From spin vertex to string vertex

In the recent publication [1] the spin vertex was introduced as a new approach for computing three-point functions in N = 4 $$ \mathcal{N}=4 $$ SYM. In this note we consider the BMN limit of the spin vertex for scalar excitations and show that it reproduces the string vertex in the light-cone string field theory which describes the string interactions in the pp-wave background at the leading order of λ ′ expansion. This is achieved by introducing a polynomial representation for the spin vertex. We derive the Neumann coefficients from the spin vertex at weak coupling and show they match with the Neumann coefficients from the string field theory