Spinning strings in [Formula Presented] New integrable system relations

Abstract

A general class of rotating closed string solutions in [Formula Presented] 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 [Formula Presented] 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 [Formula Presented] and three [Formula Presented] 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 [Formula Presented] 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. © 2004 The American Physical Society.