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

Hollands, Stefan and Lechner, Gandalf ORCID: https://orcid.org/0000-0002-8829-3121 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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Abstract

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 (http://creativecommons.org/licenses/by/4.0/), 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:	05 May 2023 09:55
URI:	https://orca.cardiff.ac.uk/id/eprint/88666

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