On exact superpotentials in confining vacua

Abstract

We consider the N=1 super-Yang–Mills theory with gauge group U( N) or SU( N) and one adjoint Higgs field with an arbitrary polynomial superpotential. We provide a purely field theoretic derivation of the exact effective superpotential W( S) for the glueball superfield S=− W aα W a α /(32 Nπ 2) in the confining vacua. We show that the result matches with the Dijkgraaf–Vafa matrix model proposal. The proof brings to light a deep relationship between non-renormalization theorems first discussed by Intriligator, Leigh and Seiberg, and the fact that W( S) is given by a sum over planar diagrams.