Phase transitions at strong coupling in the 2+1-d abelian Higgs model

Abstract

We study, using numerical Monte-Carlo simulations, an effective description of the 2+1 dimensional Abelian Higgs model which is valid at strong coupling, in the broken symmetry sector. In this limit, the massive gauge boson and the massive neutral Higgs decouple leaving only the massive vortices. The vortices have no long range interactions. We find a phase transition as the mass of the vortices is made lighter and lighter. At the transition, the contributions to the functional integral come from a so-called infinite vortex anti-vortex loop. Adding the Chern-Simons term simply counts the linking number between the vortices. We find that the Wilson loop exhibits perimeter law behaviour in both phases, although the polarization cloud increases by an order of magnitude at the transition. We also study the 't Hooft loop. We find the 't Hooft loop exhibits perimeter law behaviour in the presence of the Chern-Simons term but is trivial in its absence. Thus we have a theory with perimeter law for both the Wilson loop and the 't Hooft loop, but contains no massless particles.