Poincaré Constraints on Celestial Amplitudes

TL;DR

$ ext{Poincaré symmetry}$ on the celestial sphere imposes strong, universal constraints on 2-, 3-, and 4-point celestial amplitudes for massless and massive external states. The authors derive distribution-valued structures for massless cases, reveal recurrence relations among coefficient functions, and show how Gaussian-like delta constraints encode momentum conservation in the celestial representation. For massive scalars, the results reproduce familiar conformal correlator forms with additional momentum-induced shifts, and yield explicit expressions for two- and three-point coefficients (including a gluon three-point coefficient) via symmetry arguments alone. The work clarifies key structural differences between Poincaré-invariant celestial dynamics and standard CFT correlators, discusses convergence issues of the inverse celestial transform, and provides a framework for cross-checking explicit celestial-amplitude calculations. Overall, it advances non-perturbative, symmetry-based control of celestial amplitudes in flat space holography.

Abstract

The functional structure of celestial amplitudes as constrained by Poincaré symmetry is investigated in $2,3,$ and $4$-point cases for massless external particles of various spin, as well as massive external scalars. Functional constraints and recurrence relations are found (akin to the findings in arXiv:1901.01622) that must be obeyed by the respective permissible correlator structures and function coefficients. In specific three-point cases involving massive scalars the resulting recurrence relations can be solved, e.g. reproducing purely from symmetry a three-point function coefficient known in the literature. Additionally, as a byproduct of the analysis, the three-point function coefficient for gluons in Minkowski signature is obtained from an amplitude map to the celestial sphere.