obeys the Coulomb asymptotics at large
distances from its core. It is shown that the observable rest mass of the
fermion arises as a result of interaction of the fields with the physical
vacuum. The spinor and scalar field components of the solution decay
exponentially outside the core; therefore they can be regarded as internal
degrees of freedom which can only be probed at sufficiently large scales of
energy and momentum. Apart from conventional Fermi particles, our model can
find applications in a theory of exotic localized objects, such as U(1) gauged
Q-balls with half-integer spin. | Introductory Lectures on Quantum Field Theory: In these lectures we present a few topics in Quantum Field Theory in detail.
Some of them are conceptual and some more practical. They have been selected
because they appear frequently in current applications to Particle Physics and
String Theory. |
Centrally extended symmetry algebra of asymptotically Goedel spacetimes: We define an asymptotic symmetry algebra for three-dimensional Goedel
spacetimes supported by a gauge field which turns out to be the semi-direct sum
of the diffeomorphisms on the circle with two loop algebras. A class of fields
admitting this asymptotic symmetry algebra and leading to well-defined
conserved charges is found. The covariant Poisson bracket of the conserved
charges is then shown to be centrally extended to the semi-direct sum of a
Virasoro algebra and two affine algebras. | Tachyonic Kink and Lump-like Solutions in Superstring Field Theory: We construct a kink solution on a non-BPS D-brane using Berkovits'
formulation of superstring field theory in the level truncation scheme. The
tension of the kink reproduces 95% of the expected BPS D-brane tension. We also
find a lump-like solution which is interpreted as a kink--antikink pair, and
investigate some of its properties. These results may be considered as
successful tests of Berkovits' superstring field theory combined with the
modified level truncation scheme. |
Transport Properties of Solitons: We calculate in this article the transport coefficients which characterize
the dynamics of solitons in quantum field theory using the methods of
dissipative quantum systems. We show how the damping and diffusion coefficients
of soliton-like excitations can be calculated using the integral functional
formalism. The model obtained in this article has new features which cannot be
obtained in the standard models of dissipation in quantum mechanics. | AKSZ-BV Formalism and Courant Algebroid-induced Topological Field
Theories: We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz-
Zaboronsky superfield formalism using the language of graded manifolds. As a
main illustarting example, to every Courant algebroid structure we associate
canonically a three-dimensional topological sigma-model. Using the AKSZ
formalism, we construct the Batalin-Vilkovisky master action for the model. |
Higher N-point Amplitudes in Open Superstring Theory: In this work we report on recent progress in the calculation of open
superstring scattering amplitudes, at tree level, with more than four external
massless states. We also report on the corresponding terms in the low energy
effective lagrangian. | Run-away solutions in relativistic spin 1/2 quantum electrodynamics: The existence of run-away solutions in classical and non-relativistic quantum
electrodynamics is reviewed. It is shown that the less singular high energy
behavior of relativistic spin 1/2 quantum electrodynamics precludes an
analogous behavior in that theory. However, a Landau-like anomalous pole in the
photon propagation function or in the electron-massive photon foward scattering
amplitude would generate a new run-away, characterized by an energy scale omega
~ m_e exp (1/alpha). This contrasts with the energy scale omega ~ (m_e/alpha)
associated with the classical and non-relativistic quantum run-aways. |
Bosonic vacuum wave functions from the BCS-type wave function of the
ground state of the massless Thirring model: A BCS-type wave function describes the ground state of the massless Thirring
model in the chirally broken phase. The massless Thirring model with fermion
fields quantized in the chirally broken phase bosonizes to the quantum field
theory of the free massless (pseudo)scalar field (Eur. Phys. J. C20, 723
(2001)). The wave functions of the ground state of the free massless
(pseudo)scalar field are obtained from the BCS-type wave function by averaging
over quantum fluctuations of the Thirring fermion fields. We show that these
wave functions are orthogonal, normalized and non-invariant under shifts of the
massless (pseudo)scalar field. This testifies the spontaneous breaking of the
field-shift symmetry in the quantum field theory of a free massless
(pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude
calculated for the bosonized BCS-type wave functions coincides with the
generating functional of Green functions defined only by the contribution of
vibrational modes (Eur. Phys. J. C 24, 653 (2002)) . This confirms the
assumption that the bosonized BCS-type wave function is defined by the
collective zero-mode (hep-th/0212226). We argue that the obtained result is not
a counterexample to the Mermin-Wagner-Hohenberg and Coleman theorems. | Construction of New D=3, N=4 Quiver Gauge Theories: In this paper we propose a special class of 3-algebras, called
double-symplectic 3-algebras. We further show that a consistent contraction of
the double-symplectic 3-algebra gives a new 3-algebra, called an N=4
three-algebra, which is then identified as the exact gauged three-algebra in
the N=4 quiver gauge theories. A systematic construction is proposed for the
3-brackets and fundamental identities used in building up the N=4 theories, by
starting with two superalgebras whose bosonic parts share at least one simple
factor or U(1) factor. This leads to a systematic way of constructing D=3, N=4
quiver theories, of which several examples with new gauge groups are presented
in detail. The general N=4 superconformal Chern-Simons matter theories in terms
of ordinary Lie algebras can be also re-derived in our new 3-algebra approach. |
Virasoro Characters from Bethe Equations for the Critical Ferromagnetic
Three-State Potts Model: We obtain new fermionic sum representations for the Virasoro characters of
the confromal field theory describing the ferromagnetic three-state Potts spin
chain. These arise from the fermionic quasi-particle excitations derived from
the Bethe equations for the eigenvalues of the hamiltonian. In the conformal
scaling limit, the Bethe equations provide a description of the spectrum in
terms of one genuine quasi-particle, and two ``ghost'' excitations with a
limited microscopic momentum range. This description is reflected in the
structure of the character formulas, and suggests a connection with the
integrable perturbation of dimensions (2/3,2/3)$^+$ which breaks the $S_3$
symmetry of the conformal field theory down to $Z_2$. | Possible Contributions to the Bulk Casimir Energy in Heterotic M-theory: Some possible ways for the study of the contributions of some background
fields to the bulk Casimir energy have been probed in the framework of the 5D
heterotic M-theory. |
On-Shell Electric-Magnetic Duality and the Dual Graviton: Using on-shell amplitude methods, we explore 4-dimensional Electric-Magnetic
duality and its double copy. We show explicitly that the on-shell scattering
amplitudes know about `dual' photons (and dual gravitons), that the off-shell
photon propagator double copies to the graviton propagator and that the
magnetic part of the propagator is essential for the double copy to hold. We
also show that there is an equivalent gravito-magnetic part of the graviton
propagator which is essential in giving rise to solutions with either angular
momentum or NUT charge. Furthermore, we comment on the so-called Weinberg
paradox, which states that scattering amplitudes involving the mixing of
electric and magnetic monopoles cannot be Lorentz invariant, and would seem to
preclude the existence of the 't Hooft-Polyakov (topological) monopole. We
trace this paradox to the magnetic part of the propagator, showing that it can
be eliminated if one restricts to proper orthochronous Lorentz transformations.
Finally, we compute the fully relativistic cross-section for arbitrary spin
dyons using the recently formulated on-shell duality transformation and show
that this is always fully Lorentz invariant. | Renormalisability of the matter determinants in noncommutative gauge
theory in the enveloping-algebra formalism: We consider noncommutative gauge theory defined by means of Seiberg-Witten
maps for an arbitrary semisimple gauge group. We compute the one-loop UV
divergent matter contributions to the gauge field effective action to all
orders in the noncommutative parameters $\theta$. We do this for Dirac fermions
and complex scalars carrying arbitrary representations of the gauge group. We
use path-integral methods in the framework of dimensional regularisation and
consider arbitrary invertible Seiberg-Witten maps that are linear in the matter
fields. Surprisingly, it turns out that the UV divergent parts of the matter
contributions are proportional to the noncommutative Yang-Mills action where
traces are taken over the representation of the matter fields; this result
supports the need to include such traces in the classical action of the gauge
sector of the noncommutative theory. |
Path Integral for the Dirac Equation: A path integral representation is given for the solutions of the 3+1
dimensional Dirac equation. The regularity of the trajectories, the
non-relativistic limit and the semiclassical approximation are briefly
mentioned. | Holographic Aspects of Non-minimal $RF^{(a)}_{μα}F^{(a)μ
α} $ Black Brane: In this paper, we consider Einstein-Hilbert gravity in the presence of
cosmological constant and an electric field of Yang-Mills type, which is
minimally coupled to gravity. We couple the Ricci scalar to the Yang-Mills
invariant to obtain a modified theory of gravity. The black brane solution of
this model is introduced up to the first order of the $RF^{(a)}_{\mu \alpha
}F^{(a)\mu \alpha} $ term. Then, the color non-abelian direct current (DC)
conductivity and the ratio of shear viscosity to entropy density are calculated
for this solution. Our results recover the Yang-Mills Schwarzschild AdS black
brane in the limit of $q_2 \to 0$. |
Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma
models: We conjecture that a non-flat $D$-real-dimensional compact Calabi-Yau
manifold, such as a quintic hypersurface with D=6, or a K3 manifold with D=4,
has locally length minimizing closed geodesics, and that the number of these
with length less than L grows asymptotically as L^{D}. We also outline the
physical arguments behind this conjecture, which involve the claim that all
states in a nonlinear sigma model can be identified as "momentum" and "winding"
states in the large volume limit. | A Specific N = 2 Supersymmetric Quantum Mechanical Model: Supervariable
Approach: By exploiting the supersymmetric invariant restrictions on the chiral and
anti-chiral supervariables, we derive the off-shell nilpotent symmetry
transformations for a specific (0 + 1)-dimensional N = 2 supersymmetric quantum
mechanical model which is considered on a (1, 2)-dimensional supermanifold
(parametrized by a bosonic variable t and a pair of Grassmannian variables
(\theta, \bar\theta). We also provide the geometrical meaning to the symmetry
transformations. Finally, we show that this specific N = 2 SUSY quantum
mechanical model is a model for Hodge theory. |
Supergravity flows and D-brane stability: We investigate the correspondence between existence/stability of BPS states
in type II string theory compactified on a Calabi-Yau manifold and BPS
solutions of four dimensional N=2 supergravity. Some paradoxes emerge, and we
propose a resolution by considering composite configurations. This in turn
gives a smooth effective field theory description of decay at marginal
stability. We also discuss the connection with 3-pronged strings, the Joyce
transition of special Lagrangian submanifolds, and Pi-stability. | All-Order Quantum Gravity in Two Dimensions: We derive curvature counterterms in two-dimensional gravity coupled to
conformal matter up to infinite order. By construction the higher-order action
is equivalent to a finite first-order theory with auxiliary scalar. Due to this
equivalence it shares the following remarkable properties: There is no need for
gravitational dressing of the cosmological constant, quantization is consistent
for any conformal anomaly $c$ of the coupled matter system, and if the coupled
matter system is a $c=d~$-dimensional string theory in a Euclidean background
then the effective string theory is $D=d+2~$-dimensional with Minkowski
signature $(1,D-1)$. The resulting quantum theory favours flat geometries and
suppresses both parabolic and hyperbolic singularities. |
Supersymmetry Constraints and String Theory on K3: We study supervertices in six dimensional (2,0) supergravity theories, and
derive supersymmetry non-renormalization conditions on the 4- and 6-derivative
four-point couplings of tensor multiplets. As an application, we obtain exact
non-perturbative results of such effective couplings in type IIB string theory
compactified on K3 surface, extending previous work on type II/heterotic
duality. The weak coupling limit thereof, in particular, gives certain
integrated four-point functions of half-BPS operators in the nonlinear sigma
model on K3 surface, that depend nontrivially on the moduli, and capture
worldsheet instanton contributions. | An Early Proposal of "Brane World": Here we place the TeX-typeset version of the old preprint SMC-PHYS-66 (1982),
which was published in K. Akama, "Pregeometry", in Lecture Notes in Physics,
176, Gauge Theory and Gravitation, Proceedings, Nara, 1982, edited by K.
Kikkawa, N. Nakanishi and H. Nariai, (Springer-Verlag) 267--271. In the paper,
we presented the picture that we live in a "brane world" (in the present-day
terminology) i.e. in a dynamically localized 3-brane in a higher dimensional
space. We adopt, as an example, the dynamics of the Nielsen-Olesen vortex type
in six dimensional spacetime to localize our space-time within a 3-brane. At
low energies, everything is trapped in the 3-brane, and the Einstein gravity is
induced through the fluctuations of the 3-brane. The idea is important because
it provides a way basically distinct from the "compactification" to hide the
extra dimensions which become necessary for various theoretical reasons. |
A Remark on the Geometry of Two-Dimensional Anisotropic Non-Linear
Sigma-Models: One discusses here the connection between \sigma-model gauge anomalies and
the existence of a connection with torsion that does not flatten the Ricci
tensor of the target manifold, by considering a number of non-symmetric coset
spaces. The influence of an eventual anisotropy on a certain direction of the
target manifold is also contemplated. | The Gaussian entropy of fermionic systems: We consider the entropy and decoherence in fermionic quantum systems. By
making a Gaussian Ansatz for the density operator of a collection of fermions
we study statistical 2-point correlators and express the entropy of a system
fermion in terms of these correlators. In a simple case when a set of N
thermalised environmental fermionic oscillators interacts bi-linearly with the
system fermion we can study its time dependent entropy, which also represents a
quantitative measure for decoherence. We then consider a relativistic fermionic
quantum field theory and take a mass mixing term as a simple model for the
Yukawa interaction. It turns out that even in this Gaussian approximation, the
fermionic system decoheres quite effectively, such that in a large coupling and
high temperature regime the system field approaches the temperature of the
environmental fields. |
A varying gravitational constant map in asymptotically AdS black hole
thermodynamics: We propose a sequence of steps and a generic transformation for connecting
common thermodynamic quantities considered in asymptotically anti-de Sitter
black hole thermodynamics in the bulk and those that are appropriate for CFT
thermodynamics in the boundary. We do this by constructing a "varying-$G$ map",
where $G$ is the gravitational constant, and demonstrate its usefulness by
considering various examples. | High spin baryon in hot strongly coupled plasma: We consider a strings-junction holographic model of probe baryon in the
finite-temperature supersymmetric Yang-Mills dual of the AdS-Schwarzschild
black hole background. In particular, we investigate the screening length for
high spin baryon composed of rotating N_c heavy quarks. To rotate quarks by
finite force, we put hard infrared cutoff in the bulk and give quarks finite
mass. We find that N_c microscopic strings are embedded reasonably in the bulk
geometry when they have finite angular velocity \omega, similar to the meson
case. By defining the screening length as the critical separation of quarks, we
compute the \omega dependence of the baryon screening length numerically and
obtain a reasonable result which shows that baryons with high spin dissociate
more easily. Finally, we discuss the relation between J and E^2 for baryons. |
Duality in Non-Trivially Compactified Heterotic Strings: We study the implications of duality symmetry on the analyticity properties
of the partition function as it depends upon the compactification length. In
order to obtain non-trivial compactifications, we give a physical prescription
to get the Helmholtz free energy for any heterotic string supersymmetric or
not. After proving that the free energy is always invariant under the duality
transformation $R\rightarrow \alpha^{'}/(4R)$ and getting the zero temperature
theory whose partition function corresponds to the Helmholtz potential, we show
that the self-dual point $R_{0}=\sqrt{\alpha^{'}}/2$ is a generic singularity
as the Hagedorn one. The main difference between these two critical
compactification radii is that the term producing the singularity at the
self-dual point is finite for any $R \neq R_{0}$. We see that this behavior at
$R_{0}$ actually implies a loss of degrees of freedom below that point. | Low Energy Dynamics of N=2 Supersymmetric Monopoles: It is argued that the low-energy dynamics of $k$ monopoles in N=2
supersymmetric Yang-Mills theory are determined by an N=4 supersymmetric
quantum mechanics based on the moduli space of $k$ static monople solutions.
This generalises Manton's ``geodesic approximation" for studying the low-energy
dynamics of (bosonic) BPS monopoles. We discuss some aspects of the
quantisation and in particular argue that dolbeault cohomology classes of the
moduli space are related to bound states of the full quantum field theory. |
The Superconformal Index of the E_6 SCFT: We derive an integral representation for the superconformal index of the
strongly-coupled N=2 superconformal field theory with E_6 flavor symmetry. The
explicit expression of the index allows highly non-trivial checks of
Argyres-Seiberg duality and of a class of S-dualities conjectured by Gaiotto. | On the BRST Operator Structure of the N=2 String: The BRST operator cohomology of $N=2$ $2d$ supergravity coupled to matter is
presented. Descent equations for primary superfields of the matter sector are
derived. We find one copy of the cohomology at ghost number one, two
independent copies at ghost number two, and conjecture that there is a copy at
ghost number three. The $N=2$ string has a twisted $N=4$ superconformal
symmetry generated by the $N=2$ superstress tensor, the BRST supercurrent, the
antighost superfield, and the ghost number supercurrent. |
On the problem of inflation in nonlinear multidimensional cosmological
models: We consider a multidimensional cosmological model with nonlinear quadratic
$R^2$ and quartic $R^4$ actions. As a matter source, we include a monopole form
field, D-dimensional bare cosmological constant and tensions of branes located
in fixed points. In the spirit of the Universal Extra Dimensions models, the
Standard Model fields are not localized on branes but can move in the bulk. We
define conditions which ensure the stable compactification of the internal
space in zero minimum of the effective potentials. Such effective potentials
may have rather complicated form with a number of local minima, maxima and
saddle points. Then, we investigate inflation in these models. It is shown that
$R^2$ and $R^4$ models can have up to 10 and 22 e-foldings, respectively. These
values are not sufficient to solve the homogeneity and isotropy problem but big
enough to explain the recent CMB data. Additionally, $R^4$ model can provide
conditions for eternal topological inflation. However, the main drawback of the
given inflationary models consists in a value of spectral index $n_s$ which is
less than observable now $n_s\approx 1$. For example, in the case of $R^4$
model we find $n_s \approx 0.61$. | Fuzzy Ring from M2-brane Giant Torus: We construct spinning dual M2 giant gravitons in AdS_4 x S^7, which
generically become 1/16 BPS states, and show that their world-volumes become
torii. By taking an orbifold, we obtain spinning dielectric D2-brane
configurations in AdS_4 x CP^3 dual to specific BPS operators in ABJM theory.
This reveals a novel mechanism how to give an angular momentum to a dielectric
D2-brane. We also find that when its angular momentum in the AdS_4 becomes
large, it approaches to a ring-like object. Our result might suggest an
existence of supersymmetric black rings in the AdS_4 background. We will also
discuss dual giant gravitons in AdS_4 x CP^3. |
Supersymmetric Chaplygin gas: Using a Kaluza-Klein framework, we consider a relativistic fluid whose
projection yields the supersymmetric non-relativistic Chaplygin gas introduced
by Bergner-Jackiw-Polychronakos and by Hoppe. The conserved (super)charges of
the Chaplygin gas are obtained as the projection of those arising in the
extended model. | Gauge theory, topological strings, and S-duality: We offer a derivation of the duality between the topological U(1) gauge
theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold.
This duality was conjectured recently by Iqbal, Nekrasov, Okounkov, and Vafa.
We deduce it from the S-duality of the IIB superstring. We also argue that the
mirror version of this duality relates the topological B-model on a Calabi-Yau
3-fold and a topological sector of the Type IIA Little String Theory on the
same manifold. |
Fermionic currents in AdS spacetime with compact dimensions: We derive a closed expression for the vacuum expectation value (VEV) of the
fermionic current density in a (D+1)-dimensional locally AdS spacetime with an
arbitrary number of toroidally compactified Poincare spatial dimensions and in
the presence of a constant gauge field. The latter can be formally interpreted
in terms of a magnetic flux treading the compact dimensions. In the compact
subspace, the field operator obeys quasiperiodicity conditions with arbitrary
phases. The VEV of the charge density is zero and the current density has
nonzero components along the compact dimensions only. They are periodic
functions of the magnetic flux with the period equal to the flux quantum and
tend to zero on the AdS boundary. Near the horizon, the effect of the
background gravitational field is small and the leading term in the
corresponding asymptotic expansion coincides with the VEV for a massless field
in the locally Minkowski bulk. Unlike the Minkowskian case, in the system
consisting an equal number of fermionic and scalar degrees of freedom, with
same masses, charges and phases in the periodicity conditions, the total
current density does not vanish. In these systems, the leading divergences in
the scalar and fermionic contributions on the horizon are canceled and, as a
consequence of that, the charge flux, integrated over the coordinate
perpendicular to the AdS boundary, becomes finite. We show that in odd
spacetime dimensions the fermionic fields realizing two inequivalent
representations of the Clifford algebra and having equal phases in the
periodicity conditions give the same contribution to the VEV of the current
density. Combining the contributions from these fields, the current density in
odd-dimensional C-,P- and T -symmetric models are obtained. As an application,
we consider the ground state current density in curved carbon nanotubes. | Five-loop renormalization-group expansions for two-dimensional Euclidean
λφ^4 theory: The renormalization-group functions of the two-dimensional n-vector \lambda
\phi^4 model are calculated in the five-loop approximation. Perturbative series
for the \beta-function and critical exponents are resummed by the
Pade-Borel-Leroy techniques. An account for the five-loop term shifts the
Wilson fixed point location only briefly, leaving it outside the segment formed
by the results of the lattice calculations. This is argued to reflect the
influence of the non-analytical contribution to the \beta-function. The
evaluation of the critical exponents for n = 1, n = 0 and n = -1 in the
five-loop approximation and comparison of the results with known exact values
confirm the conclusion that non-analytical contributions are visible in two
dimensions. For the 2D Ising model, the estimate \omega = 1.31 for the
correction-to-scaling exponent is found. |
Neveu-Schwarz Five-Branes at Orbifold Singularities and Holography: We consider Type IIB Neveu-Schwarz five-branes transverse to C^2/Z_n
orbifolds and conjecture that string theory on the near horizon geometry is
dual to the decoupled theory on the branes. We analyze the conformal field
theory describing the near horizon region and the world volume non-critical
string theory. The modular invariance consistency condition of string theory is
exactly reproduced as the gauge anomaly cancellation condition in the little
string theories. We comment on aspects of the holographic nature of this
duality. | Gravitational lensing and shadow of charged black holes in the
low-energy limit of string theory: In this work, we investigate the shadow cast and strong field gravitational
lensing of a new class of black hole solutions in dilaton gravity where dilaton
field is coupled with nonlinear Maxwell invariant [Younesizadeh et al. in Int J
Mod Phys A 34(35):1950239]. The space-time is a stationary axisymmetric
geometry. The key part in our investigations is finding the effect of dilaton
parameter N on the size of shadows and the energy emission rate. As the N
parameter increases, the size of black hole shadow increases. Also, the energy
emission rate increases with increase in the dilaton parameter N. By supposing
the gravitational field of the supermassive object at the heart of Milky Way
galaxy described by this metric, we estimated the numerical values of the
observables for gravitational lensing in the strong field limit. |
The Momentum Amplituhedron: In this paper we define a new object, the momentum amplituhedron, which is
the long sought-after positive geometry for tree-level scattering amplitudes in
$\mathcal{N}=4$ super Yang-Mills theory in spinor helicity space. Inspired by
the construction of the ordinary amplituhedron, we introduce bosonized spinor
helicity variables to represent our external kinematical data, and restrict
them to a particular positive region. The momentum amplituhedron
$\mathcal{M}_{n,k}$ is then the image of the positive Grassmannian via a map
determined by such kinematics. The scattering amplitudes are extracted from the
canonical form with logarithmic singularities on the boundaries of this
geometry. | Summing the Instantons in Half-Twisted Linear Sigma Models: We study half-twisted linear sigma models relevant to (0,2) compactifications
of the heterotic string. Focusing on theories with a (2,2) locus, we examine
the linear model parameter space and the dependence of genus zero half-twisted
correlators on these parameters. We show that in a class of theories the
correlators and parameters separate into A and B types, present techniques to
compute the dependence, and apply these to some examples. These results should
bear on the mathematics of (0,2) mirror symmetry and the physics of the moduli
space and Yukawa couplings in heterotic compactifications. |
Twisted sectors from plane partitions: Twisted sectors arise naturally in the bosonic higher spin CFTs at their free
points, as well as in the associated symmetric orbifolds. We identify the coset
representations of the twisted sector states using the description of W_\infty
representations in terms of plane partitions. We confirm these proposals by a
microscopic null-vector analysis, and by matching the excitation spectrum of
these representations with the orbifold prediction. | Gluing II: Boundary Localization and Gluing Formulas: We describe applications of the gluing formalism discussed in the companion
paper. When a $d$-dimensional local theory $\text{QFT}_d$ is supersymmetric,
and if we can find a supersymmetric polarization for $\text{QFT}_d$ quantized
on a $(d-1)$-manifold $W$, gluing along $W$ is described by a non-local
$\text{QFT}_{d-1}$ that has an induced supersymmetry. Applying supersymmetric
localization to $\text{QFT}_{d-1}$, which we refer to as the boundary
localization, allows in some cases to represent gluing by finite-dimensional
integrals over appropriate spaces of supersymmetric boundary conditions. We
follow this strategy to derive a number of `gluing formulas' in various
dimensions, some of which are new and some of which have been previously
conjectured. First we show how gluing in supersymmetric quantum mechanics can
reduce to a sum over a finite set of boundary conditions. Then we derive two
gluing formulas for 3D $\mathcal{N}=4$ theories on spheres: one providing the
Coulomb branch representation of gluing, and another providing the Higgs branch
representation. This allows to study various properties of their
$(2,2)$-preserving boundary conditions in relation to Mirror Symmetry. After
that we derive a gluing formula in 4D $\mathcal{N}=2$ theories on spheres, both
squashed and round. First we apply it to predict the hemisphere partition
function, then we apply it to the study of boundary conditions and domain walls
in these theories. Finally, we mention how to glue half-indices of 4D
$\mathcal{N}=2$ theories. |
Classical Theorems in Noncommutative Quantum Field Theory: Classical results of the axiomatic quantum field theory - Reeh and
Schlieder's theorems, irreducibility of the set of field operators and
generalized Haag's theorem are proven in SO(1,1) invariant quantum field
theory, of which an important example is noncommutative quantum field theory.
In SO(1,3) invariant theory new consequences of generalized Haag's theorem are
obtained. It has been proven that the equality of four-point Wightman functions
in two theories leads to the equality of elastic scattering amplitudes and thus
the total cross-sections in these theories. | Generalizations of normal ordering and applications to quantization in
classical backgrounds: A nonlocal method of extracting the positive (or the negative) frequency part
of a field, based on knowledge of a 2-point function, leads to certain natural
generalizations of the normal ordering of quantum fields in classical
gravitational and electromagnetic backgrounds and illuminates the origin of the
recently discovered nonlocalities related to a local description of particles.
A local description of particle creation by gravitational backgrounds is given,
with emphasis on the case of black-hole evaporation. The formalism reveals a
previously hidden relation between various definitions of the particle current
and those of the energy-momentum tensor. The implications to particle creation
by classical backgrounds, as well as to the relation between vacuum energy,
dark matter, and cosmological constant, are discussed. |
Tensor supercurrent in QCD: An external Abelian magnetic field excites in the QCD vacuum a tensor
supercurrent that represents the tensor polarization of the chiral condensate.
This tensor supercurrent can be deduced from the chiral lagrangian in the
presence of anomalies; a similar tensor supercurrent emerges in rotating
systems at finite chemical potential. We discuss the microscopic origin of this
supercurrent and argue that it screens the instanton--anti-instanton $I\bar{I}$
molecules in the QCD vacuum, similarly to the vector supercurrent screening
Abrikosov vortices in a superconductor. A number of possible experimental
manifestations of the tensor supercurrent are discussed: {\it i}) spin
alignment of axial-vector and vector mesons in heavy ion collisions; {\it ii})
tensor charge of the nucleon; {\it iii}) transversity of quark distributions in
polarized nucleons. | Three-Dimensional Extended Bargmann Supergravity: We show that three-dimensional General Relativity, augmented with two vector
fields, allows for a non-relativistic limit, different from the standard limit
leading to Newtonian gravity, that results into a well-defined action which is
of the Chern-Simons type. We show that this three-dimensional `Extended
Bargmann Gravity', after coupling to matter, leads to equations of motion
allowing a wider class of background geometries than the ones that one
encounters in Newtonian gravity. We give the supersymmetric generalization of
these results and point out an important application in the context of
calculating partition functions of non-relativistic field theories using
localization techniques. |
More about F-term uplifting: We study moduli stabilization and a realization of de Sitter vacua in
generalized F-term uplifting scenarios of the KKLT-type anti-de Sitter vacuum,
where the uplifting sector X directly couples to the light K\"ahler modulus T
in the superpotential through, e.g., stringy instanton effects. F-term
uplifting can be achieved by a spontaneous supersymmetry breaking sector, e.g.,
the Polonyi model, the O'Raifeartaigh model and the Intriligator-Seiberg-Shih
model. Several models with the X-T mixing are examined and qualitative features
in most models {\it even with such mixing} are almost the same as those in the
KKLT scenario. One of the quantitative changes, which are relevant to the
phenomenology, is a larger hierarchy between the modulus mass m_T and the
gravitino mass $m_{3/2}$, i.e., $m_T/m_{3/2} = {\cal O}(a^2)$, where $a \sim 4
\pi^2$. In spite of such a large mass, the modulus F-term is suppressed not
like $F^T = {\cal O}(m_{3/2}/a^2)$, but like $F^T = {\cal O}(m_{3/2}/a)$ for
$\ln (M_{Pl}/m_{3/2}) \sim a$, because of an enhancement factor coming from the
X-T mixing. Then we typically find a mirage-mediation pattern of gaugino masses
of ${\cal O}(m_{3/2}/a)$, while the scalar masses would be generically of
${\cal O}(m_{3/2})$. | Non-Volkov solutions for a charge in a plane wave: We focus our attention, once again, on the Klein--Gordon and Dirac equations
with a plane-wave field. We recall that for the first time a set of solutions
of these equations was found by Volkov. The Volkov solutions are widely used in
calculations of quantum effects with electrons and other elementary particles
in laser beams. We demonstrate that one can construct sets of solutions which
differ from the Volkov solutions and which may be useful in physical
applications. For this purpose, we show that the transversal charge motion in a
plane wave can be mapped by a special transformation to transversal free
particle motion. This allows us to find new sets of solutions where the
transversal motion is characterized by quantum numbers different from Volkov's
(in the Volkov solutions this motion is characterized by the transversal
momentum). In particular, we construct solutions with semiclassical transversal
charge motion (transversal squeezed coherent states). In addition, we
demonstrate how the plane-wave field can be eliminated from the transversal
charge motion in a more complicated case of the so-called combined
electromagnetic field (a combination of a plane-wave field and constant
colinear electric and magnetic fields). Thus, we find new sets of solutions of
the Klein--Gordon and Dirac equations with the combined electromagnetic field. |
Exact beta function and glueball spectrum in large-N Yang Mills theory: In the pure large-N Yang-Mills theory there is a quasi-BPS sector that is
exactly solvable at large N. It follows an exact beta function and the glueball
spectrum in this sector. The main technical tool is a new holomorphic loop
equation for quasi-BPS Wilson loops, that occurs as a non-supersymmetric
analogue of Dijkgraaf-Vafa holomorphic loop equation for the glueball
superpotential of n=1 SUSY gauge theories. The new holomorphic loop equation is
localized, i.e. reduced to a critical equation, by a deformation of the loop
that is a vanishing boundary in homology, somehow in analogy with Witten's
cohomological localization by a coboundary deformation in SUSY gauge theories. | Brane Descent Relations in K-theory: The various descent and duality relations among BPS and non-BPS D-branes are
classified using topological K-theory. It is shown how the descent procedures
for producing type-II D-branes from brane-antibrane bound states by tachyon
condensation and $\klein$ projections arise as natural homomorphisms of
K-groups generating the brane charges. The transformations are generalized to
type-I theories and type-II orientifolds, from which the complete set of vacuum
manifolds and field contents for tachyon condensation is deduced. A new set of
internal descent relations is found which describes branes over orientifold
planes as topological defects in the worldvolumes of brane-antibrane pairs on
top of planes of higher dimension. The periodicity properties of these
relations are shown to be a consequence of the fact that all fundamental bound
state constructions and hence the complete spectrum of brane charges are
associated with the topological solitons which classify the four Hopf
fibrations. |
Equivalence between light-cone and conformal gauge in the
two-dimensional string: Aiming towards understanding the question of the discrete states in the
light-cone gauge in the theory of two-dimensional strings with a linear
background charge term, we study the path-integral formulation of the theory.
In particular, by gauge fixing Polyakov's path-integral expression for the 2-d
strings, we show that the light-cone gauge-fixed generating functional is the
same as the conformal gauge-fixed one and is critical for the same value of the
background charge (Q=2 $\sqrt 2 $). Since the equivalence is shown at the
generating functional level, one expects that the spectra of the two theories
are the same. The zero modes of the ratio of the determinants are briefly
analyzed and it is shown that only the constant mode survives in this
formulation. This is an indication that the discrete states may lie in these
zero modes. This result is not particular to the light-cone gauge, but it holds
for the conformal gauge as well. | The Wheeler Propagator: We study the half advanced and half retarded Wheeler Green function and its
relation to Feynman propagators. First for massless equation. Then, for
Klein-Gordon equations with arbitrary mass parameters; real, imaginary or
complex. In all cases the Wheeler propagator lacks an on-shell free
propagation. The Wheeler function has support inside the light-cone (whatever
the mass). The associated vacuum is symmetric with respect to annihilation and
creation operators.
We show with some examples that perturbative unitarity holds, whatever the
mass (real or complex). Some possible applications are discussed. |
Note About Non-BPS and BPS Dp-branes in Near Horizon Region of N
Dk-Branes: In this paper we will consider the dynamics of BPS and non-BPS Dp-branes in
the background of N Dk-branes. Our approach is based on an existence of the new
symmetry of D-brane effective actions that naturally emerges in the near
horizon region of the stack of N Dk-branes. Since generally this scaling
symmetry is explicitly broken in the Lagrangian we will find the equation that
determines the time evolution of the generator of this transformations. Then we
will argue that in case when the tachyon living on the worldvolume of unstable
D-brane reaches the stable minimum the time evolution of this generator can be
easily determined. With the help of the knowledge of the time dependence of
this charge we will determine the trajectory of the non-BPS D-brane in the near
horizon region of N Dk-branes. In case of BPS Dp-brane probe we will aruge that
such a broken scaling symmetry exists as well and the existence of the explicit
time dependence of the generator of this symmetry can be used in the solving
the equation of motion of the probe Dp-brane in the near horizon region of N
Dk-branes. | Consistent sphere reductions of gravity to two dimensions: Consistent reductions of higher-dimensional (matter-coupled) gravity theories
on spheres have been constructed and classified in an important paper by
Cveti\v{c}, L\"u and Pope. We close a gap in the classification and study the
case when the resulting lower-dimensional theory is two-dimensional. We
construct the consistent reduction of Einstein-Maxwell-dilaton gravity on a
$d$-sphere $S^d$ to two-dimensional dilaton-gravity coupled to a gauged sigma
model with target space ${\rm SL}(d+1)/{\rm SO}(d+1)$. The truncation contains
solutions of type AdS$_2\times \Sigma_d$ where the internal space $\Sigma_d$ is
a deformed sphere. In particular, the construction includes the consistent
truncation around the near-horizon geometry of the boosted Kerr string. In
turn, we find that an AdS$_2\times S^d$ background with the round $S^d$ within
a consistent truncation requires $d>3$ and an additional cosmological term in
the higher-dimensional theory. |
Circuit Complexity in an interacting quenched Quantum Field Theory: In this work, we explore the effects of a quantum quench on the circuit
complexity for a quenched quantum field theory having weakly coupled quartic
interaction. We use the invariant operator method, under a perturbative
framework, for computing the ground state of this system}. We give the
analytical expressions for specific reference and target states using the
ground state of the system. Using a particular cost functional, we show the
analytical computation of circuit complexity for the quenched and interacting
field theory. Further, we give a numerical estimate of circuit complexity with
respect to the quench rate, $\delta t$ for two coupled oscillators. The
parametric variation of the unambiguous contribution of the circuit complexity
for an arbitrary number of oscillators has been studied with respect to the
dimensionless parameter $(t/\delta t$). We comment on the variation of circuit
complexity for different values of coupling strength, different number of
oscillators, and even in different dimensions. | $KBc$ algebra and the gauge invariant overlap in open string field
theory: We study in detail the evaluation of the gauge invariant overlap for analytic
solutions constructed out of elements in the $KBc$ algebra in open string field
theory. We compute this gauge invariant observable using analytical and
numerical techniques based on the sliver frame $\mathcal{L}_0$ and traditional
Virasoro $L_0$ level expansions of the solutions. |
Heterotic geometry without isometries: We present some properties of hyperkahler torsion (or heterotic) geometry in
four dimensions that make it even more tractable than its hyperkahler
counterpart. We show that in $d=4$ hypercomplex structures and weak torsion
hyperkahler geometries are the same. We present two equivalent formalisms
describing such spaces, they are stated in the propositions of section 1. The
first is reduced to solve a non-linear system for a doublet of potential
functions, first found by Plebanski and Finley. The second is equivalent to
finding the solutions of a quadratic Ashtekar-Jacobson-Smolin like system, but
without a volume preserving condition. This is why heterotic spaces are simpler
than usual hyperkahler ones. We also analyze the strong version of this
geometry. Certain examples are presented, some of them are metrics of the
Callan-Harvey-Strominger type and others are not. In the conclusion we discuss
the benefits and disadvantages of both formulations in detail. | 6D F-theory models and elliptically fibered Calabi-Yau threefolds over
semi-toric base surfaces: We carry out a systematic study of a class of 6D F-theory models and
associated Calabi-Yau threefolds that are constructed using base surfaces with
a generalization of toric structure. In particular, we determine all smooth
surfaces with a structure invariant under a single C^* action (sometimes called
"T-varieties" in the mathematical literature) that can act as bases for an
elliptic fibration with section of a Calabi-Yau threefold. We identify 162,404
distinct bases, which include as a subset the previously studied set of
strictly toric bases. Calabi-Yau threefolds constructed in this fashion include
examples with previously unknown Hodge numbers. There are also bases over which
the generic elliptic fibration has a Mordell-Weil group of sections with
nonzero rank, corresponding to non-Higgsable U(1) factors in the 6D
supergravity model; this type of structure does not arise for generic elliptic
fibrations in the purely toric context. |
Infinite Distance Networks in Field Space and Charge Orbits: The Swampland Distance Conjecture proposes that approaching infinite
distances in field space an infinite tower of states becomes exponentially
light. We study this conjecture for the complex structure moduli space of
Calabi-Yau manifolds. In this context, we uncover significant structure within
the proposal by showing that there is a rich spectrum of different infinite
distance loci that can be classified by certain topological data derived from
an associated discrete symmetry. We show how this data also determines the
rules for how the different infinite distance loci can intersect and form an
infinite distance network. We study the properties of the intersections in
detail and, in particular, propose an identification of the infinite tower of
states near such intersections in terms of what we term charge orbits. These
orbits have the property that they are not completely local, but depend on data
within a finite patch around the intersection, thereby forming an initial step
towards understanding global aspects of the distance conjecture in field
spaces. Our results follow from a deep mathematical structure captured by the
so-called orbit theorems, which gives a handle on singularities in the moduli
space through mixed Hodge structures, and is related to a local notion of
mirror symmetry thereby allowing us to apply it also to the large volume
setting. These theorems are general and apply far beyond Calabi-Yau moduli
spaces, leading us to propose that similarly the infinite distance structures
we uncover are also more general. | Large-Small Equivalence in String Theory: The simplest toroidally compactified string theories exhibit a duality
between large and small radii: compactification on a circle, for example, is
invariant under R goes to 1/R. Compactification on more general Lorentzian
lattices (i.e. toroidal compactification in the presence of background metric,
antisymmetric tensor, and gauge fields) yields theories for which large-small
invariance is not so simple. Here an equivalence is demonstrated between large
and small geometries for all toroidal compactifications. By repeatedly
transforming the momentum mode corresponding to the smallest winding length to
another mode on the lattice, it is possible to increase the volume to exceed a
finite lower bound. |
Dyonic Non-Abelian Vortices: We study three-dimensional Yang-Mills-Higgs theories with and without a
Chern-Simons interaction. We find that these theories admit a rich spectrum of
vortex solitons carrying both a topological charge and a global flavour charge.
We further derive a low-energy description of the vortex dynamics from a gauged
linear sigma model on the vortex worldline. | SO(10) GUTs with large tensor representations on Noncommutative
Space-time: We construct a noncommutative version of a general renormalizable SO(10) GUT
with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and
a Peccei-Quinn symmetry. Thus, we formulate the noncommutative counterpart of a
non-supersymmetric SO(10) GUT which has recently been shown to be consistent
with all the physics below $M_{GUT}$. The simplicity of our construction --the
simplicity of the Yukawa terms, in particular-- stems from the fact that the
Higgses of our GUT can be viewed as elements of the Clifford algebra
$\mathbb{C}\rm{l}_{10}(\mathbb{C})$; elements on which the SO(10) gauge
transformations act by conjugation. The noncommutative GUT we build contains
tree-level interactions among different Higgs species that are absent in their
ordinary counterpart as they are forbidden by SO(10) and Lorentz invariance.
The existence of these interactions helps to clearly distinguish noncommutative
Minkowski space-time from ordinary Minkowski space-time. |
A non-relativistic limit of M-theory and 11-dimensional membrane
Newton-Cartan geometry: We consider a non-relativistic limit of the bosonic sector of
eleven-dimensional supergravity, leading to a theory based on a covariant
`membrane Newton-Cartan' (MNC) geometry. The local tangent space is split into
three `longitudinal' and eight `transverse' directions, related only by
Galilean rather than Lorentzian symmetries. This generalises the
ten-dimensional stringy Newton-Cartan (SNC) theory. In order to obtain a finite
limit, the field strength of the eleven-dimensional four-form is required to
obey a transverse self-duality constraint, ultimately due to the presence of
the Chern-Simons term in eleven dimensions. The finite action then gives a set
of equations that is invariant under longitudinal and transverse rotations,
Galilean boosts and local dilatations. We supplement these equations with an
extra Poisson equation, coming from the subleading action. Reduction along a
longitudinal direction gives the known SNC theory with the addition of RR gauge
fields, while reducing along a transverse direction yields a new
non-relativistic theory associated to D2 branes. We further show that the MNC
theory can be embedded in the U-duality symmetric formulation of exceptional
field theory, demonstrating that it shares the same exceptional Lie algebraic
symmetries as the relativistic supergravity, and providing an alternative
derivation of the extra Poisson equation. | Anomalous transport from equilibrium partition functions: We summarize recent advances in the application of the equilibrium partition
function formalism for the study of the transport coefficients of relativistic
fluids induced by quantum anomalies, at first and second order in the
hydrodynamic expansion. We provide results for theories with Abelian and
non-Abelian chiral fermions, and discuss some features of the corresponding
constitutive relations. |
Remarks on the 2nd order Seiberg-Witten maps: In this report, we discuss the Seiberg-Witten maps up to the second order in
the noncommutative parameter $\theta$. They add to the recently published
solutions in [1]. Expressions for the vector, fermion and Higgs fields are
given explicitly. | A Nonlocal Approach to the Cosmological Constant Problem: We construct a model in which the cosmological constant is canceled from the
gravitational equations of motion. Our model relies on two key ingredients: a
nonlocal constraint on the action, which forces the spacetime average of the
Lagrangian density to vanish, and a dynamical way for this condition to be
satisfied classically with arbitrary matter content. We implement the former
condition with a spatially-constant Lagrange multiplier associated with the
volume form and the latter by including a free four-form gauge field strength
in the action. These two features are enough to remove the cosmological
constant from the Einstein equation. The model is consistent with all
cosmological and experimental bounds on modification of gravity and allows for
both cosmic inflation and the present epoch of acceleration. |
Tower of subleading dual BMS charges: We supplement the recently found dual gravitational charges with dual charges
for the whole BMS symmetry algebra. Furthermore, we extend the dual charges
away from null infinity, defining subleading dual charges. These subleading
dual charges complement the subleading BMS charges in the literature and
together account for all the Newman-Penrose charges. | Kaluza-Klein Spectrometry from Exceptional Field Theory: Exceptional field theories yield duality-covariant formulations of
higher-dimensional supergravity. They have proven to be an efficient tool for
the construction of consistent truncations around various background
geometries. In this paper, we demonstrate how the formalism can moreover be
turned into a powerful tool for computing the Kaluza-Klein mass spectra around
these backgrounds. Most of these geometries have little to no remaining
symmetries and their spectra are accessible to standard methods only in
selected subsectors. The present formalism not only grants access to the full
Kaluza-Klein spectra but also provides the scheme to identify the resulting
mass eigenstates in higher dimensions. As a first illustration, we rederive in
compact form the mass spectrum of IIB supergravity on $S^5$. We further discuss
the application of our formalism to determine the mass spectra of higher
Kaluza-Klein multiplets around the warped geometries corresponding to some
prominent ${\cal N}=2$ and ${\cal N}=0$ AdS vacua in maximal supergravity. |
Chiral geometries of (2+1)-d AdS gravity: Pure gravity in (2+1)-dimensions with negative cosmological constant is
classically equivalent Chern-Simons gauge theory with gauge group SO(2; 2),
which may be realized on chiral and antichiral gauge connections. This paper
looks at half-AdS geometries i.e. those with a trivial rightmoving gauge
connection while the left-moving connection is a standard (Banados-Teitelboim-
Zanelli) BTZ connection. These are shown to be related by diffeomorphism to a
BTZ geometry with different mass and angular momentum. Generically this is
over-spinning, leading to a naked closed timelike curves. Other closely related
solutions are also studied. These results suggest that the measure of the
Chern-Simons path integral cannot factorize in a chiral way, if it is to
represent a sum over physically sensible states. | From the WZWN Model to the Liouville Equation: Exact String Dynamics in
Conformally Invariant AdS Background: It has been known for some time that the SL(2,R) WZWN model reduces to
Liouville theory. Here we give a direct and physical derivation of this result
based on the classical string equations of motion and the proper string size.
This allows us to extract precisely the physical effects of the metric and
antisymmetric tensor, respectively, on the {\it exact} string dynamics in the
SL(2,R) background. The general solution to the proper string size is also
found. We show that the antisymmetric tensor (corresponding to conformal
invariance) generally gives rise to repulsion, and it precisely cancels the
dominant attractive term arising from the metric.
Both the sinh-Gordon and the cosh-Gordon sectors of the string dynamics in
non-conformally invariant AdS spacetime reduce here to the Liouville equation
(with different signs of the potential), while the original Liouville sector
reduces to the free wave equation. Only the very large classical string size is
affected by the torsion. Medium and small size string behaviours are unchanged.
We also find illustrative classes of string solutions in the SL(2,R)
background: dynamical closed as well as stationary open spiralling strings, for
which the effect of torsion is somewhat like the effect of rotation in the
metric. Similarly, the string solutions in the 2+1 BH-AdS background with
torsion and angular momentum are fully analyzed. |
Anomaly and Exotic Statistics in One Dimension: We study the influence of the anomaly on the physical quantum picture of the
chiral Schwinger model (CSM) defined on $S^1$. We show that such phenomena as
the total screening of charges and the dynamical mass generation characteristic
for the standard Schwinger model do not take place here. Instead of them, the
anomaly results in the background linearly rising electric field or,
equivalently, in the exotic statistics of the physical matter field. We
construct the algebra of the Poincare generators and show that it differs from
the Poincare one. For the CSM on $R^1$, the anomaly influences only the mass
generation mechanism. | Wilson Loops in string duals of Walking and Flavored Systems: We consider the VEV of Wilson loop operators by studying the behavior of
string probes in solutions of Type IIB string theory generated by Nc D5 branes
wrapped on an internal manifold. In particular, we focus on solutions to the
background equations that are dual to field theories with a walking gauge
coupling as well as for flavored systems. We present in detail our walking
solution and emphasize various general aspects of the procedure to study Wilson
loops using string duals. We discuss the special features that the strings show
when probing the region associated with the walking of the field theory
coupling. |
Exact results on N=2 supersymmetric gauge theories: This is the introduction to the collection of review articles "Exact results
on N=2 supersymmetric gauge theories". The first three sections are intended to
give a general overview over the physical motivations behind this direction of
research, and some of the developments that initiated this project. These
sections are written for a broad audience of readers with interest in quantum
field theory, assuming only very basic knowledge of supersymmetric gauge
theories and string theory. This will be followed by a brief overview over the
different chapters collected in this volume, while the last section indicates
some related developments that we were unfortunately not able to cover. | Membrane Matrix models and non-perturbative checks of gauge/gravity
duality: We compare the bosonic and maximally supersymmetric membrane models. We find
that in Hoppe regulated form the bosonic membrane is well approximated by
massive Gaussian quantum matrix models. In contrast the similarly regulated
supersymmetric membrane, which is equivalent to the BFSS model, has a gravity
dual description. We sketch recent progress in checking gauge/gravity duality
in this context. |
Quantum mechanics of a generalised rigid body: We consider the quantum version of Arnold's generalisation of a rigid body in
classical mechanics. Thus, we quantise the motion on an arbitrary Lie group
manifold of a particle whose classical trajectories correspond to the geodesics
of any one-sided-invariant metric. We show how the derivation of the spectrum
of energy eigenstates can be simplified by making use of automorphisms of the
Lie algebra and (for groups of Type I) by methods of harmonic analysis. We show
how the method can be extended to cosets, generalising the linear rigid rotor.
As examples, we consider all connected and simply-connected Lie groups up to
dimension 3. This includes the universal cover of the archetypical rigid body,
along with a number of new exactly-solvable models. We also discuss a possible
application to the topical problem of quantising a perfect fluid. | Effective Lagrangians and Chiral Random Matrix Theory: Recently, sum rules were derived for the inverse eigenvalues of the Dirac
operator. They were obtained in two different ways: i) starting from the
low-energy effective Lagrangian and ii) starting from a random matrix theory
with the symmetries of the Dirac operator. This suggests that the effective
theory can be obtained directly from the random matrix theory. Previously, this
was shown for three or more colors with fundamental fermions. In this paper we
construct the effective theory from a random matrix theory for two colors in
the fundamental representation and for an arbitrary number of colors in the
adjoint representation. We construct a fermionic partition function for
Majorana fermions in Euclidean space time. Their reality condition is
formulated in terms of complex conjugation of the second kind. |
Ternary Virasoro - Witt Algebra: A 3-bracket variant of the Virasoro-Witt algebra is constructed through the
use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets
acting on other 3-brackets in the algebra are discussed and verified in various
situations. | Microstates of a Neutral Black Hole in M Theory: We consider vacuum solutions in M theory of the form of a five-dimensional
Kaluza-Klein black hole cross T^6. In a certain limit, these include the
five-dimensional neutral rotating black hole (cross T^6). From a IIA
standpoint, these solutions carry D0 and D6 charges. We show that there is a
weakly coupled D-brane description which precisely reproduces the
Hawking-Bekenstein entropy in the extremal limit, even though supersymmetry is
completely broken. |
Phenomenological studies in the matrix models: Matrix models are a promising candidate for a nonperturbative formulation of
the superstring theory. It is possible to study how the standard model and
other phenomenological models appear from the matrix model, and estimate the
probability distribution of their appearance. This article mainly addresses
studies in toroidal compactifications with magnetic fluxes. | Duality Invariance of the Hawking Temperature and Entropy: We consider solutions to low energy string theory which have a horizon and a
spacelike symmetry. Each of these solutions has a geometrically different dual
description. We show that the dual solution has a horizon with exactly the same
Hawking temperature (surface gravity) and entropy (area) as the original
solution. |
A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic
Structure: Starting from a one-particle quasi-exactly solvable system, which is
characterized by an intrinsic sl(2) algebraic structure and the
energy-reflection symmetry, we construct a daughter N-body Hamiltonian
presenting a deformation of the Calogero model. The features of this
Hamiltonian are (i) it reduces to a quadratic combination of the generators of
sl(N+1); (ii) the interaction potential contains two-body terms and interaction
with the force center at the origin; (iii) for quantized values of a certain
cohomology parameter n it is quasi-exactly solvable, the multiplicity of states
in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry
of the parent system is preserved. | Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory
R-flux backgrounds: We introduce a magnetic analogue of the seven-dimensional nonassociative
octonionic R-flux algebra that describes the phase space of M2-branes in
four-dimensional locally non-geometric M-theory backgrounds. We show that these
two algebras are related by a Spin(7) automorphism of the 3-algebra that
provides a covariant description of the eight-dimensional M-theory phase space.
We argue that this algebra also underlies the phase space of electrons probing
a smeared magnetic monopole in quantum gravity by showing that upon appropriate
contractions, the algebra reduces to the noncommutative algebra of a spin foam
model of three-dimensional quantum gravity, or to the nonassociative algebra of
electrons in a background of uniform magnetic charge. We realise this set-up in
M-theory as M-waves probing a delocalised Kaluza-Klein monopole, and show that
this system also has a seven-dimensional phase space. We suggest that the
smeared Kaluza-Klein monopole is non-geometric because it cannot be described
by a local metric. This is the magnetic analogue of the local non-geometry of
the R-flux background and arises because the smeared Kaluza-Klein monopole is
described by a U(1)-gerbe rather than a U(1)-fibration. |
Moduli Space Dynamics of Noncommutative U(2) Instantons: We consider the low energy dynamics of charge two instantons on
noncommutative $\mathbb{R}^{2}_{NC}\times\mathbb{R}^{2}_{NC}$ in U(2)
5-dimensional super-Yang-Mills, using the Manton approximation for slow-moving
instantons to calculate the moduli space metric. By employing the ADHM
construction, we are able to understand some aspects of the geometry and
topology of the system. We also consider the effect of adding a potential to
the moduli space, giving scattering results for noncommutative dyonic
instantons. | Giant gravitons in non-supersymmetric backgrounds: We consider giant gravitons as probes of a class of ten-dimensional solutions
of type IIB supergravity which arise as lifts of solutions of U(1)^3 gauged N=2
supergravity in five-dimensions. Surprisingly it is possible to solve exactly
for minimum energy configurations of these spherical D3-brane probes in the
compact directions, even in backgrounds which preserve no supersymmetry. The
branes behave as massive charged particles in the five non-compact dimensions.
As an example we probe geometries which are believed to represent the
supergravity background of coherent states of giant gravitons. We comment on
the apparently repulsive nature of the naked singularities in these geometries. |
The non-linear coupled spin 2 - spin 3 Cotton equation in three
dimensions: In the context of three-dimensional conformal higher spin theory we derive,
in the frame field formulation, the full non-linear spin 3 Cotton equation
coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge
theory system of equations, that is, using $F=0$ to eliminate all auxiliary
fields and thus expressing the Cotton equation in terms of just the spin 3
frame field and spin 2 covariant derivatives and tensors (Schouten). In this
derivation we neglect the spin 4 and higher spin sectors and approximate the
star product commutator by a Poisson bracket. The resulting spin 3 Cotton
equation is complicated but can be related to linearized versions in the metric
formulation obtained previously by other authors. The expected symmetry (spin 3
"translation", "Lorentz" and "dilatation") properties are verified for Cotton
and other relevant tensors but some perhaps unexpected features emerge in the
process, in particular in relation to the non-linear equations. We discuss the
structure of this non-linear spin 3 Cotton equation but its explicit form is
only presented here, in an exact but not completely refined version, in
appended files obtained by computer algebra methods. Both the frame field and
metric formulations are provided. | Properties of the Faddeev-Popov operator in the Landau gauge, matter
confinement and soft BRST breaking: In light of the development of the Gribov issue for pure Euclidean gauge
theories and of the recent lattice measurement of soft breaking of the BRST
invariance in Yang-Mills theories in the Landau gauge, we consider
non-perturbative features in the gauge-interacting matter sector and their
relation with general properties of the Faddeev-Popov operator. A signature for
BRST breaking in the matter sector is proposed and a local and renormalizable
framework is constructed, accommodating this signature and predicting
non-perturbative matter propagators that are consistent with available lattice
data for adjoint scalars and quarks. |
On Kreimer's Hopf algebra structure of Feynman graphs: We reinvestigate Kreimer's Hopf algebra structure of perturbative quantum
field theories with a special emphasis on overlapping divergences. Kreimer
first disentangles overlapping divergences into a linear combination of
disjoint and nested ones and then tackles that linear combination by the Hopf
algebra operations. We present a formulation where the Hopf algebra operations
are directly defined on any type of divergence. We explain the precise relation
to Kreimer's Hopf algebra and obtain thereby a characterization of their
primitive elements. | Power-law cosmological solution derived from DGP brane with a brane
tachyon field: By studying a tachyon field on the DGP brane model, in order to embed the 4D
standard Friedmann equation with a brane tachyon field in 5D bulk, the metric
of the 5D spacetime is presented. Then, adopting the inverse square potential
of tachyon field, we obtain an expanding universe with power-law on the brane
and an exact 5D solution. |
Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum
Electrodynamics: The critical exponent corresponding to the renormalization of the composite
operator $\bar{\psi}\psi$ is computed in quantum electrodynamics at
$O(1/\Nf^2)$ in arbitrary dimensions and covariant gauge at the non-trivial
zero of the $\beta$-function in the large $\Nf$ expansion and the exponent
corresponding to the anomalous dimension of the electron mass which is a gauge
independent object is deduced. Expanding in powers of $\epsilon$ $=$ $2$ $-$
$d/2$ we check it is consistent with the known three loop perturbative
structure and determine the subsequent coefficients in the coupling constant | CFT(4) Partition Functions and the Heat Kernel on AdS(5): We explicitly reorganise the partition function of an arbitrary CFT in four
spacetime dimensions into a heat kernel form for the dual string spectrum on
AdS(5). On very general grounds, the heat kernel answer can be expressed in
terms of a convolution of the one-particle partition function of the
four-dimensional CFT. Our methods are general and would apply for arbitrary
dimensions, which we comment on. |
Problems with Duality in N=2 Super-Yang-Mills Theory: Actual calculations of monopole and dyon spectra have previously been
performed in N=4 SYM and in N=2 SYM with gauge group SU(2), and are in total
agreement with duality conjectures for the finite theories. These calculations
are extended to N=2 SYM with higher rank gauge groups, and it turns out that
the SU(2) model with four fundamental hypermultiplet is an exception in that
its soliton spectrum supports duality. This may be an indication that the other
perturbatively finite N=2 theories have non-perturbative contributions to the
beta-function. This talk contains a short summary of recent results. | Matter-gravity coupling for fuzzy geometry and the Landau-Hall problem: We consider a set of physical degrees of freedom coupled to a
finite-dimensional Hilbert space, which may be taken as modeling a fuzzy space
or as the lowest Landau level of a Landau-Hall problem. These may be viewed as
matter fields on a fuzzy space. Sequentially generalizing to arbitrary
backgrounds, we argue that the effective action is given by the Chern-Simons
form associated with the Dirac index density (with gauge and gravitational
fields), with an abelian gauge field shifted by the Poincar\'e-Cartan form for
matter dynamics. The result is an action for matter fields where the Lagrangian
is integrated with a density which is a specific polynomial in the curvatures. |
Moyal dynamics of constraint systems: Quantization of constraint systems within the Weyl-Wigner-Groenewold-Moyal
framework is discussed. Constraint dynamics of classical and quantum systems is
reformulated using the skew-gradient projection formalism. The quantum
deformation of the Dirac bracket is generalized to match smoothly the classical
Dirac bracket in and outside of the constraint submanifold in the limit $\hbar
\to 0$. | On the origin of the holographic universe: In this work, we reexamine the holographic dark energy concept proposed
already for cosmological applications. By considering, more precisely, the
bounds on the entropy arising from lattice field theory on one side and
Bekenstein-Hawking entropy of black holes on another side, it is shown that the
so-called holographic dark energy cannot be mimicked as easily as claimed in
the literature. In addition, the limits on the electron $(g-2)$ experiments are
taken into account again. It is shown that the corrections to the electron
magnetic momentum are of the order of ${\mathcal{O}}(10^{-23})$. |
Link polynomial calculus and the AENV conjecture: Using the recently proposed differential hierarchy (Z-expansion) technique,
we obtain a general expression for the HOMFLY polynomials in two arbitrary
symmetric representations of link families, including Whitehead and Borromean
links. Among other things, this allows us to check and confirm the recent
conjecture of arXiv:1304.5778 that the large representation limit (the same as
considered in the knot volume conjecture) of this quantity matches the
prediction from mirror symmetry consideration. We also provide, using the
evolution method, the HOMFLY polynomial in two arbitrary symmetric
representations for an arbitrary member of the one-parametric family of
2-component 3-strand links, which includes the Hopf and Whitehead links. | Magnetic Strings In Five Dimensional Gauged Supergravity Theories: Magnetic BPS string solutions preserving quarter of supersymmetry are
obtained for all abelian gauged d=5 N=2 supergravity theories coupled to vector
supermultiplets. Due to a ``generalised Dirac quantization'' condition
satisfied by the minimized magnetic central charge, the string metric takes a
universal form for all five dimensional gauged theories. |
Holographic KMS relations at finite density: We extend the holographic Schwinger-Keldysh prescription introduced in
arXiv:1812.08785 to charged black branes, with a view towards studying Hawking
radiation in these backgrounds. Equivalently we study real-time fluctuations of
the dual CFT held at finite temperature and finite chemical potential. We check
our prescription using charged Dirac probe fields. We solve the Dirac equation
in a boundary derivative expansion extending the results in arXiv:2011.07039.
The Schwinger-Keldysh correlators derived using this prescription automatically
satisfy the appropriate KMS relations with Fermi-Dirac factors. | RPA for Light-Front Hamiltonian Field Theory: A self-consistent random phase approximation (RPA) is proposed as an
effective Hamiltonian method in Light-Front Field Theory (LFFT). We apply the
general idea to the light-front massive Schwinger model to obtain a new bound
state equation and solve it numerically. |
Symmetries of the Free Schrödinger Equation in the Non-Commutative
Plane: We study all the symmetries of the free Schr\"odinger equation in the
non-commutative plane. These symmetry transformations form an
infinite-dimensional Weyl algebra that appears naturally from a two-dimensional
Heisenberg algebra generated by Galilean boosts and momenta. These infinite
high symmetries could be useful for constructing non-relativistic interacting
higher spin theories. A finite-dimensional subalgebra is given by the
Schr\"odinger algebra which, besides the Galilei generators, contains also the
dilatation and the expansion. We consider the quantization of the symmetry
generators in both the reduced and extended phase spaces, and discuss the
relation between both approaches. | Energy Flux Positivity and Unitarity in CFTs: We show that in most conformal field theories the condition of the energy
flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence
of ghosts. At finite temperature and large energy and momenta, the two-point
functions of the stress energy tensor develop lightlike poles. The residues of
the poles can be computed, as long as the only spin two conserved current,
which appears in the stress energy tensor OPE and acquires nonvanishing
expectation value at finite temperature, is the stress energy tensor. The
condition for the residues to stay positive and the theory to remain ghost free
is equivalent to the condition of positivity of energy flux. |
Topological T-duality via Lie algebroids and $Q$-flux in
Poisson-generalized geometry: It is known that the topological T-duality exchanges $H$ and $F$-fluxes. In
this paper, we reformulate the topological T-duality as an exchange of two Lie
algebroids in the generalized tangent bundle. Then, we apply the same
formulation to the Poisson-generalized geometry, which is introduced in
arXiv:1408.2649 to define $R$-fluxes as field strength associated with
$\beta$-transformations. We propose a definition of $Q$-flux associated with
$\beta$-diffeomorphisms, and show that the topological T-duality exchanges $R$
and $Q$-fluxes. | Duality Between Hydrogen Atom and Oscillator Systems via Hidden SO(d,2)
Symmetry and 2T-physics: The relation between motion in $-1/r$ and $r^{2}$ potentials, known since
Newton, can be demonstrated by the substitution $r\rightarrow r^{2}$ in the
classical/quantum radial equations of the Kepler/Hydrogen problems versus the
harmonic oscillator. This suggests a duality-type relationship between these
systems. However, when both radial and angular components of these systems are
included the possibility of a true duality seems to be remote. Indeed,
investigations that explored and generalized Newton's radial relation,
including algebraic approaches based on noncompact groups such as SO(4,2), have
never exhibited a full duality consistent with Newton's. On the other hand,
2T-physics predicts a host of dualities between pairs of a huge set of systems
that includes Newton's two systems. These dualities take the form of rather
complicated canonical transformations that relate the full phase spaces of
these respective systems in all directions. In this paper we focus on Newton's
case by imposing his radial relation to find an appropriate basis for
2T-physics dualities, and then construct the full duality. Using the techniques
of 2T-physics, we discuss the hidden symmetry of the actions (beyond the
symmetry of Hamiltonians) for the Hydrogen atom in $D$-dimensions and the
harmonic oscillator in $\bar{D}$ dimensions. The symmetries lead us to find the
one-to-one relation between the quantum states, including angular degrees of
freedom, for specific values of $\left( D,\bar{D}\right) $, and construct the
explicit quantum canonical transformation in those special cases. We find that
the canonical transformation has itself a hidden gauge symmetry that is crucial
for the respective phase spaces to be dual even when $D\neq\bar{D}$. In this
way we display the surprising beautiful symmetry of the full duality that
generalizes Newton's radial duality. |
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