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

TL;DR

This work tests a two-loop, factorised S-matrix conjecture for the planar sl(2) sector of N=4 SYM by performing a direct perturbative calculation in N=2 superspace with SSDR. Focusing on spin-3, twist-3 operators, the authors compute the leading-N anomalous dimensions via operator mixing and renormalisation, and find exact agreement with integrability-based predictions. The calculation leverages a simplified N=2 supergraph framework and the Mincer algorithm to evaluate up to three-loop momentum-space integrals, showing that BPS-like diagrams do not affect the first nontrivial anomalous dimensions. The results support the proposed higher-loop Bethe-ansatz and provide a concrete pathway toward constructing the planar two-loop dilatation operator for the sl(2) sector, with plans to extend to higher spins and longer operators.

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.