Conformally invariant nonlinear electrodynamic actions and its non-abelian extensions

In this work, formal theoretical aspects concerning conformally invariant functional actions of electrodynamics are presented and discussed. In particular, the origin of the conformal and duality invariant Lagrangians of [I. Bandos et al., J. High Energy Phys. 10 (2021) 031; I. Bandos, K. Lechner, D. Sorokin and P. Townsend, Phys. Rev. D 102 (2020) 121703] (e.g. ModMax) and also Born-Infeld types are analyzed being its non-abelian counterpart presented and discussed explicitly for the gauge group SU(2). Implications on the properties of the gravitational field are briefly discussed by means of new symmetries of the field equations.