Shadow Celestial Amplitude

TL;DR

This paper explores shadow celestial amplitudes in conformal field theory, demonstrating their locality, OPE behavior, and conformal block expansion, providing new insights into scattering amplitudes in a conformal basis.

Contribution

It introduces the study of shadow celestial amplitudes, analyzing their locality, OPE limits, and conformal block expansion, highlighting advantages over the original basis.

Findings

Shadow celestial amplitudes exhibit manifest locality on the celestial sphere.

OPE limits of three-point and multi-point shadow celestial amplitudes are characterized.

Conformal block expansion coefficients factorize into products of OPE coefficients.

Abstract

We study scattering amplitudes in the shadow conformal primary basis, which satisfies the same defining properties as the original conformal primary basis and has many advantages over it. The shadow celestial amplitudes exhibit locality manifestly on the celestial sphere, and behave like correlation functions in conformal field theory under the operator product expansion (OPE) limit. We study the OPE limits for three-point shadow celestial amplitude, and general $2\to n-2$ shadow celestial amplitudes from a large class of Feynman diagrams. In particular, we compute the conformal block expansion of the $s$-channel four-point shadow celestial amplitude of massless scalars at tree-level, and show that the expansion coefficients factorize as products of OPE coefficients.