Covariant procedures for perturbative non-linear deformation of   duality-invariant theories
  We analyze a recent conjecture regarding the perturbative construction of non-linear 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 non-linear 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 non-linear Born-Infeld type duality, or to constrain the finiteness of N=8 supergravity. 
John Joseph M. Carrasco, Renata Kallosh, and Radu Roiban
hep-th