Structure of large spin expansion of anomalous dimensions at strong coupling

The anomalous dimensions of planar N=4 SYM theory operators like tr(ΦD+SΦ) expanded in large spin S have the asymptotics γ=flnS+fc+1S(f11lnS+f10)+⋯ , where f (the universal scaling function or cusp anomaly), fc and fmn are given by power series in the 't Hooft coupling λ. The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing γ 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 AdS5. The large spin expansion of the classical string energy happens to have exactly the same structure as that of γ 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 fc, f11, f10 and verify the functional/reciprocity relations at subleading 1λ 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.