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We introduce a bosonic ambitwistor string theory in AdS space. Even thoughthe theory is anomalous at the quantum level, one can nevertheless use it inthe classical limit to derive a novel formula for correlation functions ofboundary CFT operators in arbitrary space-time dimensions. The resultingconstruction can be treated as a natural extension of the CHY formalism for theflat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS asintegrals over the moduli space of Riemann spheres with punctures. Theseintegrals localize on an operator-valued version of scattering equations, whichwe derive directly from the ambitwistor string action on a coset manifold. As atesting ground for this formalism we focus on the simplest case of ambitwistorstring coupled to two current algebras, which gives bi-adjoint scalarcorrelators in AdS. In order to evaluate them directly, we make use of a seriesof contour deformations on the moduli space of punctured Riemann spheres andcheck that the result agrees with tree level Witten diagram computations to allmultiplicity. We also initiate the study of eigenfunctions of scatteringequations in AdS, which interpolate between conformal partial waves indifferent OPE channels, and point out a connection to an elliptic deformationof the Calogero-Sutherland model.

Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions