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Journal of High Energy Physics

, 2019:131 | Cite as

Gluing two affine Yangians of 𝔤𝔩1

  • Wei LiEmail author
  • Pietro Longhi
Open Access
Regular Article - Theoretical Physics

Abstract

We construct a four-parameter family of affine Yangian algebras by gluing two copies of the affine Yangian of 𝔤𝔩1. Our construction allows for gluing operators with arbitrary (integer or half integer) conformal dimension and arbitrary (bosonic or fermionic) statistics, which is related to the relative framing. The resulting family of algebras is a two-parameter generalization of the \( \mathcal{N} \) = 2 affine Yangian, which is isomorphic to the universal enveloping algebra of 𝔲 (1)⊕ 𝒲\( {}_{\infty}^{\mathcal{N}=2}\left[\lambda \right] \). All algebras that we construct have natural representations in terms of “twin plane partitions”, a pair of plane partitions appropriately joined along one common leg. We observe that the geometry of twin plane partitions, which determines the algebra, bears striking similarities to the geometry of certain toric Calabi-Yau threefolds.

Keywords

Conformal and W Symmetry Quantum Groups Topological Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsChinese Academy of SciencesBeijingP.R. China
  2. 2.Institut für Theoretische PhysikETH ZurichZürichSwitzerland

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