The supersymmetric affine Yangian

Monday, 20 November, 2017

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The affine Yangian of \mathfrak{gl}_1 is known to be isomorphic to {\cal W}_{1+\infty}, the W-algebra that characterizes the bosonic higher spin -- CFT duality. In this paper we propose defining relations of the Yangian that is relevant for the N=2 superconformal version of {\cal W}_{1+\infty}. Our construction is based on the observation that the N=2 superconformal {\cal W}_{1+\infty} algebra contains two commuting bosonic {\cal W}_{1+\infty} 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{gl}_1 by adding in generators that transform appropriately.


Matthias R. Gaberdiel
Wei Li
Cheng Peng
Hong Zhang