Compositio Mathematica



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


Giovanni Felder a1, Jürg Fröhlich a2, Jürgen Fuchs a3 and Christoph Schweigert a4
a1 Department of Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland
a2 Institute for Theoretical Physics, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
a3 Institute for Theoretical Physics, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
a4 LPTHE, Université Paris VI, 4, place Jussieu, F-75252 Paris Cedex 05, France

Article author query
felder g   [Google Scholar] 
fröhlich j   [Google Scholar] 
fuchs j   [Google Scholar] 
schweigert c   [Google Scholar] 
 

Abstract

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.


Key Words: conformal field theory; modular categories; topological field theory.