Publication : t23/031

Abstract:
We consider the generalization of a matrix integral with arbitrary spectral curve ρ0(E) to a 0+1D theory of matrix quantum mechanics (MQM). Using recent techniques for 1D quantum systems at large-N, we formulate a hydrodynamical effective theory for the eigenvalues. The result is a simple 2D free boson BCFT on a curved background, describing the quantum fluctuations of the eigenvalues around ρ0(E), which is now the large-N limit of the quantum expectation value of the eigenvalue density operator ρ^(E). The average over the ensemble of random matrices becomes a quantum expectation value. Equal-time density correlations reproduce the results (including non-perturbative corrections) of random matrix theory. This suggests an interpretation of JT gravity as dual to a one-time-point reduction of MQM. As an application, we compute the Rényi entropy associated to a bipartition of the eigenvalues. We match a previous result by Hartnoll and Mazenc for the c=1 matrix model dual to two-dimensional string theory and extend it to arbitrary ρ0(E). The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory. The entropy is naturally finite and displays a large amount of short range entanglement, proportional to the microcanonical entropy. We also compute the reduced density matrix for a subset of n Année de publication : 2023
Preprint : arXiv:2301.02259
Keywords : High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)
Langue : Anglais

Fichier(s) à télécharger :

publi.pdf