Confining gauge theories with adjoint scalars on R³ × S¹

Recent work on QCD-like gauge theories on R³ × S ¹ has shown that we can study confinement both perturbatively using the effective potential of the Polyakov loop and nonperturbativley using the semi-classical evaluation of monopoles and instantons. We extend the theory with an adjoint scalar field and use a deformation potential inspired by two-dimensional fermions with periodic boundary conditions, which unlike the previous models give a second-order phase transition. The model shows a rich phase structure, including a new confined phase where the Polyakov loop mixes with the scalar field. This new phase in turn shows that the confined phase is incompatible with the Higgs phase. Moreover, the mixing gives rise to topological objects that generalize the instanton constituents of BPS and KK monopoles in Euclidean space, which are then related to infinite sum of Julia-Zee dyons in Minkowski space by Poisson duality. All phases in the model are connected by a dilute monopole gas, and the string tension associated with Wilson loops orthogonal to the compact direction can be computed using Abelian duality.