Ambitwistor Strings and the Scattering Equations on AdS$_3\times$S$^3$

TL;DR

The paper builds a Type II ambitwistor string on AdS3×S3 with pure NS flux and shows anomaly freedom is ensured by the AdS background Einstein equations, yielding a spectrum of linearized supergravity fluctuations with no higher-string states.It translates n-point tree-level AdS amplitudes into the spectral problem of an sl2 Gaudin integrable system, where worldsheet insertion points act as spectral parameters and the scattering equations take the same form as flat space, controlled by Gaudin eigenvalues τij.Worldsheet correlators for gluons and gravitons are evaluated in a chiral setting, producing AdS-CHY-like integrands involving D-functions and Gaudin Hamiltonians; a heterotic version indicates a Yang–Mills–CS sector on AdS3×S3.The work establishes a concrete link between ambitwistor strings on curved backgrounds and quantum integrable systems, while outlining major open problems, notably constructing a complete basis of Gaudin eigenstates and connecting to Mellin/Mellin-like representations and flat-space limits.

Abstract

We construct an ambitwistor string that describes Type II supergravity on AdS$_3\times$S$^3$ with pure NS flux. The background Einstein equations ensure that the model is anomaly free. The spectrum consists of supergravity fluctuations around this background, with no higher string states. This theory transforms the problem of computing $n$-point tree-level amplitudes on AdS$_3$ into that of understanding an $\mathfrak{sl}_2$ Gaudin integrable system, whose representations are determined by the dual boundary operators and whose spectral parameters correspond to the worldsheet insertion points. The scattering equations take a similar form to flat space, with $n(n-3)/2$ parameters $τ_{ij}$ parametrizing the eigenvalues of the Gaudin model.