Tree-level gluon amplitudes on the celestial sphere

TL;DR

This paper maps tree-level gluon scattering amplitudes to celestial sphere correlators using Mellin transforms, revealing hypergeometric function structures for different amplitude types.

Contribution

It extends the celestial holography framework to arbitrary n-point gluon amplitudes, providing explicit Mellin transform representations.

Findings

MHV amplitudes expressed as hypergeometric functions on Grassmannian Gr(4,n)

Non-MHV amplitudes involve Gelfand A-hypergeometric functions

Demonstrates the applicability of celestial holography to gluon scattering amplitudes

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.