On structure constants and fusion rules in the $SL(2,\BC)/SU(2)$ WZNW model

TL;DR

This paper derives a closed formula for structure constants in the SL(2,C)/SU(2) WZNW model, enabling precise computation of n-point functions on genus zero surfaces.

Contribution

It introduces a novel method to compute structure constants and proposes fusion rules for the SL(2,C)/SU(2) WZNW model based on canonical quantization.

Findings

Derived a closed formula for structure constants.

Proposed fusion rules from reflection amplitudes.

Enabled unambiguous definition of genus zero n-point functions.

Abstract

A closed formula for the structure constants in the SL(2,C)/SU(2) WZNW model is derived by a method previously used in Liouville theory. With the help of a reflection amplitude that follows from the structure constants one obtains a proposal for the fusion rules from canonical quantization. Taken together these pieces of information allow an unambigous definition of any genus zero n-point function.