Confinement and deconfinement for any gauge group from dyons viewpoint

Abstract

Basing on a semiclassical picture of dyons, we present a nonperturbative model of a pure Yang--Mills theory at any temperatures, for an arbitrary simple gauge group. We argue that at low temperatures dyons drive the Yang--Mills system for all groups to a phase where the `eigenphases' of the Polyakov line are, as a vector, proportional to the Weyl vector being the half sum of positive roots. For most gauge groups it means confinement, in particular for `quarks' in any N-ality nonzero representation of the SU(N) gauge group. At a critical temperature there is a 1st order phase transition for all groups (except SU(2) where the transition is 2nd order), characterized by a jump of Polyakov lines, irrespectively of whether the gauge group has a nontrivial center, or not.