Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone's theorem at finite temperature

TL;DR

This paper demonstrates that the presence of localized near-zero Dirac modes at finite temperature can suppress Goldstone bosons, affecting chiral symmetry breaking in gauge theories.

Contribution

It reveals how localized Dirac eigenmodes influence Goldstone's theorem and chiral symmetry breaking at finite temperature, a novel insight into gauge theory behavior.

Findings

Localized near-zero Dirac modes can eliminate Goldstone bosons at finite temperature.

Chiral symmetry breaking is affected by the density of localized modes.

Goldstone's theorem may not hold in the presence of certain localized eigenmodes.

Abstract

I show that a finite density of near-zero localised Dirac modes in the chirally broken phase of a gauge theory can lead to the disappearance of the massless excitations predicted by the Goldstone theorem at finite temperature.