Twistor Parametrization of Locally BPS Super-Wilson Loops

We consider the kinematics of the locally BPS super-Wilson loop in $\mathcal{N}=4$ super-Yang-Mills with scalar coupling from a twistorial point of view. We find that the kinematics can be described either as supersymmetrized pure spinors or as a point in $G_{2\vert 2}(4\vert 4) \times G_{2\vert 2}(4\vert 4)$. In this description of the kinematics the scalar–scalar correlation function appearing in the one-loop evaluation of the super-Wilson loop can be neatly written as a sum of four super-determinants.