Gromov–Witten invariants of $\mathbb{P}^1$ and Eynard–Orantin invariants

Abstract

We prove that genus-zero and genus-one stationary Gromov–Witten invariants of ${\mathbb{P}}^1$ arise as the Eynard–Orantin invariants of the spectral curve $x=z+1∕z$, $y=lnz$. As an application we show that tautological intersection numbers on the moduli space of curves arise in the asymptotics of large-degree Gromov–Witten invariants of ${\mathbb{P}}^1$.