Uniqueness from locality and BCFW shifts

TL;DR

The paper investigates whether Yang-Mills tree amplitudes are uniquely determined by locality and constructability, using a polarization-aware BCFW shift to build amplitudes recursively. It proves, at leading order in the soft expansion, that the only consistent local object obeying the prescribed large-z behavior is the Yang-Mills amplitude, with unitarity emerging from these principles. The authors demonstrate that potential B-type contributions vanish under the imposed constraints and that C-type terms are fixed by lower-point data, yielding a precise leading-order expression for the (n+1)-point amplitude in terms of the n-point one. These results suggest a deep connection between locality, shift constructability, and unitarity, and point to extensions to gravity and other theories, as well as new on-shell computation strategies.

Abstract

We introduce a BCFW shift which can be used to recursively build the full Yang-Mills tree-level amplitude as a function of polarization vectors. Furthermore, in line with the recent results of arXiv:1612.02797, we conjecture that the Yang-Mills tree-level scattering amplitude is uniquely fixed by locality and demanding the usual asymptotic behavior under a sufficient number of shifts. Unitarity therefore emerges from locality and constructability. We prove this statement at the leading order in the soft expansion.