Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities

Tobias Ekholm; Piotr Kucharski; Pietro Longhi

doi:10.1007/jhep02(2020)018

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arXiv · 1910.06193

Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities

Tobias Ekholm·Piotr Kucharski·Pietro Longhi

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Abstract

The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of holomorphic disks on a Lagrangian brane are observed to generate dual quiver descriptions of the geometry. Embedding into M-theory, a large class of dualities of 3d $\mathcal{N}=2$ theories associated to quivers is obtained. The multi-cover skein relation admits a compact formulation in terms of quantum torus algebras associated to the quiver and in this language the relations are similar to wall-crossing identities of Kontsevich and Soibelman.

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Tobias Ekholm, Piotr Kucharski, Pietro Longhi. 2019-10-14. Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities. https://doi.org/10.1007/jhep02(2020)018

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