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

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  • Published: 27 July 2017
  • volume 357, pages 159–202 (2018)
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\({{SO(d,1)}}\)-Invariant Yang–Baxter Operators and the dS/CFT Correspondence
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  • Stefan Hollands  ORCID: orcid.org/0000-0001-6627-28081 &
  • Gandalf Lechner  ORCID: orcid.org/0000-0002-8829-31212 
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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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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Leipzig, Leipzig, Germany

    Stefan Hollands

  2. School of Mathematics, Cardiff University, Cardiff, UK

    Gandalf Lechner

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  1. Stefan Hollands
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  2. Gandalf Lechner
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Correspondence to Gandalf Lechner.

Additional information

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

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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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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  • Received: 27 August 2016

  • Accepted: 24 May 2017

  • Published: 27 July 2017

  • Issue Date: January 2018

  • DOI: https://doi.org/10.1007/s00220-017-2942-6

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