Coxeter and Dynkin Diagrams and Their Associated Twisted Partition Functions for the Virasoro Minimal Models

Abstract

To a pair (G′, G″) of ADE Dynkin diagrams one can associate five types of sesquilinear forms on the space of Virasoro characters. These forms can be interpreted, in terms of minimal models, as twisted partition functions. Our classification rests on the possibility of twisting the “torus structures” of the two diagrams G′ and G″. For the torus structure of a given diagram, one can introduce a single twist, two twists, or no twist at all. We describe the general situation and study an example pertaining to the case of the Virasoro minimal models.