Localization of Dirac Fermions in Finite-Temperature Gauge Theory

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.

Open-boundary conditions in the deconfined phase

In this work, we consider open-boundary conditions at high temperatures, as they can potentially be of help to measure the topological susceptibility. In particular, we measure the extent of the boundary effects at T = 1.5 T c and T = 2.7 T c . In the first case, it is larger than at T = 0 while we find it to be smaller in the second case. The length of this "boundary zone" is controlled by the screening masses. We use this fact to measure the scalar and pseudo-scalar screening masses at these two temperatures. We observe a mass gap at T = 1.5 T c but not at T = 2.7 T c . Finally, we use our pseudo-scalar channel analysis to estimate the topological susceptibility. The results at T = 1.5 T c are in good agreement with the literature. At T = 2.7 T c , they appear to suffer from topological freezing, which prevents us from providing a precise determination of the topological susceptibility.