Chiral Massive News: Null Boundary Symmetries in Topologically Massive Gravity

TL;DR

This paper investigates the boundary symmetries and surface charges in three-dimensional topologically massive gravity, revealing a Heisenberg plus Virasoro algebra structure and the role of chiral gravitons as boundary news.

Contribution

It constructs the solution phase space for null boundaries in TMG, identifying the symmetry algebra and the conditions for charge integrability, highlighting the role of chiral gravitons.

Findings

Surface charges form a Heisenberg plus Virasoro algebra.

The chiral massive graviton flux appears as boundary news.

Two surface charges are always integrable, one depends on graviton flux.

Abstract

We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtain Heisenberg $\oplus$ Virasoro algebra {with} a central charge proportional to the gravitational Chern-Simons term of TMG. We also discuss that the flux of the chiral massive gravitons appears as the (Bondi) news through the null surface.