Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II

TL;DR

This paper explores how the effective superpotential in a spontaneously broken N=2 supersymmetric U(N) gauge model relates to matrix model free energy, revealing a deformation of the Dijkgraaf-Vafa relation due to broken supersymmetry.

Contribution

It demonstrates a novel deformation of the Dijkgraaf-Vafa relation in the context of spontaneously broken N=2 supersymmetry, connecting superpotential and matrix model free energy.

Findings

Effective superpotential relates to planar free energy with a deformation term.

Deformation involves couplings of the original prepotential and matrix model.

Shows how supersymmetry breaking affects the gauge-matrix model correspondence.

Abstract

We consider the matter induced part of the effective superpotential of N=2, U(N) gauge model in which N=2 supersymmetry is spontaneously broken to N=1, by using the properties of the chiral ring and the generalized Konishi anomaly equations derived in our previous paper arXiv:0704.1060. It is shown that the effective superpotential is related to the planar free energy of the matrix model by a formula which consists of two parts -- the well-known part due to Dijkgraaf-Vafa and the part that acts as a deformation of the couplings. These couplings are those of the original bare prepotential in the action and at the same time matrix model couplings.