Anderson Localization in high temperature QCD: background configuration properties and Dirac eigenmodes

Abstract

We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the Möbius domain-wall fermion operator on configurations generated for the $SU(3)$ gauge theory with two flavors of fermions, in the temperature range $[0.9,1.9]T_c$. We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop $P_L$, in the high temperature sea of $P_L\sim 1$. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures.

27 pages, 16 figures, 2 tables, minor corrections and typos

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• Deconfinement, chiral transition and localisation in a QCD-like model
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• Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory
• Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature
• Localization and chiral properties near the ordering transition of an Anderson-like toy model for QCD
• 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
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• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• 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