- 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

Dark higher-form portals and duality

Cypris Plantier* and Christopher Smith†

  • *Contact author: cplantier@lpsc.in2p3.fr
  • †Contact author: chsmith@lpsc.in2p3.fr
PDF

Phys. Rev. D 112, 075043 – Published 23 October, 2025

DOI: https://doi.org/10.1103/yfh1-zms8

Abstract

Light scalar or vector particles are among the most studied dark matter candidates. Yet, those are always described as scalar or vector fields. In this paper, we explore instead the embedding of the scalar particle in an antisymmetric rank-three tensor field, and the dark photon into an antisymmetric rank-two tensor field (a so-called Kalb-Ramond field), and construct minimal bases of effective interactions with Standard Model fields. Then, keeping phenomenological applications as our main objective, a number of theoretical aspects are clarified, in particular related to the impact of existing dualities among the corresponding free theories, and concerning their Stueckelberg representations. Besides, for the rank-two field, we present for the first time its full propagator, accounting for the possible presence of a pseudoscalar mass term. Thanks to these results, and with their different kinematics, gauge-invariant limits, and Lorentz properties, we show that these higher-form fields provide genuine alternative frameworks, with different couplings and expected signatures at low-energy or at colliders.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (44)

  1. M. Schumann, Direct detection of WIMP dark matter: Concepts and status, J. Phys. G 46, 103003 (2019).
  2. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of QCD axion models, Phys. Rep. 870, 1 (2020).
  3. C. Smith, The strong CP puzzle and axions, Proc. Sci. DIS2024 (2025) 013 [arXiv:2411.09529].
  4. A. Arbey and F. Mahmoudi, Dark matter and the early Universe: A review, Prog. Part. Nucl. Phys. 119, 103865 (2021).
  5. B. Holdom, Two U(1)’s and epsilon charge shifts, Phys. Lett. 166B, 196 (1986).
  6. M. Fabbrichesi, E. Gabrielli, and G. Lanfranchi, The Physics of the Dark Photon: A Primer (Springer International Publishing, New York, 2021).
  7. J. Polchinski, String Theory. Vol. 2: Superstring Theory and Beyond, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2007).
  8. P. Svrcek and E. Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  9. M. Kalb and P. Ramond, Classical direct interstring action, Phys. Rev. D 9, 2273 (1974).
  10. F. Lund and T. Regge, Unified approach to strings and vortices with soliton solutions, Phys. Rev. D 14, 1524 (1976).
  11. V. I. Ogievetsky and I. V. Polubarinov, The notoph and its possible interactions, Yad. Fiz. 4, 216 (1966).
  12. T. L. Curtright and P. G. O. Freund, Massive dual fields, Nucl. Phys. B172, 413 (1980).
  13. T. Curtright, Generalized gauge fields, Phys. Lett. 165B, 304 (1985).
  14. N. Kemmer, On the theory of particles of spin 1, Helv. Phys. Acta 33, 829 (1960).
  15. A. Aurilia and Y. Takahashi, Generalized Maxwell equations and the gauge mixing mechanism of mass generation, Prog. Theor. Phys. 66, 693 (1981).
  16. A. Aurilia and H. Umezawa, Theory of high-spin fields, Phys. Rev. 182, 1682 (1969).
  17. E. C. G. Stueckelberg, Interaction energy in electrodynamics and in the field theory of nuclear forces, Helv. Phys. Acta 11, 225 (1938).
  18. H. Ruegg and M. Ruiz-Altaba, The Stueckelberg field, Int. J. Mod. Phys. A 19, 3265 (2004).
  19. E. Cremmer and J. Scherk, Spontaneous dynamical breaking of gauge symmetry in dual models, Nucl. Phys. B72, 117 (1974).
  20. S. E. Hjelmeland and U. Lindstrom, Duality for the nonspecialist, arXiv:hep-th/9705122.
  21. Y. Takahashi and R. Palmer, Gauge-independent formulation of a massive field with spin one, Phys. Rev. D 1, 2974 (1970).
  22. A. Smailagic and E. Spallucci, The dual phases of massless/massive Kalb-Ramond fields: Letter to the editor, J. Phys. A 34, L435 (2001).
  23. F. A. d. S. Barbosa, Canonical analysis of Kalb–Ramond–Proca duality, Eur. Phys. J. Plus 137, 678 (2022).
  24. K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974).
  25. S. Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries, Phys. Rep. 1063, 1 (2024).
  26. L. Bhardwaj, L. E. Bottini, L. Fraser-Taliente, L. Gladden, D. S. W. Gould, A. Platschorre, and H. Tillim, Lectures on generalized symmetries, Phys. Rep. 1051, 1 (2024).
  27. F. Quevedo and C. A. Trugenberger, Phases of antisymmetric tensor field theories, Nucl. Phys. B501, 143 (1997).
  28. P. C. Malta, J. P. S. Melo, and C. A. D. Zarro, Experimental signatures of Kalb-Ramond-like particles, J. High Energy Phys. 05 (2025) 093.
  29. S. Tiwary and R. Dick, Constraints on antisymmetric tensor fields from Bhabha scattering, Eur. Phys. J. C 81, 1115 (2021).
  30. A. Hell, On the duality of massive Kalb-Ramond and Proca fields, J. Cosmol. Astropart. Phys. 01 (2022) 056.
  31. J. F. Kamenik and C. Smith, FCNC portals to the dark sector, J. High Energy Phys. 03 (2012) 090.
  32. M. Williams, C. P. Burgess, A. Maharana, and F. Quevedo, New constraints (and motivations) for Abelian gauge bosons in the MeV-TeV mass range, J. High Energy Phys. 08 (2011) 106.
  33. A. J. Magnus, J. G. Fenwick, and R. Dick, Antisymmetric tensor portals to dark matter, J. Subatomic Part. Cosmol. 3, 100022 (2025).
  34. M. Blau and G. Thompson, Topological gauge theories of antisymmetric tensor fields, Ann. Phys. (N.Y.) 205, 130 (1991).
  35. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  36. L. C. Papaloucas, J. Rembielinski, and W. Tybor, Free notoph theory in longitudinal gauge, Acta Phys. Pol. B 22, 429 (1991), https://www.actaphys.uj.edu.pl/R/22/5/429/pdf.
  37. D. Dalmazi and R. C. Santos, Spin-1 duality in D-dimensions, Phys. Rev. D 84, 045027 (2011).
  38. H. Casini, R. Montemayor, and L. F. Urrutia, Duality for symmetric second rank tensors. 1. The massive case, Phys. Rev. D 66, 085018 (2002).
  39. A. Sugamoto, Dual transformation in gauge theories, Phys. Rev. D 19, 1820 (1979).
  40. G. B. de Gracia, Renormalized Kalb-Ramond model: Duality and generalized potential, Nucl. Phys. B1001, 116498 (2024).
  41. J. F. Kamenik and C. Smith, Could a light Higgs boson illuminate the dark sector?, Phys. Rev. D 85, 093017 (2012).
  42. G. Dvali, Three-form gauging of axion symmetries and gravity, arXiv:hep-th/0507215.
  43. G. Dvali, Strong-cp with and without gravity, arXiv:2209.14219.
  44. J. Baez and J. P. Muniain, Gauge Fields, Knots and Gravity (World Scientific, River Edge, NJ, 1995).

Outline

Information

Phys. Rev. D 112, 075043– Published 23 October, 2025
  • Received 18 June 2025
  • Accepted 30 September 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