Cardy algebras and sewing constraints, I

Details Cardy algebras and sewing constraints, I Cardy algebras and sewing constraints, I

2008-07-21

arxiv.org/abs/0807.3356v2

Commun.Math.Phys.292:871-912,2009

Mathematics

Quantum Algebra

43 pages, several figures; v2: minor corrections and changes to references, version to appear in CMP

Scientific paper

10.1007/s00220-009-0901-6

This is part one of a two-part work that relates two different approaches to two-dimensional open-closed rational conformal field theory. In part one we review the definition of a Cardy algebra, which captures the necessary consistency conditions of the theory at genus 0 and 1. We investigate the properties of these algebras and prove uniqueness and existence theorems. One implication is that under certain natural assumptions, every rational closed CFT is extendable to an open-closed CFT. The relation of Cardy algebras to the solutions of the sewing constraints is the topic of part two.

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