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

TL;DR

This paper explores the relationship between Dirac eigenmode localization and confinement in gauge theories, focusing on QCD at imaginary chemical potential near the Roberge-Weiss transition, confirming the link between mode localization and deconfinement.

Contribution

It provides new numerical evidence for the localization transition of Dirac eigenmodes at the deconfinement point in a physical setup with dynamical fermions.

Findings

Low Dirac modes become localized at the deconfinement transition.

Localization of eigenmodes correlates with confinement properties.

Results support Dirac eigenmodes as tools to study confinement mechanisms.

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.