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.

Holography in $$ \hat{\textrm{CGHS}} $$ supergravity

“…Recently the CGHS theory is conjectured to acquire a dual quantum matrix ensemble description similar to JT gravity [27,28,53] which can potentially capture non-perturbative effects. Finally, it would be interesting to embed more dilaton-gravity theories in the 2D holography setup -see recent papers [54][55][56] and their references.…”

“…The construction of the CGHS model is based on the BF gauge theory formulation of Cangemi and Jackiw which was first introduced as a string-inspired model for gravity on a line [25]. This authenticates the name CJ gravity to this model as well [26][27][28]. 1 In contrast to the JT model, boundary conditions in CGHS JHEP03(2023)009…”

Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals

“…As a generalization, one could investigate Poisson diffeomorphisms for larger target space manifolds such as for the Cangemi-Jackiw or CGHS model [55,60]. In this case, the target space is four-dimensional with the fourth dimension corresponding to an additional (topological) Maxwell field.…”