Celestial geometry
Sebastian Mizera, Sabrina Pasterski
Abstract
A bstract Celestial holography expresses $$ \mathcal{S} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> -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 ≥ 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.