Spectrum of the U(1) staggered Dirac operator in four dimensions

TL;DR

This study compares the low-lying eigenvalue spectrum of the staggered Dirac operator in 4D U(1) gauge theory to chiral random matrix theory, confirming theoretical predictions about eigenvalue scaling and chiral condensate contributions.

Contribution

It provides the first detailed comparison of U(1) gauge theory eigenvalues with chiral random matrix theory, confirming the universality class and scaling behavior.

Findings

Agreement with chiral unitary ensemble below Thouless energy

Eigenvalues contribute to chiral condensate similarly to SU(2) and SU(3)

Thouless energy scales with lattice size as predicted

Abstract

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate similar as for the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.