Quivers for 3-manifolds: the correspondence, BPS states, and 3d $$ \mathcal{N} $$ = 2 theories
Piotr Kucharski
Abstract
A bstract 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 $$ \hat{Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Z</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:math> ). Apart from assigning quivers to complements of T (2 , 2 p +1) torus knots, we study the physical interpretation in terms of the BPS spectrum and general structure of 3d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.