Abstract
Relations between the various formulations of nonlinear p-form electrodynamics with conformal-invariant weak-field and strong-field limits are clarified, with a focus on duality invariant (2n − 1)-form electrodynamics and chiral 2n-form electrodynamics in Minkowski spacetime of dimension D = 4n and D = 4n + 2, respectively. We exhibit a new family of chiral 2-form electrodynamics in D = 6 for which these limits exhaust the possibilities for conformal invariance; the weak-field limit is related by dimensional reduction to the recently discovered ModMax generalisation of Maxwell’s equations. For n > 1 we show that the chiral ‘strong-field’ 2n-form electrodynamics is related by dimensional reduction to a new Sl(2; ℝ)-duality invariant theory of (2n − 1)-form electrodynamics.
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References
D. Berman, M5 on a torus and the three-brane, Nucl. Phys. B 533 (1998) 317 [hep-th/9804115] [INSPIRE].
A. Nurmagambetov, Duality symmetric three-brane and its coupling to type IIB supergravity, Phys. Lett. B 436 (1998) 289 [hep-th/9804157] [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].
I. Bialynicki-Birula, Nonlinear electrodynamics: variations on a theme by Born and Infeld, in Quantum theory of particles and fields: birthday volume dedicated to Jan Lopuszanski, B. Jancewicz and J. Lukierski eds., World Scientific, Singapore (1984), pg. 31.
G. W. Gibbons and P. C. West, The metric and strong coupling limit of the M5-brane, J. Math. Phys. 42 (2001) 3188 [hep-th/0011149] [INSPIRE].
P. K. Townsend, An interacting conformal chiral 2-form electrodynamics in six dimensions, Proc. Roy. Soc. Lond. A 476 (2020) 20190863 [arXiv:1911.01161] [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].
G. Buratti, K. Lechner and L. Melotti, Duality invariant self-interactions of Abelian p-forms in arbitrary dimensions, JHEP 09 (2019) 022 [arXiv:1906.07094] [INSPIRE].
G. Buratti, K. Lechner and L. Melotti, Self-interacting chiral p-forms in higher dimensions, Phys. Lett. B 798 (2019) 135018 [arXiv:1909.10404] [INSPIRE].
D. Chruscinski, Strong field limit of the Born-Infeld p-form electrodynamics, Phys. Rev. D 62 (2000) 105007 [hep-th/0005215] [INSPIRE].
P. K. Townsend, Manifestly Lorentz invariant chiral boson action, Phys. Rev. Lett. 124 (2020) 101604 [arXiv:1912.04773] [INSPIRE].
M. Henneaux and C. Teitelboim, Dynamics of chiral (selfdual) p-forms, Phys. Lett. B 206 (1988) 650 [INSPIRE].
E. Bergshoeff, D. P. Sorokin and P. K. Townsend, The M5-brane Hamiltonian, Nucl. Phys. B 533 (1998) 303 [hep-th/9805065] [INSPIRE].
N. Marcus and J. H. Schwarz, Field theories that have no manifestly Lorentz invariant formulation, Phys. Lett. B 115 (1982) 111 [INSPIRE].
M. Perry and J. H. Schwarz, Interacting chiral gauge fields in six-dimensions and Born-Infeld theory, Nucl. Phys. B 489 (1997) 47 [hep-th/9611065] [INSPIRE].
P. Pasti, D. P. Sorokin and M. Tonin, Duality symmetric actions with manifest space-time symmetries, Phys. Rev. D 52 (1995) 4277 [hep-th/9506109] [INSPIRE].
P. Pasti, D. P. Sorokin and M. Tonin, On Lorentz invariant actions for chiral p-forms, Phys. Rev. D 55 (1997) 6292 [hep-th/9611100] [INSPIRE].
A. Maznytsia, C. R. Preitschopf and D. P. Sorokin, Duality of selfdual actions, Nucl. Phys. B 539 (1999) 438 [hep-th/9805110] [INSPIRE].
M. K. Gaillard and B. Zumino, Duality rotations for interacting fields, Nucl. Phys. B 193 (1981) 221 [INSPIRE].
S. Deser and O. Sarioglu, Hamiltonian electric/magnetic duality and Lorentz invariance, Phys. Lett. B 423 (1998) 369 [hep-th/9712067] [INSPIRE].
X. Bekaert and M. Henneaux, Comments on chiral p-forms, Int. J. Theor. Phys. 38 (1999) 1161 [hep-th/9806062] [INSPIRE].
X. Bekaert, Interactions of chiral two forms, PoS(tmr99)007 (1999) [hep-th/9911109] [INSPIRE].
R. Courant and D. Hilbert, Methods of mathematical physics: partial differential equations, volume 2, Interscience, (1962), pg. 91.
M. Hatsuda, K. Kamimura and S. Sekiya, Electric magnetic duality invariant Lagrangians, Nucl. Phys. B 561 (1999) 341 [hep-th/9906103] [INSPIRE].
R. Floreanini and R. Jackiw, Selfdual fields as charge density solitons, Phys. Rev. Lett. 59 (1987) 1873 [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, (1997), pg. 33 [hep-th/9712103] [INSPIRE].
S. M. Kuzenko and S. Theisen, Supersymmetric duality rotations, JHEP 03 (2000) 034 [hep-th/0001068] [INSPIRE].
X. Bekaert and S. Cucu, Deformations of duality symmetric theories, Nucl. Phys. B 610 (2001) 433 [hep-th/0104048] [INSPIRE].
E. A. Ivanov and B. M. Zupnik, New representation for Lagrangians of selfdual nonlinear electrodynamics, in 4th international workshop on supersymmetry and quantum symmetries: 16th Max Born symposium, (2002), pg. 235 [hep-th/0202203] [INSPIRE].
E. A. Ivanov and B. M. Zupnik, New approach to nonlinear electrodynamics: dualities as symmetries of interaction, Phys. Atom. Nucl. 67 (2004) 2188 [Yad. Fiz. 67 (2004) 2212] [hep-th/0303192] [INSPIRE].
S. M. Kuzenko, Manifestly duality-invariant interactions in diverse dimensions, Phys. Lett. B 798 (2019) 134995 [arXiv:1908.04120] [INSPIRE].
V. Arnold, Mathematical methods of classical mechanics, 2nd edition, Springer, (1989).
P. A. M. Dirac, Generalized Hamiltonian dynamics, Can. J. Math. 2 (1950) 129 [INSPIRE].
I. Bialynicki-Birula, Field theory of photon dust, Acta Phys. Polon. B 23 (1992) 553 [INSPIRE].
S. Deser and C. Teitelboim, Duality transformations of Abelian and non-Abelian gauge fields, Phys. Rev. D 13 (1976) 1592 [INSPIRE].
L. Mezincescu and P. K. Townsend, DBI in the IR, J. Phys. A 53 (2020) 044002 [arXiv:1907.06036] [INSPIRE].
J. H. Schwarz and A. Sen, Duality symmetric actions, Nucl. Phys. B 411 (1994) 35 [hep-th/9304154] [INSPIRE].
W. Siegel, Manifest Lorentz invariance sometimes requires nonlinearity, Nucl. Phys. B 238 (1984) 307 [INSPIRE].
A. R. Kavalov and R. L. Mkrtchian, Lagrangian of the selfduality equation and d = 10, N = 2b supergravity, Sov. J. Nucl. Phys. 46 (1987) 728 [Yad. Fiz. 46 (1987) 1246] [INSPIRE].
B. McClain, F. Yu and Y. S. Wu, Covariant quantization of chiral bosons and OSp(1, 1|2) symmetry, Nucl. Phys. B 343 (1990) 689 [INSPIRE].
C. Wotzasek, The Wess-Zumino term for chiral bosons, Phys. Rev. Lett. 66 (1991) 129 [INSPIRE].
I. Bengtsson and A. Kleppe, On chiral p-forms, Int. J. Mod. Phys. A 12 (1997) 3397 [hep-th/9609102] [INSPIRE].
N. Berkovits, Manifest electromagnetic duality in closed superstring field theory, Phys. Lett. B 388 (1996) 743 [hep-th/9607070] [INSPIRE].
N. Berkovits, Local actions with electric and magnetic sources, Phys. Lett. B 395 (1997) 28 [hep-th/9610134] [INSPIRE].
D. Belov and G. W. Moore, Holographic action for the self-dual field, hep-th/0605038 [INSPIRE].
D. M. Belov and G. W. Moore, Type II actions from 11-dimensional Chern-Simons theories, hep-th/0611020 [INSPIRE].
A. Sen, Covariant action for type IIB supergravity, JHEP 07 (2016) 017 [arXiv:1511.08220] [INSPIRE].
A. Sen, Self-dual forms: action, Hamiltonian and compactification, J. Phys. A 53 (2020) 084002 [arXiv:1903.12196] [INSPIRE].
K. Mkrtchyan, On covariant actions for chiral p-forms, JHEP 12 (2019) 076 [arXiv:1908.01789] [INSPIRE].
E. Andriolo, N. Lambert and C. Papageorgakis, Geometrical aspects of an Abelian (2, 0) action, JHEP 04 (2020) 200 [arXiv:2003.10567] [INSPIRE].
P. Vanichchapongjaroen, Covariant M5-brane action with self-dual 3-form, arXiv:2011.14384 [INSPIRE].
A. Maznytsia, C. R. Preitschopf and D. P. Sorokin, Dual actions for chiral bosons, in 10th summer school/seminar (Volga-10) on recent problems in theoretical and mathematical physics, (1998) [hep-th/9808049] [INSPIRE].
S.-L. Ko and P. Vanichchapongjaroen, A covariantisation of M5-brane action in dual formulation, JHEP 01 (2018) 072 [arXiv:1712.06408] [INSPIRE].
D. Zwanziger, Local Lagrangian quantum field theory of electric and magnetic charges, Phys. Rev. D 3 (1971) 880 [INSPIRE].
I. A. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. P. Sorokin and M. Tonin, Covariant action for the superfive-brane of M-theory, Phys. Rev. Lett. 78 (1997) 4332 [hep-th/9701149] [INSPIRE].
M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, World volume action of the M-theory five-brane, Nucl. Phys. B 496 (1997) 191 [hep-th/9701166] [INSPIRE].
I. Bandos, On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology, JHEP 08 (2014) 048 [arXiv:1406.5185] [INSPIRE].
H. Isono, Note on the self-duality of gauge fields in topologically nontrivial spacetime, PTEP 2014 (2014) 093B05 [arXiv:1406.6023] [INSPIRE].
P. S. Howe and E. Sezgin, D = 11, p = 5, Phys. Lett. B 394 (1997) 62 [hep-th/9611008] [INSPIRE].
P. S. Howe, E. Sezgin and P. C. West, Covariant field equations of the M-theory five-brane, Phys. Lett. B 399 (1997) 49 [hep-th/9702008] [INSPIRE].
P. S. Howe, E. Sezgin and P. C. West, The six-dimensional selfdual tensor, Phys. Lett. B 400 (1997) 255 [hep-th/9702111] [INSPIRE].
I. A. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. P. Sorokin and M. Tonin, On the equivalence of different formulations of the M-theory five-brane, Phys. Lett. B 408 (1997) 135 [hep-th/9703127] [INSPIRE].
P. Pasti, D. Sorokin and M. Tonin, Covariant actions for models with non-linear twisted self-duality, Phys. Rev. D 86 (2012) 045013 [arXiv:1205.4243] [INSPIRE].
C. Lee and H. Min, SL(2, R) duality-symmetric action for electromagnetic theory with electric and magnetic sources, Annals Phys. 339 (2013) 328 [arXiv:1306.5520] [INSPIRE].
P. Vanichchapongjaroen, Dual formulation of covariant nonlinear duality-symmetric action of kappa-symmetric D3-brane, JHEP 02 (2018) 116 [arXiv:1712.06425] [INSPIRE].
S.-L. Ko and P. Vanichchapongjaroen, The dual formulation of M5-brane action, JHEP 06 (2016) 022 [arXiv:1605.04705] [INSPIRE].
S.-L. Ko, D. Sorokin and P. Vanichchapongjaroen, The M5-brane action revisited, JHEP 11 (2013) 072 [arXiv:1308.2231] [INSPIRE].
P.-M. Ho and Y. Matsuo, M5 from M2, JHEP 06 (2008) 105 [arXiv:0804.3629] [INSPIRE].
P.-M. Ho, Y. Imamura, Y. Matsuo and S. Shiba, M5-brane in three-form flux and multiple M2-branes, JHEP 08 (2008) 014 [arXiv:0805.2898] [INSPIRE].
I. A. Bandos and P. K. Townsend, Light-cone M5 and multiple M2-branes, Class. Quant. Grav. 25 (2008) 245003 [arXiv:0806.4777] [INSPIRE].
I. A. Bandos and P. K. Townsend, SDiff gauge theory and the M2 condensate, JHEP 02 (2009) 013 [arXiv:0808.1583] [INSPIRE].
P. Pasti, I. Samsonov, D. Sorokin and M. Tonin, BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D = 6 and M5-branes, Phys. Rev. D 80 (2009) 086008 [arXiv:0907.4596] [INSPIRE].
B. P. Kosyakov, Nonlinear electrodynamics with the maximum allowable symmetries, Phys. Lett. B 810 (2020) 135840 [arXiv:2007.13878] [INSPIRE].
D. Flores-Alfonso, B. A. González-Morales, R. Linares and M. Maceda, Black holes and gravitational waves sourced by non-linear duality rotation-invariant conformal electromagnetic matter, Phys. Lett. B 812 (2021) 136011 [arXiv:2011.10836] [INSPIRE].
A. B. Bordo, D. Kubiznak and T. R. Perche, Taub-NUT solutions in conformal electrodynamics, arXiv:2011.13398 [INSPIRE].
D. Flores-Alfonso, R. Linares and M. Maceda, Nonlinear extensions of gravitating dyons: from NUT wormholes to Taub-Bolt instantons, arXiv:2012.03416 [INSPIRE].
Z. Amirabi and S. H. Mazharimousavi, Black-hole solution in nonlinear electrodynamics with the maximum allowable symmetries, arXiv:2012.07443 [INSPIRE].
B. Zumino, Effective Lagrangians and broken symmetries, in Lectures on elementary particles and quantum field theory, volume 2, Brandeis Univ., Cambridge, MA, U.S.A. (1970), pg. 437.
S. Faci, Conformal invariance: from Weyl to SO(2, d), EPL 101 (2013) 31002 [arXiv:1206.4362] [INSPIRE].
V. I. Denisov, E. E. Dolgaya, V. A. Sokolov and I. P. Denisova, Conformal invariant vacuum nonlinear electrodynamics, Phys. Rev. D 96 (2017) 036008 [INSPIRE].
I. P. Denisova, B. D. Garmaev and V. A. Sokolov, Compact objects in conformal nonlinear electrodynamics, Eur. Phys. J. C 79 (2019) 531 [arXiv:1901.05318] [INSPIRE].
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Bandos, I., Lechner, K., Sorokin, D. et al. On p-form gauge theories and their conformal limits. J. High Energ. Phys. 2021, 22 (2021). https://doi.org/10.1007/JHEP03(2021)022
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DOI: https://doi.org/10.1007/JHEP03(2021)022