\({{SO(d,1)}}\)-Invariant Yang–Baxter Operators and the dS/CFT Correspondence

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 \({\mathbb{R}^{d-1}}\), 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 de Sitter spacetime. Our constructions use semi-local generator fields defined in terms of R and abstract methods from operator algebras.

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Correspondence to Gandalf Lechner.

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Communicated by D. Buchholz, K. Fredenhagen, Y. Kawahigashi.

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Hollands, S., Lechner, G. \({{SO(d,1)}}\)-Invariant Yang–Baxter Operators and the dS/CFT Correspondence. Commun. Math. Phys. 357, 159–202 (2018). https://doi.org/10.1007/s00220-017-2942-6

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