Dynkin Diagrams of ${CP}^1$ Orbifolds

TL;DR

This paper studies the soliton spectra of N=2 supersymmetric sigma model orbifolds of the sphere, using topological fusion, and classifies them via extended Dynkin diagrams linked to finite subgroups of SO(3).

Contribution

It introduces a method to compute generalized Dynkin diagrams for N=2 superconformal orbifold theories, connecting soliton spectra to finite subgroup classifications.

Findings

Dynkin diagrams correspond to finite subgroups of SO(3)

Computed soliton spectra for sphere orbifold theories

Classified massive superconformal theories using these diagrams

Abstract

We investigate $N=2$ supersymmetric sigma model orbifolds of the sphere in the large radius limit. These correspond to $N=2$ superconformal field theories. Using the equations of topological-anti-topological fusion for the topological orbifold, we compute the generalized Dynkin diagrams of these theories - i.e., the soliton spectrum - which was used in the classification of massive superconformal theories. They correspond to the extended Dynkin diagrams associated to finite subgroups of $SO(3).$