Celestial Geometry

Abstract

Celestial holography expresses $\mathcal{S}$-matrix elements as correlators in a CFT living on the night sky. Poincaré 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.

27 pages, 6 figures

References in corpus (4)

• Evidence for a New Soft Graviton Theorem
• Gluon Amplitudes as 2d Conformal Correlators
• Symmetries of Celestial Amplitudes
• Four-point correlators of light-ray operators in CCFT

Cited by in corpus (8)

• Bridging Carrollian and Celestial Holography
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial Supersymmetry
• Celestial amplitudes in an ambidextrous basis
• Celestial Recursion
• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism
• A Celestial Route to AdS Bulk Locality
• Celestial Eikonal Amplitudes in the Near-Horizon Region