Structure of large spin expansion of anomalous dimensions at strong coupling

The anomalous dimensions of planar N = 4 SYM theory operators like tr(phi D-+(s)phi) expanded in large spin S have the asymptotics gamma = f In S + f(c) + 1/S (f(11) In S + f(10)) + ..., where f (the universal scaling function or cusp anomaly), f(c) and f(mn) are given by power series in the 't Hooft coupling gimel. The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing gamma in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS(5). The large spin expansion of the classical string energy happens to have exactly the same structure as that of gamma in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f(c), f(11), f(10) and verify the functional/reciprocity relations at subleading 1/root gimel order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions. (C) 2008 Elsevier B.V. All rights reserved.