Derivation of the Konishi anomaly relation from Dijkgraaf-Vafa with (Bi-)fundamental matters

TL;DR

This paper derives Feynman rules for N=1 super Yang-Mills theories with various matter representations and demonstrates that expectation values satisfy the Konishi anomaly relation, connecting Dijkgraaf-Vafa methods to anomaly relations.

Contribution

It explicitly formulates Feynman rules for complex gauge theories with multiple matter representations and verifies the Konishi anomaly relation using these rules.

Findings

Feynman rules for super Yang-Mills with adjoint, fundamental, and bi-fundamental matter

Verification that expectation values satisfy the Konishi anomaly relation

Application of Dijkgraaf-Vafa approach to these gauge theories

Abstract

We explicitly write down the Feynman rules following the work of Dijkfraaf, Vafa and collaborators for N=1 super Yang-Mills having products of SU groups as the gauge group and matter chiral superfields in adjoint, fundamental, and bi-fundamental representations without baryonic perturbations. As an application of this, we show expectation values calculated by these methods satisfy the Konishi anomaly relation.