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TFT construction of RCFT correlators I: Partition functions | | Jürgen Fuchs
; Ingo Runkel
; Christoph Schweigert
; | | Date: |
18 Apr 2002 | | Journal: | Nucl.Phys. B646 (2002) 353-497 DOI: 10.1016/S0550-3213(02)00744-7 | | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | | Abstract: | 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. | | Source: | arXiv, hep-th/0204148 | | Services: | Forum | Review | PDF | Favorites | |
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