Structure of large spin expansion of anomalous dimensions at strong coupling

Abstract

The anomalous dimensions of planar N = 4 SYM theory operators like tr ( Φ D + S Φ ) expanded in large spin S have the asymptotics γ = f ln S + f c + 1 S ( f 11 ln S + f 10 ) + ⋯ , where f (the universal scaling function or cusp anomaly), f c and f m n 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 AdS 5 . 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 f c , f 11 , f 10 and verify the functional/reciprocity relations at subleading 1 λ 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.