The generalized scaling function of AdS/CFT and semiclassical string theory

TL;DR

This paper explores the large j limit of an integral equation related to anomalous dimensions in N=4 SYM, connecting it with the semiclassical string theory limit, and provides analytical and numerical evidence of agreement at loop levels.

Contribution

It analyzes the large j limit of the FRS integral equation and links it with the fast long string limit in AdS/CFT, including weak coupling computations.

Findings

Agreement between gauge theory and string theory at one loop

Numerical results support two-loop correspondence

Protection of certain classical and one-loop string results

Abstract

Recently, Freyhult, Rej and Staudacher (FRS) proposed an integral equation determining the leading logarithmic term of the anomalous dimension of sl(2) twist-operators in N=4 SYM for large Lorentz spin M and twist L at fixed j = L/log(M). We discuss the large j limit of the FRS equation. This limit can be matched with the {\em fast long string} limit of AdS_5 X S^5 superstring perturbation theory at all couplings. In particular, a certain part of the classical and one-loop string result is known to be protected and can be computed in the weakly coupled large-j limit of the FRS equation. We present various analytical and numerical results supporting agreement at one and two loops in the gauge theory.