We review the general formalism of duality rotations for N-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with N≥0. Self-dual models for a vector field (N=0) and for N=1 and 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 U(1) duality-invariant model is demonstrated to be self-dual with respect to a Legendre transformation. Methods are described 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 this review, we make use of the formalism of conformal (super)space, which is the geometric setting to describe the gauge theory of the (super)conformal group.
Sergei M. Kuzenko (Mon,) studied this question.