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

March 18, 2016

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 deSitter 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 deSitter spacetime.
b) A (non-unitary) Euclidean conformal quantum field theory on ${\mathbb R}^{d-1}$, 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 ${\mathbb R}^{d-1}$ as conformal infinity of deSitter spacetime. Our constructions use semi-local generator fields defined in terms of $R$ and abstract methods from operator algebras.

open access link
doi:10.1007/s00220-017-2942-6

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@article{Hollands:2016aha,
author = "Hollands, Stefan and Lechner, Gandalf",
title = "{$SO(d,1)$ -Invariant Yangâ€“Baxter Operators and the
dS/CFT Correspondence}",
journal = "Commun. Math. Phys.",
volume = "357",
year = "2018",
number = "1",
pages = "159-202",
doi = "10.1007/s00220-017-2942-6",
eprint = "1603.05987",
archivePrefix = "arXiv",
primaryClass = "gr-qc",
SLACcitation = "%%CITATION = ARXIV:1603.05987;%%"
}

Keywords:

*none*