Abstract
We construct 3D mathcal{N} = 2 abelian gauge theories on mathbbm{S} 2 × mathbbm{S} 1 labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored Jones polynomials of knots in mathbbm{S} 3. The colored Jones polynomials are obtained as the Wilson loop expectation values along knots in SU(2) Chern-Simons gauge theories on mathbbm{S} 3, and then our construction provides an explicit correspondence between 3D mathcal{N} = 2 abelian gauge theories and 3D SU(2) Chern-Simons gauge theories. We verify, in particular, the applicability of our constructions to a class of tangle diagrams of 2-bridge knots with certain specific twists.
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