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

Stefan Hollands, Gandalf Lechner
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
%%% contains utf-8, see: %%% add \usepackage[utf8]{inputenc} to your latex preamble @article{Hollands:2016aha, author = "Hollands, Stefan and Lechner, Gandalf", title = "{$SO(d,1)$ -Invariant Yang–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;%%" }