Abstract
We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of the action, we characterize the Lagrangians giving rise to duality-invariant theories up to the eight-derivative level, providing the complete list of operators that one needs to include in the action. We also characterize the set of duality-invariant theories whose action is quadratic in the Maxwell field strength but which are non-minimally coupled to the curvature. Then we explore the effect of field redefinitions and we show that, to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators. We conjecture that this is a general phenomenon at all orders, i.e., that any duality-invariant extension of Einstein-Maxwell theory is perturbatively equivalent to a higher-derivative gravity minimally coupled to Maxwell theory. Finally, we study charged black hole solutions in the six-derivative theory and we investigate additional constraints on the couplings motivated by the weak gravity conjecture.
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References
A. Sen, O(d) × O(d) symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys. Lett. B 271 (1991) 295 [INSPIRE].
E. Bergshoeff, B. Janssen and T. Ortín, Solution generating transformations and the string effective action, Class. Quant. Grav. 13 (1996) 321 [hep-th/9506156] [INSPIRE].
K. A. Meissner, Symmetries of higher order string gravity actions, Phys. Lett. B 392 (1997) 298 [hep-th/9610131] [INSPIRE].
C. Eloy, O. Hohm and H. Samtleben, Duality Invariance and Higher Derivatives, Phys. Rev. D 101 (2020) 126018 [arXiv:2004.13140] [INSPIRE].
Z. Elgood and T. Ortín, T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′, JHEP 10 (2020) 097 [Erratum ibid. 06 (2021) 105] [arXiv:2005.11272] [INSPIRE].
T. Ortín, O(n, n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in α′, JHEP 01 (2021) 187 [arXiv:2005.14618] [INSPIRE].
T. Codina, O. Hohm and D. Marques, String Dualities at Order α′3, Phys. Rev. Lett. 126 (2021) 171602 [arXiv:2012.15677] [INSPIRE].
D. Marques and C. A. Núñez, T-duality and α’-corrections, JHEP 10 (2015) 084 [arXiv:1507.00652] [INSPIRE].
W. H. Baron, J. J. Fernandez-Melgarejo, D. Marques and C. Núñez, The Odd story of α′-corrections, JHEP 04 (2017) 078 [arXiv:1702.05489] [INSPIRE].
H. Razaghian and M. R. Garousi, R4 terms in supergravities via T-duality constraint, Phys. Rev. D 97 (2018) 106013 [arXiv:1801.06834] [INSPIRE].
O. Hohm and B. Zwiebach, Duality invariant cosmology to all orders in α′, Phys. Rev. D 100 (2019) 126011 [arXiv:1905.06963] [INSPIRE].
O. Hohm and B. Zwiebach, Non-perturbative de Sitter vacua via α′ corrections, Int. J. Mod. Phys. D 28 (2019) 1943002 [arXiv:1905.06583] [INSPIRE].
C. Krishnan, de Sitter, α′-Corrections \& Duality Invariant Cosmology, JCAP 10 (2019) 009 [arXiv:1906.09257] [INSPIRE].
H. Bernardo, R. Brandenberger and G. Franzmann, O(d, d) covariant string cosmology to all orders in α′, JHEP 02 (2020) 178 [arXiv:1911.00088] [INSPIRE].
C. A. Núñez and F. E. Rost, New non-perturbative de Sitter vacua in α′-complete cosmology, JHEP 03 (2021) 007 [arXiv:2011.10091] [INSPIRE].
M. K. Gaillard and B. Zumino, Duality Rotations for Interacting Fields, Nucl. Phys. B 193 (1981) 221 [INSPIRE].
M. Henneaux and C. Teitelboim, Dynamics of Chiral (Selfdual) P Forms, Phys. Lett. B 206 (1988) 650 [INSPIRE].
M. J. Duff, Duality Rotations in String Theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].
M. J. Duff and J. X. Lu, Duality Rotations in Membrane Theory, Nucl. Phys. B 347 (1990) 394 [INSPIRE].
A. Sen, Electric magnetic duality in string theory, Nucl. Phys. B 404 (1993) 109 [hep-th/9207053] [INSPIRE].
J. H. Schwarz and A. Sen, Duality symmetric actions, Nucl. Phys. B 411 (1994) 35 [hep-th/9304154] [INSPIRE].
B. de Wit, Electric magnetic dualities in supergravity, Nucl. Phys. B Proc. Suppl. 101 (2001) 154 [hep-th/0103086] [INSPIRE].
T. Ortín, Gravity and Strings, Cambridge Monographs on Mathematical Physics, second edition, Cambridge University Press, Cambridge U.K. (2015), [INSPIRE].
C. M. Hull and P. K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
C. M. Hull and A. Van Proeyen, Pseudoduality, Phys. Lett. B 351 (1995) 188 [hep-th/9503022] [INSPIRE].
C. I. Lazaroiu and C. S. Shahbazi, Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds, Rev. Math. Phys. 30 (2018) 1850012 [arXiv:1609.05872] [INSPIRE].
C. I. Lazaroiu and C. S. Shahbazi, Four-dimensional geometric supergravity and electromagnetic duality: a brief guide for mathematicians, arXiv:2006.16157 [INSPIRE].
G. W. Gibbons and D. A. Rasheed, Electric-magnetic duality rotations in nonlinear electrodynamics, Nucl. Phys. B 454 (1995) 185 [hep-th/9506035] [INSPIRE].
M. K. Gaillard and B. Zumino, Selfduality in nonlinear electromagnetism, Lect. Notes Phys. 509 (1998) 121 [hep-th/9705226] [INSPIRE].
M. K. Gaillard and B. Zumino, Nonlinear electromagnetic selfduality and Legendre transformations, in A Newton Institute Euroconference on Duality and Supersymmetric Theories, Cambridge U.K. (1997), pg. 33 [hep-th/9712103] [INSPIRE].
M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A 144 (1934) 425.
E. Schrödinger, Contributions to Born’s new theory of the electromagnetic field, Proc. Roy. Soc. Lond. A 150 (1935) 465.
I. Bialynicki-Birula, Field theory of photon dust, Acta Phys. Polon. B 23 (1992) 553 [INSPIRE].
W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98 (1936) 714 [physics/0605038] [INSPIRE].
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 (2020) 121703 [arXiv:2007.09092] [INSPIRE].
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 (1996) 46 [hep-th/9509141] [INSPIRE].
M. Hatsuda, K. Kamimura and S. Sekiya, Electric magnetic duality invariant Lagrangians, Nucl. Phys. B 561 (1999) 341 [hep-th/9906103] [INSPIRE].
D. Brace, B. Morariu and B. Zumino, Duality invariant Born-Infeld theory, hep-th/9905218 [INSPIRE].
C. Bunster and M. Henneaux, Sp(2n,R) electric-magnetic duality as off-shell symmetry of interacting electromagnetic and scalar fields, PoS(HRMS2010)028 (2010) [arXiv:1101.6064] [INSPIRE].
W. Chemissany, R. Kallosh and T. Ortín, Born-Infeld with Higher Derivatives, Phys. Rev. D 85 (2012) 046002 [arXiv:1112.0332] [INSPIRE].
K. Babaei Velni and H. Babaei-Aghbolagh, On SL(2, R) symmetry in nonlinear electrodynamics theories, Nucl. Phys. B 913 (2016) 987 [arXiv:1610.07790] [INSPIRE].
Y. Hamada, T. Noumi and G. Shiu, Weak Gravity Conjecture from Unitarity and Causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [INSPIRE].
B. Bellazzini, M. Lewandowski and J. Serra, Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity, Phys. Rev. Lett. 123 (2019) 251103 [arXiv:1902.03250] [INSPIRE].
P. A. Cano and A. Murcia, Electromagnetic Quasitopological Gravities, JHEP 10 (2020) 125 [arXiv:2007.04331] [INSPIRE].
S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins, Normal forms for tensor polynomials. 1: The Riemann tensor, Class. Quant. Grav. 9 (1992) 1151 [INSPIRE].
P. Bueno, P. A. Cano, J. Moreno and A. Murcia, All higher-curvature gravities as Generalized quasi-topological gravities, JHEP 11 (2019) 062 [arXiv:1906.00987] [INSPIRE].
S. Deser, M. Henneaux and C. Teitelboim, Electric-magnetic black hole duality, Phys. Rev. D 55 (1997) 826 [hep-th/9607182] [INSPIRE].
R. M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
C. Cheung, J. Liu and G. N. Remmen, Proof of the Weak Gravity Conjecture from Black Hole Entropy, JHEP 10 (2018) 004 [arXiv:1801.08546] [INSPIRE].
A. M. Charles, The Weak Gravity Conjecture, RG Flows, and Supersymmetry, arXiv:1906.07734 [INSPIRE].
G. J. Loges, T. Noumi and G. Shiu, Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture, Phys. Rev. D 102 (2020) 046010 [arXiv:1909.01352] [INSPIRE].
P. A. Cano, T. Ortín and P. F. Ramirez, On the extremality bound of stringy black holes, JHEP 02 (2020) 175 [arXiv:1909.08530] [INSPIRE].
P. A. Cano, S. Chimento, R. Linares, T. Ortín and P. F. Ramírez, α′ corrections of Reissner-Nordström black holes, JHEP 02 (2020) 031 [arXiv:1910.14324] [INSPIRE].
S. Andriolo, T.-C. Huang, T. Noumi, H. Ooguri and G. Shiu, Duality and axionic weak gravity, Phys. Rev. D 102 (2020) 046008 [arXiv:2004.13721] [INSPIRE].
G. J. Loges, T. Noumi and G. Shiu, Duality and Supersymmetry Constraints on the Weak Gravity Conjecture, JHEP 11 (2020) 008 [arXiv:2006.06696] [INSPIRE].
G. Goon and R. Penco, Universal Relation between Corrections to Entropy and Extremality, Phys. Rev. Lett. 124 (2020) 101103 [arXiv:1909.05254] [INSPIRE].
P. A. Cano and A. Murcia, Exact electromagnetic duality with nonminimal couplings, arXiv:2105.09868 [INSPIRE].
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Cano, P.A., Murcia, Á. Duality-invariant extensions of Einstein-Maxwell theory. J. High Energ. Phys. 2021, 42 (2021). https://doi.org/10.1007/JHEP08(2021)042
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DOI: https://doi.org/10.1007/JHEP08(2021)042