The Classification of SU(3) Modular Invariants Revisited

Abstract

The SU(3) modular invariant partition functions were first completely classified in Ref.\ \SU. The purpose of these notes is four-fold: \item{(i)} Here we accomplish the SU(3) classification using only the most basic facts: modular invariance; $M_{\laμ}\in{\bf Z}_{\ge}$; and $M_{00}=1$. In \SU{} we made use of less elementary results from Moore-Seiberg, in addition to these 3 basic facts. \item{(ii)} Ref.\ \SU{} was completed well over a year ago. Since then I have found a number of significant simplifications to the general argument. They are all included here. \item{(iii)} A number of people have complained that some of the arguments in \SU{} were hard to follow. I have tried here to be as explicit and as clear as possible. \item{(iv)} Hidden in \SU{} were a number of smaller results which should be of independent value. These are explicitly mentioned here.

33 pp (plain tex)

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• Meromorphic c=24 Conformal Field Theories
• su(3)k fusion coefficients
• WZW Commutants, Lattices, and Level 1 Partition Functions
• Implications of an arithmetical symmetry of the commutant for modular invariants
• On the Classification of Diagonal Coset Modular Invariants
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