Fusion products of twisted modules in permutation orbifolds

Abstract

Let V V be a vertex operator algebra, k k a positive integer and σ \sigma a permutation automorphism of the vertex operator algebra V ⊗ k V^{\otimes k} . In this paper, we determine the fusion product of any V ⊗ k V^{\otimes k} -module with any σ \sigma -twisted V ⊗ k V^{\otimes k} -module.