Structure of large spin expansion of anomalous dimensions at strong coupling

TL;DR

Beccaria et al. study the large-$S$ expansion of anomalous dimensions in planar ${\mathcal N}=4$ SYM at strong coupling using AdS/CFT, focusing on folded spinning strings in $AdS_5$ to test the functional relation and reciprocity that organize subleading terms. They show that the classical large-$S$ expansion of the string energy has the same logarithmic structure as the gauge theory, with $\gamma(S)=f\ln S+f_c+\frac{f_{11}\ln S+f_{10}}{S}+\cdots$, and that universal relations among the coefficients, such as $f_{11}=\tfrac{1}{2}f^2$, hold at leading order; these relations connect to the cusp function $f$ and survive the strong-coupling expansion. They compute leading string 1-loop corrections to $f_c,f_{11},f_{10}$ and verify that the functional/reciprocity constraints persist at order $1/\sqrt{\lambda}$, supporting universality across weak and strong coupling. The authors also explore cases with nonzero $J$ and spiky strings, finding that reciprocity can fail for non-minimal trajectories, thereby delineating the limits of these symmetry constraints. Altogether, the work strengthens the view that the large-spin expansion and its symmetry structure are intrinsic to the AdS/CFT correspondence and provides concrete strong-coupling data for the subleading 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 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.