Spinning superstrings at two loops: Strong-coupling corrections to dimensions of large-twist super Yang-Mills operators

We consider folded (S,J) spinning strings in AdS5×S5 (with one spin component in AdS5 and a one in S5) corresponding to the Tr(DSΦJ) operators in the sl(2) sector of the N=4 super Yang-Mills theory in the special scaling limit in which both the string mass ∼λln S and J are sent to infinity with their ratio fixed. Expanding in the parameter =Jλln S we compute the 2-loop string sigma-model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena. We suggest that a resummation of the logarithmic 2lnn terms is necessary in order to establish an interpolation to the weakly coupled gauge-theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multispin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite "renormalization" of the relation between the parameters of the classical solution and the fixed spins, i.e., the charges of the SO(2,4)×SO(6) symmetry.