Refining the Proof of Planar Equivalence

TL;DR

This paper provides a comprehensive non-perturbative proof of planar equivalence between certain large-N gauge theories, extending previous results and connecting supersymmetric and non-supersymmetric theories.

Contribution

It offers a full non-perturbative proof of planar equivalence, including cases with Majorana and Dirac fermions, generalizing earlier results to broader classes of theories.

Findings

Confirmed planar equivalence for a wide class of theories.

Extended previous results to non-perturbative regimes.

Connected super-Yang--Mills theory with non-supersymmetric orientifold theories.

Abstract

We outline a full non-perturbative 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 non-supersymmetric ``orientifold field theory.'' The latter theory becomes one-flavor massless QCD at N=3.