Structure of large spin expansion of anomalous dimensions at strong coupling

Abstract

The anomalous dimensions of planar N=4 SYM theory operators like tr(Phi D^S Phi) 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_mn 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 invariance (or reciprocity) property of the function expressing γin 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 the same structure as that of γin 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 λ^{-1/2} 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.

arXiv comment43 pages. v2: minor comments added, misprints corrected; v3: one-loop coefficients are expressed in terms of one constant not fixed by our method of computation, conclusion about parity invariance is unchanged, note added; v4: minor correctionsin eq (3.34) and below (3.37)

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