The Classification of Affine SU(3) Modular Invariant Partition Functions

A complete classification of the WZNW modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of SU(2), and level 1 of all simple algebras. In this paper we solve the classification problem for SU(3) modular invariant partition functions. Our approach will also be applicable to other affine Lie algebras, and we include some preliminary work in that direction, including a sketch of a new proof for SU(2)