Comments on Effective Superpotentials via Matrix Models

TL;DR

This paper investigates the conjecture that effective superpotentials in certain supersymmetric gauge theories can be computed using matrix models, confirming the conjecture through exact calculations and geometric interpretations.

Contribution

It provides exact evaluations of effective superpotentials for specific gauge theories using matrix models and string theory, validating the Dijkgraaf-Vafa conjecture in these cases.

Findings

Exact superpotentials match matrix model predictions.

Superpotentials agree with closed string theory on Calabi-Yau geometries.

Supports the conjecture linking gauge theories, matrix models, and string theory.

Abstract

Dijkgraaf and Vafa have conjectured that the effective superpotentials for N=1 four-dimensional supersymmetric gauge theories can be given by the planar diagrams of matrix models. We examine some special models with cubic and quartic tree level superpotentials for adjoint chiral superfield \Phi. We consider the effective superpotentials for the classical vacuum \Phi=0 for U(N) and SO(N)/Sp(N) gauge theories. We evaluate the effective superpotentials exactly in terms of the matrix model and in terms of closed string theory on Calabi-Yau geometry with fluxes. As a result we find their perfect agreements.