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We consider folded spinning strings in AdS_5xS^5 (with one spin component Sin AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2)sector of the N=4 SYM theory in the special scaling limit in which both thestring mass M ~ \sqrt \lambda \ln S and J are sent to infinity with their ratiofixed. Expanding in the parameter \el= J/M we compute the 2-loop string sigmamodel correction to the string energy and show that it agrees with theexpression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest thata resummation of the logarithmic \el^2 \ln^n \el terms is necessary in order toestablish an interpolation to the weakly coupled gauge theory results. In theprocess, we set up a general framework for the calculation of higher loopcorrections to the energy of multi-spin string configurations. In particular,we find that in addition to the direct 2-loop term in the string energy thereis a contribution from lower loop order due to a finite ``renormalization'' ofthe relation between the parameters of the classical solution and the fixedspins, i.e. the charges of the SO(2,4) x SO(6) symmetry.

Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators