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

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

1992-12-18

arxiv.org/abs/hep-th/9212114v1

Nucl.Phys.B399:514-526,1993

Physics

High Energy Physics

High Energy Physics - Theory

14 pages (LaTeX) + 4 postscript figures encoded through uufiles. PUPT-1354, TAUP-2013-92

Scientific paper

10.1016/0550-3213(93)90507-L

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.

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