Formalism of gauge-invariant curvatures and constructing the cubic vertices for massive spin-3/2 field in AdS₄ space

We study the interaction of a massive spin-3/2 field with electromagnetic and gravitational fields in the four dimensional AdS space and construct the corresponding cubic vertices. The construction is based on a generalization of Fradkin–Vasiliev formalism, developed for massless higher spin fields, to massive fermionic higher spin fields. The main ingredients of this formalism are the gauge-invariant curvatures. We build such curvatures for the massive theory under consideration and show how the cubic vertices are written in their terms.