New massive gravity, extended

TL;DR

This paper develops a generalized three-dimensional massive gravity theory with higher curvature corrections, ensuring holographic consistency, matching black hole entropy, and addressing ghost modes, thus extending the framework of new massive gravity.

Contribution

It introduces a systematic way to include arbitrary higher curvature corrections in 3D gravity while maintaining holographic c-theorem and controlling ghost modes, generalizing new massive gravity.

Findings

Derived a general form of higher curvature gravity in 3D with three invariants.

Fixed coefficients to satisfy the holographic c-theorem at all orders.

Constructed black hole solutions and matched their entropy with central charge calculations.

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.