AUTOMORPHISM MODULAR INVARIANTS OF CURRENT-ALGEBRAS

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