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Holography from the Wheeler-DeWitt equation
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 03 March 2022

Holography from the Wheeler-DeWitt equation

  • Chandramouli Chowdhury1,
  • Victor Godet  ORCID: orcid.org/0000-0002-2057-08741,
  • Olga Papadoulaki2 &
  • …
  • Suvrat Raju1 

Journal of High Energy Physics volume 2022, Article number: 19 (2022) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to a given configuration of matter fields and the metric on a spatial slice. These wavefunctionals must obey a set of constraints as a consequence of the diffeomorphism invariance of the theory, the most important of which is known as the Wheeler-DeWitt equation. We study these constraints perturbatively by expanding them to leading nontrivial order in Newton’s constant about a background AdS spacetime. We show that, even within perturbation theory, any wavefunctional that solves these constraints must have specific correlations between a component of the metric at infinity and energetic excitations of matter fields or transverse-traceless gravitons. These correlations disallow strictly localized excitations. We prove perturbatively that two states or two density matrices that coincide at the boundary for an infinitesimal interval of time must coincide everywhere in the bulk. This analysis establishes a perturbative version of holography for theories of gravity coupled to matter in AdS.

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Authors and Affiliations

  1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Shivakote, Bengaluru, 560089, India

    Chandramouli Chowdhury, Victor Godet & Suvrat Raju

  2. International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy

    Olga Papadoulaki

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  1. Chandramouli Chowdhury
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  2. Victor Godet
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Correspondence to Victor Godet.

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Chowdhury, C., Godet, V., Papadoulaki, O. et al. Holography from the Wheeler-DeWitt equation. J. High Energ. Phys. 2022, 19 (2022). https://doi.org/10.1007/JHEP03(2022)019

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  • Received: 21 September 2021

  • Revised: 22 January 2022

  • Accepted: 07 February 2022

  • Published: 03 March 2022

  • DOI: https://doi.org/10.1007/JHEP03(2022)019

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Keywords

  • AdS-CFT Correspondence
  • Models of Quantum Gravity
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