TFT construction of RCFT correlators I: Partition functions
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.
Cite
@article{arxiv.hep-th/0204148,
title = {TFT construction of RCFT correlators I: Partition functions},
author = {Jürgen Fuchs and Ingo Runkel and Christoph Schweigert},
journal= {arXiv preprint arXiv:hep-th/0204148},
year = {2008}
}
Comments
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