Anderson localisation of Dirac eigenmodes in high temperature QCD

We investigate the properties of 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 M\"obius domain-wall fermion operator on configurations generated for the $SU(3)$ gauge theory with two flavors of fermions. We identify the source of localization of the eigenmodes with gauge configurations that are approximately self-dual and support local negative fluctuations of the Polyakov loop $P_L(x)$, in the bulk of $P_L\sim 1$. We investigate the dependence of these observations on the boundary conditions of the valence operator and interpret the results in terms of monopole-instanton structures. The results presented here are from \cite{Cossu:2016scb}, where we describe more details on the methods and conclusions.