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 finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional 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 e-prints
- Pub Date:
- September 2014
- DOI:
- 10.48550/arXiv.1409.8672
- arXiv:
- arXiv:1409.8672
- Bibcode:
- 2014arXiv1409.8672B
- Keywords:
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- Mathematical Physics;
- Mathematics - Operator Algebras;
- Mathematics - Quantum Algebra;
- 81T05;
- 46L37;
- 46M05 (Primary);
- 81T40;
- 46L60;
- 81R10 (Secondary)
- E-Print:
- Updated to published version