On nonlinear self-duality in $4p$ dimensions

TL;DR

The paper addresses extending self-dual nonlinear electrodynamics from four dimensions to higher even dimensions $d=4p$ by leveraging the Gaillard–Zumino framework. It shows that any four-dimensional self-dual model can be extended to $d=4p>4$ within a restricted $L(F)=\mathcal{L}(S,P)$ form, and provides a constructive scheme using an Omega-rotation $\Omega = S\cosh\gamma + \sqrt{S^{2}+P^{2}}\sinh\gamma$ to generate new duality-invariant theories $\mathcal{L}_\gamma = \mathcal{L}(\Omega,P)$, including higher-dimensional Born–Infeld and ModMax generalizations. Explicit examples demonstrate the method: $\mathcal{L}_{BI}$ and the conformal ModMax theory $\mathcal{L}_{MM}$, along with a recipe that yields a higher-dimensional ModMax–Born theory. The results imply a broad family of $\mathsf{U}(1)$-duality-invariant nonlinear electrodynamics in $4p$ dimensions, with connections to recent $T\overline{T}$-like flow results and potential extensions beyond the $S,P$ invariants.

Abstract

We demonstrate that every model for self-dual nonlinear electrodynamics in four dimensions has a $\mathsf{U}(1)$ duality-invariant extension to $4p>4$ dimensions.