Counterterms vs. dualities

We investigate and clarify the mutual compatibility of the higher order corrections arising in supergravity and string theory effective actions and the non-linear duality symmetries of these theories. Starting from a conventional tree level action leading to duality invariant equations of motion, we show how to accommodate duality invariant counterterms given as functionals of both electric and magnetic fields in a perturbative expansion, and to deduce from them a non-polynomial bona fide action satisfying the Gaillard-Zumino (NGZ) constraint. There exists a corresponding consistency constraint in the non-covariant Henneaux-Teitelboim formalism which ensures that one can always restore diffeomorphism invariance by perturbatively solving this functional identity. We illustrate how this procedure works for the R ²δFδF and F⁴ counterterms in Maxwell theory.