- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Gauge dependence of momentum running in higher-derivative gravity

Diego Buccio*

Gustavo P. de Brito†

Luca Parente‡

  • Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
  • Institute for Theoretical Physics, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany

  • Departamento de Física, Universidade Estadual Paulista (Unesp), Campus Guaratinguetá, Avenida Doutor Ariberto Pereira da Cunha, 333, Guaratinguetá, São Paulo, Brazil

  • *Contact author: diego.buccio@ru.nl
  • †Contact author: gp.brito@unesp.br
  • ‡Contact author: luca.parente@phd.unipi.it
PDF

Phys. Rev. D 112, 126024 – Published 26 December, 2025

DOI: https://doi.org/10.1103/v9ff-g69f

Abstract

Recent works [D. Buccio et al., Phys. Rev. Lett. 133, 021604 (2024)and D. Buccio et al., Phys. Rev. D 111, 065022 (2025)] have argued that improved one-loop beta-functions capturing the physical momentum dependence of one-loop corrected higher-derivative gravity theories are the most suitable to describe their high-energy behavior. This work critically tests the validity of this claim. We compute the explicit gauge dependence of the one-loop momentum running of curvature-squared operators in quadratic gravity and conformal gravity using the background field method. We find them to be gauge dependent, and we discuss the implications of this result for the theory and its physical predictivity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. D. Buccio, J. F. Donoghue, G. Menezes, and R. Percacci, Phys. Rev. Lett. 133, 021604 (2024).
  2. D. Buccio, L. Parente, and O. Zanusso, Phys. Rev. D 111, 065022 (2025).
  3. D. Buccio, J. F. Donoghue, and R. Percacci, Phys. Rev. D 109, 045008 (2024).
  4. H. Kawai and N. Ohta, Phys. Lett. B 868, 139781 (2025).
  5. S. Weinberg, Phys. Rev. 140, B516 (1965).
  6. D. Buccio, Renormalization and running couplings in higher derivative theories, Ph.D. thesis, SISSA, Trieste, 2025.
  7. A. Salvio, A. Strumia, and M. Vitti, arXiv:2507.08803.
  8. B. S. DeWitt, Phys. Rev. 162, 1195 (1967).
  9. S. Weinberg, The Quantum Theory of Fields. Vol. 2: Modern Applications (Cambridge University Press, Cambridge, England, 2013).
  10. J. F. Donoghue, Phys. Rev. D 105, 105025 (2022).
  11. U. G. Aglietti and D. Anselmi, Eur. Phys. J. C 77, 84 (2017).
  12. L. Buoninfante, J. High Energy Phys. 02 (2025) 186.
  13. K. S. Stelle, Phys. Rev. D 16, 953 (1977).
  14. M. Ostrogradsky, Mem. Acad. St. Petersbourg 6, 385 (1850).
  15. C. Deffayet, A. Held, S. Mukohyama, and A. Vikman, J. Cosmol. Astropart. Phys. 11 (2023) 031.
  16. A. Held, arXiv:2509.18049.
  17. R. P. Woodard, Scholarpedia 10, 32243 (2015).
  18. D. Anselmi and M. Piva, J. High Energy Phys. 05 (2018) 027.
  19. P. D. Mannheim, Int. J. Mod. Phys. D 29, 2043009 (2020).
  20. J. F. Donoghue and G. Menezes, Phys. Rev. D 104, 045010 (2021).
  21. A. Salvio and A. Strumia, Eur. Phys. J. C 76, 227 (2016).
  22. B. Holdom and J. Ren, Phys. Rev. D 93, 124030 (2016).
  23. R. Percacci, An Introduction to Covariant Quantum Gravity and Asymptotic Safety, 100 Years of General Relativity, Vol. 3 (World Scientific, Singapore, 2017).
  24. N. Ohta, R. Percacci, and A. D. Pereira, Eur. Phys. J. C 77, 611 (2017).
  25. N. Ohta and R. Percacci, Classical Quantum Gravity 31, 015024 (2014).
  26. A. O. Barvinsky and G. A. Vilkovisky, Nucl. Phys. B333, 471 (1990).
  27. A. Codello and O. Zanusso, J. Math. Phys. (N.Y.) 54, 013513 (2013).
  28. I. G. Avramidi and A. O. Barvinsky, Phys. Lett. 159B, 269 (1985).
  29. E. S. Fradkin and A. A. Tseytlin, Nucl. Phys. B201, 469 (1982).
  30. A. O. Barvinsky and G. A. Vilkovisky, Phys. Rep. 119, 1 (1985).
  31. G. ’t Hooft and M. J. G. Veltman, Ann. Inst. H. Poincare A 20, 69 (1974).
  32. J. Julve and M. Tonin, Nuovo Cimento Soc. Ital. Fis. 46B, 137 (1978).
  33. G. de Berredo-Peixoto and I. L. Shapiro, Phys. Rev. D 71, 064005 (2005).
  34. I. G. Avramidi, Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher derivative quantum gravity, Ph.D. thesis, Moscow State Lomonosov University, 1986.
  35. I. L. Shapiro and A. G. Zheksenaev, Phys. Lett. B 324, 286 (1994).
  36. G. de Berredo-Peixoto and I. L. Shapiro, Phys. Rev. D 70, 044024 (2004).
  37. N. Ohta and R. Percacci, Classical Quantum Gravity 33, 035001 (2016).
  38. B. L. Voronov and I. V. Tyutin, Yad. Fiz. 39, 998 (1984).
  39. B. Holdom, Phys. Rev. D 105, 046008 (2022).

Outline

Information

Phys. Rev. D 112, 126024– Published 26 December, 2025
  • Received 9 August 2025
  • Accepted 24 November 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation