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# JT gravity with matter, generalized ETH, and Random Matrices

Sep 2022

We present evidence for a duality between Jackiw-Teitelboim gravity minimallycoupled to a free massive scalar field and a single-trace two-matrix model. Onematrix is the Hamiltonian $H$ of a holographic disorder-averaged quantummechanics, while the other matrix is the light operator $\cal O$ dual to thebulk scalar field. The single-boundary observables of interest are thermalcorrelation functions of $\cal O$. We study the matching of the genus zero one-and two-boundary expectation values in the matrix model to the disk andcylinder Euclidean path integrals. The non-Gaussian statistics of the matrixelements of $\cal O$ correspond to a generalization of the ETH ansatz. We describe multiple ways to construct double-scaled matrix models thatreproduce the gravitational disk correlators. One method involves imposing anoperator equation obeyed by $H$ and $\cal O$ as a constraint on the twomatrices. Separately, we design a model that reproduces certain double-scaledSYK correlators that may be scaled once more to obtain the disk correlators. We show that in any single-trace, two-matrix model, the genus zerotwo-boundary expectation value, with up to one $\cal O$ insertion on eachboundary, can be computed directly from all of the genus zero one-boundarycorrelators. Applied to the models of interest, we find that these cylinderobservables depend on the details of the double-scaling limit. To the extent wehave checked, it is possible to reproduce the gravitational double-trumpet,which is UV divergent, from a systematic classification of matrix model `tHooft diagrams. The UV divergence indicates that the matrix integral saddle ofinterest is perturbatively unstable. A non-perturbative treatment of the matrixmodels discussed in this work is left for future investigations.

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