The generalised scaling function: a systematic study

We describe a procedure which aims at determining, for all the values of the coupling constant, all the generalised scaling functions arising in the high spin limit for long operators in the sl(2) sector of N = 4 SYM. All the relevant information is encoded in infinite linear systems, each easily connected with the previous ones. Therefore, the solution may be written in a recursive form and then explicitly worked out in the strong coupling regime. In this case, we carefully detail the peculiar convergence of different ’masses’ to the unique O(6) mass gap, by also analysing the departure from this limiting theory. E-mail: [email protected], [email protected], [email protected] 1