Lattice study of planar equivalence: The quark condensate

We study quenched $SU(N)$ gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colors those theories become nonperturbatively equivalent. We prove the equivalence assuming that the charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then carry out a quenched lattice simulation of the quark condensate in the symmetric, antisymmetric and the adjoint representations for $SU(2)$, $SU(3)$, $SU(4)$, $SU(6)$, and $SU(8)$. We show that the data support the equivalence and discuss the size of subleading corrections.