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arXiv · 1302.2604

Conformal nets I: coordinate-free nets

Arthur Bartels·Christopher L. Douglas·André Henriques
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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.

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Arthur Bartels, Christopher L. Douglas, André Henriques. 2013-02-11. Conformal nets I: coordinate-free nets. https://arxiv.org/abs/1302.2604

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