Search

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. [ABSTRACT FROM AUTHOR]

We present a semiclassical approach to the SU (N) Yang–Mills theory whose partition function at nonzero temperatures is approximated by a saddle point—an ensemble of an infinite number of interacting dyons of N kinds. The ensemble is governed by an exactly solvable 3d quantum field theory, allowing calculation of correlations functions relevant to confinement. We show that all known criteria of confinement are satisfied in this semiclassical approximation: (i) the average Polyakov line is zero below some critical temperature, and nonzero above it, (ii) a quark-antiquark pair has linear rising potential energy, (iii) the average spatial Wilson loop falls off exponentially with the area, (iv) N2 gluons are canceled out from the spectrum, (v) the critical deconfinement temperature is in good agreement with lattice data. Using the same approximation, we find confinement for the exceptional gauge group G(2) and a first-order deconfinement transition, also in agreement with lattice findings. [ABSTRACT FROM AUTHOR]