On exact superpotentials in confining vacua

TL;DR

This paper derives the exact effective superpotential for confining vacua in N=1 super Yang-Mills theories with adjoint matter, confirming its match with matrix model predictions and revealing deep theoretical connections.

Contribution

It provides a purely field theoretic derivation of the exact superpotential, linking non-renormalization theorems to planar diagram sums and confirming the Dijkgraaf-Vafa proposal.

Findings

Exact superpotential W(S) derived for confining vacua.

Matching with Dijkgraaf-Vafa matrix model results.

Revealed relationship between non-renormalization theorems and planar diagrams.

Abstract

We consider the N=1 super Yang-Mills theory with gauge group U(Nc) or SU(Nc) 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 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.