Conformal Block Expansion in Celestial CFT

TL;DR

This paper develops a method to expand 4D massless scalar scattering amplitudes into 2D conformal blocks using celestial CFT techniques, including spinning and scalar exchanges, revealing the structure of celestial amplitudes.

Contribution

It introduces a conformal block expansion for celestial amplitudes involving spinning light-ray states and scalar states, providing a new framework for analyzing celestial CFTs.

Findings

Conformal blocks include spinning light-ray and scalar exchanges.

Prefactors are quadratic in celestial OPE coefficients.

Method enables decomposition of celestial amplitudes into conformal blocks.

Abstract

The 4D 4-point scattering amplitude of massless scalars via a massive exchange is expressed in a basis of conformal primary particle wavefunctions. This celestial amplitude is expanded in a basis of 2D conformal partial waves on the unitary principal series, and then rewritten as a sum over 2D conformal blocks via contour deformation. The conformal blocks include intermediate exchanges of spinning light-ray states, as well as scalar states with positive integer conformal weights. The conformal block prefactors are found as expected to be quadratic in the celestial OPE coefficients.