Chiral Massive News: Null Boundary Symmetries in Topologically Massive Gravity

TL;DR

This work extends the null boundary symmetry program to topologically massive gravity in three dimensions, constructing a maximal boundary phase space for an arbitrary null surface. It identifies four boundary functions, including a propagating chiral graviton mode, and derives three boundary charges whose integrability depends on the presence or absence of bulk flux, with a Heisenberg ⊕ Virasoro symmetry algebra governed by the gravitational Chern-Simons term. In the vanishing-Cotton (VCT) sector, charges can be rendered integrable via a careful Y-ambiguity choice, yielding a central Virasoro charge tied to the CS coupling; in the non-vanishing Cotton (NVCT) sector, a nonzero flux (chiral massive news) appears and is captured by a generalized charge conservation equation (GCCE) and a modified Barnich-Troessaert bracket. Axisymmetric examples, BTZ in TMG, warped solutions, and non-expanding backgrounds illustrate how flux and central terms shape the charge algebra, including regimes where the algebra reduces to Heisenberg ⊕ Virasoro or to a U(1) Kac-Moody with vanishing Virasoro central charge. Overall, the paper provides a concrete framework linking boundary symmetries, bulk propagating modes, and flux through null surfaces, with implications for black hole microphysics and holography in topologically massive gravity.

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.