Celestial amplitudes in an ambidextrous basis

TL;DR

This paper develops a new conformally covariant celestial amplitude framework in an ambidextrous basis, enabling explicit computation of multi-point massless scattering amplitudes with improved covariance and insights into holographic duals.

Contribution

It introduces a conformally covariant celestial transform in an ambidextrous basis and computes explicit 2, 3, and 4-point amplitudes, including the 4-gluon case, with applications to holography.

Findings

Non-distributional celestial amplitudes in all channels

Explicit 4-gluon amplitude in ambidextrous basis

Insights into operator dictionary and CFT data

Abstract

We start by constructing a conformally covariant improvement of the celestial light transform which keeps track of the mixing between incoming and outgoing states under finite Lorentz transformations in $\mathbb{R}^{2,2}$. We then compute generic 2, 3 and 4-point celestial amplitudes for massless external states in the ambidextrous basis prepared by composing this $\mathrm{SL}(2,\mathbb{R})$ intertwiner with the usual celestial map between momentum and boost eigenstates. The results are non-distributional in the celestial coordinates $(z,\bar{z})$ and conformally covariant in all scattering channels. Finally, we focus on the tree level 4-gluon amplitude where we present a streamlined route to the ambidextrous correlator based on Grassmannian formulae and examine its alpha space representation. In the process, we gain insights into the operator dictionary and CFT data of the holographic dual.