Frank Ferrari: Random Disks of Constant Curvature and Jackiw-Teitelboim Quantum Gravity

vendredi 7 févr. 2025, 14:00 → 15:00 Europe/Paris

112 (Bat. Braconnier)

Jackiw-Teitelboim quantum gravity is a model of two-dimensional gravity for which the bulk curvature is fixed but the extrinsic curvature of the boundaries is free to fluctuate. The negative curvature model has been studied extensively in the recent physics literature, in a particular "Schwarzian" limit, because of its relevance in describing near-extremal quantum black holes and their SYK-like duals. 

 

The Schwarzian description applies only to the negative curvature case and is an effective theory valid on distances much larger than the curvature length scale of the bulk geometry. Our goal will be to present a microscopic, UV-complete approach to the theory, valid for the three versions of the model (negative, zero or positive curvature), from two different points of view. We focus on the disk topology. 

 

The first point of view is based on a lattice formulation. The theory is shown to be equivalent to a new model of so-called self-overlapping random polygons. By definition, these polygons must bound a disk immersed in the plane. They must be counted with an appropriate multiplicity. The combinatorial solution of the model is shown to be encoded in a new ``dually weighted’’ Hermitian matrix model. The second point of view is based on a direct continuum approach, adapting the framework used to solve Liouville quantum gravity in the 80s and 90s. We find that the model is described in terms of a boundary log-correlated field. The conjectured equivalence between the lattice and continuum formulations yields non trivial predictions, for example for the critical exponents of the self-overlapping polygon models, and open the path to a wide range of potential applications.