String scattering in flat space and a scaling limit of Yang-Mills correlators

TL;DR

This work establishes a precise link between flat-space string scattering in type IIB theory and a scaling limit of ${\mathcal N}=4$ SYM four-point functions, derived via the flat-space limit of AdS/CFT. It presents two independent derivations—one from strings to YM and one from YM to strings—showing that the boundary scaling function ${\mathcal F}$ is related to the bulk amplitude ${\mathcal T}$ through a Bessel-kernel transform, with an explicit inverse transform. The analysis covers tree-level and hard-scattering regimes, demonstrating the analytic structure of ${\mathcal F}$ (an entire function in $\xi$) and making concrete predictions for the gauge theory correlator from known string amplitudes. The paper also discusses the challenges of testing these ideas in strongly coupled gauge theories and outlines directions for extending the framework to higher-point functions and massive external states, aiming toward a holographic understanding of flat space.

Abstract

We use the flat space limit of the AdS/CFT correspondence to derive a simple relation between the 2 to 2 scattering amplitude of massless string states in type IIB superstring theory on ten-dimensional Minkowski space and a scaling limit of the N=4 super Yang-Mills four point functions. We conjecture that this relation holds non-perturbatively and at arbitrarily high energy.

Figures (2)

• Figure 1: (a) Causal relations between the operator insertion points used in the flat space limit: $x_{12}$ and $x_{34}$ are spacelike and $x_3$ and $x_4$ are in the future of both $x_1$ and $x_2$. (b) Example of configuration providing the flat space limit of the correlator. The auxiliary point $x_0$ is null related to all the insertion points. The conformal invariants for this configuration are $\rho=0$ and $\sigma=\sin^2(\theta/2)$ where $\theta$ is shown in the figure.
• Figure 2: Integration contour used in equation \ref{['TofFgeneral']}.