Two-loop commuting charges and the string/gauge duality

TL;DR

This paper reviews integrability in AdS/CFT, showing agreement of commuting charges between string and gauge theories up to two loops, but discrepancies arise at three loops, highlighting limits of current integrability techniques.

Contribution

It provides new computations of hidden commuting charges for spinning strings, confirming agreement up to two loops and revealing discrepancies at three loops.

Findings

Agreement of charges up to two loops

Disagreement at three loops

Highlights limits of integrability in AdS/CFT

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.