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

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 $\mathrm{SU}(N_f{)}_A$ 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.

1+72 pages (40 + appendices and bibliography), 1 figure; to be published in JHEP

References in corpus (29)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4
• On the order of the QCD chiral phase transition for different numbers of quark flavours
• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Anderson Localization in Quark-Gluon Plasma
• Thermal quarkonium physics in the pseudoscalar channel
• Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit
• Unusual Features of QCD Low-Energy Modes in IR Phase
• Chiral dynamics in the low-temperature phase of QCD
• An Ising-Anderson model of localisation in high-temperature QCD
• Ideal topological gas in the high temperature phase of SU(3) gauge theory
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Deconfinement, chiral transition and localisation in a QCD-like model
• Second order chiral phase transition in three flavor quantum chromodynamics?
• Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite Temperature
• Localization with overlap fermions
• Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory
• Anderson Metal-to-Critical Transition in QCD
• Anderson localization in QCD-like theories
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Super-Universality in Anderson Localization
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Localised Dirac eigenmodes, chiral symmetry breaking, and Goldstone's theorem at finite temperature
• Short distance singularities and automatic O($a$) improvement: the cases of the chiral condensate and the topological susceptibility

Cited by in corpus (3)

• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Goldstone bosons at non-zero temperature
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories