Fusion of twisted representations

TL;DR

This paper generalizes the fusion product formula for chiral algebra representations to include twisted cases, establishing a tensor product structure and analyzing the Ramond sector of superconformal algebras.

Contribution

It extends the fusion formula to twisted representations and characterizes the associated algebraic structures, including the Ramond sector of superconformal algebras.

Findings

Generalized fusion formula for twisted representations

Defined tensor product with desired properties

Analyzed Ramond sector of superconformal algebra

Abstract

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and determine the analogue of Zhu's algebra for arbitrary twisted representations. As an example we study the fusion of representations of the Ramond sector of the N=1 and N=2 superconformal algebra. In the latter case, certain subtleties arise which we describe in detail.