Celestial Geometry

TL;DR

This paper explores the geometric structure of celestial amplitudes in celestial holography, revealing how Poincaré invariance constrains the support of correlators on the celestial sphere and connecting 4D kinematics with 2D CFT crossing symmetry.

Contribution

It introduces geometric rules for celestial amplitude support and shows how crossing channels tile the celestial sphere for n≥5, advancing understanding of celestial correlator analyticity.

Findings

Supported correlator patches depend on operator in/out status.

Crossing channels form tilings of the celestial sphere for n≥5.

Provides a geometric framework for celestial amplitude analysis.

Abstract

Celestial holography expresses $\mathcal{S}$-matrix elements as correlators in a CFT living on the night sky. Poincar\'e invariance imposes additional selection rules on the allowed positions of operators. As a consequence, $n$-point correlators are only supported on certain patches of the celestial sphere, depending on the labeling of each operator as incoming/outgoing. Here we initiate a study of the celestial geometry, examining the kinematic support of celestial amplitudes for different crossing channels. We give simple geometric rules for determining this support. For $n\ge 5$, we can view these channels as tiling together to form a covering of the celestial sphere. Our analysis serves as a stepping off point to better understand the analyticity of celestial correlators and illuminate the connection between the 4D kinematic and 2D CFT notions of crossing symmetry.