2008/07/31 by Liang Kong, Ingo Runkel · 2 citations
Mathematics · Physics and Astronomy · #hep-th #math.CT #math.QA #msc:16D90 #msc:17B69 #msc:18D10 #msc:81T40
paper · pdf · doi:10.1007/s00220-009-0901-6
published as Commun.Math.Phys.292:871-912,2009 · 43 pages, several figures; v2: minor corrections and changes to references, version to appear in CMP
arxiv created 2009/10/26 · arxiv updated 2009/12/01
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.