Covariant procedures for perturbative nonlinear deformation of duality-invariant theories

We analyze a recent conjecture regarding the perturbative construction of nonlinear deformations of all classically duality-invariant theories, including N=8 supergravity. Starting with an initial quartic deformation, we engineer a procedure that generates a particular nonlinear deformation (Born-Infeld) of the Maxwell theory. This procedure requires the introduction of an infinite number of modifications to a constraint which eliminates degrees of freedom consistent with the duality and field content of the system. We discuss the extension of this procedure to N=1 and N=2 supersymmetric theories, and comment on its potential to either construct new supergravity theories with nonlinear Born-Infeld type duality, or to constrain the finiteness of N=8 supergravity.