Phase Structure of Confining Theories on R³ x S¹

Recent work on QCD-like theories on R^3 x S^1 has revealed that a confined phase can exist when the circumference L of S^1 is sufficiently small. Adjoint QCD and double-trace deformation theories with certain conditions are such theories, and we present some new results for their phase diagrams. First we show the connection between the large-L and small-L confined regions in the phase diagram of SU(3) adjoint QCD using Polyakov-Nambu-Jona Lasinio models. Then we consider an SU(2) double-trace deformation theory with adjoint scalars and study conflicts between the Higgs and small-L confined phase.