Representation theory of a W-algebra from generalised DS reduction

Details Representation theory of a W-algebra from generalised DS reduction Representation theory of a W-algebra from generalised DS reduction

1994-03-25

arxiv.org/abs/hep-th/9403157v1

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, Latex file, DTP-94-5

Scientific paper

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

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