The Extended Algebra of the SU(2) Wess-Zumino-Witten Models

Details The Extended Algebra of the SU(2) Wess-Zumino-Witten Models The Extended Algebra of the SU(2) Wess-Zumino-Witten Models

2006-09-29

arxiv.org/abs/hep-th/0609226v2

Nucl.Phys.B765:201-239,2007

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, 2 figures; added further motivational material and corrected typos

Scientific paper

10.1016/j.nuclphysb.2006.11.019

The Wess-Zumino-Witten model defined on the group SU(2) has a unique (non-trivial) simple current of conformal dimension k/4 for each level k. The extended algebra defined by this simple current is carefully constructed in terms of generalised commutation relations, and the corresponding representation theory is investigated. This extended algebra approach is proven to realise a faithful ("free-field-type") representation of the SU(2) model. Subtleties in the formulation of the extended theory are illustrated throughout by the k=1, 2 and 4 models. For the first two cases, bases for the modules of the extended theory are given and rigorously justified.

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