ModMax meets GCA

TL;DR

This paper introduces a Galilean-invariant extension of the ModMax nonlinear electrodynamics theory, preserving Galilean conformal symmetry and expanding the understanding of symmetry structures in non-linear electromagnetism.

Contribution

It constructs a covariant Galilean cousin of ModMax theory, demonstrating its invariance under Galilean Conformal Algebra and involving Galilean electromagnetic invariants.

Findings

The Galilean ModMax theory is explicitly invariant under Galilean Conformal Symmetries.

The construction involves new Galilean electromagnetic invariants.

The classical structure of the theory remains invariant under GCA.

Abstract

A maximally symmetric non-linear extension of Maxwell's theory in four dimensions called ModMax has been recently introduced in the literature. This theory preserves both electromagnetic duality and conformal invariance of the linear theory. In this short paper, we introduce a Galilean cousin of the ModMax theory, written in a covariant formalism, that is explicitly shown to be invariant under Galilean Conformal Symmetries. We discuss the construction of such a theory involving Galilean electromagnetic invariants, and show how the classical structure of the theory is invariant under the action of Galilean Conformal Algebra (GCA).