Flat JT Gravity and the BMS-Schwarzian

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.

30 pages; v2: numerous extra details in sections 3-4 and appendix B; typos fixed; references added

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• One-loop partition function of gravity with leaky boundary conditions
• Holography in CGHS supergravity
• Boundary Conditions for $\mathrm{Ad}{\mathrm{S}}_2$ Dilaton Gravity
• A note on the action with the Schwarzian at the stretched horizon
• Unimodular time in JT gravity: a holographic clock