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

Hollands S, Lechner G (2018)

Publication Type: Journal article

Publication year: 2018


Book Volume: 357

Pages Range: 159-202

Journal Issue: 1

DOI: 10.1007/s00220-017-2942-6


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.

Authors with CRIS profile

Additional Organisation(s)

Involved external institutions

How to cite


Hollands, S., & Lechner, G. (2018). SO(d, 1) -Invariant Yang–Baxter Operators and the dS/CFT Correspondence. Communications in Mathematical Physics, 357(1), 159-202.


Hollands, Stefan, and Gandalf Lechner. "SO(d, 1) -Invariant Yang–Baxter Operators and the dS/CFT Correspondence." Communications in Mathematical Physics 357.1 (2018): 159-202.

BibTeX: Download