Localisation of Dirac eigenmodes and confinement in gauge theories: the Roberge-Weiss transition

Abstract

Ample numerical evidence from lattice calculations shows a strong connection between the confining properties of gauge theories at finite temperature and the localisation properties of the low-lying Dirac eigenmodes. In this contribution we discuss recent progress on this topic, focussing on results for QCD at imaginary chemical potential ${\mu }_I/T=\pi$ at temperatures above the Roberge-Weiss transition temperature. These confirm the general picture of low modes turning from delocalised to localised at the deconfinement transition, in a previously unexplored setup with a genuine, physical transition in the presence of dynamical fermions. This further supports the use of Dirac eigenmodes as a tool to investigate the mechanisms behind confinement and the deconfinement transition.

8 pages, 4 figures; contribution to the proceedings of the XVth Quark Confinement and Hadron Spectrum conference (ConfXV), 1-6 August 2022, University of Stavanger, Stavanger (Norway)

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