Classification of the N=1 Seiberg-Witten Theories

TL;DR

This paper systematically classifies N=1 supersymmetric gauge theories in the Coulomb phase with simple gauge groups and no superpotential, providing their low-energy solutions via hyperelliptic Seiberg-Witten curves.

Contribution

It offers a complete classification and solution for a broad class of N=1 theories, extending previous work to include all theories with matter index less than the adjoint.

Findings

Derived all such theories based on simple gauge groups.

Provided explicit low-energy solutions using hyperelliptic Seiberg-Witten curves.

Completed the classification for theories with matter index less than the adjoint.

Abstract

We present a systematic study of N=1 supersymmetric gauge theories which are in the Coulomb phase. We show how to find all such theories based on a simple gauge group and no tree-level superpotential. We find the low-energy solution for the new theories in terms of a hyperelliptic Seiberg-Witten curve. This work completes the study of all N=1 supersymmetric gauge theories where the Dynkin index of the matter fields equals the index of the adjoint (mu=G), and consequently all theories for which mu<G.