Fusion Rules for Extended Current Algebras

TL;DR

This paper derives explicit fusion rules and S matrices for extended current algebras in rational conformal field theory, revealing cases with sensible fusion rules and others with fractional constants.

Contribution

It provides explicit formulas for fusion rules and S matrices for extended current algebras, advancing understanding of their structure in conformal field theory.

Findings

Explicit formulas for S matrix and fusion rules

Identification of cases with sensible fusion rules

Discovery of fractional fusion constants in some cases

Abstract

The initial classification of fusion rules have shown that rational conformal field theory is very limited. In this paper we study the fusion rules of extend ed current algebras. Explicit formulas are given for the S matrix and the fusion rules, based on the full splitting of the fixed point fields. We find that in s ome cases sensible fusion rules are obtained, while in others this procedure lea ds to fractional fusion constants.