Localisation of Dirac eigenmodes in finite-temperature lattice gauge theory

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 low-lying Dirac eigenmodes. In all the models investigated so far, low modes turn from delocalised to localised when the system deconfines, exactly at the critical temperature when deconfinement takes place through a genuine phase transition. In this talk I review recent progress on this topic, including an improved understanding of the underlying localisation mechanism, and the determination of how low-mode localisation affects the quasi-pion spectrum in the chiral limit. These findings further support the use of Dirac eigenmodes as a tool to investigate the mechanisms behind confinement and the deconfinement transition, and the connection between confining and chiral properties in finite-temperature gauge theories.