Chiral Rings, Anomalies and Electric-Magnetic Duality

TL;DR

This paper explores electric-magnetic duality in supersymmetric gauge theories with chiral rings, analyzing how duality manifests in different vacua and matching effective superpotentials using the Dijkgraaf-Vafa approach.

Contribution

It provides a detailed analysis of duality in chiral rings, including offshell duality and the structure of resolvents across vacua, extending understanding of supersymmetric gauge theories.

Findings

Dual magnetic solutions correspond to electric vacua.

Effective superpotentials match via Dijkgraaf-Vafa method.

Duality can hold offshell in certain cases.

Abstract

We study electric-magnetic duality in the chiral ring of a supersymmetric U(N_c) gauge theory with adjoint and fundamental matter, in presence of a general confining phase superpotential for the adjoint and the mesons. We find the magnetic solution corresponding to both the pseudoconfining and higgs electric vacua. By means of the Dijkgraaf-Vafa method, we match the effective glueball superpotentials and show that in some cases duality works exactly offshell. We give also a picture of the analytic structure of the resolvents in the magnetic theory, as we smoothly interpolate between different higgs vacua on the electric side.