Abstract
Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates z, overline{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 overline{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 Nk−2MHV amplitudes take the form of Euler-type integrals over regions in Gr(k, n) cut out by positive energy constraints.
Highlights
Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates z, z
One could ask the even more basic question: what is the analogue of light transforms for momentum eigenstates? It turns out that answering this question thrusts us head first into the world of half-Fourier transforms and twistor space!
We describe half-Mellin and half-Fourier transforms that take boost eigenstates to the appropriate notion of conformal primary twistor eigenstates. We show that these twistor eigenstates are equivalent to a linear combination of two light transformed boost eigenstates
Summary
Boost eigenstates are defined as Mellin transforms of momentum eigenstates [4]. Having labeled it by its conformal weights (h, h) = ( ∆2+ , ∆2− ) We write this as |z, z, h, h, when working with affine coordinates z, z. The CCFT operator dual to |ζ, ζ, h, h, will be called Oh,h(ζ, ζ) or equivalently Oh,h(z, z) It can be viewed as a field of homogeneity (−2h, −2h) in (ζα, ζα ) in the embedding formalism for CFTs [31]. Celestial amplitudes An of massless particles are defined as the scattering amplitudes of such states. They are obtained by Mellin transforming n-point momentum space amplitudes An(λi, λi, i) [4, 26]: An(ζi, ζi, ∆i, i, i) =. At 4 points or less, the resulting amplitudes are generically distributional in the zi, zi [26]
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