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

Lechner G, Scotford C (2022)

Publication Language: English

Publication Status: Submitted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2022

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

URI: https://link.springer.com/article/10.1007/s00220-022-04324-x

DOI: 10.1007/s00220-022-04324-x

Open Access Link: https://link.springer.com/article/10.1007/s00220-022-04324-x

Abstract

We construct explicit examples of half-sided modular inclusions ⊂ 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 ⊂ with large relative commutant and construct a one-parameter family κ⊂κ, κ≥0, of half-sided inclusions such that 0=, 0= and ′κ∩κ=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.

Authors with CRIS profile

Gandalf Lechner Lehrstuhl für Mathematik (Operatoralgebren)

Involved external institutions

Cardiff University

United Kingdom (GB)

How to cite

APA:

Lechner, G., & Scotford, C. (2022). Deformations of half-sided modular inclusions and non-local chiral field theories. Communications in Mathematical Physics. https://doi.org/10.1007/s00220-022-04324-x

MLA:

Lechner, Gandalf, and Charley Scotford. "Deformations of half-sided modular inclusions and non-local chiral field theories." Communications in Mathematical Physics (2022).

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