English

3d-3d correspondence and abelian flat connection

High Energy Physics - Theory 2026-03-06 v1 Mathematical Physics Geometric Topology math.MP

Abstract

We realize a homological block of a knot complement in S3S^3 for GC=SL(2,C)G_{\mathbb{C}}=SL(2,\mathbb{C}) as a half-index of a 3d N=2\mathcal{N}=2 theory via an expression of the homological block as an inverted Habiro series by working out some examples, which we expect to extend to general knots. Also, by choosing a certain set of poles in the integral expression of the half-index, we obtain the colored Jones polynomial.

Cite

@article{arxiv.2603.05236,
  title  = {3d-3d correspondence and abelian flat connection},
  author = {Hee-Joong Chung},
  journal= {arXiv preprint arXiv:2603.05236},
  year   = {2026}
}

Comments

23 pages

R2 v1 2026-07-01T11:04:59.966Z