Related papers: A geometric approach to singularity confinement an…
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis…
The `deautonomisation' of an integrable mapping of the plane consists in treating the free parameters in the mapping as functions of the independent variable, the precise expressions of which are to be determined with the help of a suitable…
Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The…
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R…
We consider charged black holes in four dimensional AdS space, in the presence of a Weyl correction. We obtain the solution including the effect of back-reaction, perturbatively up to first order in the Weyl coupling, and study its…
We treat spherically symmetric black holes in Gauss-Bonnet gravity by imposing boundary conditions on fluctuating metric on the horizon. Obtained effective two-dimensional theory admits Virasoro algebra near the horizon. This enables, with…
We investigate the entanglement entropy in gravity duals of confining large $N_c$ gauge theories using the proposal of arXiv:hep-th/0603001, arXiv:hep-th/0605073. Dividing one of the directions of space into a line segment of length $l$ and…
We investigate the behavior of the entanglement entropy of a confining gauge theory near cosmological singularities using gauge/gravity duality. As expected, the coefficients of the UV divergent terms are given by simple geometric…
We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…
Let $G$ be a connected semisimple algebraic group over an algebraically closed field of characteristic zero, and let $\th$ be an automorphism of $G$. We give a characterization of $\th$-twisted spherical conjugacy classes in $G$ by a…
The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time…
We explore 4-dimensional SU(N) gauge theory with a Weyl fermion in an irreducible self-conjugate representation. This theory, in general, has a discrete chiral symmetry. We use 't Hooft anomaly matching condition of the center symmetry and…
In this paper we introduce a non autonomous generalization of the $\QV$ equation introduced by Viallet. All the equations of Boll's classification appear in it for special choices of the parameters. Using the algebraic entropy test we infer…
The information content of the two-particle one- and two-dimensional Calogero model is studied using the von Neumann and R\'enyi entropies. The one-dimensional model is shown to have non-monotonic entropies with finite values in the large…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of…
We apply the Weyl method, as sanctioned by Palais' symmetric criticality theorems, to obtain those -highly symmetric -geometries amenable to explicit solution, in generic gravitational models and dimension. The technique consists of…
Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler-Lagrange equations. Hamel's equations, on the…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
This paper investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. We prove by a new unified method the pointwise boundary H\"{o}lder regularity under proper…