On the Strong Coupling Scaling Dimension of High Spin Operators

TL;DR

This work provides an exact analytic solution for the strong-coupling limit of the BES equation governing the universal scaling function f(g) of high spin operators in N=4 SYM. By combining numerical insight with a careful 1/g expansion, the authors obtain a leading-density solution in the t- and u-rapidity representations, showing a constant density inside |u|<1 and a concrete outside behavior, in strong agreement with string theory (GKP) predictions. The results establish a robust framework for perturbative corrections around strong coupling and offer an independent derivation that highlights the role of the dressing phase. The analysis also clarifies the structure of the density in the rapidity plane and sets the stage for higher-order strong-coupling perturbation theory and deeper AdS/CFT comparisons.

Abstract

We give an exact analytic solution of the strong coupling limit of the integral equation which was recently proposed to describe the universal scaling function of high spin operators in N = 4 gauge theory. The solution agrees with the prediction from string theory, confirms the earlier numerical analysis and provides a basis for developing a systematic perturbation theory around strong coupling.