Generalisations of the Russo-Townsend formulation

As a generalisation of the recent construction by Russo and Townsend, we propose a new approach to generate U ( 1 ) duality-invariant models for nonlinear electrodynamics. It is based on the use of two building blocks: (i) a fixed (but otherwise arbitrary) model for self-dual nonlinear electrodynamics with Lagrangian L ( F μν ; g ) depending on a duality-invariant parameter g ; and (ii) an arbitrary potential W ( ψ ), with ψ an auxiliary scalar field. It turns out that the model L ( F μ ν ; ψ ) = L ( F μ ν ; ψ ) + W ( ψ ) leads to a self-dual theory for nonlinear electrodynamics upon elimination of ψ . As an illustration, we work out two examples in which the seed Lagrangian L ( F μν ; g ) corresponds to the Born-Infeld model and two particular potentials W ( ψ ) are chosen such that integrating out ψ gives: (i) the ModMaxBorn theory; and (ii) the ModMax theory. We also briefly discuss supersymmetric generalisations of the proposed formulation. To the memory of Kelly Stelle