On Yangian symmetry of scattering amplitudes and the dilatation operator in N=4 super Yang-Mills

TL;DR

This paper demonstrates that the Yangian symmetry of the tree-level S-matrix in N=4 super Yang-Mills theory implies a near-invariance of the one-loop dilatation operator, linking scattering amplitudes and operator spectrum symmetries.

Contribution

It establishes a direct connection between the Yangian symmetry of scattering amplitudes and the invariance properties of the one-loop dilatation operator in N=4 super Yang-Mills.

Findings

Yangian symmetry of tree-level S-matrix implies invariance of the one-loop dilatation operator

Boundary terms prevent exact Yangian invariance at one loop

The result links amplitude symmetries with operator spectrum in N=4 SYM

Abstract

It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S-matrix of N=4 super Yang-Mills. 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 N=4 super Yang-Mills implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator.