# The supersymmetric affine Yangian

Journal of High Energy Physics, May 2018

Abstract The affine Yangian of gl1 is known to be isomorphic to $${\mathcal{W}}_{1+\infty }$$, the W-algebra that characterizes the bosonic higher spin — CFT duality. In this paper we propose some of the defining relations of the Yangian that are relevant for the $$\mathcal{N}=2$$ superconformal version of $${\mathcal{W}}_{1+\infty }$$. Our construction is based on the observation that the $$\mathcal{N}=2$$ superconformal $${\mathcal{W}}_{1+\infty }$$ algebra contains two commuting bosonic W1+∞ algebras, and that the additional generators transform in bi-minimal representations with respect to these two algebras. The corresponding affine Yangian can therefore be built up from two affine Yangians of $$\mathfrak{g}{\mathfrak{l}}_1$$ by adding in generators that transform appropriately.

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Matthias R. Gaberdiel, Wei Li, Cheng Peng, Hong Zhang. The supersymmetric affine Yangian, Journal of High Energy Physics, 2018, 200, DOI: 10.1007/JHEP05(2018)200