Integrability and Maximally Helicity Violating Diagrams in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory

We apply maximally helicity violating (MHV) diagrams to the derivation of the one-loop dilatation operator of $\mathcal{N}=4$ supersymmetric Yang-Mills theory in the SO(6) sector. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularization. This provides the first application of MHV diagrams to an off-shell quantity. We also discuss other applications of the method and future directions.

Figure 1

The particular one-loop integral in configuration space contributing to the dilatation operator.

Figure 2

The double-bubble integral relevant for the computation of $I(x_{12})$.

Figure 3

The single MHV diagram contributing to the dilatation operator at one loop.