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

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.

arXiv comment43+5 pages

References in corpus (16)

• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Knot Invariants and Topological Strings
• Vortex Counting and Lagrangian 3-manifolds
• Branes and N=2 Theories in Two Dimensions
• Spectral networks
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Knots, links and branes at large N
• Polynomial invariants for torus knots and topological strings
• Cohomological Hall algebra of a symmetric quiver
• Wild Wall Crossing and BPS Giants
• Topological Strings, D-Model, and Knot Contact Homology
• Topological strings, strips and quivers
• Donaldson-Thomas invariants, torus knots, and lattice paths
• BPS Graphs: From Spectral Networks to BPS Quivers
• Semi-Stable Chow-Hall Algebras of Quivers and Quantized Donaldson-Thomas Invariants
• On explicit formulae of LMOV invariants

Cited by in corpus (14)

• $\hat{Z}$ at large $N$: from curve counts to quantum modularity
• Quivers for 3-manifolds: the correspondence, BPS states, and 3d $\mathcal{N}$=2 theories
• Stable maps to Looijenga pairs
• Branes, quivers and wave-functions
• Harer-Zagier formulas for knot matrix models
• Nahm sums, quiver A-polynomials and topological recursion
• Quiver diagonalization and open BPS states
• Revisiting the Melvin-Morton-Rozansky Expansion, or There and Back Again
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• Refined open topological strings revisited
• Combinatorics of Nahm sums, quiver resultants and the K-theoretic condition
• Open/Closed BPS Correspondence and Integrality
• The colored Jones polynomials as vortex partition functions
• Permutohedra for knots and quivers