TFT construction of RCFT correlators I: Partition functions

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dc.creatorFuchs, Jürgen
dc.creatorRunkel, Ingo
dc.creatorSchweigert, Christoph
dc.date2002-04-18
dc.date2002-08-13
dc.date.accessioned2026-07-07T10:53:47Z
dc.date.available2026-07-07T10:53:47Z
dc.descriptionWe 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.
dc.description123 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
dc.identifierhttps://arxiv.org/abs/hep-th/0204148
dc.identifierhttp://arxiv.org/abs/hep-th/0204148
dc.identifierNucl.Phys.B646:353-497,2002
dc.identifierdoi:10.1016/S0550-3213(02)00744-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185601
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleTFT construction of RCFT correlators I: Partition functions
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