Lionel Mason, University of Oxford
Holography identifies scattering amplitudes at strong coupling with areas of minimal surfaces in AdS whose boundaries are pinned to a null polygon in the boundary at infinity. This motivates the task of trying to compute the area as a function of the boundary data. Classic work of Alday-Maldacena reduces the calculation of the such areas to a so-called Y-system. This talk presents the Y-system, and explains how it defines a twistor space for the space of boundary data. This leads to a simple proof that the area satsifies a Plebanski equations defining a Pseudo-hyperkahler metric on the space of boundary data that is nicely compatible with its structures as a product of cluster varieties of type A_k for k odd.