Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups

Abstract

Using the twisted partition function on ${{\mathbb{R}}^3}$ × ${{\mathbb{S}}^1}$, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(N _c ) gauge theory for arbitrary N _c , and theories without a center symmetry, such as G ₂ gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-instantons generate attraction among the eigenvalues of the Wilson line. This is counter-acted by neutral bions — topological excitations which generate eigenvalue repulsion for all simple groups. The transition is driven by the competition between these three effects. We study the transition in more detail for the gauge groups SU(N _c ), N _c ≥ 3, and G ₂. In the case of G ₂ there is no change of symmetry, but the expectation value of the Wilson line exhibits a discontinuity. We also examine the effect of the θ-angle on the phase transition and critical temperature T _c (θ). The critical temperature is a multi-branched function, which has a minimum at θ = π as a result of topological interference.