AdS/CFT v.s. String Loops

TL;DR

This paper computes one-loop string corrections to certain states and compares them with gauge theory predictions, finding partial agreement and notable absence of higher power corrections in the t'Hooft coupling.

Contribution

It introduces an improved 3-string vertex for light-cone string field theory and compares string loop corrections with non-planar gauge theory results.

Findings

Agreement at leading order between string and gauge theory

Discrepancy at second order in Yang-Mills loops

Absence of 3/2 and 5/2 powers in the coupling expansion

Abstract

The one string-loop correction to the energies of two impurity BMN states are computed using IIB light-cone string field theory with an improved 3-string vertex that has been proposed by Dobashi and Yoneya. As in previous published computations, the string vertices are truncated to the 2-impurity channel. The result is compared with the prediction from non-planar corrections in the BMN limit of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It is found to agree at leading order -- one-loop in Yang-Mills theory -- and is close but not quite in agreement at order two Yang-Mills loops. Furthermore, in addition to the leading 1/2 power in the t'Hooft coupling, which is generic in string field theory, and which we have previously argued cancels, we find that the 3/2 and 5/2 powers are also miraculously absent.