On the new massive gravity and AdS/CFT

TL;DR

This work demonstrates that enforcing a holographic c-theorem in 2+1D higher-derivative gravity singles out New Massive Gravity (NMG) at the four-derivative level and admits a six-derivative extension preserving a monotonic c-function. It links the c-function to the Weyl anomaly central charge, constructs AdS black-hole solutions, and validates thermodynamics and Wald entropy against 1+1D CFT expectations. The analysis highlights a persistent tension between bulk unitarity and positive boundary central charge, though a special parameter choice yields two-derivative dynamics that can mitigate this issue. The authors also outline eight-derivative extensions and Lifshitz solutions, suggesting broader holographic applications and directions toward 1+1D holographic quantum liquids.

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.