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

2016/03/31 by Stefan Hollands, Gandalf Lechner
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Anti-de Sitter space #Black Holes and Theoretical Physics #Conformal field theory #Conformal group #Conformal map #Conformal symmetry #Lie group #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Spacetime #Unitarity #Unitary representation #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s00220-017-2942-6

Minor changes in formulations and presentation. 48 pages

openalex created_date 2016/06/24 · arxiv created 2017/05/30 · openalex publication_date 2017/07/27 · arxiv updated 2017/09/13 · openalex updated_date 2026/08/05

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 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 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.

Citations

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