SO(3) versus SU(2) lattice gauge theory

TL;DR

This paper demonstrates the equivalence of SO(3) and SU(2) lattice gauge theories at weak coupling through an analytic path, clarifies the mysterious phase of SO(3), and measures the dual string tension using advanced Monte Carlo methods.

Contribution

It provides an analytic connection between SO(3) and SU(2) gauge theories and measures the dual string tension in SO(3) using multicanonical Monte Carlo, clarifying the phase structure.

Findings

SO(3) theory is equivalent to SU(2) summed over twist sectors.

Large lattices (~700^4) are needed to probe the confined phase.

The dual string tension can be measured in SO(3) gauge theory.

Abstract

We consider the SO(3) lattice gauge theory at weak coupling, in the Villain action. We exhibit an analytic path in coupling space showing the equivalence of the SO(3) theory with SU(2) summed over all twist sectors. This clarifies the ``mysterious phase'' of SO(3). As order parameter, we consider the dual string tension or center vortex free energy, which we measure in SO(3) using multicanonical Monte Carlo. This allows us to set the scale, indicating that ${\cal O}(700)^4$ lattices are necessary to probe the confined phase. We consider the relevance of our findings for confinement in other gauge groups with trivial center.