Supersymmetric large-N reduced model with multiple matter

TL;DR

This paper extends the large-N reduction and supermatrix model approach to a broader class of supersymmetric gauge theories with multiple matter representations, linking their free energy to prepotentials.

Contribution

It generalizes the large-N reduction framework to gauge theories with product groups and bifundamental or fundamental matter, establishing supermatrix models for these theories.

Findings

Supermatrix models reproduce the prepotentials of the gauge theories.

The approach applies in the Veneziano limit with fixed matter-to-color ratio.

Generalization from single adjoint matter to multiple matter representations.

Abstract

We showed in hep-th/0303210 that the Dijkgraaf-Vafa theory can be regarded as large-N reduction in the case of $\mathcal{N}=1$ supersymmetric U(N) gauge theories, with single adjoint matter. We generalize this to gauge theories with gauge groups being the products of some unitary groups coupled to bifundamental or fundamental matter. We show that some large-N reduced models of these theories are supermatrix models, whose free energy is equivalent to the prepotentials of the original gauge theories. The supermatrix model in our approach should be taken in the Veneziano limit $N_c,N_f \to \infty $ with $N_f/N_c$ fixed.