Residual Local Supersymmetry and the Soft Gravitino

TL;DR

The paper analyzes residual local supersymmetry in four-dimensional N=1 supergravity on asymptotically flat spacetimes. By constructing the Noether two-form and analyzing boundary conditions in the 1.5 order formalism, it identifies an infinite set of angle-dependent asymptotic supersymmetries whose charges generate a supersymmetric extension of BMS translations. The authors derive the corresponding Ward identities and show they reproduce the soft limit of the gravitino, establishing a gravitino soft factor and linking it to LSZ-reduced S-matrix elements. This work unifies asymptotic symmetry charges with soft gravitino physics, illustrating supersymmetry at every angle and its impact on gravitational scattering amplitudes.

Abstract

We show that there exists an infinite tower of fermionic symmetries in pure $d=4$, $\mathcal{N}=1$ supergravity on an asymptotically flat background. The Ward identities associated with these symmetries are equivalent to the soft limit of the gravitino and to the statement of supersymmetry at every angle. Additionally, we show that these charges commute into charges associated with the (unextended) BMS group, providing a supersymmetrization of the BMS translations.