The Dirac operator spectrum: a perturbative approach

TL;DR

This paper uses Numerical Stochastic Perturbation Theory to analyze the Dirac operator spectrum, providing insights into the eigenvalue distribution and its relation to chiral symmetry breaking.

Contribution

It introduces a perturbative approach to study the Dirac spectrum, shedding light on the eigenvalue repulsion mechanism behind the Bank-Casher relation.

Findings

Numerical Stochastic Perturbation Theory effectively reshuffles eigenvalues.

Eigenvalue repulsion is confirmed as a key factor in the spectrum.

The approach offers new insights into chiral symmetry breaking mechanisms.

Abstract

By computing the Dirac operator spectrum by means of Numerical Stochastic Perturbation Theory, we aim at throwing some light on the widely accepted picture for the mechanism which is behind the Bank-Casher relation. The latter relates the chiral condensate to an accumulation of eigenvalues in the low end of the spectrum. This can be in turn ascribed to the usual mechanism of repulsion among eigenvalues which is typical of quantum interactions. First results appear to confirm that NSPT can indeed enable us to inspect a huge reshuffling of eigenvalues due to quantum repulsion.