Conservation and integrability in topological massive gravity

Abstract

In this work, following the paper by Romain Ruzziconi and Céline Zwikel [4] we extend the questions of conservation, integrability and renormalization in asymptotically locally anti-de Sitter in three spacetime dimensions (AdS3) in Bondi gauge and in Einstein gravity to the theory of topological massive gravity. We construct the phase space and renormalize the divergences arising within the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are finite, conserved (under the Dirichlet boundary conditions) and can be made integrable by using a particular slicing of the phase space. Then, we obtain the algebra of AdS3 boundary with a central charges the same as the Brown-Henneaux central charges.