Super orbifold theory

TL;DR

This paper investigates the structure of modules over simple vertex operator superalgebras under finite automorphism groups, classifies irreducible modules, and establishes a super quantum Galois theory with explicit computations of quantum dimensions and the S-matrix.

Contribution

It provides a classification of irreducible modules over fixed-point subalgebras and develops a super quantum Galois theory for vertex operator superalgebras.

Findings

Classification of irreducible $V^G$-modules

Determination of quantum dimensions of modules

Computation of the $S$-matrix for $V^G$

Abstract

Let $V$ be a simple vertex operator superalgebra and $G$ a finite automorphism group of $V$ containing the canonical automorphism $\sigma$ 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 $g\in G$ and the irreducible $V^G$-modules are classified. Moreover, the quantum dimensions of irreducible $V^G$-modules are determined, a global dimension formula for $V$ in terms of twisted modules is obtained and a super quantum Galois theory is established. In addition, the $S$-matrix of $V^G$ is computed