Global symmetries and partial confinement

In gauge theories, spontaneous breaking of the centre symmetry provides a precise definition of deconfinement. In large-N gauge theories, evidence has emerged recently that between confined and deconfined phases a partially-deconfined phase can appear, in which only a subset of colours deconfine. In the partially-deconfined phase, the centre symmetry is spontaneously broken, raising the question of whether an order parameter exists that can distinguish completely- and partially-deconfined phases. We present two examples in gauge theories of global symmetries that are spontaneously broken in the confined phase and preserved in the deconfined phase, and we show that this symmetry is spontaneously broken in the partially-deconfined phase. As a result, in these theories the transition from complete to partial deconfinement is accompanied by the spontaneous breaking of a global symmetry. The two examples are CP symmetry in N = 1 super-Yang-Mills with a massive gluino and theta-angle theta = pi, and chiral symmetry in a strongly-coupled lattice gauge theory. For N = 1 SYM we also present numerical evidence that the same phenomenon occurs at finite N >= 30. We thus conjecture that global symmetries may provide order parameters to distinguish completely and partially deconfined phases generically, including at finite N.

Automated summary

This study investigates the phenomenon of spontaneous breaking of the center symmetry in gauge theories and the distinction between completely and partially deconfined phases. Two examples are presented to demonstrate the spontaneous breaking of a global symmetry in the confined phase and its preservation in the deconfined phase, as well as its spontaneous breaking in the partially-deconfined phase. This suggests that global symmetries may serve as order parameters to distinguish between completely and partially deconfined phases.