Recursion relations from soft theorems

TL;DR

This work extends on-shell recursion by leveraging soft theorems to control large-$z$ behaviour, enabling construction of tree-level amplitudes that were previously inaccessible due to bad asymptotics. By introducing soft-BCFW shifts and regulator factors $F_n^{(\sigma)}(z)$, the authors derive new recursion relations that incorporate soft-theorem residues, applicable not only to scalars but also to fermions in the Akulov-Volkov theory and to dilaton-related actions from spontaneously broken conformal symmetry. The framework covers both vanishing and non-vanishing soft limits, including cases with non-Goldstone particles, and is demonstrated through explicit examples such as AV six-point amplitudes and dilaton EFT amplitudes, with connections to conformal DBI and two-scalar models. These results establish a more universal notion of on-shell constructibility for EFTs constrained by soft theorems and open avenues for SUSY extensions and applications to gravity-like theories with higher-derivative terms. Overall, the paper provides a versatile, symmetry-driven method to build higher-point amplitudes from lower-point data in theories where soft behavior supplies the essential boundary information.

Abstract

We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory, amplitudes containing dilatons of spontaneously-broken conformal symmetry.