Some Correlators of $SU(3)_3$ WZW Models on Higher-Genus Riemann Surfaces

TL;DR

This paper develops a method to compute correlators of $SU(3)_3$ WZW models on higher-genus Riemann surfaces using conformal embedding and symmetry properties, applicable to all $k>1$ models embedded in $k=1$ models.

Contribution

It introduces a novel approach leveraging conformal embedding and symmetry properties to calculate correlators for $SU(3)_3$ and similar WZW models on complex surfaces.

Findings

Expressed $SU(3)_3$ characters via $SO(8)_1$ characters.

Calculated correlators on arbitrary Riemann surfaces.

Applicable to all $k>1$ WZW models with conformal embedding.

Abstract

Using the conformal embedding on the torus, we can express some characters of $SU(3)_3$ in terms of $SO(8)_1$ characters. Then with the help of crossing symmetry, modular transformation and factorization properties of Green functions, we will calculate a class of correlators of $SU(3)_3$ on arbitrary Riemann surfaces. This method can apply to all $k>1$ WZW models which can be conformally embedded in some $k=1$ WZW models.