Yangian Form-alism for Planar Gauge Theories

TL;DR

This paper explores the Yangian symmetry in planar N=4 supersymmetric Yang-Mills theory, examining its potential extension to deformed models and analyzing the invariance properties of the action and equations of motion.

Contribution

It provides a detailed cohomological derivation of Yangian invariance and investigates how twist deformations affect symmetry properties in the theory.

Findings

Equations of motion remain covariant under the deformation.

Action invariance holds only for the uncharged Yangian subalgebra.

Yangian symmetry can be partially preserved under certain deformations.

Abstract

In this article, we reconsider the formulation of Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory, and we investigate to what extent this symmetry lifts to the beta/gamma-deformation of the model. We first apply cohomology of variational forms towards a thorough derivation of the invariance statement for the undeformed action from covariance of the equations of motion under the Yangian algebra. We then apply a twist deformation to these statements paying particular attention to cyclicity aspects. We find that the equations of motion remain covariant while invariance of the action only holds for the Yangian subalgebra that is uncharged under the twist.