  We compute the tree-level connected six-point function of identical scalar
fluctuations of the AdS$_2$ string worldsheet dual to the half-BPS Wilson line
in planar ${\cal N}=4$ Super Yang-Mills. The calculation can be carried out
analytically in the conformal gauge approach, where the boundary
reparametrization mode of the string plays a crucial role. We also study the
analytic continuation of the six-point function to an out-of-time-order
configuration, which is related to a 3-to-3 scattering amplitude in flat space.
As a check of our results, we also numerically compute the six-point function
using the Nambu-Goto action in static gauge, finding agreement with the
conformal gauge answer.
