- 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

Bulk model for dissipation and fixing EFT equations on its boundary

A. Besharat1,2,*, L. Lehner2,†, and J. Radkovski2,3,4,‡

  • *Contact author: abeshara@ualberta.ca
  • †Contact author: llehner@perimeterinstitute.ca
  • ‡Contact author: jradkovski@perimeterinstitute.ca
PDF

Phys. Rev. D 114, 076006 – Published 5 October, 2026

DOI: https://doi.org/10.1103/wk9q-srg4

Abstract

Effective field theories (EFTs) with higher derivatives often yield equations of motion that define ill-posed problems. We present an action-based approach that supplements a recent well-posed formulation of Figueras et al. with selective dissipation: the EFT field is coupled to an auxiliary field living in one extra dimension, into which the energy of short-wavelength modes can dissipate. The construction is tested numerically on a scalar EFT with a known UV completion. We observe a reduction in spurious oscillations, and, for large couplings, in error. We also compare with the fixing-the-equations approach, and outline the extension to gravity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (65)

  1. Steven Weinberg, The Quantum Theory of Fields. Vol. 1: Foundations (Cambridge University Press, Cambridge, England, 2005).
  2. C. P. Burgess, Introduction to Effective Field Theory (Cambridge University Press, Cambridge, 2020).
  3. John F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50, 3874 (1994).
  4. John F. Donoghue, Mikhail M. Ivanov, and Andrey Shkerin, EPFL lectures on general relativity as a quantum field theory, arXiv:1702.00319.
  5. Petr Horava, Membranes at quantum criticality, J. High Energy Phys. 03 (2009) 020.
  6. Petr Horava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79, 084008 (2009).
  7. M. Herrero-Valea, The status of Hořava gravity, Eur. Phys. J. Plus 138, 968 (2023).
  8. R. Abbott et al., Tests of general relativity with GWTC-3, Phys. Rev. D 112, 084080 (2025).
  9. N. V. Krishnendu and Frank Ohme, Testing general relativity with gravitational waves: An overview, Universe 7, 497 (2021).
  10. A. G. Abac et al., GWTC-4.0: Tests of general relativity. I. Overview and general tests, arXiv:2603.19019.
  11. Enrico Barausse, Carlos Palenzuela, Marcelo Ponce, and Luis Lehner, Neutron-star mergers in scalar-tensor theories of gravity, Phys. Rev. D 87, 081506 (2013).
  12. Laura Bernard, Luis Lehner, and Raimon Luna, Challenges to global solutions in Horndeski’s theory, Phys. Rev. D 100, 024011 (2019).
  13. Solomon Endlich, Victor Gorbenko, Junwu Huang, and Leonardo Senatore, An effective formalism for testing extensions to general relativity with gravitational waves, J. High Energy Phys. 09 (2017) 122.
  14. Nicholas Loutrel and Nicolas Yunes, Parity violation in spin-precessing binaries: Gravitational waves from the inspiral of black holes in dynamical Chern-Simons gravity, Phys. Rev. D 106, 064009 (2022).
  15. Maxence Corman, Justin L. Ripley, and William E. East, Nonlinear studies of binary black hole mergers in Einstein-scalar-Gauss-Bonnet gravity, Phys. Rev. D 107, 024014 (2023).
  16. Ramiro Cayuso, Pau Figueras, Tiago França, and Luis Lehner, Self-consistent modeling of gravitational theories beyond general relativity, Phys. Rev. Lett. 131, 111403 (2023).
  17. Kristen Schumacher, Scott Ellis Perkins, Ashley Shaw, Kent Yagi, and Nicolás Yunes, Gravitational wave constraints on Einstein-æther theory with LIGO/Virgo data, Phys. Rev. D 108, 104053 (2023).
  18. Félix-Louis Julié, Lorenzo Pompili, and Alessandra Buonanno, Inspiral-merger-ringdown waveforms in Einstein-scalar-Gauss-Bonnet gravity within the effective-one-body formalism, Phys. Rev. D 111, 024016 (2025).
  19. Laura Bernard, Suvendu Giri, Luis Lehner, and Riccardo Sturani, Generic EFT-motivated beyond general relativity gravitational wave tests and their curvature dependence: From observation to interpretation, Phys. Rev. D 112, 124013 (2025).
  20. Gary T. Horowitz, Maciej Kolanowski, Grant N. Remmen, and Jorge E. Santos, Extremal Kerr black holes as amplifiers of new physics, Phys. Rev. Lett. 131, 091402 (2023).
  21. Juan Cayuso, Néstor Ortiz, and Luis Lehner, Fixing extensions to general relativity in the nonlinear regime, Phys. Rev. D 96, 084043 (2017).
  22. Justin L. Ripley and Frans Pretorius, Hyperbolicity in spherical gravitational collapse in a Horndeski theory, Phys. Rev. D 99, 084014 (2019).
  23. Nicola Franchini, Miguel Bezares, Enrico Barausse, and Luis Lehner, Fixing the dynamical evolution in scalar-Gauss-Bonnet gravity, Phys. Rev. D 106, 064061 (2022).
  24. Gwyneth Allwright and Luis Lehner, Towards the nonlinear regime in extensions to GR: assessing possible options, Classical Quantum Gravity 36, 084001 (2019).
  25. Ramiro Cayuso and Luis Lehner, Nonlinear, noniterative treatment of EFT-motivated gravity, Phys. Rev. D 102, 084008 (2020).
  26. Maxence Corman, Luis Lehner, William E. East, and Guillaume Dideron, Nonlinear studies of modifications to general relativity: Comparing different approaches, Phys. Rev. D 110, 084048 (2024).
  27. Michal P. Heller et al., Stable evolution of relativistic hydrodynamics order-by-order in gradients, arXiv:2511.08582.
  28. Ingo Muller, Zum Paradoxon der Warmeleitungstheorie, Z. Phys. 198, 329 (1967).
  29. W. Israel, Nonstationary irreversible thermodynamics: A causal relativistic theory, Ann. Phys. (N.Y.) 100, 310 (1976).
  30. W. Israel and J. M. Stewart, Thermodynamics of nonstationary and transient effects in a relativistic gas, Phys. Lett. 58A, 213 (1976).
  31. W. Israel and J. M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. (N.Y.) 118, 341 (1979).
  32. W. A. Hiscock and L. Lindblom, Stability and causality in dissipative relativistic fluids, Ann. Phys. (N.Y.) 151, 466 (1983).
  33. Rudolf Baier, Paul Romatschke, Dam Thanh Son, Andrei O Starinets, and Mikhail A Stephanov, Relativistic viscous hydrodynamics, conformal invariance, and holography, J. High Energy Phys. 04 (2008) 100.
  34. G. S. Denicol, H. Niemi, E. Molnár, and D. H. Rischke, Derivation of transient relativistic fluid dynamics from the Boltzmann equation, Phys. Rev. D 85, 114047 (2012); G. S. Denicol et al.91, 039902(E) (2015).
  35. Akash Jain and Pavel Kovtun, Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics, J. High Energy Phys. 01 (2024) 162.
  36. Fábio S. Bemfica, Marcelo M. Disconzi, and Jorge Noronha, Causality and existence of solutions of relativistic viscous fluid dynamics with gravity, Phys. Rev. D 98, 104064 (2018).
  37. Pavel Kovtun, First-order relativistic hydrodynamics is stable, J. High Energy Phys. 10 (2019) 034.
  38. Fábio S. Bemfica, Marcelo M. Disconzi, and Jorge Noronha, Nonlinear causality of general first-order relativistic viscous hydrodynamics, Phys. Rev. D 100, 104020 (2019); Fábio S. Bemfica et al.105, 069902(E) (2022).
  39. Raphael E. Hoult and Pavel Kovtun, Stable and causal relativistic Navier-Stokes equations, J. High Energy Phys. 06 (2020) 067.
  40. Fabio S. Bemfica, Marcelo M. Disconzi, and Jorge Noronha, First-order general-relativistic viscous fluid dynamics, Phys. Rev. X 12, 021044 (2022).
  41. Pau Figueras, Aaron Held, and Áron D. Kovács, Well-posed initial value formulation of general effective field theories of gravity, arXiv:2407.08775.
  42. Pau Figueras, Áron D. Kovács, and Shunhui Yao, Stable non-linear evolution in regularised higher derivative effective field theories, J. High Energy Phys. 10 (2025) 150.
  43. Heinz-Otto Kreiss and Jens Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations, Classics in Applied Mathematics, Vol. 47 (Academic Press/SIAM, Boston, 1989).
  44. B. Gustafsson, H. O. Kreiss, and J. Oliger, Time-Dependent Problems and Difference Methods, Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts (Wiley, New York, 2013).
  45. Walter D. Goldberger and Ira Z. Rothstein, Effective field theory of gravity for extended objects, Phys. Rev. D 73, 104029 (2006).
  46. Rafael A. Porto, The effective field theorist’s approach to gravitational dynamics, Phys. Rep. 633, 1 (2016).
  47. J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numer. 10, 357 (2001).
  48. Ari Stern et al., Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms, Geometry, Mechanics, and Dynamics (Springer, New York, 2015), pp. 437–475.
  49. Chad R. Galley, Classical mechanics of nonconservative systems, Phys. Rev. Lett. 110, 174301 (2013).
  50. David Tsang, Chad R. Galley, Leo C. Stein, and Alec Turner, “Slimplectic” integrators: Variational integrators for general nonconservative systems, Astrophys. J. Lett. 809, L9 (2015).
  51. Afshin Besharat, Jury Radkovski, and Sergey Sibiryakov, Effective action for dissipative and nonholonomic systems, Phys. Rev. E 109, L052103 (2024).
  52. K. D. Kokkotas and B. F. Schutz, Normal modes of a model radiating system, Gen. Relativ. Gravit. 18, 913 (1986).
  53. A. O. Caldeira and A. J. Leggett, Quantum tunneling in a dissipative system, Ann. Phys. (N.Y.) 149, 374 (1983).
  54. Horace Lamb, On a peculiarity of the wave-system due to the free vibrations of a nucleus in an extended medium, Proc. London Math. Soc. 1, 208 (1900).
  55. C. P. Burgess and M. Williams, Who you gonna call? Runaway ghosts, higher derivatives and time-dependence in EFTs, J. High Energy Phys. 08 (2014) 074.
  56. Pradip M. Bakshi and Kalyana T. Mahanthappa, Expectation value formalism in quantum field theory. 1, J. Math. Phys. (N.Y.) 4, 1 (1963).
  57. Kalyana T. Mahanthappa, Multiple production of photons in quantum electrodynamics, Phys. Rev. 126, 329 (1962).
  58. Pradip M. Bakshi and Kalyana T. Mahanthappa, Expectation value formalism in quantum field theory. II, J. Math. Phys. (N.Y.) 4, 12 (1963).
  59. L. V. Keldysh, Diagram technique for nonequilibrium processes, Sov. Phys. JETP 20, 1018 (1965).
  60. Robert Geroch, Relativistic theories of dissipative fluids, J. Math. Phys. (N.Y.) 36, 4226 (1995).
  61. Gioel Calabrese, Luis Lehner, David Neilsen, Jorge Pullin, Oscar Reula, Olivier Sarbach, and Manuel Tiglio, Novel finite-differencing techniques for numerical relativity: Application to black-hole excision, Classical Quantum Gravity 20, L245 (2003).
  62. Gioel Calabrese, Luis Lehner, Oscar Reula, Olivier Sarbach, and Manuel Tiglio, Summation by parts and dissipation for domains with excised regions, Classical Quantum Gravity 21, 5735 (2004).
  63. Walter D. Goldberger and Ira Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev. D 73, 104030 (2006).
  64. Afshin Besharat, Open quantum dynamics on lie group: An effective field theory approach, Ph.D. thesis, McMaster University, 2024.
  65. Alex Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge University Press, Cambridge, 2023).

Outline

Information

Phys. Rev. D 114, 076006– Published 5 October, 2026
  • Received 16 March 2026
  • Accepted 10 September 2026
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