Multi-cover skeins, quivers, and 3d N = 2 dualities
Tobias Ekholm, Piotr Kucharski, Pietro Longhi
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 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.
Topics & Concepts
QuiverEmbeddingSkeinCover (algebra)MathematicsCovering spaceSkein relationTorusLagrangianPure mathematicsHolomorphic functionRelation (database)Algebra over a fieldKnot (papermaking)GeometryKnot theoryComputer scienceMaterials scienceDatabaseComposite materialMechanical engineeringEngineeringArtificial intelligenceAlgebraic structures and combinatorial modelsGeometric and Algebraic TopologyHomotopy and Cohomology in Algebraic Topology