Flux tubes in three-dimensional lattice gauge theories

Measurements of flux tubes generated by sources in different representations of SU(2) and U(1) lattice gauge theory in three dimensions are reported. Heavy quarks'' are considered in three representations of SU(2): fundamental ([ital j]=1/2), adjoint ([ital j]=1), and quartet ([ital j]=3/2). Wilson loops are used to introduce a static quark-antiquark ([ital Q][sub [ital j][bar Q][ital j]]) pair. Several attributes of the fields generated by the [ital Q][sub [ital j][bar Q][ital j]] pair are measured. In particular, the first direct lattice measurements of the flux-tube cross section [ital scrA][sub [ital j]] as a junction of representation are made. It is found that [ital scrA][sub [ital j]][approx][ital const], to within about 10% (a rough estimate of the overall quality of the data). The results are consistent with a connection between the string tension [sigma][sub [ital j]] and cross section suggested by a simplified model of flux-tube formation, [sigma][sub [ital j]]=[ital g][sup 2][ital j]([ital j]+1)/(2[ital scrA][sub [ital j]]) [where [ital g] is the gauge coupling], given that the string tension scales like the Casimir constant [ital j]([ital j]+1), as observed in previous lattice studies in both three and four dimensions (and confirmed here up to the quartet representation). These results can be used to discriminate among phenomenological models of the physics underlying confinement. Flux-tube measurements are also made in compact three-dimensional QED, which exhibits electric confinement due to magnetic monopole condensation. Singly and doubly charged Wilson loops are considered. The string tension is found to scale like the squared charge, and the flux-tube cross section is found to be independent of the charge, to a good approximation.