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SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence

Hollands, Stefan and Lechner, Gandalf 2018. SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence. Communications in Mathematical Physics 357 , pp. 159-202. 10.1007/s00220-017-2942-6

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We propose a model for the dS/CFT correspondence. The model is constructed in terms of a “Yang–Baxter operator” R for unitary representations of the de Sitter group SO(d,1) . This R-operator is shown to satisfy the Yang–Baxter equation, unitarity, as well as certain analyticity relations, including in particular a crossing symmetry. With the aid of this operator we construct: (a) a chiral (light-ray) conformal quantum field theory whose internal degrees of freedom transform under the given unitary representation of SO(d,1) . By analogy with the O(N) non-linear sigma model, this chiral CFT can be viewed as propagating in a de Sitter spacetime. (b) A (non-unitary) Euclidean conformal quantum field theory on Rd−1 , where SO(d, 1) now acts by conformal transformations in (Euclidean) spacetime. These two theories can be viewed as dual to each other if we interpret Rd−1 as conformal infinity of de Sitter spacetime. Our constructions use semi-local generator fields defined in terms of R and abstract methods from operator algebras.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher: Springer Verlag
ISSN: 0010-3616
Funders: ERC
Date of First Compliant Deposit: 6 April 2016
Date of Acceptance: 24 May 2017
Last Modified: 18 Nov 2020 10:30

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