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

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 $\bp^1$.

30 pages, made minor changes

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• Remodeling the B-model
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings

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