Behrend, Roger E.  ORCID: https://orcid.org/0000-0002-6143-7439, Pearce, Paul A., Petkova, V. B. and Zuber, J. B.
2000.
Boundary conditions in rational conformal field theories.
Nuclear Physics B
579
(3)
, pp. 707-773.
10.1016/S0550-3213(00)00225-X
|
Abstract
We develop further the theory of RationalConformalFieldTheories (RCFTs) on a cylinder with specified boundaryconditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph G to each RCFT such that the conformalboundaryconditions are labelled by the nodes of G . This approach is carried to completion for sl(2) theories leading to complete sets of conformalboundaryconditions, their associated cylinder partition functions and the A -D -E classification. We also review the current status for WZW sl(3) theories. Finally, a systematic generalization of the formalism of Cardy–Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
| Publisher: | Elsevier |
| ISSN: | 0550-3213 |
| Last Modified: | 21 Oct 2022 10:10 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/39289 |
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