New massive gravity, extended

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.

4 pages

References in corpus (6)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Topologically Massive Gravity and the AdS/CFT Correspondence
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Born-Infeld extension of new massive gravity
• Note on New Massive Gravity in $Ad{S}_3$

Cited by in corpus (8)

• Holographic c-theorems in arbitrary dimensions
• Quasi Normal Modes for New Type Black Holes in New Massive Gravity
• Boundary stress tensor and counterterms for weakened AdS_3 asymptotic in New Massive Gravity
• New Massive Gravity and AdS_4 counterterms
• Charged Black Holes in New Massive Gravity
• Higgs Mechanism for New Massive Gravity and Weyl Invariant Extensions of Higher Derivative Theories
• All Bulk and Boundary Unitary Cubic Curvature Theories in Three Dimensions
• Generalised massive gravity one-loop partition function and AdS/(L)CFT