Confinement in partially broken abelian Chern-Simons theories

TL;DR

This paper studies how confinement phenomena in certain abelian Chern-Simons theories depend on the presence of CS terms for unbroken gauge fields, revealing conditions under which particles are confined or free.

Contribution

It demonstrates that confinement in partially broken abelian Chern-Simons theories depends on the CS terms for unbroken gauge fields, showing how adding these terms affects confinement.

Findings

Confinement occurs for particles with specific flux and charge multiples.

Adding CS term for broken gauge fields introduces Aharonov-Bohm interactions.

Including CS term for unbroken gauge fields eliminates confinement.

Abstract

Planar Chern-Simons (CS) theories in which a compact abelian gauge group U(1) x U(1) is spontaneously broken to U(1) x Z_N 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 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.