New modular invariant partition functions for tensor products of [Formula: see text] affine Lie algebras are presented. These exceptional modular invariants can be understood in terms of automorphisms of the fusion rules of the affine algebra or of its extensions. There are three isolated cases, as well as an infinite series of new invariants. As an application, the new modular invariants are employed to produce new Gepner type compactifications of the heterotic string.
We compute the branching rules of the conformal embeddings SO{4nk) 1 DSp(2ή) k φSp(2k) n and SO(rq) ι DSO(r) q ®SO(q) r for rq even. Using this we prove that the affine algebras Sp(2n) k and Sp(2k) n have the same S matrix and modular invariants. As a second application, we show how the triality of SO(8) leads to an exceptional modular invariant for SU{2) at level 16 and for all SO(q ^ 4) at level 8.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.