Mass/electric versus NUT/magnetic charges: duality from scattering amplitudes in $D\ge 4$ and for all bosonic spins

Abstract

We revisit Kerr-NUT metrics and related spin-$s$ fields in $D\ge 4$, and study their associated scattering amplitudes. Starting in position space, we highlight the interpretation of mass and (multiple) NUT charges as being associated to distinct solutions of the rotation-deformed radial equation, which is made explicit in Cartesian multi-Kerr-Schild coordinates. This interpretation extends to electromagnetism with magnetic-type charges, and also extends to higher-spin counterparts, in accordance with the classical double or multi copy. We then establish a notion of ``electric-magnetic" duality in higher dimensions, relating mass/electric to NUT/magnetic charges, which generalises the $D=4$ case in a novel manner. For $D\ge 6$, this involves the choice where the multiple magnetic charges are equal. The duality is revealed in momentum space, by the 3-point scattering amplitudes that generate the solutions. For all spins, these amplitudes are constructed from a spin-raising operator ${\mathcal{S}}_{\mu }$ and take the form ${\epsilon }^{{\mu }_1\cdots {\mu }_s}{\mathcal{S}}_{{\mu }_1}\cdots {\mathcal{S}}_{{\mu }_s}$ acting on a scalar seed. The scalar seed of the electric sector is dual to that of the magnetic sector: where the former's rotation dependence resums to a Bessel function $J_{\frac{D-5}{2}}$, the latter resums to a Bessel function $J_{-\frac{D-5}{2}}$. Finally, we explore the notion of self-duality that arises from this picture. Studying the classical $2\mapsto 2$ amplitudes that determine leading-order scattering, we find no evidence of a higher-dimensional analogue of the integrability of $D=4$ self-dual gravity.

47 pages