Topologically Massive AdS Gravity

TL;DR

This paper analyzes (2+1)-dimensional gravity with a gravitational Chern–Simons term in an AdS$_3$ background, showing the full theory decomposes into two SL$(2,\mathbb{R})$ CS terms and has a single bulk degree of freedom, a massive mode whose mass is tunable by the parameter $\mu$ and the cosmological constant $\Lambda$. The authors demonstrate that curvature components carry chirality-dependent masses, yielding a spectrum of both scalar-like bulk modes and a positive-energy, normalizable wave-packet sector for all $|\mu|>0$, with boundary behavior governed by Fefferman–Graham expansions that constrain $\mu$ to be at least 1 for finite metric fluctuations. They reveal a pure CS reformulation of the theory, identify a special equivalence between tensor and vector excitations at $\mu=1$, and construct exact chiral pp-wave solutions that solve the full nonlinear equations. The work also discusses stability issues related to BTZ black holes in this setup and hints at a positive-energy supergravity extension that could address these concerns, linking Λ=0 and Λ<0 regimes within a coherent framework.

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.