2007/10/31 by Robert Coquereaux, Gil Schieber, G. Schieber
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1088/1742-6596/103/1/012006
published as J.Phys.Conf.Ser.103:012006,2008 · 22 pages, 3 color figures. Version 2: We changed the color of figures (ps files) in such a way that they are still understood when converted to gray levels. Version 3: Several references have been added
arxiv created 2007/12/17 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a quantum graph. For known examples, the corresponding modular invariant partition function, which is sometimes associated with a conformal embedding, provides enough information to recover the whole structure. We illustrate these notions with the example of the conformal embedding of SU(4) at level 4 into Spin (15) at level 1, leading to the exceptional quantum graph 4 ( SU (4)), and we determine its algebra of quantum symmetries.