Localization of Dirac Fermions in Finite-Temperature Gauge Theory

TL;DR

This paper reviews how Dirac fermions in non-Abelian gauge theories undergo an Anderson-type localization transition at finite temperature, affecting low-energy physics and related to deconfinement and chiral symmetry restoration.

Contribution

It provides a comprehensive review of the localization transition in Dirac fermions within lattice gauge theory, connecting it to finite-temperature phase transitions and topological gauge field excitations.

Findings

Localization transition linked to deconfinement and chiral symmetry restoration

Universality of the localization transition across models

Connection between zero modes and topological excitations

Abstract

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.