Antiself-dual gravity and supergravity from a pure connection formulation

Abstract

We consider a pure connection action plus additional algebraic constraints that are suitable for a straightforward supergroup extension. By taking as an internal group [Formula: see text], the action reduces to the Capovilla, Dell and Jacobson approach. By taking as an internal symmetry the supergroup [Formula: see text], and by means of the Bianchi identity and integrability conditions, the equations of motion are those that could be found from antiself-dual supergravity [Formula: see text] with cosmological constant sector.