A two-loop test for the factorised S-matrix of planar N=4

TL;DR

This paper verifies the two-loop integrability-based Bethe-ansatz for the sl(2) sector of planar N=4 super Yang-Mills theory through explicit perturbative calculations, confirming the theoretical predictions.

Contribution

It provides a direct two-loop perturbative check of the integrability-based Bethe-ansatz for the sl(2) sector in N=4 supersymmetric Yang-Mills theory, extending previous one-loop results.

Findings

Agreement with integrability predictions at two loops

Method applicable to operators of arbitrary twist and many fields

Detailed analysis of spin three, twist three operator mixing

Abstract

We check the recently proposed higher loop Bethe-ansatz for the sl(2) sector of N=4 at two loops by a direct perturbative calculation using N=2 superfields in supersymmetric dimensional reduction. Our method can in principle address operators built from many elementary fields and of arbitrary twist. We work out in detail the spin three, twist three operator mixing problem at leading order in N and find agreement with the prediction based on integrability.