Confinement in partially broken abelian Chern-Simons theories

Planar Chern-Simons (CS) theories in which a compact abelian gauge group U(1) × U(1) is spontaneously broken to U(1) × ZN are investigated. Among other things, it is noted that the theories just featuring the mixed CS term coupling the broken to the unbroken U(1) gauge fields in general exhibits an interesting form of confinement: only particles carrying certain multiples of the fundamental magnetic vortex flux unit and certain multiples of the fundamental charge of the unbroken U(1) gauge field can appear as free particles. Adding the usual CS term for the broken U(1) gauge fields does not change much. It merely leads to additional Aharonov-Bohm interactions among these particles. Upon introducing the CS term for the unbroken U(1) gauge fields, in contrast, the confinement phenomenon completely disappears.