On the high spin expansion in the sl(2) N=4 SYM theory

We study the form of the high spin expansion of the minimal anomalous dimension for long operators belonging to the sl(2) sector of N = 4 SYM. Keeping fixed the ratio j between the twist and the logarithm of the spin, the minimal anomalous dimension expands as gamma(g, j, s) = f (g, j) In s +f((0)) (g, j) + O(1 / In s). This particular double scaling limit is efficiently described, including the desired accuracy O((Ins)(0)), in terms of a linear integral equation. By its use, we are able to evaluate both at weak and strong coupling the subleadina scalina function f(0) (g, J) as a series in J. up to the order j(5). Thanks to these results, the possible extension of the liaison with the 0(6) non-linear signia model may be tackled on a solid ground. (C) 2009 Elsevier B.V. All rights reserved.