All genus open mirror symmetry for the projective line

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 $(\mathbb{P}^1, \mathbb{R}\mathbb{P}^1)$.

💡 Research Summary

The paper establishes an all‑genus equivariant open mirror symmetry for the pair ((\mathbb{P}^1,\mathbb{R}\mathbb{P}^1)). The authors first review the (S^1)-equivariant cohomology of the projective line, presenting it as (\mathbb{C}