  We introduce a complex pure connection action with constraints which is
diffeomorphism and gauge invariant. Taking as an internal group $SU(2)$, we
obtain, from the equations of motion, anti-self-dual Einstein spaces together
with the zero torsion condition thanks to Bianchi identity. By applying the
same procedure, we take as internal symmetry the super group $OSp(1|2)$ and by
means of the Bianchi identity and integrability conditions, the equations of
motion are those that come from anti-self-dual supergravity $N=1$ with
cosmological constant sector.
