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

TL;DR

This paper proposes a universal mechanism for deconfinement and theta-dependence in pure Yang-Mills theories across all simple gauge groups, linking phase transitions to topological excitations and eigenvalue dynamics.

Contribution

It introduces a universal, controlled framework connecting deconfinement phase transitions to topological effects for all simple gauge groups.

Findings

The phase transition mechanism is universal across simple groups.

Neutral bions generate eigenvalue repulsion, counteracting attraction from monopole-instantons.

The critical temperature T_c(theta) varies with theta, with a minimum at pi.

Abstract

Using the twisted partition function on R^3 x 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>2, 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 theta-angle on the phase transition and critical temperature T_c(theta). The critical temperature is a multi-branched function, which has a minimum at theta=pi as a result of topological intereference.