On the finite size corrections of anti-ferromagnetic anomalous dimensions in ${\cal N}=4$ SYM

TL;DR

This paper uses non-linear integral equations from Bethe Ansatz to compute finite size corrections to anomalous dimensions in ${ m extbf{N}=4}$ SYM, providing explicit formulas and numerical comparisons for scalar operators.

Contribution

It introduces a general method for calculating finite size corrections to anomalous dimensions in ${ m extbf{N}=4}$ SYM, including multi-loop corrections in the SU(2) sector.

Findings

Finite size corrections are explicitly computed for certain operators.

The method is suitable for numerical evaluation and comparison.

Results include multi-loop corrections in the SU(2) sector.

Abstract

Non-linear integral equations derived from Bethe Ansatz are used to evaluate finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and immediately lower anomalous dimensions of scalar operators in ${\cal N}=4$ SYM. In specific, multi-loop corrections are computed in the SU(2) operator subspace, whereas in the general SO(6) case only one loop calculations have been finalised. In these cases, the leading finite size corrections are given by means of explicit formul\ae and compared with the exact numerical evaluation. In addition, the method here proposed is quite general and especially suitable for numerical evaluations.