Note on New Massive Gravity in $AdS_3$

TL;DR

This paper analyzes linearized gravity in three-dimensional New Massive Gravity on AdS3, uncovering a critical mass where massive gravitons become massless and both energies and central charges vanish under Brown-Henneaux boundary conditions. It derives a factorized graviton equation yielding massless and massive branches, analyzes their representations and energies, and shows that the AdS3 vacuum may be trivial at the critical point unless alternative boundary conditions are adopted. The work highlights the delicate interplay between higher-derivative gravity, energy positivity, and holographic boundary conditions in 3D AdS spacetimes, and suggests exploring log-gravity BCs and other vacua. Overall, it raises important questions about unitarity, stability, and the physical content of NMG in AdS3.

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.