Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories

TL;DR

This paper demonstrates the classical Yangian symmetry in planar N=4 super Yang-Mills and N=6 super Chern-Simons theories, showing how bi-local generators ensure invariance of the action.

Contribution

It establishes the classical Yangian symmetry for these gauge theories and details the action of bi-local generators on the cyclic planar action.

Findings

Yangian invariance for equations of motion established

Bi-local generators act on the action to ensure invariance

Planar limit is crucial for the symmetry realization

Abstract

In this article we establish the notion of classical Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory and for related planar gauge theories. After revisiting Yangian invariance for the equations of motion, we describe how the bi-local generators act on the action of the model such that the latter becomes exactly invariant. In particular, we elaborate on the relevance of the planar limit and how to act non-linearly with bi-local generators on the cyclic action.