- 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

Emergent Lorentzian dispersion relations from a Euclidean scalar-tensor theory

Justin C. Feng*

Shinji Mukohyama

Sante Carloni

  • Central European Institute for Cosmology and Fundamental Physics (CEICO), Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 21 Prague 8, Czech Republic

  • *Contact author: feng@fzu.cz
PDF

Phys. Rev. D 112, 024066 – Published 28 July, 2025

DOI: https://doi.org/10.1103/zylg-s8lf

Abstract

Can one be fooled into thinking that space and time are fundamentally described by a Lorentzian manifold? In this article, we describe a scenario in which a theory constructed on a (Euclidean signature) Riemannian manifold can lead to degrees of freedom with Lorentzian dispersion relations, due to a nontrivial configuration of a scalar field. In particular, we perform a perturbative analysis of a renormalizable shift-symmetric scalar-tensor theory and find that it can, in principle, admit a massless tensor degree of freedom with a Lorentzian dispersion relation. While the remaining degrees of freedom in the gravity sector will, in general, satisfy Euclidean dispersion relations, we argue that they can be brought under control by elliptic equations with an appropriate choice of boundary conditions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (23)

  1. E. Anderson, Ann. Phys. (Berlin) 524, 757 (2012); C. J. Isham, NATO Sci. Ser. C 409, 157 (1993), arXiv:gr-qc/9210011.
  2. S. Mukohyama and J.-P. Uzan, Phys. Rev. D 87, 065020 (2013).
  3. M. Ishak, Living Rev. Relativity 22, 1 (2019).
  4. J. D. Bekenstein, Phys. Rev. D 48, 3641 (1993).
  5. A. White, S. Weinfurtner, and M. Visser, Classical Quantum Gravity 27, 045007 (2010).
  6. S. Mukohyama, Phys. Rev. D 87, 085030 (2013).
  7. K. Muneyuki and N. Ohta, Phys. Lett. B 725, 495 (2013).
  8. K. S. Stelle, Phys. Rev. D 16, 953 (1977).
  9. J. C. Feng, S. Mukohyama, and S. Carloni, Phys. Rev. D 109, 024040 (2024).
  10. S. Hossenfelder and L. Smolin, Phys. Rev. D 81, 064009 (2010); S. W. Hawking, Mod. Phys. Lett. A 05, 453 (1990); S. W. Hawking and R. Laflamme, Phys. Lett. B 209, 39 (1988); S. W. Hawking, Phys. Rev. D 37, 904 (1988).
  11. S. Chadha and H. B. Nielsen, Nucl. Phys. B217, 125 (1983).
  12. R. Wald, General Relativity (University of Chicago Press, Chicago, 1984); S. Hawking and G. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, England, 1973).
  13. K. Aoki and S. Mukohyama, Phys. Rev. D 100, 064061 (2019).
  14. S. Mukohyama, J. Cosmol. Astropart. Phys. 12 (2014) 011.
  15. W. Barker, C. Marzo, and C. Rigouzzo, arXiv:2406.09500.
  16. L. Buoninfante, arXiv:1610.08744.
  17. Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, Phys. Rev. D 99, 064001 (2019); Y.-C. Lin, Ghost and tachyon free gauge theories of gravity: A systematic approach, Ph.D. thesis, Apollo—University of Cambridge Repository, 2020.
  18. A. Aurilia and H. Umezawa, Phys. Rev. 182, 1682 (1969).
  19. S. Mukohyama, Phys. Rev. D 98, 104053 (2018).
  20. C. Deffayet, A. Held, S. Mukohyama, and A. Vikman, arXiv:2504.11437; J. Cosmol. Astropart. Phys. 11 (2023) 031; C. Deffayet, S. Mukohyama, and A. Vikman, Phys. Rev. Lett. 128, 041301 (2022).
  21. A. Hell, D. Lust, and G. Zoupanos, J. High Energy Phys. 08 (2023) 168; J. Maldacena, arXiv:1105.5632.
  22. R. P. Woodard, Scholarpedia 10, 32243 (2015); Eur. Phys. J. Plus 138, 1067 (2023); M. Ostrogradsky, Mem. Acad. St. Petersbourg 6, 385 (1850).
  23. J. Kehayias, S. Mukohyama, and J.-P. Uzan, Phys. Rev. D 89, 105017 (2014).

Outline

Information

Phys. Rev. D 112, 024066– Published 28 July, 2025
  • Received 8 May 2025
  • Accepted 5 July 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation