Duality-invariant (super)conformal higher-spin models

TL;DR

This paper develops a formalism for duality rotations in conformal higher-spin gauge fields in four dimensions, extending known duality-invariant electrodynamics to higher spins and supersymmetric cases, revealing new families of models.

Contribution

It introduces a general duality-invariant formalism for conformal higher-spin gauge fields, generalizing existing electrodynamics models to higher spins and supersymmetric theories.

Findings

Existence of duality-invariant models for spins s ≥ 2

Extension to supersymmetric conformal gauge fields

Generalization of ModMax Electrodynamics to higher spins

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 $n$.