A note on non-Lorentzian duality symmetries

TL;DR

This paper constructs non-Lorentzian dual actions for electromagnetism and linearised gravity in Carrollian and Galilean limits, revealing off-shell dualities and connections to kinematic algebra gauging.

Contribution

It introduces a systematic method to derive non-Lorentzian dual actions for electromagnetism and gravity, extending duality concepts beyond Lorentzian frameworks.

Findings

Dual actions for non-Lorentzian electromagnetism and gravity are constructed.

Off-shell electromagnetic duality relates electric and magnetic limits in these theories.

Dualities connect contractions of gravity to theories obtained via gauging kinematic algebras.

Abstract

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.