The strong coupling limit of the scaling function from the quantum string Bethe ansatz

Using the quantum string Bethe ansatz we derive the one-loop energy of a folded string rotating with angular momenta (S,J) in AdS3×S1⊂AdS5×S5 in the limit 1≪J≪S, z=λlog(S/J)/(πJ) fixed. The one-loop energy is a sum of two contributions, one originating from the Hernandez-Lopez phase and another one being due to spin chain finite size effects. We find a result which at the functional level exactly matches the result of a string theory computation. Expanding the result for large z we obtain the strong coupling limit of the scaling function for low twist, high spin operators of the SL(2) sector of N=4 SYM. In particular, we recover the famous −3log(2)π. Its appearance is a result of non-trivial cancellations between the finite size effects and the Hernandez-Lopez correction.