Untwisting the symmetries of $\beta$-deformed Super-Yang--Mills

TL;DR

This paper proves that the planar real-$eta$-deformed Super-Yang--Mills theory has an infinite-dimensional Yangian symmetry algebra, establishing its classical integrability by extending supersymmetry through a twisted coproduct.

Contribution

It introduces a twisted coproduct to lift the supersymmetry of the $eta$-deformed theory to its Yangian, revealing its integrable structure.

Findings

Existence of Yangian symmetry algebra in $eta$-deformed SYM

Classical integrability of the deformed theory

Extension of supersymmetry via twisted coproduct

Abstract

We demonstrate that the planar real-$\beta$-deformed Super-Yang--Mills theory possesses an infinitely-dimensional Yangian symmetry algebra and thus is classically integrable. This is achieved by the introduction of the twisted coproduct which allows us to lift the apparent $\mathcal{N}=1$ supersymmetry first to the full $\mathcal{N}=4$ symmetry of the parent $\mathcal{N} = 4$ SYM theory, and subsequently to its Yangian.