Vortices and confinement at weak coupling

We discuss the physical picture of thick vortices as the mechanism responsible for confinement at arbitrarily weak coupling in $\mathrm{SU}\left(2\right)\mathrm{}$ gauge theory. By introducing appropriate variables on the lattice we distinguish between thin, thick and “hybrid” vortices, the latter involving $Z\left(2\right)\mathrm{}$ monopole loop boundaries. We present numerical lattice simulation results that demonstrate that the full $\mathrm{SU}\left(2\right)\mathrm{}$ string tension at weak coupling arises from the presence of vortices linked to the Wilson loop. Conversely, excluding linked vortices eliminates the confining potential. The numerical results are stable under an alternate choice of lattice action as well as a smoothing procedure which removes short distance fluctuations while preserving long distance physics.