Sen's Mechanism for Self-Dual Super Maxwell theory

In several elementary particle scenarios, self-dual fields emerge as fundamental degrees of freedom. Some examples are the $D = 2$ chiral boson, $D = 10$ Type IIB supergravity, and $D = 6$ chiral tensor multiplet theory. For those models, a novel variational principle has been proposed in the work of Ashoke Sen. The coupling to supergravity of self-dual models in that new framework is rather peculiar to guarantee the decoupling of unphysical degrees of freedom. We generalize this technique to the self-dual super Maxwell gauge theory in $D = 4$ Euclidean spacetime both in the component formalism and the superspace. We use the geometric tools of rheonomy and integral forms since they are very powerful geometrical techniques for the extension to supergravity. We show the equivalence between the two formulations by choosing a different integral form defined using a Picture Changing Operator. That leads to a meaningful action functional for the variational equations. In addition, we couple the model to a non-dynamical gravitino to extend the analysis slightly beyond the free case. A full-fledged self-dual supergravity analysis will be presented elsewhere.