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arXiv · 1807.11304

Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian

Matthias R. Gaberdiel·Wei Li·Cheng Peng
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Abstract

The universal enveloping algebra of ${\cal W}_{1+\infty}$ is isomorphic to the affine Yangian of $\mathfrak{gl}_1$. We study the ${\cal N}=2$ supersymmetric version of this correspondence, and identify the full set of defining relations of the supersymmetric affine Yangian. These relations can be deduced by demanding that the algebra has a representation on twin-plane-partitions, which we construct by gluing pairs of plane partitions. We define the action of the algebra on these twin-plane-partitions explicitly.

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Matthias R. Gaberdiel, Wei Li, Cheng Peng. 2018-07-30. Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian. https://doi.org/10.1007/jhep11(2018)192

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