Lattice QCD in the epsilon-regime and random matrix theory

TL;DR

This paper investigates the connection between lattice QCD in the epsilon-regime and random matrix theory, comparing theoretical predictions with numerical data to understand eigenvalue distributions of the Dirac operator.

Contribution

It provides a detailed comparison of random matrix theory predictions with high-precision lattice QCD data in the epsilon-regime, highlighting areas of agreement and discrepancy.

Findings

Agreement with theory at volumes > 5 fm^4

Partial matching of eigenvalue distributions

Insights into universality class applicability

Abstract

In the epsilon-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm^4.