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3d-3d correspondence and abelian flat connection

Hee-Joong Chung

Abstract

We realize a homological block of a knot complement in $S^3$ for $G_{\mathbb{C}}=SL(2,\mathbb{C})$ as a half-index of a 3d $\mathcal{N}=2$ 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.

3d-3d correspondence and abelian flat connection

Abstract

We realize a homological block of a knot complement in for as a half-index of a 3d 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.
Paper Structure (8 sections, 66 equations)

This paper contains 8 sections, 66 equations.

Table of Contents

  1. Introduction
  2. Abelian flat connection and half-index of $T[M_3]$
  3. Half-index for homological block of figure-eight knot
  4. Trefoil knots
  5. Example other than a knot
  6. Critical point and contour
  7. Conclusions and discussion
  8. Additional branch in SUSY parameter space for trefoil knot