Fusion Products of Twisted Modules in Permutation Orbifolds: II

TL;DR

This paper determines the fusion products of twisted modules in permutation orbifolds of a specific class of vertex operator algebras, extending understanding of their module structure and fusion rules.

Contribution

It explicitly computes the fusion products of twisted modules for permutation orbifolds of rational, $C_2$-cofinite vertex operator algebras, generalizing previous results.

Findings

Fusion rules for twisted modules in permutation orbifolds are explicitly derived.

The results apply to a broad class of vertex operator algebras of CFT type.

Provides a foundation for further study of orbifold models in conformal field theory.

Abstract

Let $V$ be a simple, rational, $C_{2}$-cofinite vertex operator algebra of CFT type, and let $k$ be a positive integer. In this paper, we determine the fusion products of twisted modules for $V^{\otimes k}$ and $G = \left\langle g \right\rangle$ generated by any permutation $g \in S_{k}$.