Permutation orbifolds and their applications

Abstract

The theory of permutation orbifolds is reviewed and applied to the study of symmetric product orbifolds and the congruence subgroup problem. The issue of discrete torsion, the combinatorics of symmetric products, the Galois action and questions related to the classification of RCFTs are also discussed.

Invited talk at the Fields Institute workshop "Vertex Operator Algebras in Mathematics and Physics", Toronto, Canada, 23-27 October 2000