N=2 Supersymmetric SO(N)/Sp(N) Gauge Theories from Matrix Model

TL;DR

This paper employs matrix models to analyze N=2 supersymmetric SO(N)/Sp(N) gauge theories, deriving the Seiberg-Witten curve through loop equations and effective actions.

Contribution

It introduces a matrix model approach to derive the Seiberg-Witten curve for SO(N)/Sp(N) gauge theories with massive hypermultiplets.

Findings

Derived the effective action for eigenvalues.

Obtained the loop equation for the matrix model.

Reconstructed the Seiberg-Witten curve from the loop equation.

Abstract

We use the matrix model to describe the N=2 SO(N)/Sp(N) supersymmetric gauge theories with massive hypermultiplets in the fundamental representation. By taking the tree level superpotential perturbation made of a polynomial of a scalar chiral multiplet, the effective action for the eigenvalues of chiral multiplet can be obtained. By varying this action with respect to an eigenvalue, a loop equation is obtained. By analyzing this equation, we derive the Seiberg-Witten curve within the context of matrix model.