Trirefringence and the M5-brane

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.

Automated summary

This article uses the Hamiltonian formulation for nonlinear chiral 2-form electrodynamics in six-dimensional Minkowski spacetime to demonstrate that small-amplitude plane-wave perturbations of a generic uniform constant 'magnetic' background exhibit trirefringence. The dispersion relations for all three independent wave-polarisations are distinct. The unique coincidence of all three dispersion relations is observed in the chiral 2-form theory on the worldvolume of the M5-brane of M-theory, as waves propagate in a planar M5-M2-M2 bound-state preserving 16 supersymmetries. Similar results are also implied for nonlinear electrodynamics in five and four dimensions in Minkowski spacetime.