Nonlinear self-duality for arbitrary spin, superspin, and supersymmetry type

TL;DR

This paper reviews the formalism of duality rotations for superconformal gauge multiplets of various spins and supersymmetries, demonstrating the self-duality of models and proposing methods to generate such models, including higher-spin extensions.

Contribution

It introduces a comprehensive formalism for duality rotations in superconformal gauge theories of arbitrary spin and supersymmetry, and shows how to construct self-dual models and their higher-spin extensions.

Findings

All $ ext{U}(1)$ duality-invariant models are self-dual under Legendre transformation.

Self-dual models for vector and supermultiplets are formulated on general backgrounds.

Methods are proposed to generate self-dual models, including superconformal and higher-spin extensions.

Abstract

We review the general formalism of duality rotations for $\cal N$-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with ${\cal N} \geq 0$. Self-dual models for a vector field (${\cal N}=0$) and for ${\cal N}=1$ and ${\cal N}=2$ vector supermultiplets are naturally formulated on general (super)gravity backgrounds. For all other (super)spin values, the corresponding self-dual systems are realised on arbitrary conformally flat backgrounds. Every $\mathsf{U}(1)$ duality-invariant model is demonstrated to be self-dual with respect to a Legendre transformation. Methods are proposed to generate such self-dual models including superconformal ones. We show that every model for self-dual nonlinear electrodynamics admits a higher-spin extension. Throughout the review, we make use of the formalism of conformal (super)space, that is the geometric setting to describe the gauge theory of the (super)conformal group.