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arXiv · 2005.13394

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

Piotr Kucharski
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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.

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Piotr Kucharski. 2020-05-27. Quivers for 3-manifolds: the correspondence, BPS states, and 3d $\mathcal{N}$=2 theories. https://doi.org/10.1007/jhep09(2020)075

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