Theory HEP Seminar

JT Gravity as a Matrix Integral

Phil Saad

Stanford

Motivated by the question of understanding the origin of random matrix statistics in the spectra of quantum black holes, I discuss nonperturbative effects in Jackiw-Teitelboim (JT) gravity. Using a connection between Mirzakhani's recursion relations for Weil-Petersson volumes and recursion relations for the genus expansion of a certain random matrix integral, I show that partition functions of JT gravity may be reproduced by this matrix integral. The random matrix is interpreted as Hamiltonian for a boundary theory dual to JT gravity. I then discuss nonperturbative effects in the average density of states of this matrix integral. These effects are sensitive to the underlying discreteness of the matrix eigenvalues. The JT gravity description of these effects involves an infinite number of disconnected spacetime geometries.