TFT construction of RCFT correlators I: Partition functions
  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. 
J\"urgen Fuchs, Ingo Runkel, Christoph Schweigert