Superconformal nets and noncommutative geometry

Carpi, Sebastiano and Hillier, Robin and Longo, Roberto (2015) Superconformal nets and noncommutative geometry. Journal of Noncommutative Geometry, 9 (2). pp. 391-445. ISSN 1661-6960

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Abstract

This paper provides a further step in our program of studying superconformal nets over S^1 from the point of view of noncommutative geometry. For any such net A and any family Delta of localized endomorphisms of the even part A^gamma of A, we define the locally convex differentiable algebra A_Delta with respect to a natural Dirac operator coming from supersymmetry. Having determined its structure and properties, we study the family of spectral triples and JLO entire cyclic cocycles associated to elements in Delta and show that they are nontrivial and that the cohomology classes of the cocycles corresponding to inequivalent endomorphisms can be separated through their even or odd index pairing with K-theory in various cases. We illustrate some of those cases in detail with superconformal nets associated to well-known CFT models, namely super-current algebra nets and super-Virasoro nets. All in all, the result allows us to encode parts of the representation theory of the net in terms of noncommutative geometry.

Item Type: Journal Article
Journal or Publication Title: Journal of Noncommutative Geometry
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2608
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 68701
Deposited By: ep_importer_pure
Deposited On: 24 Feb 2014 09:00
Refereed?: Yes
Published?: Published
Last Modified: 01 Jan 2020 08:32
URI: https://eprints.lancs.ac.uk/id/eprint/68701

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