Localisation of Dirac modes in gauge theories and Goldstone’s theorem at finite temperature

Giordano, Matteo (2022) Localisation of Dirac modes in gauge theories and Goldstone’s theorem at finite temperature. JOURNAL OF HIGH ENERGY PHYSICS, 2022 (12). ISSN 1126-6708

Preview

Text 2206.11109.pdf Available under License Creative Commons Attribution. Download (836kB) | Preview

Abstract

I discuss the possible effects of a finite density of localised near-zero Dirac modes in the chiral limit of gauge theories with N f degenerate fermions. I focus in particular on the fate of the massless quasi-particle excitations predicted by the finite-temperature version of Goldstone’s theorem, for which I provide an alternative and generalised proof based on a Euclidean SU( N f ) A Ward-Takahashi identity. I show that localised near-zero modes can lead to a divergent pseudoscalar-pseudoscalar correlator that modifies this identity in the chiral limit. As a consequence, massless quasi-particle excitations can disappear from the spectrum of the theory in spite of a non-zero chiral condensate. Three different scenarios are possible, depending on the detailed behaviour in the chiral limit of the ratio of the mobility edge and the fermion mass, which I prove to be a renormalisation-group invariant quantity.

Actions (login required)

Edit Item