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 FK 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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Kucharski, P. Quivers for 3-manifolds: the correspondence, BPS states, and 3d \( \mathcal{N} \) = 2 theories. J. High Energ. Phys. 2020, 75 (2020). https://doi.org/10.1007/JHEP09(2020)075
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DOI: https://doi.org/10.1007/JHEP09(2020)075