Democratic Lagrangians for Nonlinear Electrodynamics

TL;DR

This paper develops a symmetric Lagrangian framework for nonlinear electrodynamics that naturally incorporates electric-magnetic duality, including the ModMax theory, and suggests a generalization to higher-dimensional forms.

Contribution

It introduces a democratic Lagrangian formulation for nonlinear electrodynamics that makes duality symmetries explicit and extends to conformally invariant theories like ModMax.

Findings

Constructed a duality-symmetric Lagrangian for nonlinear electrodynamics.

Unified electric and magnetic potentials on equal footing.

Provided a natural extension to higher-dimensional p-forms.

Abstract

We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be straightforwardly imposed, leading to a simple formulation for theories with the $SO(2)$ duality invariance. When specialized to the conformally invariant case, our construction provides a manifestly duality-symmetric formulation of the recently discovered ModMax theory. We briefly comment on a natural generalization of this approach to $p$-forms in $2p+2$ dimensions.