Spinning strings in AdS5 × S5 and integrable systems

We show that solitonic solutions of the classical string action on the AdS5 × S5 background that carry charges (spins) of the Cartan subalgebra of the global symmetry group can be classified in terms of periodic solutions of the Neumann integrable system. In the limit of large spins J, the first subleading 1/J coefficient in the expansion of the string energy is expected to be non-renormalized to all orders in the inverse string tension expansion and thus can be directly compared to the 1-loop anomalous dimensions of the corresponding composite operators in super YM theory. We identify a particular string solution whose classical energy exactly reproduces the 1-loop anomalous dimension of a certain set of SYM operators with two independent R charges J1, J2.