Conformal Block Expansion in Celestial CFT

TL;DR

This work builds a conformal block expansion for massless scalar 4-point amplitudes mediated by a massive scalar within celestial CFT in Klein space. The celestial amplitude is decomposed into a partial-wave basis on the unitary principal series, then rewritten as a sum over conformal blocks, revealing two distinct intermediate exchanges: a tower of spin-0 blocks with integer conformal weights and a continuum of light-ray blocks related to principal-series primaries via the light transform. The block coefficients are shown to be quadratic in OPE data, aligning with conformal symmetry expectations, though certain overall factors remain to be fully understood. An important finding is that even purely contact interactions can be encoded in this block language through massive-exchange limits, underscoring a stringy-like smoothing in celestial holography and illuminating the structure of CCFT operator bases and their OPEs.

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.

Figures (1)

• Figure 1: 4-point kinematics with particles $1,2$ incoming and particles $3,4$ outgoing. We will study the $13-24$ OPE limit ($z \rightarrow 0$) in the CCFT which corresponds to the collinear limit of $1$ and $3$ in the bulk.