From Spin Vertex to String Vertex

TL;DR

This paper demonstrates that the spin vertex approach in N=4 SYM reproduces the string vertex in light-cone string field theory within the BMN limit, establishing a connection between gauge theory and string interactions.

Contribution

It introduces a polynomial representation for the spin vertex and derives Neumann coefficients that match string theory results at weak coupling.

Findings

Spin vertex reproduces string vertex in the BMN limit.

Neumann coefficients derived from spin vertex match string field theory.

Establishes a link between gauge theory and string interactions.

Abstract

In the recent publication arXiv:1410.8860 the spin vertex was introduced as a new approach for computing three-point functions in 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 BMN 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.