Dynkin diagrams of CP¹ orbifolds

We investigate N = 2 supersymmetric sigma-model orbifolds of the sphere in the large-radius limit. These correspond to N = 2 superconformal field theories. We review the topological-anti-topological equations of Cecotti and Vafa and their classification of N = 2 theories with massive deformations. 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 classifying supersymmetric theories. They correspond to the extended Dynkin diagrams associated to finite subgroups of SO(3).