Uniqueness of open/closed rational CFT with given algebra of open states
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.
Keywords
Cite
@article{arxiv.hep-th/0612306,
title = {Uniqueness of open/closed rational CFT with given algebra of open states},
author = {Jens Fjelstad and Jurgen Fuchs and Ingo Runkel and Christoph Schweigert},
journal= {arXiv preprint arXiv:hep-th/0612306},
year = {2009}
}
Comments
77 pages, several figures; v2: minor corrections, version published in ATMP