  At small AdS radius, the superstring on $AdS_5\times S^5$ was conjectured by
Maldacena to be equivalent to ${\cal N}=4$ super-Yang-Mills at small `t Hooft
coupling where thickened Feynman diagrams can be used to compute scattering
amplitudes. It was previously shown that the pure spinor worldsheet action of
the $AdS_5\times S^5$ superstring can be expressed as the sum of a BRST-trivial
term and a `B-term' which is antisymmetric in worldsheet derivatives. Using the
explicit form of the pure spinor vertex operators, it will be argued here that
the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial
term where the thickened propagators are the regions of the string worldsheet
near the AdS boundary and the holes are the regions near the AdS horizon.
Evidence will then be presented that the antisymmetric B-term generates the
super-Yang-Mills vertex so that, at small radius and arbitrary genus, the
superstring amplitudes correctly reproduce the super-Yang-Mills Feynman diagram
expansion.
