Infrared behaviour of the one-loop scattering equations and supergravity integrands

The recently introduced ambitwistor string led to a striking proposal for one-loop maximal supergravity amplitudes, localised on the solutions of the ambitwistor one-loop scattering equations. However, these amplitudes have not been explicitly analysed, due to the apparent complexity of the equations that determine the localisation. In this paper we propose an analytic solution to the four-point one-loop scattering equations in the infrared (IR) regime of the amplitude. Using this solution, we compute the ambitwistor integrand and demonstrate that it correctly reproduces the four-graviton integrand in the IR regime. This solution qualitatively extends to n points. To conclude, we explain that the ambitwistor one-loop scattering equations actually correspond to the standard Gross & Mende saddle point.