One-loop amplitudes on the Riemann sphere

Understand

The scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories.

• Their derivation from ambitwistor string theory led to proposals for formulae at one loop on a torus for 10 dimensional supergravity, and we recently showed how these can be reduced to the Riemann sphere and checked in simple cases.
• We also proposed analogous formulae for other theories including maximal super-Yang-Mills theory and supergravity in other dimensions at one loop.
• We give further details of these results and extend them in two directions.