The Action of Geometric Entropy in Topologically Massive Gravity

TL;DR

This paper investigates how geometric entropy acts in topologically massive gravity, revealing it as a boundary-preserving transformation and confirming its consistency with semiclassical computations.

Contribution

It demonstrates that the geometric entropy in TMG acts as a boundary-condition-preserving kink transformation, extending previous results from Einstein-Hilbert gravity.

Findings

The action of geometric entropy in TMG matches the HRT area operator in Einstein-Hilbert gravity.

The geometric entropy acts as a boundary-condition-preserving kink transformation.

Results are consistent with semiclassical commutator computations in asymptotic AdS TMG spacetimes.

Abstract

Due to the presence of a gravitational anomaly in topologically massive gravity (TMG), the geometric entropy is no longer simply the Hubeny-Rangamani-Takayanagi (HRT) area; instead, it is given by the HRT area plus an anomalous contribution. We study the action of this geometric entropy on the covariant phase space of classical solutions for TMG with matter fields whose action is algebraic in the metric. The result agrees precisely with the action of HRT area operators in Einstein-Hilbert gravity given in arXiv:2203.04270, i.e., it is a boundary-condition-preserving kink transformation. Furthermore, we show our result to be consistent with direct computations of semiclassical commutators of geometric entropies in pure TMG spacetimes asymptotic to planar AdS, as computed in arXiv:2206.00027.