Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

A bstract We consider the generalization of a matrix integral with arbitrary spectral curve ρ 0 ( E ) to 0+1D theory quantum mechanics (MQM). Using recent techniques for 1D systems at large- N , we formulate hydrodynamical effective eigenvalues. The result is simple 2D free boson BCFT on curved background, describing fluctuations eigenvalues around ), which now limit expectation value eigenvalue density operator $$ \hat{\rho}(E) ρ ̂ E . average over ensemble random matrices becomes value. Equal-time correlations reproduce results (including non-perturbative corrections) theory. This suggests an interpretation JT gravity as dual one-time-point reduction MQM. As application, compute Rényi entropy associated bipartition match previous by Hartnoll and Mazenc c = 1 model two-dimensional string extend it ). provides clear picture emergence spacetime in two dimensional naturally finite displays large amount short range entanglement, proportional microcanonical entropy. also reduced subset n <