From Super-yang–mills Theory to Qcd: Planar Equivalence and Its Implications

We review and extend our recent work on the planar (large N) equivalence between gauge theories with varying degrees of supersymmetry. The main emphasis is on the planar equivalence between N =1 gluodynamics (super-Yang–Mills theory) and a nonsupersymmetric “orientifold field theory”. We outline an “orientifold” large N expansion, analyze its possible phenomenological consequences in one-flavor massless QCD, and make a first attempt at extending the correspondence to three massless flavors. An analytic calculation of the quark condensate in one-flavor QCD starting from the gluino condensate in N =1 gluodynamics is thoroughly discussed. We also comment on a planar equivalence involving N = 1 supersymmetry, on “chiral rings” in non-supersymmetric theories, and on the origin of planar equivalence from an underlying, non-tachyonic type-0 string theory. Finally, possible further directions of investigation, such as the gauge/gravity correspondence in large-N orientifold field theory, are briefly discussed.