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 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.

Minor changes in formulations and presentation. 48 pages

References in corpus (8)

• de Sitter tachyons and related topics
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain
• The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz
• Integrable QFT and Longo-Witten endomorphisms
• An operator expansion for integrable quantum field theories
• Conformal symmetry superalgebras
• Noncompact sl(N) spin chains: BGG-resolution, Q-operators and alternating sum representation for finite dimensional transfer matrices

Cited by in corpus (2)

• Yang-Baxter representations of the infinite symmetric group
• Modular Structure and Inclusions of Twisted Araki-Woods Algebras