Representation theory of a W-algebra from generalised DS reduction

TL;DR

This paper constructs and analyzes a specific W-algebra derived from a B2 WZW model via Drinfeld-Sokolov reduction, detailing its structure, free field realization, and representation theory including fusion rules and character formulas.

Contribution

It provides an explicit construction, free field realization, and detailed representation theory analysis of a new W-algebra from a B2 WZW model reduction.

Findings

Explicit algebra generated by three spin-2 and one spin-1 fields

Free field realization commuting with a screening charge

Fusion rules and character formulas for degenerate primary fields

Abstract

We investigate the W-algebra resulting from Drinfel'd-Sokolov reduction of a $B_2$ WZW model with respect to the grading induced by a short root. The quantum algebra, which is generated by three fields of spin-2 and a field of spin-1, is explicitly constructed. A `free field' realisation of the algebra in terms of the zero-grade currents is given, and it is shown that these commute with a screening charge. We investigate the representation theory of the algebra using a combination of the explicit fusion method of Bauer et al. and free field methods. We discuss the fusion rules of degenerate primary fields, and give various character formulae and a Kac determinant formula for the algebra