Conformal nets II: conformal blocks
Abstract
Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finitedimensional projective Hilbert spaces. We also construct infinitedimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.
 Publication:

arXiv eprints
 Pub Date:
 September 2014
 arXiv:
 arXiv:1409.8672
 Bibcode:
 2014arXiv1409.8672B
 Keywords:

 Mathematical Physics;
 Mathematics  Operator Algebras;
 Mathematics  Quantum Algebra;
 81T05;
 46L37;
 46M05 (Primary);
 81T40;
 46L60;
 81R10 (Secondary)
 EPrint:
 Updated to published version