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

Abstract

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.

arXiv comment42 pages, 2 figures; added further motivational material and corrected typos

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Cited by in corpus (11)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
• Modular Data and Verlinde Formulae for Fractional Level WZW Models II
• sl^(2)_{-1/2}: A Case Study
• Logarithmic M(2,p) Minimal Models, their Logarithmic Couplings, and Duality
• sl(2)_{-1/2} and the Triplet Model
• The Verlinde formula in logarithmic CFT
• The Extended Algebra of the Minimal Models
• W-Algebras Extending Affine gl(1|1)
• Toward logarithmic extensions of ^sl(2)_k conformal field models
• Path representation of su(2)_k states I: Operators and particles for k=1,2