S-matrix singularities and CFT correlation functions

Understand

In this note, we explore the correspondence between four-dimensional flat space S-matrix and two-dimensional CFT proposed by Pasterski et al.

• We demonstrate that the factorization singularities of an n-point cubic diagram reproduces the AdS Witten diagrams if mass conservation is imposed at each vertex.
• Such configuration arises naturally if we consider the 4-dimensional S-matrix as a compactified massless 5-dimensional theory.
• This identification allows us to rewrite the massless S-matrix in the CHY formulation, where the factorization singularities are re-interpreted as factorization limits of a Riemann sphere.