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

TL;DR

The paper tests the AdS/CFT correspondence beyond the Penrose/BMN limit by extending string/gauge comparisons to three-impurity states in the near-BMN regime. It develops a detailed perturbative and all-orders analysis of the three-impurity string spectrum, including explicit matrix elements and protected subsector projections, and compares with higher-loop BMN anomalous dimensions in N=4 SYM via spin-chain methods. The main finding is a precise two-loop agreement between string theory and gauge theory, with a robust breakdown at three loops, suggesting deeper subtlety in the duality or limiting procedures. Overall, the work provides a stringent, higher-impurity benchmark that constrains proposed resolutions of the three-loop mismatch and guides future investigations into integrability and BMN scaling.

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.