N = 1 Theories and a Geometric Master Field

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 〈TrΦp〉 are determined by a master matrix Φ0 with eigenvalue distribution ρGT (λ). ρGT (λ) is quite distinct from the eigenvalue distribution ρMM (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 ρGT (λ), knowing ρMM (λ). Nov. 2002 1 [email protected]