Generalized scaling function at strong coupling

We considered folded spinning string in AdS5 x S5 background dual to the Tr(DSΦJ) operators of N = 4 SYM theory. In the limit S,J → ∞ and l = (πJ)/(λ1/2 log S) fixed we compute the string energy with the 2-loop accuracy in the worldsheet coupling λ1/2 from the asymptotical Bethe ansatz. In the limit l → 0 the result is finite due to the massive cancellations with terms coming from the conjectured dressing phase. We also managed to compute all leading logarithm terms (l2m logn 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/λ1/2 and also at weak coupling.