A Matrix Model for Flat Space Quantum Gravity

TL;DR

This paper develops a non-perturbative matrix model for 2D dilaton gravity with black holes, enabling detailed analysis of quantum gravitational phenomena and black hole dynamics.

Contribution

It introduces a double-scaled Hermitian matrix model that captures the non-perturbative partition function and late-time observables of 2D dilaton gravity with black holes.

Findings

Constructed the gauge-invariant asymptotic phase space.

Matched the matrix model to the topological expansion of the Euclidean path integral.

Found evidence of maximal chaos in out-of-time-order correlators.

Abstract

We take a step towards the non-perturbative description of a two-dimensional dilaton-gravity theory which has a vanishing cosmological constant and contains black holes. This is done in terms of a double-scaled Hermitian random matrix model which non-perturbatively computes the partition function for the asymptotic Bondi Hamiltonian. To arrive at this connection we first construct the gauge-invariant asymptotic phase space of the theory and determine the relevant asymptotic boundary conditions, compute the classical S-matrix and, finally, shed light on the interpretation of the Euclidean path integral defined in previous works. We then construct a matrix model that matches the topological expansion of the latter, to all orders. This allows us to compute the fine-grained Bondi spectrum and other late time observables and to construct asymptotic Hilbert spaces. We further study aspects of the semi-classical dynamics of the finite cut-off theory coupled to probe matter and find evidence of maximally chaotic behavior in out-of-time-order correlators. We conclude with a strategy for constructing the non-perturbative S-matrix for our model coupled to probe matter and comment on the treatment of black holes in celestial holography.