Key points are not available for this paper at this time.
We prove that a 4d theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric g replaced by a unit-determinant metric h (F) which is a function of the field strength F, if and only if the theory enjoys electric-magnetic duality invariance. Among duality-invariant models, the Modified Maxwell (ModMax) theory is special because the associated metric h (F) produces identical equations of motion when it is coupled to the Maxwell theory via two different prescriptions which we describe. We use the field-dependent metric perspective to analyze the electric and magnetic 1-form global symmetries in models of self-dual electrodynamics. This analysis suggests that any duality-invariant theory possesses a set of conserved currents j^ which are in one-to-one correspondence with 2-forms that are harmonic with respect to the field-dependent metric h (F).
Ferko et al. (Mon,) studied this question.