Symmetries and Interactions of $\mathcal{N}=1$ SUGRA: from Constructive and BCFW to KLT formulations

TL;DR

This paper explores the interactions and symmetries of minimal $ =1$ supergravity using constructive, BCFW, and KLT methods, deriving 3- and 4-point couplings and analyzing the Compton effect.

Contribution

It introduces a comprehensive approach combining constructive, BCFW, and KLT techniques to analyze $ =1$ supergravity interactions and symmetries.

Findings

Derived 4-point couplings from BCFW

Verified 3-point interactions via KLT relations

Analyzed supergravity Compton scattering

Abstract

In this paper, we study the coupling of the gravity supermultiplet (graviton and gravitino) of minimal $\mathcal{N}=1$ SUGRA following a constructive approach. Firstly, we use the master formulae that follows from considering the scaling behavior of the spinor variables under the little group. Secondly, we derive the 4-point couplings using BFCW. Then, we verify these results for the general 3-point interactions that can be derived using the KLT-type relations, i.e., they can be written as the square of the coupling of the gluons and gluinos. Finally, we consider SUGRA Compton effect for graviton-gravitino. For completeness, we present in the appendix the $\mathcal{N}=1$ Sugra lagrangian in the 2-component Weyl formalism, including the proofs of SUSY and gauge invariance.