Title: Gauge Theory Formulation of Hyperbolic Gravity

Abstract: The talk will be based on my recent paper arXiv:2011.02108 (to appear in JHEP) and on an ongoing follow-up research. A tentative plan of the talk is as follows:

1. Introduction: we introduce the subject of JT gravity, and more generally hyperbolic gravity theories (2D quantum gravity theories for which the curvature is constrained to be a constant), trying give an overview from “old” points of view (topological gravity, Liouville models) to very modern applications (SYK, holography).
2. Motivations: we review our own motivations to study in detail the gauge theoretic point of view. In particular, we shall emphasize puzzles and/or unresolved non-trivial issues in the subject, including for the most basic instance of JT gravity on a disk. Some of these issues are well-known, like the lack of a genuine quantum mechanical interpretation, and others seem to have been overlooked in the existing literature (for instance, the relevant space of metrics on the disk has not been described properly, etc.). We suggest that there may be an interrelationship between these issues.
3. Gauge theory construction: we describe the interesting novelties associated with the gauge theory formulation of the models when boundaries are present and discuss the resulting theory.
4. We start a rigorous discussion of the quantum path integral, in particular of the famous problem of understanding the correct measure of integration.

Talk – Video

Talk – Slides