Higher Conserved Charges and Integrability for Spinning Strings in AdS_5 x S^5

TL;DR

This paper demonstrates the existence of an infinite set of conserved charges for classical spinning string solutions in AdS_5 x S^5 and shows their agreement with higher charges in N=4 super Yang-Mills theory, confirming integrability.

Contribution

It establishes the presence of an infinite number of conserved charges for classical spinning strings and confirms their correspondence with gauge theory charges, supporting integrability in AdS/CFT.

Findings

Infinite conserved charges for classical string solutions.

One-loop agreement with gauge theory higher charges.

Evidence of integrability in AdS/CFT correspondence.

Abstract

We demonstrate the existence of an infinite number of local commuting charges for classical solutions of the string sigma model on AdS_5 x S^5 associated with a certain circular three-spin solution spinning with large angular momenta in three orthogonal directions on the five-sphere. Using the AdS/CFT correspondence we find agreement to one-loop with the tower of conserved higher charges in planar N=4 super Yang-Mills theory associated with the dual composite single-trace operator in the highest weight representation (J_1,J_2,J_2) of SO(6). The agreement can be explained by the presence of integrability on both sides of the duality.