  We propose a geometric setup to study analytic aspects of a variant of the
super symmetric two-dimensional nonlinear sigma model. This functional extends
the functional of Dirac-harmonic maps by gravitino fields. The system of
Euler--Lagrange equations of the two-dimensional nonlinear sigma model with
gravitino is calculated explicitly. The gravitino terms pose additional
analytic difficulties to show smoothness of its weak solutions which are
overcome using Rivi\`ere's regularity theory and Riesz potential theory.
