N=2 supersymmetry and U(1)-duality

Understanding the consequences of the E ₇₍₇₎ duality on the UV properties of N=8 supergravity requires unravelling when and how duality-covariant actions can be constructed so as to accommodate duality-invariant counterterms. For nonsupersymmetric Abelian gauge theories exhibiting U(1)-duality, with and without derivative couplings, it was shown that such a covariant construction is always possible. In this paper we describe a similar procedure for the construction of covariant nonlinear deformations of U(1)-duality invariant theories in the presence of rigid N=2 supersymmetry. This is a concrete step towards studying the interplay of duality and extended supersymmetry.