Generalized Scaling Function at Strong Coupling

We considered folded spinning string in AdS5 × S5 background dual to the Tr ( DSΦJ ) operators of N = 4 SYM theory. In the limit S, J → ∞ and l = πJ √ λ logS fixed we compute the string energy with the 2-loop accuracy in the worldsheet coupling √ λ from the asymptotical Bethe ansatz. In the limit l → 0 the result is finite due to the massive cancelations with terms coming from the conjectured dressing phase. We also managed to compute all leading logarithm terms l 2m log l λn/2 to an arbitrary order in perturbation theory. In particular for m = 1 we reproduced results of Alday and Maldacena computed from a sigma model. The method developed in this paper could be used for a systematic expansion in 1/ √ λ and also at weak coupling.