Duality-invariant (super)conformal higher-spin models

TL;DR

This work extends the paradigm of U(1) duality-invariant nonlinear electrodynamics to conformal higher-spin fields in four dimensions by constructing a general duality framework for bosonic CHS theories with $s\ge 2$ in conformally flat backgrounds, and by developing auxiliary-field formalisms that enforce self-duality under Legendre transformations. It then elevates the construction to ${\cal N}=1$ and ${\cal N}=2$ supersymmetric conformal higher-spin multiplets, producing explicit superconformal duality-invariant actions and showing how ModMax-type deformations generalize to higher spins, with clear reductions to known $s=1$ results. The paper also discusses a superspace degauging approach and sketches a Lorentz-type duality extension, providing a robust toolkit for building and analyzing self-dual, duality-invariant higher-spin theories with potential links to low-energy effective actions in gauge theories. Overall, the results offer a systematic pathway to formulate and study continuous dualities in higher-spin, superconformal contexts, with implications for conformal geometry, supersymmetric higher-spin dynamics, and extensions of ModMax-type deformations.

Abstract

We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics developed by Gaillard and Zumino, Gibbons and Rasheed, and generalised by Ivanov and Zupnik. For each integer spin $s\geq 2$ we demonstrate the existence of families of conformal $\mathsf{U}(1)$ duality-invariant models, including a generalisation of the so called ModMax Electrodynamics ($s=1$). Our bosonic results are then extended to the $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric cases. We also sketch a formalism of duality rotations for conformal gauge fields of Lorentz type $(m/2, n/2)$, for positive integers $m $ and $n$.