# Yangian Symmetry and Integrability of Planar N=4 Super-Yang-Mills Theory

## TL;DR

This paper proves that planar N=4 super-Yang-Mills theory exhibits Yangian symmetry, which is a hallmark of integrability, and demonstrates that this symmetry criterion distinguishes integrable from non-integrable gauge theories.

## Contribution

The authors establish Yangian symmetry of planar N=4 super-Yang-Mills theory and propose an off-shell extension, providing a new criterion for integrability in planar gauge theories.

## Key findings

- Yangian symmetry is proven for classical equations of motion.
- An off-shell extension of symmetry invariance is proposed and verified.
- The criterion distinguishes integrable ABJM theory from non-integrable N=1 super-Yang-Mills.

## Abstract

In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover we propose an off-shell extension of our statement which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to integrable ABJM theory but not to non-integrable N=1 super-Yang-Mills theory.