Global symmetries and partial confinement

Abstract

In many 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-confined phase can appear, in which only a subset of colours deconfine. In the partially-confined phase, the centre symmetry is spontaneously broken, raising the question of whether an order parameter exists that can distinguish fully- and partially-confined phases. We consider two gauge theories in which a global symmetry is spontaneously broken in the confined phase and preserved in the deconfined phase, and we show that this symmetry is spontaneously broken also in the partially-confined phase. As a result, in these theories the transition from full to partial confinement 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 gaugino and theta-angle θ = π, and chiral symmetry in a strongly-coupled lattice gauge theory. We conjecture that such global symmetries may provide order parameters to distinguish fully- and partially-confined phases more generally, including at finite N.