Note on New Massive Gravity in $Ad{S}_3$

Abstract

In this note we study the properties of linearized gravitational excitations in the new massive gravity theory in asymptotically $Ad{S}_3$ 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 $Ad{S}_3$. 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 $Ad{S}_3$ 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.

v3 typos corrected, refs added, version to appear in JHEP

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• On the z=4 Horava-Lifshitz Gravity
• On the Generalized Massive Gravity in $Ad{S}_3$
• Renormalizability of Massive Gravity in Three Dimensions
• Massive Gravity with Mass Term in Three Dimensions
• Kundt spacetimes of massive gravity in three dimensions
• Renormalizability of Topologically Massive Gravity