Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM

TL;DR

This paper demonstrates that the su(2|1) sector of planar N=4 SYM exhibits Yangian symmetry at two loops, confirming its integrability through explicit construction and verification of symmetry properties.

Contribution

It provides the first explicit perturbative construction of Yangian symmetry at two loops in the su(2|1) sector of N=4 SYM, including necessary corrections to generators.

Findings

Yangian charges receive site-dependent corrections

Yangian charges commute with the dilatation operator

Serre relations are satisfied at two loops

Abstract

We present the perturbative Yangian symmetry at next-to-leading order in the su(2|1) sector of planar N=4 SYM. Just like the ordinary symmetry generators, the bi-local Yangian charges receive corrections acting on several neighboring sites. We confirm that the bi-local Yangian charges satisfy the necessary conditions: they transform in the adjoint of su(2|1), they commute with the dilatation generator, and they satisfy the Serre relations. This proves that the sector is integrable at two loops.