Conservation and Integrability in TMG

TL;DR

This paper extends the analysis of conservation, integrability, and renormalization in Bondi gauge and General Relativity to Topological Massive Gravity, constructing a finite, conserved, and integrable charge framework.

Contribution

It develops a phase space construction and holographic renormalization for TMG, demonstrating finiteness, conservation, and integrability of charges in this theory.

Findings

Charges are generically finite and conserved.

Charges can be made integrable via field-dependent redefinitions.

The work extends previous GR results to TMG in Bondi gauge.

Abstract

In this work, following the paper by Romain Ruzziconi and C\'eline Zwikel \cite{Ruzziconi:2020wrb} we extend the questions of conservation, integrability and renormalization in Bondi gauge and in GR to the theory of Topological Massive Gravity (TMG). 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 generically finite, conserved and can be made integrable by a field$-$dependent redefinition of the asymptotic symmetry parameters.