1998/03/31 by K. Barron, C. Dong, G. Mason · 2 citations
Mathematics · Physics and Astronomy · #math.QA #hep-th
paper · pdf · doi:10.1007/s002200200633
published as Commun.Math.Phys. 227 (2002) 349-384 · amslatex 34 pages, both mathematics and typos are corrected
arxiv created 1999/12/16 · arxiv updated 2009/11/30
Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V⊗ k. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V⊗ k are isomorphic to the categories of weak, weak admissible and ordinary V-modules, respectively. The main result is an explicit construction of the weak g-twisted V⊗ k-modules from weak V-modules. For an arbitrary permutation automorphism g of V⊗ k the category of weak admissible g-twisted modules for V^⊗ k is semisimple and the simple objects are determined if V is rational. In addition, we extend these results to the more general setting of γg-twisted V⊗ k-modules for γa general automorphism of V acting diagonally on V⊗ k and a g a permutation automorphism of V⊗ k.