On orbifold theory

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that VG is regular. It is proved that every irreducible VG-module occurs in an irreducible g-twisted V-module for some g∈G. Moreover, the quantum dimensions of irreducible VG-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.