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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Ekholm, T., Kucharski, P. & Longhi, P. Multi-cover skeins, quivers, and 3d \( \mathcal{N} \) = 2 dualities. J. High Energ. Phys. 2020, 18 (2020). https://doi.org/10.1007/JHEP02(2020)018
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DOI: https://doi.org/10.1007/JHEP02(2020)018