On exact superpotentials in confining vacua Original Research Article

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=−WaαWaα/(32Nπ2) 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.