Three point functions of N=4 Super Yang Mills from light cone string field theory in pp-wave

TL;DR

This work tests the pp-wave version of the AdS/CFT correspondence by computing three-string interaction amplitudes in light-cone string field theory and comparing them to free planar three-point functions of BMN operators in ${\cal N}=4$ SYM. By deriving and employing the bosonic Neumann matrices in the large $\mu p^{+} \alpha'$ limit, the authors evaluate cubic couplings for both supergravity and string modes, and express results as ratios to vacuum amplitudes. The main finding is exact agreement between the string-theory calculations and the corresponding BMN correlators for three representative cases, thereby supporting the duality in the BMN sector at leading order. The study also outlines a pathway to access subleading corrections via a systematic expansion in $1/(\mu p^{+} \alpha')$.

Abstract

In this paper we calculate three-string interaction from light cone string field theory in pp-wave. We find exact agreements with the free planar three point functions of non-chiral BMN operators of ${\cal N} = 4$ super Yang Mills. The three string interaction vertex involving the Neumann matrices was derived in a recent paper hep-th/0204146. We explicitly calculate the bosonic Neumann matrices in the limit of large $μp^{+} α^{'}$ . Using the Neumann matrices we are able to compute the cubic interactions of three string modes in a pp-wave background.