Comment on "Cosmological Topological Massive Gravitons and Photons"

TL;DR

This paper clarifies the energy properties of solutions in chiral gravity, demonstrating that certain negative-energy solutions are boundary-dependent and consistent with previous positive-energy results in global AdS3.

Contribution

It resolves a controversy by showing that negative-energy solutions are boundary-dependent and only appear smooth within the Poincare patch, aligning with prior positive-energy findings.

Findings

Negative-energy solutions are boundary-dependent.

Solutions are smooth only within the Poincare patch.

Global AdS3 analysis shows divergence at certain boundary points.

Abstract

In a recent paper (arXiv: 0801.4566) it was shown that all global energy eigenstates of asymptotically $AdS_3$ chiral gravity have non-negative energy at the linearized level. This result was questioned (arXiv: 0803.3998) by Carlip, Deser, Waldron and Wise (CDWW), who work on the Poincare patch. They exhibit a linearized solution of chiral gravity and claim that it has negative energy and is smooth at the boundary. We show that the solution of CDWW is smooth only on that part of the boundary of $AdS_3$ included in the Poincare patch. Extended to global $AdS_3$, it is divergent at the boundary point not included in the Poincare patch. Hence it is consistent with the results of (arXiv: 0801.4566).