Quark spectra, topology and random matrix theory

TL;DR

This paper investigates the spectrum of the Overlap-Dirac operator in lattice QCD, testing predictions from chiral random matrix theory in topologically non-trivial sectors, linking quark spectra to fundamental QCD properties.

Contribution

It provides the first test of chiral random matrix theory predictions for the spectrum of the Overlap-Dirac operator in topologically non-trivial gauge sectors.

Findings

Spectrum matches chiral random matrix theory predictions

Validates the use of the Overlap-Dirac operator in nonperturbative QCD studies

Links quark spectral properties to topological features of gauge fields

Abstract

Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their relation to random matrix theory are studied here. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are tested for the first time.