Logarithmic tensor category theory, V: Convergence condition for intertwining maps and the corresponding compatibility condition

TL;DR

This paper advances tensor category theory for vertex operator algebras by analyzing products and iterates of intertwining maps, establishing convergence and compatibility conditions crucial for the analytic framework.

Contribution

It introduces a new convergence condition for intertwining maps and develops the analytic approach within the tensor category framework for vertex operator algebras.

Findings

Established convergence conditions for intertwining maps

Developed the analytic approach for tensor categories

Analyzed products and iterates of logarithmic intertwining operators

Abstract

This is the fifth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part V), we study products and iterates of intertwining maps and of logarithmic intertwining operators and we begin the development of our analytic approach.