Two-loop commuting charges and the string/gauge duality

TL;DR

The paper assesses the AdS/CFT integrability program in the large-charge regime, where string and gauge computations agree at one and two loops but diverge at three loops. It strengthens the integrability link by deriving explicit two-loop matches for the full tower of commuting charges in folded and circular string sectors, using the string resolvent from Bäcklund transformations and the gauge-side Inozemtsev/Bethe Ansatz, with a universal two-loop relation between string and gauge charges. The authors further analyze the three-loop discrepancy, showing it can be captured by non-local combinations of charges, signaling limits of perturbative matching and pointing toward deeper non-perturbative structure. Overall, the work provides concrete two-loop charge correspondences and clarifies how modular transformations connect string and gauge integrable data, reinforcing the viability of the AdS/CFT integrable framework while highlighting where refinements are needed.

Abstract

We briefly review the status quo of the application of integrable systems techniques to the AdS/CFT correspondence in the large charge approximation, a rapidly evolving topic. Intricate string and gauge computations of, respectively, energies and scaling dimensions agree at the one and two-loop level, but disagree starting from three loops. To add to this pattern, we present further computations which demonstrate that for folded and circular spinning strings the full tower of infinitely many hidden commuting charges, responsible for the integrability, also agrees up to two, but not three, loops.