Jackiw-Teitelboim Gravity, Random Disks of Constant Curvature, Self-Overlapping Curves and Liouville CFT1 (Frank Ferrari, Université Libre de Bruxelles)

30.04.2024 15:15 – 17:15

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 quantum black holes and their SYK-like duals.

A first-principle approach reveals that the description used in the literature so far is an effective theory valid on distances much larger than the curvature length scale of the bulk geometry.

At the microscopic level, the theory should be defined by taking the continuum limit of a new model of random polygons. The polygons, called ``self-overlapping,'' are constrained to bound a disk immersed in the plane. They must be counted with an appropriate multiplicity. The solution of the model could be found in principle by solving a difficult ``dually weighted’' Hermitian matrix model.

Motivated by standard heuristic path integral arguments, mimicking similar arguments used for Liouville gravity in the 80s and the 90s, we conjecture that an equivalent description is obtained in terms of a boundary log-correlated field. This yields predictions for the critical exponents of the self-overlapping polygon models and open the path to a wide range of potential applications.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Maths-Physique"

entrée libre