Direct derivation of the Veneziano-Yankielowicz superpotential from matrix model

TL;DR

This paper demonstrates how to derive the Veneziano-Yankielowicz superpotential directly from a matrix model by carefully fixing the measure, clarifying its connection to ${ m N}=4$ supersymmetric Yang-Mills theory.

Contribution

It provides a direct derivation of the superpotential from the matrix model, elucidating the conditions under which the matrix model reproduces known gauge theory results.

Findings

The superpotential is derived directly from the matrix model.

The measure fixing is crucial for the derivation.

The approach clarifies the link between matrix models and gauge theories.

Abstract

We derive the Veneziano-Yankielowicz superpotential directly from the matrix model by fixing the measure precisely. The essential requirement here is that the effective superpotential of the matrix model corresponding to the ${\cal N}=4$ supersymmetric Yang-Mills theory vanishes except for the tree gauge kinetic term. Thus we clarify the reason why the matrix model reproduces the Veneziano-Yankielowicz superpotential correctly in the Dijkgraaf-Vafa theory.