Fermionic Sen's Mechanism for Self-Dual Super Maxwell theory

Abstract

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 fully satisfactory variational principle was missing until the works of Ashoke Sen. We generalize this technique to the fermionic sector of self-dual super Maxwell gauge theory in $D=4$ Euclidean spacetime both in the component formalism and in the superspace. For the latter, we use the geometric tools of rheonomy together with integral forms. We show the equivalence between the two formulations by choosing a different integral form defined by means of 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 in order to extend the analysis slightly beyond the rigid case. A full-fledged self-dual supergravity analysis will be presented elsewhere.Comment: 15 pages, no figure