Matching three-point functions of BMN operators at weak and strong coupling

TL;DR

This paper demonstrates the agreement between string theory and field theory for three-point functions of BMN operators at weak and strong coupling by calculating correlators independently in both frameworks and showing they match.

Contribution

It provides the first calculation of three-point correlators of two-impurity BMN states with all non-zero momenta in both field theory and string theory, confirming their agreement.

Findings

Field theory and string theory results are identical for the correlator.

First calculation of three-point functions with all non-zero momenta in this context.

Supports the correspondence between string theory and gauge theory at weak coupling.

Abstract

The agreement between string theory and field theory is demonstrated in the leading order by providing the first calculation of the correlator of three two-impurity BMN states with all non-zero momenta. The calculation is performed in two completely independent ways: in field theory by using the large-$N$ perturbative expansion, up to the terms subleading in finite-size, and in string theory by using the Dobashi-Yoneya 3-string vertex in the leading order of the Penrose expansion. The two results come out to be completely identical.