Chiral massive news: null boundary symmetries 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 ⊕ 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.

3d gravity in Bondi-Weyl gauge: charges, corners, and integrability

“…First of all, an additional corner potential ϑ 1 is necessary in order to obtain integrable charges. This is similar to what happens in Topologically Massive Gravity for a finite null boundary [52]. Second, there is another natural corner potential ϑ 2 which controls the Weyl part of the charges and the associated Heisenberg algebra.…”

“…This is similar to the case studied in[52] where generic boundary conditions around a finite null surface were worked out in Topologically Massive Gravity. Therein, it was shown that it exists specific choices of slicing and of a corner ambiguity for which the non-integrability of the charges is only sourced by the physical flux passing through the boundary.…”

“…These symmetries are therefore large and the phase space carries four unconstrained time-dependent charges. Until now, the maximal number of charges that were found in the metric formulation was three [23,52]. In these works however, the boundary was taken at fixed r. Here we see that this condition is too restrictive because the charge associated withk can only exist if the boundary is allowed to move.…”

“…When dealing with non-integrable charges, one possibility is to consider the modified Barnich-Troessaert bracket [66], or other proposals for a modified bracket such as that in [51]. However, as argued in [21,23,52], the fact that we are in three-dimensional gravity means that there should be no physical flux sourcing the non-integrability (since there are no degrees of freedom which can leak through the boundary). Indeed, as we are about to see, integrability can be achieved using a combination of two mechanisms: i) a change of slicing, which amounts to a (non-unique but invertible) field-dependent redefinition of the vector field generators (f, g, h, k),…”

“…On top of the usual ingredients of the covariant phase space formalism [60,63,65,79,80], the construction of finite and integrable charges has required to introduce corner terms for renormalization and integrability, and also to find an integrable slicing [23,52]. At the end of the day, in this slicing the charges are given by (3.20) (where as we have explained one can take c 2 = 0).…”