Gauge and gravity amplitudes on the celestial sphere

Nikhil Kalyanapuram

doi:10.1103/physrevd.103.085015

Abstract

The analytic structures of scattering amplitudes in gauge theory and gravity are examined on the celestial sphere. The celestial amplitudes in the two theories - computed by employing a regulated Mellin transform - can be compared at low multiplicity. It is established by direct computation that up to five external particles, the double copy relations of Kawai, Lewellen and Tye continue to hold identically, modulo certain multiplicative factors which are explicitly determined. Supersymmetric representations of the amplitudes are utilized throughout, manifesting the double copy structure between $\mathcal{N}=4$ super Yang-Mills and $\mathcal{N}=8$ supergravity on the celestial sphere.

Highlights

Scattering amplitudes of massless particles exhibit a number of properties—physical and mathematical—which make them rather interesting as objects of independent study
We have considered the Mellin basis in this note, the question is worth pondering for any basis change
There are two problems that we have considered in this article—those of preserving manifest supersymmetry and implementing the KLT relations among gauge theory and gravity amplitudes in the celestial basis

Summary

INTRODUCTION

Scattering amplitudes of massless particles exhibit a number of properties—physical and mathematical—which make them rather interesting as objects of independent study. Gravity amplitudes have very poor ultraviolet behavior, making the Mellin transform ill-defined Curing this problem requires either a consistent understanding of gravity in the ultraviolet (a tall order) or a regulated form of the transform, which corrects for the fact that gravitational amplitudes come from an effective field theory. This problem was studied in [20], where a regulated Mellin transform was proposed and in [21], where it was applied to four-particle amplitudes in gravity and the conformal soft theorems were studied. Λi always denote the weights appearing in the Mellin transform

Three-particle amplitudes

Four-particle amplitudes

Five-particle amplitudes

OBSTRUCTIONS AT HIGHER MULTIPLICITY

CONCLUSIONS