Strong coupling for planar N=4 SYM theory: An all-order result

We propose a scheme for determining a generalised scaling function, namely the Sudakov factor in a peculiar double scaling limit for high spin and large twist operators belonging to the sl(2) sector of planar N = 4 SYM. In particular. we perform explicitly the all-order computation at strong 't Hooft coupling regarding the first (contribution to the) generalised scaling function. Moreover, we compare Our asymptotic results with the numerical solutions finding a very good agreement and evaluate numerically the non-asymptotic contributions. Eventually, we illustrate the agreement and prediction on the string, side. (C) 2008 Elsevier B.V. All rights reserved.