On the new massive gravity and AdS/CFT

Abstract

Demanding the existence of a simple holographic $c$-theorem, it is shown that a general (parity preserving) theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants reduces to the new massive gravity theory. We consider extending the theory including upto six derivative curvature invariants. Black hole solutions are presented and consistency with 1+1 CFTs is checked. We present evidence that bulk unitarity is still in conflict with a positive CFT central charge for generic choice of parameters. However, for a special choice of parameters appearing in the four and six derivative terms reduces the linearized equations to be two derivative, thereby ameliorating the unitarity problem.