The generalized scaling function of AdS/CFT and semiclassical string theory

Recently, Freyhult, Rej and Staudacher ( FRS) proposed an integral equation determining the leading logarithmic term of the anomalous dimension of sl( 2) twist-operators in N = 4 SYM for large Lorentz spin M and twist L at fixed j = L/log M. We discuss the large j limit of the FRS equation. This limit can be matched with the fast long string limit of AdS(5) x S-5 superstring perturbation theory at all couplings. In particular, a certain part of the classical and one-loop string result is known to be protected and can be computed in the weakly coupled large-j limit of the FRS equation. We present various analytical and numerical results supporting agreement at one and two loops in the gauge theory.