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 Z_N for fermions in the adjoint representation and just Z_2 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 Z_N center symmetry is dynamically recovered also for fermions in the (anti)symmetric representation, by considering the theories at finite temperature.