Localization of Dirac Fermions in Finite-Temperature Gauge Theory

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.

Invited review for the special issue of Universe "Modern Approaches to Non-Perturbative QCD and other Confining Gauge Theories", ed. D. Antonov. Revised version, 47 pages, 17 figures

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Cited by in corpus (13)

• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting
• Metal-insulator transition in a 2D system of chiral unitary class
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Mobility Edge in the Anderson model on partially disordered random regular graphs
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone's theorem at finite temperature
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition