Planar limit of orientifold field theories and emergent center symmetry

We consider orientifold field theories [i.e., SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations] on R3×S1 where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills theory. The latter has ZN center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from ZN symmetric to ZN broken phase applies. At the Lagrangian level the orientifold theories have at most a Z2 center. We discuss how the full ZN center symmetry dynamically emerges in the orientifold theories in the limit N→. In the confining phase the manifestation of this enhancement is the existence of stable k strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.