A Monograph on the Classification of the Discrete Subgroups of SU(4)

TL;DR

This paper provides a comprehensive classification of all finite discrete subgroups of SU(4), including character tables for exceptional cases, aiding research in string theory, quiver theories, and related fields.

Contribution

It offers the first complete modern classification of discrete subgroups of SU(4) with detailed character tables for exceptional cases.

Findings

Classification of all finite subgroups of SU(4)

Character tables for exceptional subgroups

Resource for string and quiver theories

Abstract

We here present, in modern notation, the classification of the discrete finite subgroups of SU(4) as well as the character tables for the exceptional cases thereof (Cf. https://github.com/yanghuihe/SU4Subgroups). We hope this catalogue will be useful to works on string orbifold theories, quiver theories, WZW modular invariants, Gorenstein resolutions, nonlinear sigma-models as well as some recently proposed inter-connections among them.