Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector

TL;DR

This paper establishes the asymptotic symmetry algebra of topologically massive gravity in the spacelike stretched AdS sector, revealing a conformal symmetry structure with two Virasoro algebras and central charges.

Contribution

It introduces natural asymptotic conditions and demonstrates that the asymptotic symmetry algebra is two Virasoro algebras with central charges, confirming previous hypotheses.

Findings

Asymptotic symmetry algebra is a semi-direct sum of u(1) Kac-Moody and Virasoro algebra.

The algebra simplifies to two Virasoro algebras with central charges.

Results align with prior conjectures about the symmetry structure.

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].