Flux-tubes in three-dimensional lattice gauge theories

Abstract

Flux-tubes in different representations of SU(2) and U(1) lattice gauge theories in three dimensions are measured. Wilson loops generate heavy ``quark-antiquark'' pairs in fundamental ($j=1/2$), adjoint ($j=1$), and quartet ($j=3/2$) representations of SU(2). The first direct lattice measurements of the flux-tube cross-section ${\mathcal{A}}_j$ as a function of representation are made. It is found that ${\mathcal{A}}_j\approx \mathrm{constant}$, to about 10\%. Results are consistent with a connection between the string tension ${\sigma }_j$ and ${\mathcal{A}}_j$ suggested by a simplified flux-tube model, ${\sigma }_j=g^{2}j(j+1)/(2{\mathcal{A}}_j)$ [$g$ is the gauge coupling], given that ${\sigma }_j$ scales like the Casimir $j(j+1)$, as observed in previous lattice studies in both three and four dimensions. The results can discriminate among phenomenological models of the physics underlying confinement. Flux-tubes for singly- and doubly-charged Wilson loops in compact QED${}_3$ are also measured. It is found that the string tension scales as the squared-charge and the flux-tube cross-section is independent of charge to good approximation. These SU(2) and U(1) simulations 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.

Comments: 15 pages (REVTEX 2.1). Figures: 11, not included (available by request from trottier@sfu.ca by regular mail, postscript files, or one self-unpacking uuencoded file)