## Advances in Theoretical and Mathematical Physics

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

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

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

#### 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