Gluon Amplitudes as 2d Conformal Correlators

TL;DR

The work demonstrates that gluon tree amplitudes can be expressed as two-dimensional conformal correlators on the celestial sphere by using a conformal primary wavefunction basis obtained through a Mellin transform. It shows that low-point amplitudes (3- and 4-point) transform covariantly with 2d spin-one primaries and derives explicit forms and cross-ratio structures, including delta-function constraints tied to 4d kinematics. A conformal-space version of the BCFW recursion is formulated, linking 4pt results to products of 3pt conformal amplitudes, with careful treatment of shifts to preserve Mellin-transform well-definedness. These results illuminate the 4d–2d connection and set the stage for a block-structured celestial CFT approach to gauge theory amplitudes.

Abstract

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