Automorphism Modular Invariants of Current Algebras

Abstract

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac--Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.

32 pages, plain TeX