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Uniqueness of open/closed rational CFT with given algebra of open states

Jens Fjelstad·Jurgen Fuchs·Ingo Runkel·Christoph Schweigert
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Abstract

We study the sewing constraints for rational two-dimensional conformal field theory on oriented surfaces with possibly non-empty boundary. The boundary condition is taken to be the same on all segments of the boundary. The following uniqueness result is established: For a solution to the sewing constraints with nondegenerate closed state vacuum and nondegenerate two-point correlators of boundary fields on the disk and of bulk fields on the sphere, up to equivalence all correlators are uniquely determined by the one-, two,- and three-point correlators on the disk. Thus for any such theory every consistent collection of correlators can be obtained by the TFT approach of hep-th/0204148, hep-th/0503194. As morphisms of the category of world sheets we include not only homeomorphisms, but also sewings; interpreting the correlators as a natural transformation then encodes covariance both under homeomorphisms and under sewings of world sheets.

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Jens Fjelstad, Jurgen Fuchs, Ingo Runkel, Christoph Schweigert. 2008-11-07. Uniqueness of open/closed rational CFT with given algebra of open states. https://arxiv.org/abs/hep-th/0612306

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