A note on non-Lorentzian duality symmetries

We work out non-Lorentzian dual actions for electromagnetism and linearised gravity, both in the Carrollian and Galilean cases. This is done in the same way as for Lorentzian theories, by first constructing a parent action that reduces to a pair of dual actions. In the case of Maxwell theory, each pair of dual actions consists of the known ‘electric’ and ‘magnetic’ limits of the original theories, showing that these limits are related by an off-shell electromagnetic duality. We have obtained dualities between on one hand the non-Lorentzian contractions of linearised gravity in second-order form, and on the other hand the theories one obtains by gauging the corresponding kinematic algebras. In the Carrollian contraction, these dual actions reproduce the known ‘electric’ and ‘magnetic’ Carrollian theories of gravity, and we find a similar result in the Galilean case.