New fermionic soft theorems

TL;DR

This work extends the universality of soft theorems from scalars to fermions, showing that single-soft fermions vanish while double-soft-fermion limits in Akulov-Volkov theory and in 4D/3D supergravities mirror the scalar double-soft structure with appropriate replacements. The authors derive these results using recursion techniques (BCFW with an auxiliary graviton) and, in 3D, a symmetrized double-soft limit to control soft-graviton divergences. They also present evidence that these fermionic soft theorems do not receive loop corrections, at least for leading IR pieces, and discuss the potential implications for constraints on ultraviolet counterterms and possible hidden symmetries. Overall, the paper reveals a broader, fermionic counterpart to Goldstone-like double-soft behavior with significant implications for the structure of highly supersymmetric theories.

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.