Dual Interpretations of Seiberg-Witten and Dijkgraaf-Vafa curves

TL;DR

This paper explores dual interpretations of Seiberg-Witten and Dijkgraaf-Vafa curves in supersymmetric gauge theories, revealing a symmetry that exchanges gauge group rank with superpotential degree and relates geometric deformations to flavor constraints.

Contribution

It introduces a duality framework that interchanges gauge group rank and superpotential degree, linking geometric deformation constraints to flavor number limitations.

Findings

Duality exchanges gauge group rank with superpotential degree.

Geometric deformation constraints map to flavor number constraints.

Provides new insights into the structure of supersymmetric gauge theories.

Abstract

We give dual interpretations of Seiberg-Witten and Dijkgraaf-Vafa (or matrix model) curves in n=1 supersymmetric U(N) gauge theory. This duality interchanges the rank of the gauge group with the degree of the superpotential; moreover, the constraint of having at most log-normalizable deformations of the geometry is mapped to a constraint in the number of flavors N_f < N in the dual theory.