Symmetries and interactions of 𝒩=1 SUGRA: From constructive and BCFW to KLT formulations

In this paper, we study the couplings of the gravity supermultiplet (graviton and gravitino) of minimal [Formula: see text] supergravity (SUGRA) following a constructive approach. First, we use the master formula that follows from considering the scaling behavior of the spinor variables under the little group. Second, we derive the four-point couplings using the Britto–Cachazo–Feng–Witten (known as BCFW) recursion relations. Then, we verify these results for the general three-point interactions that can be derived using the Kawai–Lewellen–Tye relations (also known as KLT-type relations), i.e. they can be written as the square of the coupling of the gluons and gluinos. Finally, we consider the graviton–gravitino SUGRA Compton effect. For completeness, we present in the appendix the [Formula: see text] SUGRA Lagrangian in the two-component Weyl formalism, including proofs of supersymmetry (SUSY) and gauge invariances.