Flux-tubes in three-dimensional lattice gauge theories

TL;DR

This paper presents the first direct lattice measurements of flux-tube cross-sections in three-dimensional SU(2) and U(1) gauge theories, revealing constant cross-sections across representations and supporting flux-tube models of confinement.

Contribution

It provides novel lattice measurements of flux-tube cross-sections for various representations and charges, testing models of confinement and the dual superconductor hypothesis.

Findings

Flux-tube cross-section ${ m A}_j$ is approximately constant across representations.

String tension $\sigma_j$ scales with the Casimir $j(j+1)$, consistent with flux-tube models.

Flux-tube cross-section is charge-independent in compact QED$_3$.

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 ${\cal A}_j$ as a function of representation are made. It is found that ${\cal A}_j \approx {\rm constant}$, to about 10\%. Results are consistent with a connection between the string tension $\sigma_j$ and ${\cal A}_j$ suggested by a simplified flux-tube model, $\sigma_j = g^2 j(j+1) / (2 {\cal A}_j)$ [$g$ 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.