All genus open mirror symmetry for the projective line

TL;DR

This paper proves that the Chekhov-Eynard-Orantin recursion on the mirror curve of the projective line encodes all genus equivariant open Gromov-Witten invariants, establishing an all genus open mirror symmetry for this setting.

Contribution

It demonstrates that the recursion encodes all genus equivariant open Gromov-Witten invariants of (5, 5), providing a comprehensive mirror symmetry result.

Findings

Recursion encodes all genus invariants

Establishes all genus open mirror symmetry

Connects mirror curve recursion with Gromov-Witten invariants

Abstract

We prove that the Chekhov-Eynard-Orantin recursion on the mirror curve of $\mathbb{P}^1$ encodes all genus equivariant open Gromov-Witten invariants of $(\mathbb{P}^1, \mathbb{R}\mathbb{P}^1)$. This result can be viewed as an all genus equivariant open mirror symmetry for $(\mathbb{P}^1, \mathbb{R}\mathbb{P}^1)$.