The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz

TL;DR

This paper derives the one-loop energy of a folded string in AdS/CFT using the quantum string Bethe ansatz, revealing the strong coupling limit of the scaling function and confirming known results through detailed calculations.

Contribution

It provides a novel derivation of the strong coupling limit of the scaling function from the quantum string Bethe ansatz, including finite size effects and Hernandez-Lopez phase contributions.

Findings

Exact match with string theory computations at the functional level

Recovery of the -3 log(2)/π result for the scaling function

Identification of cancellations between finite size effects and Hernandez-Lopez correction

Abstract

Using the quantum string Bethe ansatz we derive the one-loop energy of a folded string rotating with angular momenta (S,J) in AdS_3 x S^1 inside AdS_5 x S^5 in the limit 1 << J << S, z=\lambda^(1/2) log(S/J) /(\pi J) fixed. The one-loop energy is a sum of two contributions, one originating from the Hernandez-Lopez phase and another one being due to spin chain finite size effects. We find a result which at the functional level exactly matches the result of a string theory computation. Expanding the result for large z we obtain the strong coupling limit of the scaling function for low twist, high spin operators of the SL(2) sector of N=4 SYM. In particular we recover the famous -3 log(2)/\pi. Its appearance is a result of non-trivial cancellations between the finite size effects and the Hernandez-Lopez correction.