On orbifold theory

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V-G is regular. It is proved that every irreducible V-G-module occurs in an irreducible g-twisted V-module for some g is an element of G. Moreover, the quantum dimensions of irreducible V-G-modules are determined and a global dimension formula for V in terms of twisted modules is obtained. In particular, the orbifold theory conjecture is completely solved if G is solvable. (c) 2017 Elsevier Inc. All rights reserved.