Modular Invariance and (Quasi)-Galois symmetry in Conformal Field Theory

Abstract

A brief heuristic explanation is given of recent work with Juergen Fuchs, Beatriz Gato-Rivera and Christoph Schweigert on the construction of modular invariant partition functions from Galois symmetry in conformal field theory. A generalization, which we call quasi-Galois symmetry, is also described. As an application of the latter, the invariants of the exceptional algebras at level $g$ (for example $E_8$ level 30) expected from conformal embeddings are presented. [Contribution to the Proceedings of the International Symposium on the Theory of Elementary Particles Wendisch-Rietz, August 30 - September 3, 1994]