Stability of warped AdS3 vacua of topologically massive gravity

TL;DR

This paper addresses the perturbative stability of warped AdS$_3$ vacua in topologically massive gravity. By classifying linearized perturbations under the background isometries and imposing Compère–Detournay boundary conditions, the authors show that spacelike stretched warped AdS$_3$ is stable for $\mu\ell>3$, since negative-energy massive gravitons are excluded and the spectrum reduces to positive-energy boundary gravitons. They construct explicit highest-weight propagating solutions, compute their energy density (finding it negative) and then demonstrate that the boundary conditions remove these modes from the physical spectrum, leaving only pure large-gauge excitations with positive energy. The results suggest a stability mechanism akin to chiral gravity, with potential implications for warped AdS/CFT, though the squashed case remains unsettled and further work is needed to understand possible dual boundary theories and nonperturbative stability.

Abstract

AdS3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point μl=1. We study the possibility that the warped vacua of TMG, which exist for all values of μ, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS3 vacua with Compere-Detournay boundary conditions are indeed stable in the range μl > 3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS3 vacuum. The situation somewhat resembles chiral gravity: although negative energy modes do exist, they are all excluded by the boundary conditions, and the perturbative spectrum solely consists of boundary (pure large gauge) gravitons.

Figures (1)

• Figure 1: A chromatic depiction of the way the fibered coordinates cover the $AdS_3$ boundary cylinder. Blue strips have $\sigma \rightarrow - \infty$ while pink strips have $\sigma \rightarrow + \infty$.