Celestial amplitudes: from UV constraints to conformal blocks

<!--HTML-->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.