Advances in Theoretical and Mathematical Physics

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

Jens Fjelstad, Jurgen Fuchs, Ingo Runkel, and Christoph Schweigert

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Abstract

We study the sewing constraints for rational two-dimensional conformal field theory on oriented surfaces with possibly nonempty 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 topological field theory approach of our papers TFT construction of RCFT correlators I: partition functions and TFT construction of RCFT correlators V: Proof of modular invariance and factorisation. 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.

Article information

Source
Adv. Theor. Math. Phys., Volume 12, Number 6 (2008), 1283-1375.

Dates
First available in Project Euclid: 19 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1221834534

Mathematical Reviews number (MathSciNet)
MR2443266

Zentralblatt MATH identifier
1151.81034

Citation

Fjelstad, Jens; Fuchs, Jurgen; Runkel, Ingo; Schweigert, Christoph. Uniqueness of open/closed rational CFT with given algebra of open states. Adv. Theor. Math. Phys. 12 (2008), no. 6, 1283--1375. https://projecteuclid.org/euclid.atmp/1221834534


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