Supergroup BF action for supergravity

Abstract

General relativity can be formulated as a SU(2) BF-theory with constraints, as has been shown, by Pleba\'nski. The cosmological constant term can be obtained from the constraint term, following from the consistency of the equations of motion, as recently shown by Krasnov. We consider an $OSp(2|1)$ invariant, supergravity extension of this theory, for which the consistency of the equations of motion and the constraints contribute as well to the cosmological constant terms of Townsend's supergravity. The Kalb-Ramond invariance is shortly discussed.