Abstract
We construct an ambitwistor string that describes Type II supergravity on AdS3×S3 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 AdS3 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 τij parametrizing the eigenvalues of the Gaudin model.
Highlights
We construct an ambitwistor string that describes Type II supergravity on AdS3×S3 with pure NS flux
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 AdS3 into that of understanding an sl2 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 τij parametrizing the eigenvalues of the Gaudin model
Summary
We begin by describing classical aspects of our model. The bosonic fields of the model are a map g : Σ → G from the worldsheet Riemann surface to a Lie group G, together with a field j ∈ Ω0(Σ, KΣ) ⊗ g∗ that is a (1,0)-form on Σ, taking values in the dual of the Lie algebra g of G. Note J transforms covariantly under right translations, but is invariant under left translations This asymmetry arose from choosing to construct the action in terms of g−1∂ ̄g rather than ∂ ̄g g−1. Unlike a WZW model, we have {g(σ), g(σ )} = 0 in the ambitwistor string These Poisson brackets confirm that j is the Kac-Moody current generating right translations on G. After imposing the constraint H0 = 0 and quotienting by the associated gauge transformations, we should consider points on G that differ by right translation along a cotangent vector j that is m-null to be equivalent This shows that the (bosonic) target space of the model is really the space of m-null geodesics in the complex Lie group G, which gives the ambitwistor string its name
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