Mirror symmetry and open/closed correspondence for the projective line

Abstract

We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line ${\mathbb{P}}^1$ with boundary condition specified by an $S^1$-invariant Lagrangian sub-manifold $L$ and the asymptotic expansion of the $I$-function of a toric surface $\mathcal{S}$.

22 pages, 3 figures