Fusion products of twisted modules in permutation orbifolds

TL;DR

This paper computes the fusion products between modules and twisted modules in permutation orbifolds of vertex operator algebras, advancing understanding of their module category structure.

Contribution

It explicitly determines the fusion rules involving twisted modules in permutation orbifolds of vertex operator algebras, a problem previously unresolved.

Findings

Fusion products involving twisted modules are explicitly calculated.

Results clarify the module category structure of permutation orbifolds.

Provides tools for further study of orbifold conformal field theories.

Abstract

Let $V$ be a vertex operator algebra, $k$ a positive integer and $\sigma$ a permutation automorphism of the vertex operator algebra $V^{\otimes k}$. In this paper, we determine the fusion product of any $V^{\otimes k}$-module with any $\sigma$-twisted $V^{\otimes k}$-module.