Supergravity as a constrained $BF$ theory

In this paper we formulate $\mathcal{N}=1$ supergravity as a constrained $BF$ theory with $OSp(4|1)$ gauge superalgebra. We derive the modified supergravity Lagrangian that, apart from standard supergravity with a negative cosmological constant, contains terms proportional to the (inverse of the) Immirzi parameter. Although these terms do not change classical field equations, they might be relevant in quantum theory. We briefly discuss the perturbation theory around the supersymmetric topological vacuum.