Localised Dirac eigenmodes and Goldstone's theorem at finite temperature

TL;DR

This paper demonstrates that localized near-zero Dirac modes at finite temperature can suppress Goldstone bosons in a gauge theory's chirally broken phase, challenging traditional expectations.

Contribution

It reveals a novel mechanism where localized Dirac modes affect the existence of Goldstone bosons at finite temperature.

Findings

Localized near-zero Dirac modes can eliminate Goldstone excitations.

Finite temperature modifies the relationship between Dirac modes and symmetry breaking.

The results impact understanding of chiral symmetry and massless modes in gauge theories.

Abstract

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