Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions

TL;DR

This paper develops a new formalism extending the CHY approach to compute scalar correlators in AdS space using scattering equations derived from ambitwistor string theory, validated against Witten diagram calculations.

Contribution

It introduces a classical-limit ambitwistor string framework in AdS for deriving correlation functions via scattering equations, extending flat-space amplitude techniques to AdS.

Findings

Derived a novel formula for AdS boundary correlators using scattering equations.

Validated the formalism by matching with Witten diagram results for bi-adjoint scalar correlators.

Explored eigenfunctions of scattering equations in AdS and their relation to conformal partial waves.

Abstract

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two current algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.