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

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 ${\tau }_{ij}$ parametrizing the eigenvalues of the Gaudin model.

arXiv comment40 pages

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• On duality of color and kinematics in (A)dS momentum space
• Covariant Color-Kinematics Duality
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• One-loop Gluon Amplitudes in AdS
• Dispersion Formulas in QFTs, CFTs, and Holography