The Grassmannian for celestial superamplitudes

Livia Ferro,Robert Moerman

doi:10.1007/jhep11(2021)187

Abstract

Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in mathcal{N} = 4 super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries.

Highlights

Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes
JHEP11(2021)187 whether we can learn more about scattering amplitudes, and further constrain the S-matrix, by understanding of the conformal field theory on the celestial sphere
If we want to retrace the path we have covered for ordinary amplitudes in momentum space, this is the first step towards the definition of geometries for celestial amplitudes

Summary

Celestial amplitudes

In the following we will consider tree-level scattering amplitudes of massless particles. To map the amplitudes from Minkowski space to the celestial sphere, we first need to introduce celestial coordinates and parametrize the massless momenta in the. Since we are working with superamplitudes, we have Grassmann variables ηAs. In the language of celestial amplitudes, they will be called τA [19]. In the language of celestial amplitudes, they will be called τA [19] After performing this change of variables, the massless scattering superamplitude is mapped on the celestial sphere via a Mellin transform [18, 19]: n∞. Where the celestial superamplitude transforms as a two-dimensional conformal correlator on the celestial sphere with weights ∆i.

Grassmannian integrals

Grassmannian on the celestial sphere

Examples