New fermionic soft theorems

TL;DR

This paper extends the concept of soft theorems from scalars to fermions, revealing universal double-soft behavior in various supersymmetric theories and exploring implications for supergravity counter terms.

Contribution

It introduces new fermionic soft theorems in four and three dimensions, demonstrating their universality and potential constraints on supergravity counter terms.

Findings

Double-soft fermion limits reproduce supersymmetry algebra.

Universal behavior observed in supergravity amplitudes.

Results suggest constraints on supergravity counter terms.

Abstract

Soft limits of massless S-matrix are known to reflect symmetries of the theory. In particular for theories with Goldstone bosons, the double-soft limit of scalars reveals the coset structure of the vacuum manifold. In this letter, we propose that such universal double-soft behavior is not only true for scalars, but also for spin-1/2 particles in four dimensions and fermions in three dimensions. We first consider Akulov-Volkov theory, and demonstrate the double soft-limit of goldstinos yields the supersymmetry algebra. More surprisingly we also find amplitudes in 3<N<=8 supergravity theories in four dimensions as well as N=16 supergravity in three dimensions behave universally in the double-soft-fermion limit, analogue to the scalar ones. The validity of the new soft theorems at loop level is also studied. The results for supergravity are beyond what is implied by SUSY Ward identities, and may impose non-trivial constraints on the possible counter terms for supergravity theories.