Refining the proof of planar equivalence

We outline a full nonperturbative proof of planar (large-$N$) equivalence between bosonic correlators in a theory with Majorana fermions in the adjoint representation and one with Dirac fermions in the two-index (anti) symmetric representation. In a particular case (one-flavor), this reduces to our previous result—planar equivalence between super-Yang-Mills theory and a nonsupersymmetric “orientifold field theory.” The latter theory becomes one-flavor massless QCD at $N=3$.