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  • Letter
  • Open Access

Novel duality-invariant theories of electrodynamics

Ángel J. Murcia*

  • *Contact author: angelmurcia@icc.ub.edu

Phys. Rev. D 112, L101902 – Published 7 November, 2025

DOI: https://doi.org/10.1103/8fyg-ljz4

Abstract

We identify new families of duality-invariant theories of electrodynamics. We achieve this in two different ways. On the one hand, we present an algorithm to construct a one-parameter family of exactly duality-invariant theories from a single seed duality-invariant theory. If the seed theory is causal, the theories constructed from this method will also be causal when the parameter is non-negative. On the other hand, we find two additional novel families of duality-invariant theories which include a nonzero term independent of the electromagnetic field. The first of them generalizes Bialynicki-Birula electrodynamics, while the second family of theories features a well-defined Maxwell limit as the term independent of the gauge field strength is sent to zero.

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References (44)

  1. M. Born and L. Infeld, Foundations of the new field theory, Proc. R. Soc. A 144, 425 (1934).
  2. W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98, 714 (1936).
  3. G. Boillat, Nonlinear electrodynamics—Lagrangians and equations of motion, J. Math. Phys. (N.Y.) 11, 941 (1970).
  4. J. Plebanski, Lectures on Non-linear Electrodynamics: An Extended Version of Lectures Given at the Niels Bohr Institute and NORDITA, Copenhagen, 1968, Lectures (Nordisk institut for teoretisk atomfysik) (NORDITA, 1970), https://books.google.es/books?id=zEZUAAAAYAAJ.
  5. I. Bialynicki-Birula, Field theory of photon dust, Acta Phys. Pol. B 23, 553 (1992).
  6. G. W. Gibbons and D. A. Rasheed, Electric—magnetic duality rotations in nonlinear electrodynamics, Nucl. Phys. B454, 185 (1995).
  7. G. W. Gibbons and D. A. Rasheed, Sl(2,R) invariance of nonlinear electrodynamics coupled to an axion and a dilaton, Phys. Lett. B 365, 46 (1996).
  8. M. K. Gaillard and B. Zumino, Selfduality in nonlinear electromagnetism, Lect. Notes Phys. 509, 121 (1998).
  9. M. K. Gaillard and B. Zumino, Nonlinear electromagnetic selfduality and Legendre transformations, in A Newton Institute Euroconference on Duality and Supersymmetric Theories (1997), pp. 33–48, .
  10. G. V. Dunne, The Heisenberg-Euler effective action: 75 years on, Int. J. Mod. Phys. A 27, 1260004 (2012).
  11. P. Gaete and J. Helayël-Neto, Remarks on nonlinear electrodynamics, Eur. Phys. J. C 74, 3182 (2014).
  12. S. Kruglov, A model of nonlinear electrodynamics, Ann. Phys. (Amsterdam) 353, 299 (2015).
  13. S. I. Kruglov, Nonlinear arcsin-electrodynamics and asymptotic Reissner-Nordström black holes, Ann. Phys. (Berlin) 528, 588 (2016).
  14. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, A non-linear duality-invariant conformal extension of Maxwell’s equations, Phys. Rev. D 102, 121703 (2020).
  15. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, On p-form gauge theories and their conformal limits, J. High Energy Phys. 03 (2021) 022.
  16. I. Gullu and S. H. Mazharimousavi, Double-logarithmic nonlinear electrodynamics, Phys. Scr. 96, 045217 (2021).
  17. T. Tahamtan, Compatibility of nonlinear electrodynamics models with Robinson-Trautman geometry, Phys. Rev. D 103, 064052 (2021).
  18. Z. Avetisyan, O. Evnin, and K. Mkrtchyan, Democratic Lagrangians for nonlinear electrodynamics, Phys. Rev. Lett. 127, 271601 (2021).
  19. D. P. Sorokin, Introductory notes on non-linear electrodynamics and its applications, Fortschr. Phys. 70, 2200092 (2022).
  20. H. Babaei-Aghbolagh, K. B. Velni, D. M. Yekta, and H. Mohammadzadeh, Emergence of non-linear electrodynamic theories from TT−-like deformations, Phys. Lett. B 829, 137079 (2022).
  21. C. Ferko, L. Smith, and G. Tartaglino-Mazzucchelli, On current-squared flows and ModMax theories, SciPost Phys. 13, 012 (2022).
  22. K. Mkrtchyan and M. Svazas, Solutions in nonlinear electrodynamics and their double copy regular black holes, J. High Energy Phys. 09 (2022) 012.
  23. K. Lechner, P. Marchetti, A. Sainaghi, and D. P. Sorokin, Maximally symmetric nonlinear extension of electrodynamics and charged particles, Phys. Rev. D 106, 016009 (2022).
  24. H. Babaei-Aghbolagh, K. Babaei Velni, D. M. Yekta, and H. Mohammadzadeh, Manifestly SL(2, R) duality-symmetric forms in ModMax theory, J. High Energy Phys. 12 (2022) 147.
  25. J. G. Russo and P. K. Townsend, Nonlinear electrodynamics without birefringence, J. High Energy Phys. 01 (2023) 039.
  26. C. Ferko, L. Smith, and G. Tartaglino-Mazzucchelli, Stress tensor flows, birefringence in non-linear electrodynamics and supersymmetry, SciPost Phys. 15, 198 (2023).
  27. J. G. Russo and P. K. Townsend, Dualities of self-dual nonlinear electrodynamics, J. High Energy Phys. 09 (2024) 107.
  28. J. G. Russo and P. K. Townsend, Born again, SciPost Phys. 16, 124 (2024).
  29. J. G. Russo and P. K. Townsend, Simplified self-dual electrodynamics, arXiv:2505.08869.
  30. B. Chen, S. He, and J. Hou, Self-dual electrodynamics via the characteristic method: Relativistic and Carrollian perspectives, arXiv:2506.03129.
  31. The general solution to this equation is known, although in an implicit way [9].

  32. M. Hatsuda, K. Kamimura, and S. Sekiya, Electric magnetic duality invariant Lagrangians, Nucl. Phys. B561, 341 (1999).
  33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/8fyg-ljz4 for a detailed discussion on duality invariance in the Hamiltonian formalism, some instances of dynamical choices for ψ for which the equations for the fields conforming ψ are covariant under duality transformations and the general perturbative resolution of the duality-invariance condition for theories homogeneous in the variables s, p and ψ, which includes Refs. [34–36].
  34. I. Bialynicki-Birula and Z. Bialynicki-Birula, Quantum Electrodynamics (Pergamon Press, Warsaw, 1975).
  35. T. Padmanabhan, Some aspects of field equations in generalised theories of gravity, Phys. Rev. D 84, 124041 (2011).
  36. P. A. Cano and Á. Murcia, Electromagnetic quasitopological gravities, J. High Energy Phys. 10 (2020) 125.
  37. H. Babaei-Aghbolagh, S. He, and H. Ouyang, Generalized TT¯-like deformations in duality-invariant nonlinear electrodynamic theories, J. High Energy Phys. 09 (2024) 137.
  38. En passant we fix a small typo present in Equation (4.1) of [6]. According to their notation, they should have βδ=−1.

  39. Note that O(s2,p2) stands for terms that, under a rescaling (s,p)→(as,ap), get an overall factor ak with k≥2.

  40. Observe that the theory is not well defined for p=0.

  41. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II (Interscience, New York, 1962).
  42. Strictly, the conclusion would be q(σ)=ℓ(eγσ)+b, for b∈R. However, this just amounts to the addition of an inoffensive constant to the Lagrangian, so we simply disregard it.

  43. J. G. Russo and P. K. Townsend, Causal self-dual electrodynamics, Phys. Rev. D 109, 105023 (2024).
  44. Again, by O(x3/2,y3/2) we denote terms that, under a rescaling (x,y)→(ax,ay), get an overall factor ak with k≥3/2.

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