Celestial Feynman Rules for Scalars

TL;DR

This paper develops Feynman rules for scalar celestial amplitudes, linking off-shell momentum space calculations to conformal partial wave decompositions on the celestial sphere, enhancing understanding of celestial holography.

Contribution

It introduces a method to transform scalar Feynman rules into celestial sphere language and relates them to conformal partial wave expansions for four-point amplitudes.

Findings

Feynman rules are reformulated as recursion relations on the celestial sphere.

Four-point celestial amplitudes are shown to be equivalent to conformal partial wave decompositions.

Derived a specific conformal partial wave expansion for a massless scalar four-point amplitude.

Abstract

Off-shell celestial amplitudes with both time-like and space-like external legs are defined. The Feynman rules for scalar amplitudes, viewed as a set of recursion relations for off-shell momentum space amplitudes, are transformed to the celestial sphere using the split representation. For four-point celestial amplitudes, the Feynman expansion is shown to be equivalent to a conformal partial wave decomposition, providing an interpretation of conformal partial wave expansion coefficients as integrals over off-shell three-point structures. A conformal partial wave decomposition for a simple four-point $s$-channel massless scalar celestial amplitude is derived.