Consistent Boundary Conditions for New Massive Gravity in $AdS_3$

TL;DR

This paper investigates boundary conditions for new massive gravity in AdS3, showing Brown-Henneaux conditions are consistent across parameters and exploring log boundary conditions at the critical point.

Contribution

It demonstrates the consistency of Brown-Henneaux boundary conditions for all mass parameters and analyzes the viability of log boundary conditions at the critical point.

Findings

Brown-Henneaux boundary conditions are consistent for all mass parameters.

Conserved charges vanish at the critical point, indicating potential triviality.

Three types of log boundary conditions are possible at the critical point.

Abstract

In this note we study the boundary conditions for the new massive gravity theory in asymptotically $AdS_3$ spacetime. We find that the Brown-Henneaux boundary conditions are consistent with the new massive gravity for all any value of the mass parameter. At the critical point where the central charge vanishes, the conserved charges vanish, too. This provides further evidence that the theory may be trivial at the critical point under Brown-Henneaux boundary conditions. The log boundary conditions are also examined and we find that we can have three kinds of log boundary conditions for this new massive gravity theory, each of which could be consistent at the critical point, while for other value of the mass parameter, the log gravity boundary condition is not consistent.