Understand
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.