Recently, spin-one wave functions in four dimensions that are conformal primaries of the Lorentz group $SL(2,\mathbb{C})$ were constructed. We compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wave functions. The answers have the same conformal covariance as correlators of spin-one primaries in a $2d$ CFT. The Britto–Cachazo–Feng–Witten (BCFW) recursion relation between three- and four-point gluon amplitudes is recast into this conformal basis.

• Received 19 September 2017

DOI:https://doi.org/10.1103/PhysRevD.96.085006