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  • Letter
  • Open Access

Exact electromagnetic duality with nonminimal couplings

Pablo A. Cano1,* and Ángel Murcia2,3,†

  • 1Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
  • 2Instituto de Física Teórica UAM/CSIC, C/ Nicolás Cabrera 13-15, C.U. Cantoblanco, E-28049 Madrid, Spain
  • 3Department of Mathematics, University of Hamburg, Bundesstraße 55, D-20146 Hamburg, Germany

  • *pabloantonio.cano@kuleuven.be
  • †angel.murcia@csic.es
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Phys. Rev. D 104, L101501 – Published 3 November, 2021

DOI: https://doi.org/10.1103/PhysRevD.104.L101501

Abstract

We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation usually represents a challenging problem. Despite that, we manage to obtain a closed form of the action for all the theories with a quadratic dependence on the vector field strength. In these theories we find that the Maxwell field couples to gravity through a curvature-dependent susceptibility tensor that takes a peculiar form, reminiscent to that of Born-Infeld Lagrangians. We study the static and spherically symmetric black hole solutions of the simplest of these models, showing that the corresponding equations of motion are invariant under rotations of the electric and magnetic charges. We compute the perturbative corrections to the Reissner-Nordström solution in this theory, and in the case of extremal black holes we determine exactly the near-horizon geometry as well as the entropy. Remarkably, the entropy only possesses a constant correction despite the action containing an infinite number of terms. In addition, we find there is a lower bound for the charge and the mass of extremal black holes. When the sign of the coupling is such that the weak gravity conjecture is satisfied, the area and the entropy of extremal black holes vanish at the minimal charge.

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References (38)

  1. M. Henneaux and C. Teitelboim, Phys. Lett. B 206, 650 (1988).
  2. M. J. Duff, Nucl. Phys. B335, 610 (1990).
  3. M. J. Duff and J. X. Lu, Nucl. Phys. B347, 394 (1990).
  4. A. Sen, Nucl. Phys. B404, 109 (1993).
  5. J. H. Schwarz and A. Sen, Nucl. Phys. B411, 35 (1994).
  6. T. Ortin, Gravity and Strings, 2nd ed., Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2015).
  7. B. de Wit, Nucl. Phys. B, Proc. Suppl. 101, 154 (2001).
  8. W. A. Chemissany, J. de Jong, and M. de Roo, J. High Energy Phys. 11 (2006) 086.
  9. P. A. Cano and A. Murcia, J. High Energy Phys. 08 (2021) 042.
  10. M. Born and L. Infeld, Proc. R. Soc. A 144, 425 (1934).
  11. E. Schrödinger, Proc. R. Soc. A 150, 465 (1935).
  12. G. W. Gibbons, AIP Conf. Proc. 589, 324 (2001).
  13. I. Bialynicki-Birula, Acta Phys. Pol. B 23, 553 (1992), https://www.actaphys.uj.edu.pl/R/23/6/553.
  14. G. W. Gibbons and D. A. Rasheed, Nucl. Phys. B454, 185 (1995).
  15. G. W. Gibbons and D. A. Rasheed, Phys. Lett. B 365, 46 (1996).
  16. M. K. Gaillard and B. Zumino, Lect. Notes Phys. 509, 121 (1998).
  17. M. K. Gaillard and B. Zumino, in A Newton Institute Euroconference on Duality and Supersymmetric Theories (1997), https://inspirehep.net/literature/452195.
  18. M. Hatsuda, K. Kamimura, and S. Sekiya, Nucl. Phys. B561, 341 (1999).
  19. D. Brace, B. Morariu, and B. Zumino, arXiv:hep-th/9905218.
  20. W. Chemissany, R. Kallosh, and T. Ortin, Phys. Rev. D 85, 046002 (2012).
  21. K. B. Velni and H. Babaei-Aghbolagh, Nucl. Phys. B913, 987 (2016).
  22. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, Phys. Rev. D 102, 121703 (2020).
  23. Z. Elgood and T. Ortin, J. High Energy Phys. 10 (2020) 097.

  24. One must ensure that the different χ(n)μνρσ are symmetric in the exchange of the pairs of indices {μν} and {ρσ}. This is guaranteed by the construction of the complete χμνρσ, but if one wants not to rely on separate results, it is possible to prove (6) and that the different χ(n)μνρσ have the appropriate symmetries through a simple induction process.

  25. Note that the parameter α can be reabsorbed in Tμν.

  26. This process is indeed equivalent to computing first the complete Einstein and Maxwell equations and evaluating them on the SSS ansatz—see Ref. [27] for a proof.

  27. P. A. Cano and A. Murcia, J. High Energy Phys. 10 (2020) 125.
  28. A. Sen, J. High Energy Phys. 03 (2006) 008.
  29. A. Sen, Gen. Relativ. Gravit. 40, 2249 (2008).
  30. C. Cheung, J. Liu, and G. N. Remmen, J. High Energy Phys. 10 (2018) 004.
  31. Y. Hamada, T. Noumi, and G. Shiu, Phys. Rev. Lett. 123, 051601 (2019).
  32. N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, J. High Energy Phys. 06 (2007) 060.
  33. A. Strominger and C. Vafa, Phys. Lett. B 379, 99 (1996).
  34. D. Kutasov, F. Larsen, and R. G. Leigh, Nucl. Phys. B550, 183 (1999).
  35. A. Dabholkar, Phys. Rev. Lett. 94, 241301 (2005).
  36. P. D. Prester and T. Terzić, J. High Energy Phys. 12 (2008) 088.
  37. P. A. Cano, S. Chimento, R. Linares, T. Ortín, and P. F. Ramírez, J. High Energy Phys. 02 (2020) 031.

  38. More precisely, both metrics are related by a redefinition gμνST=gμνours+3αTμν to first order in α, but this only means that the theories are written in different frames.

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Phys. Rev. D 104, L101501– Published 3 November, 2021
  • Received 25 May 2021
  • Accepted 5 October 2021
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