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

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.