Twisted sectors for tensor product vertex operator algebras associated to permutation groups

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-circle timesk. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V-circle timesk 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-circle timesk-modules from weak V-modules. For an arbitrary permutation automorphism g of V-circle timesk the category of weak admissible g-twisted modules for V-circle timesk is semisimple and the simple objects are determined if V is rational. In addition, we extend these results to the more general setting of gammag-twisted V-circle timesk-modules for gamma a general automorphism of V acting diagonally on V-circle timesk and g a permutation automorphism of V-circle timesk.