TH Journal Club on String Theory

Shota Komatsu - Scattering Equations in AdS

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I discuss 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 can be derived from the ambitwistor string action on a coset manifold. As a testing ground for this formalism I focus on the simplest case of ambitwistor string coupled to two current algebras, which gives bi-adjoint scalar correlators in AdS. I will then show that it reproduces tree level Witten diagram computations to all multiplicity, and discuss a connection to quantum integrable systems; the Gaudin model and an elliptic deformation of the Calogero-Sutherland model.