Quivers for 3-manifolds: the correspondence, BPS states, and 3d $\mathcal{N}$=2 theories

Abstract

We introduce and explore the relation between quivers and 3-manifolds with the topology of the knot complement. This idea can be viewed as an adaptation of the knots-quivers correspondence to Gukov-Manolescu invariants of knot complements (also known as $F_K$ or $\hat{Z}$). Apart from assigning quivers to complements of $T^{(2,2p+1)}$ torus knots, we study the physical interpretation in terms of the BPS spectrum and general structure of 3d $\mathcal{N}=2$ theories associated to both sides of the correspondence. We also make a step towards categorification by proposing a $t$-deformation of all objects mentioned above.

arXiv comment25 pages, 2 figures

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Cited by in corpus (11)

• $\hat{Z}$ at large $N$: from curve counts to quantum modularity
• Branches, quivers, and ideals for knot complements
• Branes, quivers and wave-functions
• BPS Invariants for a Knot in Seifert Manifolds
• Harer-Zagier formulas for knot matrix models
• Quiver diagonalization and open BPS states
• Knot Complement, ADO-Invariants and their Deformations for Torus Knots
• A Cable Knot and BPS-Series
• Permutohedra for knots and quivers
• Inverted state sums, inverted Habiro series, and indefinite theta functions
• Non-Semisimple TQFT's and BPS $q$-Series