Talk presented by Bernd A. Berg

Parallel Session: Theoretical Developments I

Thursday July 1st, 16.40 - 17.00, Room 8

Eigenvalues of the compact U(1) Dirac operator on the lattice and in random matrix theory

Abstract: We have calculated spectra of the staggered Dirac operator in quenched compact U(1) gauge theory in the strong coupling as well as in the Coulomb phase. In both cases the nearest-neighbor spacing distribution of adjacent eigenvalues agreed with the prediction of the chiral unitary ensemble of random matrix theory. It has also been demonstrated in SU(2) and SU(3) gauge theory that the microscopic spectral correlations of the lattice Dirac operator are given by universal functions. We have analyzed the low-lying eigenvalues of the staggered Dirac operator in quenched compact U(1) gauge theory for these correlations. The distribution of the smallest eigenvalue and the microscopic spectral density are found to be in agreement with predictions of the chiral unitary ensemble of random matrix theory. We have thus demonstrated the universality of these quantities in compact U(1) gauge theory.

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