Integrability and unitarity

TL;DR

This paper demonstrates how generalized unitarity methods can be used to compute the one-loop dilatation operator in N=4 super Yang-Mills theory, establishing a direct link between scattering amplitudes and operator anomalous dimensions.

Contribution

It introduces a novel on-shell approach to determine the one-loop dilatation operator in specific sectors of N=4 SYM using generalized unitarity, without off-shell inputs.

Findings

Successfully computed the one-loop dilatation operator in the SO(6) and SU(2|3) sectors.

Established a direct connection between scattering amplitudes and the dilatation operator.

Demonstrated the effectiveness of on-shell methods in gauge theory operator analysis.

Abstract

We show how generalised unitarity can be used to determine the one-loop dilatation operator in N=4 super Yang-Mills. Our analysis focuses on two sectors, namely the bosonic SO(6) sector and the SU(2|3) sector. The calculation is performed on shell, with no off-shell information introduced at any stage. In this way, we establish a direct connection between scattering amplitudes and the dilatation operator of the N=4 theory.