Holographically Viable Extensions of Topologically Massive and Minimal Massive Gravity?

TL;DR

This paper demonstrates that minimal massive gravity (MMG) is the unique consistent extension of topologically massive gravity (TMG) in 2+1 dimensions that avoids bulk-boundary unitarity issues, with no further higher-order curvature deformations possible.

Contribution

The authors prove the uniqueness of MMG as the only viable extension of TMG with the desired physical properties, ruling out higher-order curvature modifications.

Findings

MMG is unique among TMG extensions with the correct unitarity properties.

No consistent cubic or quartic curvature deformations of TMG or MMG exist.

MMG remains the sole extension with a single massive degree of freedom and proper bulk-boundary behavior.

Abstract

Recently, an extension of the topologically massive gravity (TMG) in $2+1$ dimensions, dubbed as minimal massive gravity (MMG), was found which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three dimensional theories. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is consistent at the level of the field equations. The only extension of TMG with the desired bulk and boundary properties having a single massive degree of freedom is MMG.