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The three-dimensional origin of the classifying algebra
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.ORCID iD: 0000-0003-4081-6234
2010 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 824, no 3, p. 333-364Article in journal (Refereed)
Abstract

It is known that reflection coefficients for bulk fields of a rational conformal field theory in the presence of an elementary boundary condition can be obtained as representation matrices of irreducible representations of the classifying algebra, a semisimple commutative associative complex algebra.

We show how this algebra arises naturally from the three-dimensional geometry of factorization of correlators of bulk fields on the disk. This allows us to derive explicit expressions for the structure constants of the classifying algebra as invariants of ribbon graphs in the three-manifold S^2 x S^1. Our result unravels a precise relation between intertwiners of the action of the mapping class group on spaces of conformal blocks and boundary conditions in rational conformal field theories

Place, publisher, year, edition, pages
2010. Vol. 824, no 3, p. 333-364
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-9831OAI: oai:DiVA.org:kau-9831DiVA, id: diva2:493338
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2017-12-07Bibliographically approved

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http://dx.doi.org/10.1016/j.nuclphysb.2009.07.017http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-4WVF6NK-4&_user=10&_coverDate=01%2F11%2F2010&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=e93597d98b5584f966c1ea37e9515082

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