N = 1 theories and a geometric master field

Abstract

We study the large-N limit of the class of U(N) N = 1 SUSY gauge theories with an adjoint scalar and a superpotential W(Φ). In each of the vacua of the quantum theory, the expectation values <TrΦ^p> are determined by a master matrix Φ₀ with eigenvalue distribution ρ_GT(λ). ρ_GT(λ) is quite distinct from the eigenvalue distribution ρ_MM(λ) of the corresponding large-N matrix model proposed by Dijkgraaf and Vafa. Nevertheless, it has a simple form on the auxiliary riemann surface of the matrix model. Thus the underlying geometry of the matrix model leads to a definite prescription for computing ρ_GT(λ), knowing ρ_MM(λ).