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 (j = 1/2), adjoint (j = 1), and quartet (j = 3/2). Wilson loops are used to introduce a static quark-antiquark (QjQj) pair. Several attributes of the fields generated by the QjQj pair are measured. In particular, the first direct lattice measurements of the flux-tube cross-section Aj as a function of representation are made. It is found that Aj ≈ constant, 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 σj and cross-section suggested by a simplified model of flux-tube formation, σj = g 2j(j + 1)/(2Aj) [where g is the gauge coupling], given that the string tension scales like the Casimir j(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 discriminate among phenomenological models of the physics underlying confinement. Flux-tube measurements are also made in compact QED3, which exhibits electric confinement due to magnetic monopole condensation. Singlyand 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 is be independent of the charge, to a good approximation. The results of these three-dimensional SU(2) and U(1) simulations taken together lend some support, albeit indirectly, to a conjecture that the dual superconductor mechanism underlies confinement in compact gauge theories in both three and four dimensions.