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Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities
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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.
Forward citations
Cited by 2 Pith papers
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Wild wall-crossing and symmetric quivers in 4d and 3d $\mathcal{N}=2$ field theories
The paper derives a tree-of-unlinkings formula for wild Donaldson-Thomas invariants of m-Kronecker quivers from wall-crossing identities rewritten through symmetric quivers and diagonalization.
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Quantum invariants of 3-manifolds and links: a review
This is a survey, not a new result: it reviews the q-series invariants Zhat, F_K, F_L and their supergroup analogues, collecting known conjectures, theorems, and examples.
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