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

• We study the sewing constraints for rational two-dimensional conformal fieldtheory on oriented surfaces with possibly non-empty boundary. The boundarycondition is taken to be the same on all segments of the boundary.The following uniqueness result is established: For a solution to the sewingconstraints with nondegenerate closed state vacuum and nondegenerate two-pointcorrelators of boundary fields on the disk and of bulk fields on the sphere, upto equivalence all correlators are uniquely determined by the one-, two,- andthree-point correlators on the disk. Thus for any such theory every consistentcollection of correlators can be obtained by the TFT approach of [hep-th/0204148] and [hep-th/0503194].As morphisms of the category of world sheets we includenot only homeomorphisms, but also sewings; interpreting the correlatorsas a natural transformation then encodes covariance both under homeomorphismsand under sewings of world sheets.

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NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

NATURVETENSKAP  -- Fysik -- Subatomär fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Subatomic Physics (hsv//eng)

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Fysik

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