Anomalous Dimensions from the $\mathcal{N}=4$ Supersymmetric Yang-Mills Hexagon

We consider the correlator $⟨\mathcal{L}\mathcal{K}\tilde{\mathcal{K}}⟩$ of the Lagrange operator of $\mathcal{N}=4$ super Yang-Mills theory and two conjugate two-excitation operators in an su(2) sector. We recover the planar one-loop anomalous dimension of the renormalized operators from this hexagon computation.

Figure 1

Splitting a three-point function into two hexagons.