A Matrix Model for Flat Space Quantum Gravity

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.

53+20 pages, 13 figures

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Cited by in corpus (7)

• Near-Extremal Limits of de Sitter Black Holes
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• Non-Perturbative Random Matrix Model of $\mathcal{N}=2$ JT Supergravity
• Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals
• Entanglement Rényi entropies in celestial holography
• Unimodular time in JT gravity: a holographic clock
• CFT reconstruction of local bulk operators in half-Minkowski space