New massive gravity, extended

TL;DR

The authors extend New Massive Gravity to an infinite family of higher-curvature theories in three dimensions by building invariants from the traceless part of the Ricci tensor and organizing them via partitions. They impose a holographic c-theorem to fix coefficients, deriving AdS$_3$ vacua and a central-charge function that monotonically increases under the null energy condition, with the vacuum central charge matching Weyl anomaly and black-hole entropy via Wald's formula. Perturbation theory around AdS$_3$ reveals a two-derivative sector when a parameter $\gamma$ is set to zero, ensuring bulk and boundary unitarity, while nonzero $\gamma$ introduces ghost-like massive modes and possible LCFT behavior at $\hat{c}=0$. The framework provides a tractable, algebraic construction of higher-curvature gravity in 3D with clear holographic interpretations and avenues for exploring stress-tensor correlators in the dual CFT.

Abstract

We consider gravity in three dimensions with an arbitrary number of curvature corrections. We show that such corrections are always functions of only three independent curvature invariants. Demanding the existence of a holographic c-theorem we show how to fix the coefficients in the action for an arbitrarily high order, recovering the new massive gravity lagrangian at quadratic order. We calculate the central charge $c$ and show that using Cardy's formula it matches the entropy of black hole solutions, which we construct. We also consider fluctuations about an AdS background, and find that it is possible to obtain two derivative equations by imposing a single constraint, thereby lifting the pathologic massive modes of new massive gravity. If we do not impose this, there is a set of ghosty massive modes propagating in the bulk. However, at $c=0$ these become massless and it is expected that these theories encode the dynamics of the spin two sector of strongly coupled logarithmic CFT's.