{{SO(d,1)}}-Invariant Yang\u2013Baxter 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.