Spinning strings in AdS_5 x S^5: new integrable system relations

TL;DR

This paper demonstrates that a broad class of rotating string solutions in AdS_5 x S^5 can be described by an integrable Neumann-Rosochatius system, revealing new solutions and potential insights into the AdS/CFT correspondence.

Contribution

It establishes a connection between rotating string solutions and the Neumann-Rosochatius integrable system, and finds new circular solutions with specific spin configurations.

Findings

New circular rotating string solutions with multiple spins.

Large-spin energy corrections proportional to the square of the 't Hooft coupling.

Reduction of the sigma model to an integrable oscillator system.

Abstract

A general class of rotating closed string solutions in AdS_5 x S^5 is shown to be described by a Neumann-Rosochatius one-dimensional integrable system. The latter represents an oscillator on a sphere or a hyperboloid with an additional ``centrifugal'' potential. We expect that the reduction of the AdS_5 x S^5 sigma model to the Neumann-Rosochatius system should have further generalizations and should be useful for uncovering new relations between integrable structures on the two sides of the AdS/CFT duality. We find, in particular, new circular rotating string solutions with two AdS_5 and three S^5 spins. As in other recently discussed examples, the leading large-spin correction to the classical energy turns out to be proportional to the square of the string tension or the 't Hooft coupling \lambda, suggesting that it can be matched onto the one-loop anomalous dimensions of the corresponding ``long'' operators on the SYM side of the AdS/CFT duality.