Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit

TL;DR

This paper investigates higher-order curvature corrections in the AdS/CFT correspondence within the near-BMN limit, confirming agreement at two loops but revealing discrepancies at three loops for states with three impurities.

Contribution

It extends previous tests of the AdS/CFT correspondence to include three-impurity states and higher-order curvature corrections, providing more rigorous validation of the duality.

Findings

Agreement between string theory and gauge theory at two-loop order

Discrepancies at three-loop order for three-impurity states

Validation of the near-BMN limit as a testing ground for AdS/CFT

Abstract

The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena conjecture to a new regimen of direct tests. In one line of pursuit, finite-radius curvature corrections to the Penrose limit (which appear in inverse powers of the string angular momentum J) have been found to induce a complicated system of interaction perturbations to string theory on the pp-wave; these have been successfully matched to corresponding corrections to the BMN dimensions of N=4 super Yang-Mills (SYM) operators to two loops in the 't Hooft coupling lambda. This result is tempered by a well-established breakdown in the correspondence at three loops. Notwithstanding the third-order mismatch, we proceed with this line of investigation by subjecting the string and gauge theories to new and significantly more rigorous tests. Specifically, we extend our earlier results at O(1/J) in the curvature expansion to include string states and SYM operators with three worldsheet or R-charge impurities. In accordance with the two-impurity problem, we find a perfect and intricate agreement between both sides of the correspondence to two-loop order in lambda and, once again, the string and gauge theory predictions fail to agree at third order.