Flat JT Gravity and the BMS-Schwarzian

TL;DR

This paper explores Minkowskian JT gravity with non-zero vacuum energy, revealing its asymptotic symmetries form a BMS$_2$ extension, leading to a unique coadjoint orbit, a zero-mode boundary action, and a one-loop exact partition function.

Contribution

It introduces the BMS$_2$ extension of asymptotic symmetries in flat JT gravity, analyzes the BMS-Schwarzian action, and computes an exact gravitational partition function.

Findings

BMS$_2$ has a single coadjoint orbit with real, non-zero central charges.

The BMS-Schwarzian action lacks saddle points and differs from the boundary action by a zero-mode.

The gravitational partition function is one-loop exact due to the zero-mode.

Abstract

We consider Minkowskian Jackiw-Teitelboim (JT) gravity in Bondi gauge at finite temperature, with non-zero vacuum energy. Its asymptotic symmetries span an extension of the warped Virasoro group, dubbed "BMS$_2$", which we investigate in detail. In particular, we show that this extension has a single coadjoint orbit when central charges are real and non-zero. The ensuing BMS-Schwarzian action has no saddle points, and only coincides with the boundary action functional of flat JT gravity up to a crucial dilatonic zero-mode that ensures the existence of a well-defined bulk variational principle. We evaluate the corresponding gravitational partition function, which turns out to be one-loop exact precisely thanks to the presence of such a zero-mode.