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Path integral measure and RG equations for gravity

Carlo Branchina1,*, Vincenzo Branchina2,†, Filippo Contino2,‡, and Arcangelo Pernace2,§

  • *Contact author: carlo.branchina@unical.it
  • †Contact author: branchina@ct.infn.it
  • ‡Contact author: filippo.contino@ct.infn.it
  • §Contact author: arcangelo.pernace@ct.infn.it
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Phys. Rev. D 111, 125021 – Published 25 June, 2025

DOI: https://doi.org/10.1103/wqv2-j5dt

Abstract

Considering the Einstein-Hilbert truncation for the running action in (Euclidean) quantum gravity, we derive the renormalization group equations for the cosmological and Newton constant. We find that these equations admit only the Gaussian fixed point with a UV-attractive and a UV-repulsive eigendirection, and that there is no sign of the nontrivial UV-attractive fixed point of the asymptotic safety scenario. Crucial to our analysis is a careful treatment of the measure in the path integral that defines the running action and a proper introduction of the physical running scale k. We also show why and how in usual implementations of the RG equations the aforementioned UV-attractive fixed point is generated.

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Path integral measure and the cosmological constant

Carlo Branchina, Vincenzo Branchina, Filippo Contino, and Arcangelo Pernace
Phys. Rev. D 111, 105018 (2025)

Article Text

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Outline

Information

Phys. Rev. D 111, 125021– Published 25 June, 2025
  • Received 22 April 2025
  • Accepted 28 May 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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