Gromov-Witten invariants of $\bp^1$ and Eynard-Orantin invariants

TL;DR

This paper establishes a connection between Gromov-Witten invariants of the projective line and Eynard-Orantin invariants of a specific spectral curve, revealing new links between enumerative geometry and topological recursion.

Contribution

It proves that stationary Gromov-Witten invariants of P^1 correspond to Eynard-Orantin invariants of a particular spectral curve, and relates large degree invariants to tautological intersection numbers.

Findings

Gromov-Witten invariants of P^1 are described by Eynard-Orantin invariants.

Asymptotics of large degree Gromov-Witten invariants encode tautological intersection numbers.

The spectral curve x=z+1/z, y=ln z captures the invariants' structure.

Abstract

We prove that stationary Gromov-Witten invariants of $\bp^1$ arise as the Eynard-Orantin invariants of the spectral curve $x=z+1/z$, $y=\ln{z}$. 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 $\bp^1$.