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Gravitational SL(2, ℝ) algebra on the light cone

  • Regular Article - Theoretical Physics
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  • Published: 12 July 2021
  • volume 2021, Article number: 57 (2021)
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Gravitational SL(2, ℝ) algebra on the light cone
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  • Wolfgang Wieland  ORCID: orcid.org/0000-0003-1371-34321 

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A preprint version of the article is available at arXiv.

Abstract

In a region with a boundary, the gravitational phase space consists of radiative modes in the interior and edge modes at the boundary. Such edge modes are necessary to explain how the region couples to its environment. In this paper, we characterise the edge modes and radiative modes on a null surface for the tetradic Palatini-Holst action. Our starting point is the definition of the action and its boundary terms. We choose the least restrictive boundary conditions possible. The fixed boundary data consists of the radiative modes alone (two degrees of freedom per point). All other boundary fields are dynamical. We introduce the covariant phase space and explain how the Holst term alters the boundary symmetries. To infer the Poisson brackets among Dirac observables, we define an auxiliary phase space, where the SL(2, ℝ) symmetries of the boundary fields are manifest. We identify the gauge generators and second-class constraints that remove the auxiliary variables. All gauge generators are at most quadratic in the fundamental SL(2, ℝ) variables on phase space. We compute the Dirac bracket and identify the Dirac observables on the light cone. Finally, we discuss various truncations to quantise the system in an effective way.

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Authors and Affiliations

  1. Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria

    Wolfgang Wieland

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Correspondence to Wolfgang Wieland.

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Wieland, W. Gravitational SL(2, ℝ) algebra on the light cone. J. High Energ. Phys. 2021, 57 (2021). https://doi.org/10.1007/JHEP07(2021)057

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  • Received: 20 April 2021

  • Accepted: 25 June 2021

  • Published: 12 July 2021

  • DOI: https://doi.org/10.1007/JHEP07(2021)057

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Keywords

  • Classical Theories of Gravity
  • Models of Quantum Gravity
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