Tree-level gluon amplitudes on the celestial sphere

TL;DR

The paper extends the celestial-sphere mapping of massless scattering to arbitrary n-point tree-level gluon amplitudes via a Mellin transform, building on prior three- and four-point results. It shows that n-point MHV amplitudes map to Aomoto–Gelfand generalized hypergeometric functions on the Grassmannian Gr(4,n), with a dual (4,n) representation, and that the 6-point case reduces to the Lauricella function ${\hat\varphi}_D$.For NMHV amplitudes, the celestial correlators involve Gelfand $A$-hypergeometric functions ${\hat{\mathcal F}}(\{\alpha\},x)$, reflecting a Gauss–Manin/KZ-type structure, and generalize to higher $N^k\!\mathrm{MHV}$ with increasingly intricate multivariate hypergeometric integrals.The results provide explicit analytic representations of celestial amplitudes in terms of well-studied hypergeometric functions, highlighting a rich mathematical structure and potential links to string amplitudes and Knizhnik–Zamolodchikov-type equations, with implications for holography in flat spacetime.

Abstract

Pasterski, Shao and Strominger have recently proposed that massless scattering amplitudes can be mapped to correlators on the celestial sphere at infinity via a Mellin transform. We apply this prescription to arbitrary $n$-point tree-level gluon amplitudes. The Mellin transforms of MHV amplitudes are given by generalized hypergeometric functions on the Grassmannian $Gr(4,n)$, while generic non-MHV amplitudes are given by more complicated Gelfand $A$-hypergeometric functions.