Topologically Massive AdS Gravity

TL;DR

This paper studies (2+1)-dimensional AdS gravity with a Chern--Simons term, revealing a single massive scalar mode, chiral propagating modes, and exact solutions, enriching understanding of topologically massive gravity.

Contribution

It provides a detailed analysis of topologically massive AdS gravity, showing how the theory can be expressed as two higher derivative Chern-Simons terms and identifying the physical bulk mode as a single massive scalar.

Findings

Single massive scalar mode in the bulk spectrum.

Chiral propagating modes with mass depending on parameters.

Existence of exact chiral pp-wave solutions.

Abstract

We analyze (2+1)-dimensional gravity with a Chern--Simons term and a negative cosmological constant, primarily at the weak field level. The full theory is expressible as the sum of two higher derivative SL(2,R) "vector" Chern-Simons terms, while the physical bulk degrees of freedom correspond to a single massive scalar field, just as for Lambda=0. The interplay of Lambda and the mass parameter mu can be studied, and any physical mass--including the conformal value with null propagation--is accessible by tuning mu. The single bulk mode yields a complete set of normalizable positive energy wave packets, as long as one chooses the usual, "wrong" sign of G necessary to connect smoothly with the known Lambda=0 limit. The chiral Chern--Simons coupling leads to gauge invariant linearized curvatures propagating with chirality-dependent masses. Linearized metric fluctuations have a finite asymptotic Fefferman--Graham expansion about the Poincar'e metric for any mass value greater or equal to a "critical" one, where various amusing effects appear, such as vanishing of one of the two "vector" Chern-Simons terms and an equivalence between tensor and vector excitations. We also find a set of chiral, pp-wave metrics that exactly solve the full nonlinear equations.