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N=1{\cal N}=1 Theories and a Geometric Master Field

Abstract

We study the large NN limit of the class of U(N) {\CN}=1 SUSY gauge theories with an adjoint scalar and a superpotential W()W(\P). In each of the vacua of the quantum theory, the expectation values \laTrΦp\Phi^p\ra are determined by a master matrix Φ0\Phi_0 with eigenvalue distribution \rho_{GT}(\l). \rho_{GT}(\l) is quite distinct from the eigenvalue distribution \rho_{MM}(\l) of the corresponding large NN 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 \rho_{GT}(\l), knowing \rho_{MM}(\l).Comment: 16 pages; v2. Further elaboration in Sec. 5 on the relation between gauge and matrix eigenvalue distributions, v3: Minor change

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