Integrability and on-shell methods

It is widely expected that the integrability of the planar anomalous dimension problem and the hidden structures and symmetries of scattering amplitudes in N=4 super Yang-Mills are related in some interesting way. Here we take some steps towards unravelling this potential connection. In the first part of the talk we apply a method originally devised for computing scattering amplitudes known as MHV diagrams to the derivation of the one-loop dilatation operator of N=4 super Yang-Mills in the SO(6) sector, originally obtained by Minahan and Zarembo. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularisation. Next we perform the same calculation in a fully on-shell way using generalised unitarity. This calculation establishes a direct connection between scattering amplitudes and the dilatation operator of N=4 super Yang-Mills theory.