Abstract
The Hamiltonian formulation for nonlinear chiral 2-form electrodynamics in six-dimensional Minkowski spacetime is used to show that small-amplitude plane-wave perturbations of a generic uniform constant ‘magnetic’ background exhibit trirefringence: all three independent wave-polarisations have distinct dispersion relations. While two coincide for Lorentz invariant theories, all three coincide uniquely for the chiral 2-form theory on the worldvolume of the M5-brane of M-theory. We argue that this is because, in this M-theory context, the waves propagate in a planar M5-M2-M2 bound-state preserving 16 supersymmetries. We also show how our results imply analogous results for nonlinear electrodynamics in a Minkowski spacetime of five and four dimensions.
Article PDF
Similar content being viewed by others
References
I. Bialynicki-Birula, Nonlinear Electrodynamics: Variations on a theme by Born and Infeld in Quantum Theory of Particles and Fields, B. Jancewicz and J. Lukierski eds., World Scientific (1983), p. 31–48 [INSPIRE].
M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A 144 (1934) 425 [INSPIRE].
G. Boillat, Vitesses des ondes électrodynamiques et lagrangiens exceptionnels, Ann. Inst. H. Poincare Phys. Theor. 5 (1966) 217 [INSPIRE].
G. Boillat, Nonlinear electrodynamics — Lagrangians and equations of motion, J. Math. Phys. 11 (1970) 941 [INSPIRE].
J. Plebanski, Lectures on non-linear electrodynamics, RX-476 (1970) [INSPIRE].
J.G. Russo and P.K. Townsend, Nonlinear electrodynamics without birefringence, JHEP 01 (2023) 039 [arXiv:2211.10689] [INSPIRE].
M. Henneaux and C. Teitelboim, Dynamics of Chiral (Selfdual) P Forms, Phys. Lett. B 206 (1988) 650 [INSPIRE].
I. Bandos, K. Lechner, D. Sorokin and P.K. Townsend, On p-form gauge theories and their conformal limits, JHEP 03 (2021) 022 [arXiv:2012.09286] [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].
A.A. Tseytlin, Selfduality of Born-Infeld action and Dirichlet three-brane of type IIB superstring theory, Nucl. Phys. B 469 (1996) 51 [hep-th/9602064] [INSPIRE].
I.A. Bandos et al., 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].
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].
E. Bergshoeff, D.P. Sorokin and P.K. Townsend, The M5-brane Hamiltonian, Nucl. Phys. B 533 (1998) 303 [hep-th/9805065] [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].
C. Ferko, L. Smith and G. Tartaglino-Mazzucchelli, Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry, arXiv:2301.10411 [INSPIRE].
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].
I. Bialynicki-Birula, Field theory of photon dust, Acta Phys. Polon. B 23 (1992) 553 [INSPIRE].
G.W. Gibbons and P.K. Townsend, Vacuum interpolation in supergravity via super p-branes, Phys. Rev. Lett. 71 (1993) 3754 [hep-th/9307049] [INSPIRE].
D.P. Sorokin and P.K. Townsend, M Theory superalgebra from the M five-brane, Phys. Lett. B 412 (1997) 265 [hep-th/9708003] [INSPIRE].
E. Bergshoeff, R.-G. Cai, N. Ohta and P.K. Townsend, M brane interpolations and (2, 0) renormalization group flow, Phys. Lett. B 495 (2000) 201 [hep-th/0009147] [INSPIRE].
J.M. Izquierdo, N.D. Lambert, G. Papadopoulos and P.K. Townsend, Dyonic membranes, Nucl. Phys. B 460 (1996) 560 [hep-th/9508177] [INSPIRE].
D. Mateos and P.K. Townsend, Supertubes, Phys. Rev. Lett. 87 (2001) 011602 [hep-th/0103030] [INSPIRE].
R. Emparan, D. Mateos and P.K. Townsend, Supergravity supertubes, JHEP 07 (2001) 011 [hep-th/0106012] [INSPIRE].
D. Mateos, S. Ng and P.K. Townsend, Tachyons, supertubes and brane/anti-brane systems, JHEP 03 (2002) 016 [hep-th/0112054] [INSPIRE].
U. Lindstrom and R. von Unge, A Picture of D-branes at strong coupling, Phys. Lett. B 403 (1997) 233 [hep-th/9704051] [INSPIRE].
J.P. Gauntlett, J. Gomis and P.K. Townsend, BPS bounds for world volume branes, JHEP 01 (1998) 003 [hep-th/9711205] [INSPIRE].
S. Deser, J.G. McCarthy and O. Sarioglu, ‘Good propagation’ constraints on dual invariant actions in electrodynamics and on massless fields, Class. Quant. Grav. 16 (1999) 841 [hep-th/9809153] [INSPIRE].
Acknowledgments
IB and DS have been partially supported by Spanish AEI MCIN and FEDER (ERDF EU) under grant PID2021-125700NB-C21 and by the Basque Government Grant IT1628-22. PKT has been partially supported by STFC consolidated grant ST/T000694/1.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2303.11485
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bandos, I., Lechner, K., Sorokin, D. et al. Trirefringence and the M5-brane. J. High Energ. Phys. 2023, 171 (2023). https://doi.org/10.1007/JHEP06(2023)171
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2023)171