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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 (1) , 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
Publisher: Springer Verlag
ISSN: 0010-3616
Funders: ERC
Date of First Compliant Deposit: 6 April 2016
Date of Acceptance: 24 May 2017
Last Modified: 03 Apr 2019 11:10

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