2002/04/30 by Jürgen Fuchs, Ingo Runkel, Christoph Schweigert · 9 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-th #math.QA
paper · pdf · doi:10.1016/s0550-3213(02)00744-7
published as Nucl.Phys.B646:353-497,2002 · 123 pages, table of contents, several figures. v2: Role of unitarity in sections 3.2 and 3.3 stated more explicitly; remark on Brauer groups added in section 3.5
arxiv created 2002/08/13 · openalex publication_date 2002/11/12 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We formulate rational conformal field theory in terms of a symmetric special Frobenius algebra A and its representations. A is an algebra in the modular tensor category of Moore-Seiberg data of the underlying chiral CFT. The multiplication on A corresponds to the OPE of boundary fields for a single boundary condition. General boundary conditions are A-modules, and (generalised) defect lines are A-A-bimodules. The relation with three-dimensional TFT is used to express CFT data, like structure constants or torus and annulus coefficients, as invariants of links in three-manifolds. We compute explicitly the ordinary and twisted partition functions on the torus and the annulus partition functions. We prove that they satisfy consistency conditions, like modular invariance and NIM-rep properties. We suggest that our results can be interpreted in terms of non-commutative geometry over the modular tensor category of Moore-Seiberg data.