Spinning strings in AdS5xS5:: New integrable system relations -: art. no. 086009

A general class of rotating closed string solutions in AdS(5)xS(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)xS(5) sigma model to the Neumann-Rosochatius system should have further generalizations and should be useful for uncovering new relations between integrable structures on two sides of the AdS/conformal field theory (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 super-Yang-Mills side of the AdS/CFT duality.