On Link Invariants and Topological String Amplitudes

TL;DR

This paper demonstrates that newly computed polynomial invariants for knots with up to nine crossings align with the Ooguri-Vafa conjecture, linking Chern-Simons theory to topological string theory on the conifold resolution.

Contribution

It provides explicit verification that knot invariants agree with the Ooguri-Vafa conjecture for knots up to nine crossings.

Findings

Polynomial invariants match the Ooguri-Vafa conjecture for knots up to nine crossings.

Supports the connection between Chern-Simons gauge theory and topological string theory.

Validates theoretical predictions with explicit calculations.

Abstract

We explicitly show that the new polynomial invariants for knots, upto nine crossings, agree with the Ooguri-Vafa conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold.