Conformal nets I: coordinatefree nets
Abstract
We describe a coordinatefree perspective on conformal nets, as functors from intervals to von Neumann algebras. We discuss an operation of fusion of intervals and observe that a conformal net takes a fused interval to the fiber product of von Neumann algebras. Though coordinatefree nets do not a priori have vacuum sectors, we show that there is a vacuum sector canonically associated to any circle equipped with a conformal structure. This is the first in a series of papers constructing a 3category of conformal nets, defects, sectors, and intertwiners.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 arXiv:
 arXiv:1302.2604
 Bibcode:
 2013arXiv1302.2604B
 Keywords:

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