Structure of large spin expansion of anomalous dimensions at strong coupling

TL;DR

This paper investigates the large spin expansion of anomalous dimensions in N=4 SYM at strong coupling using AdS/CFT, confirming the structure and relations known at weak coupling also hold at strong coupling through string theory calculations.

Contribution

It demonstrates that the large spin expansion structure and functional relations are preserved at strong coupling via string theory, extending known weak coupling results.

Findings

Large spin expansion structure matches between gauge theory and string theory.

Functional and reciprocity relations hold at strong coupling.

Computed leading string 1-loop corrections to key coefficients.

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 \gamma= 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 \lambda. The subleading coefficients appear to be related by the so called functional relation and parity invariance (or 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 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 \lambda^{-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.