Confinement in a Higgs Model on $R^{3}\times S^{1}$

Understand

We determine the phase structure of an SU(2) gauge theory with an adjoint scalar on $R^{3}\times S^{1}$ using semiclassical methods.

• There are two global symmetries: a $Z(2)_{H}$ symmetry associated with the Higgs field and a $Z(2)_{C}$ center symmetry.
• We analyze the order of the deconfining phase transition when different deformation terms are used.
• After finding order parameters for the global symmetries, we show that there are four distinct phases: a deconfined phase, a confined phase, a Higgs phase, and a mixed confined phase.