Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-04-18
Nucl.Phys.B646:353-497,2002
Physics
High Energy Physics
High Energy Physics - Theory
123 pages, table of contents, several figures. v2: Role of unitarity in sections 3.2 and 3.3 stated more explicitly; remark on
Scientific paper
10.1016/S0550-3213(02)00744-7
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.
Fuchs J"urgen
Runkel Ingo
Schweigert Christoph
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