# S-matrix singularities and CFT correlation functions

## TL;DR

This paper investigates the connection between 4D flat space S-matrix singularities and 2D CFT correlation functions, revealing how factorization properties relate to AdS diagrams and CHY formulations, suggesting a 2D/2D correspondence.

## Contribution

It demonstrates that S-matrix factorization singularities reproduce AdS Witten diagrams under mass conservation, linking 4D S-matrix to 2D CFT via CHY and Riemann sphere limits.

## Key findings

- Factorization singularities match AdS Witten diagrams with mass conservation.
- S-matrix can be expressed in the CHY formulation highlighting 2D structures.
- Reveals a 2D/2D correspondence between S-matrix and CFT correlation functions.

## Abstract

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. In this light, the map is recast into a form of 2d/2d correspondence.