Topological recursion for the conifold transition of a torus knot

TL;DR

This paper proves a mirror symmetry conjecture linking open Gromov-Witten invariants of a conifold transition of a torus knot to topological recursion on a spectral curve, advancing understanding in mathematical physics.

Contribution

It establishes a new mirror symmetry correspondence for torus knots involving topological recursion and Gromov-Witten invariants.

Findings

Proof of the mirror symmetry conjecture for torus knots

Connection between open Gromov-Witten invariants and topological recursion

Extension of previous conjectures by Brini-Eynard-Mariño and Diaconescu-Shende-Vafa

Abstract

In this paper we prove a mirror symmetry conjecture based on the work of Brini-Eynard-Mari\~no \cite{BEM} and Diaconescu-Shende-Vafa \cite{DSV}. This conjecture relates open Gromov-Witten invariants of the conifold transition of a torus knot to the topological recursion on the B-model spectral curve.