Les Houches lectures on two-dimensional gravity and holography

TL;DR

This paper provides an overview of exact methods for calculating the gravitational path integral in two-dimensional dilaton-gravity and supergravity, highlighting their connections to random matrix models and black hole physics.

Contribution

It introduces techniques for exact gravitational path integrals in 2D gravity and supergravity, with applications to black holes and links to matrix models and moduli spaces.

Findings

Exact path integral methods for 2D dilaton-gravity and supergravity.

Application of these methods to black hole physics.

Brief discussion on connections to random matrix models.

Abstract

Lecture notes prepared for the Les Houches school "Quantum Geometry: Mathematical Methods for Gravity, Gauge Theories and Non-Perturbative Physics" that took place during the summer 2024. We cover the techniques to perform the exact gravitational path integral of two-dimensional dilaton-gravity, and supergravity, over spacetimes with arbitrary topology, with an application to black holes. We discuss the connection with random matrix models and moduli spaces of hyperbolic surfaces briefly, since those concepts were covered in other lectures of the school.