Yangian Symmetry of Scattering Amplitudes and the Dilatation Operator in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory

It is known that the Yangian of $PSU(2,2|4)$ is a symmetry of the tree-level $S$ matrix of $\mathcal{N}=4$ super Yang-Mills theory. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi, and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level $S$ matrix of $\mathcal{N}=4$ super Yang-Mills theory implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator.

Figure 1

In Ref. [13] it was shown that the harmonic action (4) is recovered via the sewing together of a tree-level four-point superamplitude $A$ and a tree-level form factor $P$ corresponding to the particular two-site spin-chain state under consideration.