Abstract
We analyze deformations of mathcal{N} = 1 Jackiw-Teitelboim (JT) supergravity by adding a gas of defects, equivalent to changing the dilaton potential. We compute the Euclidean partition function in a topological expansion and find that it matches the perturbative expansion of a random matrix model to all orders. The matrix model implements an average over the Hamiltonian of a dual holographic description and provides a stable non-perturbative completion of these theories of mathcal{N} = 1 dilaton-supergravity. For some range of deformations, the supergravity spectral density becomes negative, yielding an ill-defined topological expansion. To solve this problem, we use the matrix model description and show the negative spectrum is resolved via a phase transition analogous to the Gross-Witten-Wadia transition. The matrix model contains a rich and novel phase structure that we explore in detail, using both perturbative and non-perturbative techniques.
Highlights
Models of two dimensional dilaton-gravity in asymptotically AdS2 [1–6] provide a very simple theoretical laboratory to study interesting questions about quantum gravity and black holes, with Jackiw-Teitelboim (JT) gravity as a prototypical example which is, among other things, exactly solvable [7–11]
We compute the Euclidean partition function in a topological expansion and find that it matches the perturbative expansion of a random matrix model to all orders
We use the matrix model description and show the negative spectrum is resolved via a phase transition analogous to the GrossWitten-Wadia transition
Summary
Models of two dimensional dilaton-gravity in asymptotically AdS2 [1–6] provide a very simple theoretical laboratory to study interesting questions about quantum gravity and black holes, with Jackiw-Teitelboim (JT) gravity as a prototypical example which is, among other things, exactly solvable [7–11]. The purpose of this paper is to study several examples in which this puzzle arises and show that whenever a negativity of the spectrum appears, the problem is resolved by properly accounting for a phase transition This resolution is made possible by a non-perturbative completion of the gravity theory via a random matrix model. Using the loop equations and a properly defined measure for the ensemble average, we show the equivalence between the average of these operators and the topological expansion of the deformed Type 0A/0B theories to all orders in the perturbative expansion in e−S0 This is the natural extension of the ξ = 0 matching previously obtained in [19] for the undeformed case.. Apart from putting together many results scattered in the literature, this appendix includes some new technical results, like the precise method for computing the matrix model kernel and observables for double scaled and double-cut Hermitian matrix models
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