BV description of $N=1$, $D=4$ Supergravity in the first order formalism

This note examines the BV formulation of $N=1$, $D=4$ supergravity in the first-order Palatini–Cartan framework. Challenges in achieving an off-shell formulation are addressed by introducing corrections to the rank 2 BV action, offering in addition a solid foundation for the study of the theory on manifolds with boundary.