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

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.

Comments: Revised version: title changed; error corrected in Eq. 11, conclusions unchanged; discussion improved, comments added about symmetry breaking and relation with Goldstone's theorem; published version, 13 pages