Operator Algebras and Conformal Field Theory III. Fusion of positive energy representations of LSU(N) using bounded operators

TL;DR

This paper explores the fusion of positive energy representations of LSU(N) through von Neumann algebra techniques, primary fields, and solutions to the Knizhnik-Zamolodchikov equation, advancing the mathematical understanding of conformal field theory.

Contribution

It introduces a novel approach to fusion using Connes' tensor product and explicit solutions of the KZ equation, connecting operator algebras with conformal field theory.

Findings

Fusion computed via primary fields and KZ solutions

Established a new operator algebra framework for fusion

Enhanced understanding of positive energy representations

Abstract

Fusion of positive energy representations is defined using Connes' tensor product for bimodules over a von Neumann algebra. Fusion is computed using the analytic theory of primary fields and explicit solutions of the Knizhnik-Zamolodchikov equation.