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One-loop exactness of gravity partition function

Andrés Goya1,*, Mauricio Leston1,2,†, and Mario Passaglia2,‡

  • *Contact author: agoya@iafe.uba.ar
  • †Contact author: mauricio@iafe.uba.ar
  • ‡Contact author: mpassaglia@cbc.uba.ar
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Phys. Rev. D 112, 106014 – Published 25 November, 2025

DOI: https://doi.org/10.1103/r6q6-f79b

Abstract

In a previous work, we showed that the two- and three-loop contributions to the partition function of three-dimensional gravity in flat space vanish. This is in agreement with the expected one-loop exactness dictated by the underlying symmetry at the quantum level. To highlight the distinctive nature of the D=3 case, we extend the three-loop computation to arbitrary spacetime dimensions D. In higher dimensions, the number of contributions increases substantially, reinforcing the view that one-loop exactness is a unique feature of three-dimensional gravity.

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See Also

3D Quantum Gravity Partition Function at Three Loops

Mauricio Leston, Andrés Goya, Guillem Pérez-Nadal, Mario Passaglia, and Gaston Giribet
Phys. Rev. Lett. 131, 181601 (2023)

Article Text

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Phys. Rev. D 112, 106014– Published 25 November, 2025
  • Received 22 August 2025
  • Accepted 30 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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