Uniqueness from locality and BCFW shifts

Understand

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.