Ambidextrous light transforms for celestial amplitudes

TL;DR

This paper introduces a new light transform basis for celestial amplitudes, resolving distributional issues and revealing conformal structures, with applications to gluon and graviton scattering at various multiplicities.

Contribution

It systematically applies light transforms to celestial amplitudes, establishing a connection with twistor space and deriving Grassmannian integral representations for higher-point amplitudes.

Findings

Recasts celestial amplitudes into conformally covariant forms.

Provides Grassmannian integral formulas for n-point amplitudes.

Establishes a link between light transforms and twistor space techniques.

Abstract

Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates $z,\bar z$. We provide a new systematic remedy to this situation by studying celestial amplitudes in a basis of light transformed boost eigenstates. Motivated by a novel equivalence between light transforms and Witten's half-Fourier transforms to twistor space, we light transform every positive helicity state in the coordinate $z$ and every negative helicity state in $\bar z$. With examples, we show that this "ambidextrous" prescription beautifully recasts two- and three-point celestial amplitudes in terms of standard conformally covariant structures. These are used to extract examples of celestial OPE for light transformed operators. We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. The formulae for $n$-point N$^{k-2}$MHV amplitudes take the form of Euler-type integrals over regions in Gr$(k,n)$ cut out by positive energy constraints.