Note on New Massive Gravity in $AdS_3$

TL;DR

This paper investigates linearized gravitational excitations in new massive gravity in asymptotically AdS_3, revealing a critical point where gravitons become massless and the theory appears trivial under Brown-Henneaux boundary conditions.

Contribution

It identifies a critical point in new massive gravity in AdS_3 where gravitons become massless and the theory's central charges vanish, suggesting a trivial phase under standard boundary conditions.

Findings

Massive gravitons become massless at the critical point.

Central charges vanish at the critical point.

The theory appears trivial under Brown-Henneaux boundary conditions.

Abstract

In this note we study the properties of linearized gravitational excitations in the new massive gravity theory in asymptotically $AdS_3$ spacetime and find that there is also a critical point for the mass parameter at which massive gravitons become massless as in topological massive gravity in $AdS_3$. However, at this critical point in the new massive gravity the energy of all branches of highest weight gravitons vanish and the central charges also vanish within the Brown-Henneaux boundary conditions. The new massive gravity in asymptotically $AdS_3$ spacetime seems to be trivial at this critical point under the Brown-Henneaux boundary conditions if the Brown-Henneaux boundary conditions can be consistent with this theory. At this point, the boundary conditions of log gravity may be preferred.