On nonlinear self-duality in $4p$ dimensions

Building on the earlier work by Araki and Tanii, Aschieri {\it et al.}, and Buratti {\it et al.}, 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 and construct new self-dual nonlinear theories for a gauge $(2p-1)$-form. We present a family of models for self-dual nonlinear $(2p-1)$-form electrodynamics in which the trace of the energy-momentum tensor determines the flow with respect to a duality-invariant deformation parameter. Finally, we propose the interesting problem of computing the so-called induced action in the case that self-dual $(2p-1)$-form electrodynamics is coupled to dilaton and axion fields and the compact duality group $\mathsf{U}(1)$ is enhanced to the non-compact group $\mathsf{SL}(2, {\mathbb R})$.