Conformal nets I: coordinate-free nets

2013/02/28 by Arthur Bartels, Christopher L. Douglas, André Henriques · 2 citations
Mathematics · Physics and Astronomy · #math-ph #math.MP #math.OA #msc:46L37 #msc:46L60 #msc:46M05 #msc:81R10 #msc:81T05 #msc:81T40

paper · pdf

published as Int. Math. Res. Not. 13 (2015), 4975-5052 · Updated to published version

arxiv created 2016/11/08 · arxiv updated 2017/01/23

Abstract

We describe a coordinate-free 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 coordinate-free 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 3-category of conformal nets, defects, sectors, and intertwiners.

Cited by

• Twisted representations of conformal nets and crossed balanced tensor categories
• Balanced tensor categories of representations of fixed-points conformal nets