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

TL;DR

This paper proves the uniqueness of rational conformal field theories with given boundary conditions, showing that all correlators are determined by basic correlators and can be constructed via a topological field theory approach.

Contribution

It establishes a uniqueness theorem for rational CFT correlators with boundary conditions, linking them to a topological field theory framework.

Findings

Correlators are uniquely determined by 1-, 2-, and 3-point functions.

The theory's correlators are fully characterized by the TFT approach.

Includes sewings as morphisms, ensuring covariance under boundary modifications.

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.