Deformations of half-sided modular inclusions and non-local chiral field theories

Lechner, Gandalf ORCID: https://orcid.org/0000-0002-8829-3121 and Scotford, Charley 2022. Deformations of half-sided modular inclusions and non-local chiral field theories. Communications in Mathematical Physics 391 , pp. 269-291. 10.1007/s00220-022-04324-x

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Abstract

We construct explicit examples of half-sided modular inclusions N⊂M of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms of an algebra localized at infinity, we consider a second quantization inclusion N⊂M with large relative commutant and construct a one-parameter family Nκ⊂Mκ, κ≥0, of half-sided inclusions such that N0=N, M0=M and N′κ∩Mκ=C1 for κ>0. The technique we use is an explicit deformation procedure (warped convolution), and we explain the relation of this result to the construction of chiral conformal quantum field theories on the real line and on the circle.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher:	Springer
ISSN:	0010-3616
Date of First Compliant Deposit:	7 March 2022
Date of Acceptance:	28 December 2021
Last Modified:	06 Jan 2024 04:24
URI:	https://orca.cardiff.ac.uk/id/eprint/148062

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