- 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

Gravity-induced photon interactions and infrared consistency in any dimensions

Pedro Bittar1,*, Sylvain Fichet2,†, and Lucas de Souza3,‡

  • *Contact author: pedro.bittar.souza@usp.br
  • †Contact author: sylvain.fichet@ufabc.edu.br
  • ‡Contact author: souza.l@ufabc.edu.br
PDF

Phys. Rev. D 112, 045009 – Published 21 August, 2025

DOI: https://doi.org/10.1103/p8k8-vz2h

Abstract

We compute the four-photon (F4) operators generated by loops of charged particles of spin 0, 12, 1 in the presence of gravity and in any spacetime dimension d. To this end, we expand the one-loop effective action via the heat kernel coefficients, which capture both the gravity-induced renormalization of the F4 operators and the low-energy Einstein-Maxwell effective field theory (EFT) produced by massive charged particles. We set positivity bounds on the F4 operators using standard arguments from extremal black holes (for d≥4) and from infrared (IR) consistency of four-photon scattering (for d≥3). We find that both approaches yield nearly equivalent results, even though in the amplitudes we discard the graviton t-channel pole and use the vanishing of the Gauss-Bonnet term at quadratic order for any d. The positivity bounds constrain the charge-to-mass ratio of the heavy particles. If the Planckian F4 operators are sufficiently small or negative, such bounds produce a version of the d-dimensional weak gravity conjecture (WGC) in most, but not all, dimensions. In the special case of d=6, the gravity-induced beta functions of F4 operators from charged particles of any spin are positive, leading to WGC-like bounds with a logarithmic enhancement. In d=9, 10, the WGC fails to guarantee extremal black hole decay in the infrared EFT, thereby requiring the existence of sufficiently large Planckian F4 operators.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (81)

  1. T. N. Pham and T. N. Truong, Evaluation of the derivative quartic terms of the meson chiral Lagrangian from forward dispersion relation, Phys. Rev. D 31, 3027 (1985).
  2. B. Ananthanarayan, D. Toublan, and G. Wanders, Consistency of the chiral pion pion scattering amplitudes with axiomatic constraints, Phys. Rev. D 51, 1093 (1995).
  3. A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, J. High Energy Phys. 10 (2006) 014.
  4. N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang, The EFT-Hedron, J. High Energy Phys. 05 (2021) 259.
  5. L. Alberte, C. de Rham, S. Jaitly, and A. J. Tolley, Positivity bounds and the massless spin-2 pole, Phys. Rev. D 102, 125023 (2020).
  6. L. Alberte, C. de Rham, S. Jaitly, and A. J. Tolley, QED positivity bounds, Phys. Rev. D 103, 125020 (2021).
  7. J. Henriksson, B. McPeak, F. Russo, and A. Vichi, Rigorous bounds on light-by-light scattering, J. High Energy Phys. 06 (2022) 158.
  8. J. Henriksson, B. McPeak, F. Russo, and A. Vichi, Bounding violations of the weak gravity conjecture, J. High Energy Phys. 08 (2022) 184.
  9. B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau, and F. Riva, Positive moments for scattering amplitudes, Phys. Rev. D 104, 036006 (2021).
  10. S. Caron-Huot, D. Mazac, L. Rastelli, and D. Simmons-Duffin, AdS bulk locality from sharp CFT bounds, arXiv:2106.10274.
  11. B. Bellazzini, M. Riembau, and F. Riva, IR side of positivity bounds, Phys. Rev. D 106, 105008 (2022).
  12. S. Caron-Huot and V. Van Duong, Extremal effective field theories, J. High Energy Phys. 05 (2021) 280.
  13. S. Caron-Huot, D. Mazac, L. Rastelli, and D. Simmons-Duffin, Sharp boundaries for the swampland, J. High Energy Phys. 07 (2021) 110.
  14. J. Davighi, S. Melville, and T. You, Natural selection rules: New positivity bounds for massive spinning particles, J. High Energy Phys. 02 (2022) 167.
  15. C. de Rham, S. Melville, and J. Noller, Positivity bounds on dark energy: When matter matters, J. Cosmol. Astropart. Phys. 08 (2021) 018.
  16. S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez, and D. Simmons-Duffin, Causality constraints on corrections to Einstein gravity, J. High Energy Phys. 05 (2023) 122.
  17. A. J. Tolley, Z.-Y. Wang, and S.-Y. Zhou, New positivity bounds from full crossing symmetry, J. High Energy Phys. 05 (2021) 255.
  18. C. de Rham, A. J. Tolley, and J. Zhang, Causality constraints on gravitational effective field theories, Phys. Rev. Lett. 128, 131102 (2022).
  19. C. de Rham, S. Kundu, M. Reece, A. J. Tolley, and S.-Y. Zhou, Snowmass white paper: UV constraints on IR physics, in Snowmass 2021 (2022), arXiv:2203.06805.
  20. L.-Y. Chiang, Y.-t. Huang, L. Rodina, and H.-C. Weng, De-projecting the EFThedron, arXiv:2204.07140.
  21. S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez, and D. Simmons-Duffin, Graviton partial waves and causality in higher dimensions, Phys. Rev. D 108, 026007 (2023).
  22. K. Häring, A. Hebbar, D. Karateev, M. Meineri, and J. a. Penedones, Bounds on photon scattering, arXiv:2211.05795.
  23. Y. Hamada, R. Kuramochi, G. J. Loges, and S. Nakajima, On (scalar QED) gravitational positivity bounds, arXiv:2301.01999.
  24. B. Bellazzini, G. Isabella, S. Ricossa, and F. Riva, Massive gravity is not positive, Phys. Rev. D 109, 024051 (2024).
  25. A. Eichhorn, A. O. Pedersen, and M. Schiffer, Application of positivity bounds in asymptotically safe gravity, arXiv:2405.08862.
  26. B. Knorr and A. Platania, Unearthing the intersections: Positivity bounds, weak gravity conjecture, and asymptotic safety landscapes from photon-graviton flows, arXiv:2405.08860.
  27. Y. Kats, L. Motl, and M. Padi, Higher-order corrections to mass-charge relation of extremal black holes, J. High Energy Phys. 12 (2007) 068.
  28. C. Cheung, J. Liu, and G. N. Remmen, Proof of the weak gravity conjecture from black hole entropy, J. High Energy Phys. 10 (2018) 004.
  29. G. J. Loges, T. Noumi, and G. Shiu, Thermodynamics of 4D dilatonic black holes and the weak gravity conjecture, Phys. Rev. D 102, 046010 (2020).
  30. G. Goon and R. Penco, Universal relation between corrections to entropy and extremality, Phys. Rev. Lett. 124, 101103 (2020).
  31. C. R. T. Jones and B. McPeak, The black hole weak gravity conjecture with multiple charges, J. High Energy Phys. 06 (2020) 140.
  32. G. J. Loges, T. Noumi, and G. Shiu, Duality and supersymmetry constraints on the weak gravity conjecture, J. High Energy Phys. 11 (2020) 008.
  33. N. Arkani-Hamed, Y.-t. Huang, J.-Y. Liu, and G. N. Remmen, Causality, unitarity, and the weak gravity conjecture, J. High Energy Phys. 03 (2022) 083.
  34. Q.-H. Cao and D. Ueda, Entropy constraint on effective field theory, arXiv:2201.00931.
  35. V. De Luca, J. Khoury, and S. S. C. Wong, Implications of the weak gravity conjecture for tidal Love numbers of black holes, arXiv:2211.14325.
  36. N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The string landscape, black holes and gravity as the weakest force, J. High Energy Phys. 06 (2007) 060.
  37. M. van Beest, J. Calderón-Infante, D. Mirfendereski, and I. Valenzuela, Lectures on the swampland program in string compactifications, Phys. Rep. 989, 1 (2022).
  38. M. Graña and A. Herráez, The swampland conjectures: A bridge from quantum gravity to particle physics, Universe 7, 273 (2021).
  39. N. B. Agmon, A. Bedroya, M. J. Kang, and C. Vafa, Lectures on the string landscape and the swampland, arXiv:2212.06187.
  40. C. Cheung and G. N. Remmen, Infrared consistency and the weak gravity conjecture, J. High Energy Phys. 12 (2014) 087.
  41. B. Bellazzini, C. Cheung, and G. N. Remmen, Quantum gravity constraints from unitarity and analyticity, Phys. Rev. D 93, 064076 (2016).
  42. C. Cheung and G. N. Remmen, Positivity of curvature-squared corrections in gravity, Phys. Rev. Lett. 118, 051601 (2017).
  43. Y. Hamada, T. Noumi, and G. Shiu, Weak gravity conjecture from unitarity and causality, Phys. Rev. Lett. 123, 051601 (2019).
  44. B. Bellazzini, M. Lewandowski, and J. Serra, Positivity of amplitudes, weak gravity conjecture, and modified gravity, Phys. Rev. Lett. 123, 251103 (2019).
  45. W.-M. Chen, Y.-T. Huang, T. Noumi, and C. Wen, Unitarity bounds on charged/neutral state mass ratios, Phys. Rev. D 100, 025016 (2019).
  46. Z. Bern, D. Kosmopoulos, and A. Zhiboedov, Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude, J. Phys. A 54, 344002 (2021).
  47. P. B. Gilkey, The spectral geometry of a Riemannian manifold, J. Diff. Geom. 10, 601 (1975).
  48. D. V. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rep. 388, 279 (2003).
  49. A. E. M. van de Ven, Explicit counter action algorithms in higher dimensions, Nucl. Phys. B250, 593 (1985).
  50. E. s. Fradkin and A. a. Tseytlin, Quantization and dimensional reduction: One loop results for superYang-Mills and supergravities in D≥4, Phys. Lett. 123B, 231 (1983).
  51. R. R. Metsaev and A. A. Tseytlin, On loop corrections to string theory effective actions, Nucl. Phys. B298, 109 (1988).
  52. F. Bastianelli, J. M. Davila, and C. Schubert, Gravitational corrections to the Euler-Heisenberg Lagrangian, J. High Energy Phys. 03 (2009) 086.
  53. A. Ritz and R. Delbourgo, The low-energy effective Lagrangian for photon interactions in any dimension, Int. J. Mod. Phys. A 11, 253 (1996).
  54. D. Hoover and C. P. Burgess, Ultraviolet sensitivity in higher dimensions, J. High Energy Phys. 01 (2006) 058.
  55. Y. Abe, T. Noumi, and K. Yoshimura, Black hole extremality in nonlinear electrodynamics: A lesson for weak gravity and Festina Lente bounds, J. High Energy Phys. 09 (2023) 024.
  56. S. Barbosa, S. Fichet, and L. de Souza, On the black hole weak gravity conjecture and extremality in the strong-field regime, arXiv:2503.20910.
  57. E. Palti, The swampland: Introduction and review, Fortschr. Phys. 67, 1900037 (2019).
  58. A. V. Manohar, Effective field theories, Lect. Notes Phys. 479, 311 (1997).
  59. A. V. Manohar, Introduction to effective field theories, arXiv:1804.05863.
  60. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).
  61. B. Zwiebach, Curvature squared terms and string theories, Phys. Lett. 156B, 315 (1985).
  62. W. A. Hiscock and L. D. Weems, Evolution of charged evaporating black holes, Phys. Rev. D 41, 1142 (1990).
  63. S. Barbosa, P. Brax, S. Fichet, and L. de Souza, Running Love numbers and the effective field theory of gravity, arXiv:2501.18684.
  64. M. Carrillo González, C. de Rham, S. Jaitly, V. Pozsgay, and A. Tokareva, Positivity-causality competition: A road to ultimate EFT consistency constraints, J. High Energy Phys. 06 (2024) 146.
  65. G. N. Remmen and N. L. Rodd, Consistency of the standard model effective field theory, J. High Energy Phys. 12 (2019) 032.
  66. J. A. Strathdee, Extended poincare supersymmetry, Int. J. Mod. Phys. A 02, 273 (1987).
  67. S. Fichet and G. von Gersdorff, Anomalous gauge couplings from composite Higgs and warped extra dimensions, J. High Energy Phys. 03 (2014) 102.
  68. I. T. Drummond and S. J. Hathrell, QED vacuum polarization in a background gravitational field and its effect on the velocity of photons, Phys. Rev. D 22, 343 (1980).
  69. W. Heisenberg and H. Euler, Consequences of dirac theory of the positron, Zeitschr. Phys. 98, 714 (1936).
  70. G. V. Dunne, Heisenberg-Euler Effective Lagrangians: Basics and Extensions (World Scientific Publishing, 2004), pp. 445–522.
  71. S. Fichet, G. von Gersdorff, B. Lenzi, C. Royon, and M. Saimpert, Light-by-light scattering with intact protons at the LHC: From standard model to new physics, J. High Energy Phys. 02 (2015) 165.
  72. N. Birrell and P. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1984).
  73. B. Grinstein, D. Stone, A. Stergiou, and M. Zhong, Challenge to the a theorem in six dimensions, Phys. Rev. Lett. 113, 231602 (2014).
  74. B. Grinstein, A. Stergiou, D. Stone, and M. Zhong, Two-loop renormalization of multiflavor ϕ3 theory in six dimensions and the trace anomaly, Phys. Rev. D 92, 045013 (2015).
  75. J. H. Schwarz, Superstring theory, Phys. Rep. 89, 223 (1982).
  76. J. Polchinski, String Theory. Vol. 2: Superstring Theory and Beyond, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2007).
  77. M. de Roo and M. G. C. Eenink, The effective action for the four point functions in Abelian open superstring theory, J. High Energy Phys. 08 (2003) 036.
  78. E. S. Fradkin and A. A. Tseytlin, Nonlinear electrodynamics from quantized strings, Phys. Lett. 163B, 123 (1985).
  79. J. M. Davila, C. Schubert, and M. A. Trejo, Photonic processes in Born-Infeld theory, Int. J. Mod. Phys. A 29, 1450174 (2014).
  80. M. Born and L. Infeld, Foundations of the new field theory, Proc. R. Soc. A 144, 425 (1934).
  81. S. Fichet, G. von Gersdorff, O. Kepka, B. Lenzi, C. Royon, and M. Saimpert, Probing new physics in diphoton production with proton tagging at the Large Hadron Collider, Phys. Rev. D 89, 114004 (2014).

Outline

Information

Phys. Rev. D 112, 045009– Published 21 August, 2025
  • Received 12 November 2024
  • Accepted 18 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. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation