Celestial amplitudes: from UV constraints to conformal blocks

About

Celestial amplitudes describe scattering in a basis of boost eigenstates. In this basis, 4-point scattering is characterized by two variables: the sum over the boost weights $\beta$ which is dual to the center of mass energy, and a cross ratio $z$ related to the bulk scattering angle. In this talk I will describe two aspects of the physics captured by the $\beta$ and $z$ dependence. I will first show that the UV behavior of 4-point scattering is encoded in the analytic structure of celestial amplitudes in the complex $\beta$ plane. The residues of the poles at negative even integer $\beta$ are related to coefficients of higher-dimension operators in the low-energy effective action hence subject to positivity constraints, while poles at positive even integer $\beta$ arise from UV asymptotics. I will then show that the $z$ dependence contains information about the celestial spectrum and three-point couplings. For scalar 4-point scattering mediated by massive exchange, the conformal blocks include massive scalar states with positive integer conformal weights, as well as intermediate exchanges of spinning light-ray states..

0:00:00 Slide 1

0:05:37 Slide 2

0:11:13 Slide 3

0:16:49 Slide 4

0:22:26 Slide 5

0:28:02 Slide 6

0:33:38 Slide 7

0:39:15 Slide 8

0:44:51 Slide 9

0:50:27 Slide 10

0:56:04 Slide 11