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Correlation Functions and Boundary Conditions in Rational Conformal Field Theory and Three-Dimensional Topology

Published online by Cambridge University Press:  04 December 2007

Giovanni Felder ,
Jürg Fröhlich ,
Jürgen Fuchs  and
Christoph Schweigert
Giovanni Felder
Affiliation:
Department of Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland
Jürg Fröhlich
Affiliation:
Institute for Theoretical Physics, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
Jürgen Fuchs
Affiliation:
Institute for Theoretical Physics, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
Christoph Schweigert
Affiliation:
LPTHE, Université Paris VI, 4, place Jussieu, F-75252 Paris Cedex 05, France
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Abstract

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We give a general construction of correlation functions in rational conformal field theory on a possibly nonorientable surface with boundary in terms of three-dimensional topological field theory. The construction applies to any modular category in the sense of Turaev. It is proved that these correlation functions obey modular invariance and factorization rules. Structure constants are calculated and expressed in terms of the data of the modular category.

Keywords

conformal field theorymodular categoriestopological field theory
Type
Research Article
Information
Compositio Mathematica , Volume 131 , Issue 2 , April 2002 , pp. 189 - 238
Copyright
© 2002 Kluwer Academic Publishers