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conformal net

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Idea

A conformal net is a local net of observables that describes (2-dimensional) conformal field theory in the framework of AQFT.

Definition

(…)

Properties

3-Category of conformal nets

(…)

Examples

Free fermion

(DH, section 4)

Fer n(I)≔Cl(L 2(I,ℝ n⊗S))Fer_n(I) \coloneqq Cl(L^2(I, \mathbb{R}^n \otimes S))

References

Fundamentals

Standard AQFT references on conformal nets include

and lots of others…

A somewhat novel take on conformal nets is presented and studied in

where conformal nets are arranged into a tricategory with symmetric monoidal structure that is a delooping of the bicategory of von Neumann algebras and bimodules between these. Among other things, this work connects the AQFT notion of conformal nets with the FQFT notion of cobordism representations.

More on this in

Relation to 2-spectral triples is discussed in

Classification

Representation theory

Articles that discuss the representation theory of conformal nets include

  • Sebastiano Carpi, Roberto Conti, Robin Hillier, Mihaly Weiner, Representations of Conformal Nets, Universal C *-Algebras and K-Theory (arXiv:1202.2543)

Revised on May 7, 2013 23:42:15 by Urs Schreiber (67.216.17.3)
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