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Quantum null geometry and gravity

  • Regular Article - Theoretical Physics
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  • Published: 03 December 2024
  • Volume 2024, article number 28, (2024)
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Quantum null geometry and gravity
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  • Luca Ciambelli  ORCID: orcid.org/0000-0001-6631-836X1,
  • Laurent Freidel1 &
  • Robert G. Leigh2,1 

  • 579 Accesses

  • 5 Citations

  • 4 Altmetric

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A preprint version of the article is available at arXiv.

Abstract

In this work, we demonstrate that quantizing gravity on a null hypersurface leads to the emergence of a CFT associated with each null ray. This result stems from the ultralocal nature of null physics and is derived through a canonical analysis of the Raychaudhuri equation, interpreted as a constraint generating null time reparametrizations. The CFT exhibits a non-zero central charge, providing a mechanism for the quantum emergence of time in gravitational systems and an associated choice of vacuum state. Our analysis reveals that the central charge quantifies the degrees of freedom along each null ray. Throughout our investigation, the area element of a cut plays a crucial role, necessitating its treatment as a quantum operator due to its dynamic nature in phase space or because of quantum backreaction. Furthermore, we show that the total central charge diverges in a perturbative analysis due to the infinite number of null generators. This divergence is resolved if there is a discrete spectrum for the area form operator. We introduce the concept of ‘embadons’ to denote these localized geometric units of area, the fundamental building blocks of geometry at a mesoscopic quantum gravity scale.

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Acknowledgments

We are thankful to Ivan Agullo, Abhay Ashtekar, Ana-Maria Raclariu, Gautam Satishchandran, Antony Speranza, Simone Speziale, Aron Wall, and Kathryn Zurek for discussions and constructive criticisms. LC thanks Miguel Campiglia and Juan Maldacena for important discussions on related projects. Similarly, RGL thanks Marc Klinger for discussions on ongoing related collaborations. We are grateful to BIRS (Banff) for the warm hospitality during our focused research group initiatives of November 2022, where this work was initiated, and of November 2023. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. The work of RGL is partially supported by the U.S. Department of Energy under contract DE-SC0015655, and RGL thanks the Perimeter Institute for supporting collaborative visits. This work was supported by the Simons Collaboration on Celestial Holography.

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  1. Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5, Canada

    Luca Ciambelli, Laurent Freidel & Robert G. Leigh

  2. Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois, 1110 West Green St., Urbana, IL, 61801, USA

    Robert G. Leigh

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  1. Luca Ciambelli
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Ciambelli, L., Freidel, L. & Leigh, R.G. Quantum null geometry and gravity. J. High Energ. Phys. 2024, 28 (2024). https://doi.org/10.1007/JHEP12(2024)028

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  • Received: 12 September 2024

  • Revised: 12 November 2024

  • Accepted: 15 November 2024

  • Published: 03 December 2024

  • DOI: https://doi.org/10.1007/JHEP12(2024)028

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Keywords

  • Classical Theories of Gravity
  • Models of Quantum Gravity
  • Scale and Conformal Symmetries
  • Space-Time Symmetries
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