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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Gaberdiel, M.R., Li, W., Peng, C. et al. The supersymmetric affine Yangian. J. High Energ. Phys. 2018, 200 (2018). https://doi.org/10.1007/JHEP05(2018)200
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DOI: https://doi.org/10.1007/JHEP05(2018)200