A theory of tensor products for module categories for a vertex operator algebra, II

TL;DR

This paper completes the development of a tensor product theory for module categories of vertex operator algebras by providing detailed proofs for the results introduced in the first part, establishing a rigorous foundation.

Contribution

It supplies the missing proofs for the $Q(z)$-tensor product constructions in the previous work, solidifying the theoretical framework for tensor products in vertex operator algebra modules.

Findings

Proofs of $Q(z)$-tensor product results are provided.

The theory of tensor products for vertex operator algebra modules is rigorously established.

Foundational results enable further research in module category tensor structures.

Abstract

This is the second part in a series of papers presenting a theory of tensor products for module categories for a vertex operator algebra. In Part I (hep-th/9309076), the notions of $P(z)$- and $Q(z)$-tensor product of two modules for a vertex operator algebra were introduced and under a certain hypothesis, two constructions of a $Q(z)$-tensor product were given, using certain results stated without proof. In Part II, the proofs of those results are supplied.