# Celestial Amplitudes: Conformal Partial Waves and Soft Limits

## TL;DR

This paper explores the structure of celestial amplitudes derived from massless scattering in 4D Minkowski space, focusing on conformal partial waves, crossing relations, and soft limits, to deepen understanding of their conformal properties.

## Contribution

It introduces a detailed analysis of conformal partial wave decomposition, crossing relations, and soft limits for celestial amplitudes, advancing the theoretical framework of celestial holography.

## Key findings

- Derived conformal partial wave decomposition for celestial amplitudes
- Established crossing relations for massless four-point functions
- Formulated soft limits analogous to traditional scattering amplitudes

## Abstract

Massless scattering amplitudes in four-dimensional Minkowski spacetime can be Mellin transformed to correlation functions on the celestial sphere at null infinity called celestial amplitudes. We study various properties of massless four-point scalar and gluon celestial amplitudes such as conformal partial wave decomposition, crossing relations and optical theorem. As a byproduct, we derive the analog of the single and double soft limits for all gluon celestial amplitudes.