Center symmetry and the orientifold planar equivalence

We study the center symmetry of SU(N) gauge theories with fermions in the two–index representations, by computing the effective potential of the Polyakov loop in the large–mass expansion on the lattice. In the large–N limit and at non–zero temperature, we find that the center symmetry is ZN for fermions in the adjoint representation and just Z2 for fermions in the (anti)symmetric representation. We discuss the fact that our results do not contradict the orientifold planar equivalence, which relates a common sector defined by the bosonic gauge–invariant C–even states of theories with fermions in different two–index representations. Our results complement the work of Armoni et al. (2007), who showed how at zero temperature a ZN center symmetry is dynamically recovered also for fermions in the (anti)symmetric representation, by considering the theories at finite temperature.