Uniqueness from locality and BCFW shifts

TL;DR

This paper introduces a BCFW shift for constructing Yang-Mills amplitudes and conjectures their uniqueness is guaranteed by locality and asymptotic behavior, with proof at leading soft order.

Contribution

It presents a new BCFW shift method and proposes a conjecture that Yang-Mills amplitudes are uniquely determined by locality and asymptotic conditions.

Findings

Introduces a BCFW shift for Yang-Mills amplitudes

Conjectures uniqueness of amplitudes from locality and asymptotic behavior

Proves the conjecture at leading order in soft expansion

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.