  Recently, a worldsheet dual to free ${\cal N}=4$ Super Yang-Mills has been
proposed in terms of twistor variables for ${\rm AdS}_5$, in parallel to that
for the ${\rm AdS}_3$ dual to the free symmetric orbifold CFT. In the latter
case, holomorphic covering maps play a central role in determining correlators
and are associated to Feynman diagrams. After recasting these maps in terms of
the worldsheet twistor variables for ${\rm AdS}_3$, we generalise to ${\rm
AdS}_5$. We propose stringy incidence relations and appropriate reality
conditions for the twistor covering maps. For some special kinematic
configurations of correlators, we exhibit an explicit construction of the
corresponding covering map. We find that the closed string worldsheet
corresponding to this map is related to a gauge theory Feynman diagram by the
Strebel construction, as for ${\rm AdS}_3/{\rm CFT}_2$. Rather strikingly, the
regularised Strebel area of the worldsheet reproduces the Feynman propagator of
the free field theory.
