The generalised scaling function: a note

A method for determining the generalised scaling function(s) arising in the high spin behaviour of long operator anomalous dimensions in the planar sl(2) sector of N = 4 SYM is proposed. The all-order perturbative expansion around the strong coupling is detailed for the prototypical third and fourth scaling functions, showing the emergence of the O(6) Non-Linear Sigma Model mass-gap from different SYM ’mass’ functions. Remarkably, only the fourth one gains contribution from the non-BES reducible densities and also shows up, as first, NLSM interaction and specific model dependence. Finally, the computation of the n-th generalised function is sketched and might be easily finalised for checks versus the computations in the sigma model or the complete string theory. ∗E-mail: [email protected], [email protected], [email protected]