S-matrix singularities and CFT correlation functions

TL;DR

The work addresses how to relate a four-dimensional flat-space S-matrix to a two-dimensional conformal field theory description in the Pasterski–Shao–Strominger framework, showing that factorization poles of massive cubic diagrams reproduce AdS3 contact diagrams when mass is conserved at each vertex. It then reframes the S-matrix in CHY form, interpreting factorization as pinch limits on the Riemann sphere and highlighting a 2d/2d correspondence between a 2D CFT and CHY representations. Massless singularities are analyzed and found to yield factorization residues that are polynomial in kinematic invariants, signaling a more intricate interpretation than a simple bulk exchange. Overall, the paper provides a coherent 2D perspective for translating 4D S-matrix factorization into boundary CFT data, via a five-dimensional embedding and CHY machinery, while pointing to open questions for higher-spin and massless exchanges.

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.

Figures (6)

• Figure 1: The factorization singularity of $s$-channel diagram leads to a contact Witten diagram in AdS$_3$.
• Figure 2:
• Figure 3: Half Ladder Feynman diagram
• Figure 4: Benzene-type diagram
• Figure 5: One-shell one-loop diagrams