Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-12-29
Adv.Theor.Math.Phys.12:1283-1375,2008
Physics
High Energy Physics
High Energy Physics - Theory
77 pages, several figures; v2: minor corrections, version published in ATMP
Scientific paper
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.
Fjelstad Jens
Fuchs J"urgen
Runkel Ingo
Schweigert Christoph
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