Effective matter superpotentials from Wishart random matrices

TL;DR

This paper demonstrates deriving matter superpotentials in supersymmetric theories using Wishart random matrices within the Dijkgraaf-Vafa framework, connecting matrix integrals to known non-perturbative superpotentials.

Contribution

It introduces a novel approach to obtain matter superpotentials from constrained matrix integrals equivalent to Wishart random matrices, extending the matrix model techniques.

Findings

Derivation of Affleck-Dine-Seiberg superpotentials from matrix integrals.

Connection between Wishart matrices and non-perturbative superpotentials.

Extension of matrix model methods to matter field superpotentials.

Abstract

We show how within the Dijkgraaf-Vafa prescription one can derive superpotentials for matter fields. The ingredients forming the non-perturbative Affleck-Dine-Seiberg superpotentials arise from constrained matrix integrals, which are equivalent to classical complex Wishart random matrices. The mechanism is similar to the way the Veneziano-Yankielowicz superpotential arises from the matrix model measure.