Confinement and deconfinement for any gauge group from dyons viewpoint

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.