Boundary conditions in rational conformal field theories

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

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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:	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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