2006/09/30 by Pierre Mathieu, David Ridout
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Current (fluid) #Current algebra #Dimension (graph theory) #Field (mathematics) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Primary field #Pure mathematics #Representation (politics) #Representation theory #Simple (philosophy) #Type (biology) #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1016/j.nuclphysb.2006.11.019
published as Nucl.Phys.B765:201-239,2007 · 42 pages, 2 figures; added further motivational material and corrected typos
arxiv created 2006/11/15 · openalex publication_date 2006/12/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08
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.