Simple current extensions of tensor products of vertex operator algebras

TL;DR

This paper investigates how simple current extensions of tensor product vertex operator algebras relate to fusion rules, constructing chains of such extensions and exploring their irreducible twisted modules.

Contribution

It establishes the relationship between fusion rules of simple current extensions and tensor factors, and constructs chains of extensions with analysis of twisted modules.

Findings

Fusion rules for simple current extensions relate to those of tensor factors.

Constructed chains of simple current extensions in special cases.

Discussed irreducible twisted modules for these extensions.

Abstract

We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple current extension and the fusion rule for a tensor factor. In a special case, we construct a chain of simple current extensions. We discuss certain irreducible twisted modules for the simple current extension as well.