On Orbifold Theory

TL;DR

This paper explores the structure of orbifold vertex operator algebras, proving the occurrence of all irreducible modules in twisted modules, and deriving formulas for quantum and global dimensions.

Contribution

It establishes that all irreducible modules of V^G appear in twisted modules and provides formulas for their quantum and global dimensions.

Findings

All irreducible V^G-modules occur in twisted modules.

Quantum dimensions of irreducible V^G-modules are explicitly determined.

A global dimension formula for V in terms of twisted modules is derived.

Abstract

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 in G. Moreover, the quantum dimensions of each irreducible V^G-module are determined and a global dimension formula for V in terms of twisted modules is obtained.