Ground State of 2D Quantum Gravity and Spectral Density of Random Matrices

TL;DR

This paper calculates the exact spectral density of random matrices in the ground state of a 2D quantum gravity model, revealing significant non-perturbative effects and differences from semi-classical approximations.

Contribution

It provides an exact non-perturbative spectral density for 2D quantum gravity matrix models, avoiding pathologies of previous regularizations.

Findings

Non-perturbative effects dominate semi-classical results.

Exact loop averages differ from WKB approximations.

No pathologies found in the new regularization approach.

Abstract

We compute the exact spectral density of random matrices in the ground state of the quantum hamiltonian corresponding to the matrix model whose double scaling limit describes pure gravity in 2D. We show that the non-perturbative effects are very large and in certain cases dominate the semi-classical WKB contribution studied in the earlier literature. The physical observables in this model are the loop averages with respect to the spectral density. We compute their exact ground-state expectation values and show that they differ significantly from the values obtained in the WKB approximation. Unlike the alternative regularizations of the nonperturbative 2D quantum gravity, based on analytic continuation of the Painlev\'e transcendent, our solution shows no pathologies.