Understanding chiral symmetry breaking with the overlap action

TL;DR

This paper discusses the use of the overlap action for studying chiral symmetry breaking in QCD, highlighting how low Dirac operator modes relate to instantons and support an instanton liquid model.

Contribution

It demonstrates a computationally efficient method to analyze chiral symmetry breaking using the overlap action and connects low modes to instanton structures in QCD.

Findings

Low Dirac modes form a chiral density peaking at instantons.

These modes dominate correlation functions at small quark mass.

Results support the instanton liquid model of QCD.

Abstract

A chiral fermion action allows one to do very clean studies of chiral symmetry breaking in QCD. I will briefly describe how to compute with the overlap action (relatively) cheaply, and then turn to physics: Low modes of the Dirac operator show a ``lumped'' chiral density which peaks at the locations of instantons and anti-instantons. These modes dominate correlation functions at small quark mass in many channels. The picture qualitatively (and in some cases quantitatively) resembles an instanton liquid model.