Scaling function in AdS/CFT from the O(6) sigma model

TL;DR

This paper computes the scaling function in AdS/CFT by linking it to the O(6) sigma model's energy density, using two-loop corrections and Bethe ansatz, confirming some predictions but challenging others.

Contribution

It introduces a novel calculation of the AdS/CFT scaling function combining two-loop corrections with Bethe ansatz results, providing new insights into strong coupling behavior.

Findings

Agreement with thermodynamical limit of quantum string Bethe ansatz

Disagreement with two-loop string corrections to folded spinning string

Validation of the O(6) sigma model approach in AdS/CFT context

Abstract

Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N=4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional bosonic O(6) sigma model. We calculate this function by combining the two-loop correction to the energy density for the O(n) model with two-loop correction to the mass gap determined by the all-loop Bethe ansatz in N=4 SYM theory. The result is in agreement with the prediction coming from the thermodynamical limit of the quantum string Bethe ansatz equations, but disagrees with the two-loop stringy corrections to the folded spinning string solution.