Duality Symmetries for N=2 Supersymmetric QCD with Vanishing beta-Functions

TL;DR

This paper constructs duality groups for N=2 supersymmetric QCD with specific gauge groups and matter content, revealing their structure and automorphic functions that encode the duality symmetries in the Seiberg-Witten framework.

Contribution

It explicitly determines the duality groups for these theories and introduces automorphic functions representing the duality symmetries on the Seiberg-Witten curve.

Findings

Duality groups are generated by elements satisfying a specific relation, not subgroups of SL(2,Z)

Automorphic functions map the fundamental region to the Riemann sphere

Duality symmetries are faithfully represented in the Seiberg-Witten curve

Abstract

We construct the duality groups for N=2 Supersymmetric QCD with gauge group SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The groups are generated by two elements $S$ and $T$ that satisfy a relation $(STS^{-1}T)^{2n+1}=1$. Thus, the groups are not subgroups of $SL(2,Z)$. We also construct automorphic functions that map the fundamental region of the group generated by $T$ and $STS$ to the Riemann sphere. These automorphic functions faithfully represent the duality symmetry in the Seiberg-Witten curve.