Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector

TL;DR

This work analyzes the spacelike stretched AdS sector of topologically massive gravity with a cosmological constant using a canonical Dirac–Hamiltonian framework. It introduces asymptotic warped AdS conditions and derives the asymptotic symmetry algebra, finding a semidirect product of a u(1) Kac–Moody and Virasoro structure without central charges at the naive level, which is then upgraded to a central extension in the canonical realization. Through a Sugawara construction in the u(1) KM sector, the authors reveal two independent Virasoro algebras with central charges c^+ and c^- and demonstrate that Cardy entropy computed from these charges reproduces the gravitational entropy of the spacelike stretched black hole, with α fixed to match S_gr. The results confirm the holographic conjecture that the boundary dynamics in this sector is conformal at the classical level and establish the precise central charges and Virasoro content, aligning with prior hypotheses. This provides a robust classical foundation for warped AdS/CFT-like dualities in TMG_ abla and clarifies the boundary conformal structure of the spacelike stretched sector.

Abstract

We introduce a natural set of asymptotic conditions in the spacelike stretched AdS sector of topologically massive gravity. The Poisson bracket algebra of the canonical generators is shown to have the form of the semi-direct sum of a $u(1)$ Kac-Moody and a Virasoro algebra, with central charges. Using the Sugawara construction, we prove that the asymptotic symmetry coincides with the conformal symmetry, described by two independent Virasoro algebras with central charges. The result is in complete agreement with the hypothesis made in [6].