The three-dimensional origin of the classifying algebra

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Erscheinungsjahr:
2010
Medientyp:
Text
Schlagworte:
  • Boundary conditions
  • Classifying algebra
  • Conformal blocks
  • Conformal field theory
  • Factorization
Beschreibung:
  • 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 S2 × S1. 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. © 2009 Elsevier B.V. All rights reserved.
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/8d38eb31-d3c0-4726-bf55-ae1ace0c2685