Whitham Prepotential and Superpotential

TL;DR

This paper explores the connection between Whitham deformation theory and supersymmetric gauge theories, deriving matrix model curves from the prepotential's properties in a softly broken N=2 to N=1 setting.

Contribution

It introduces a novel approach linking Whitham prepotential deformations to matrix model curves in supersymmetric gauge theories.

Findings

Derived matrix model curve from Whitham prepotential conditions.

Established a correspondence between superpotential and Whitham deformation.

Provided a new perspective on N=2 to N=1 supersymmetry breaking.

Abstract

N=2 supersymmetric U(N) Yang-Mills theory softly broken to N=1 by the superpotential of the adjoint scalar fields is discussed from the viewpoint of the Whitham deformation theory for prepotential. With proper identification of the superpotential we derive the matrix model curve from the condition that the mixed second derivatives of the Whitham prepotential have a nontrivial kernel.