Identification of the Givental formula with the spectral curve topological recursion procedure

TL;DR

This paper establishes a connection between the Givental formula for Gromov-Witten potentials and the topological recursion on spectral curves, proving a conjecture related to reconstructing the stationary sector of P^1.

Contribution

It identifies the Givental formula with a spectral curve topological recursion, providing a new perspective and proof for a conjecture on P^1s Gromov-Witten potential reconstruction.

Findings

Proved the equivalence between Givental formula and topological recursion for spectral curves.

Confirmed the conjecture of Norbury and Scott on P^1.

Established a method for reconstructing Gromov-Witten potentials via spectral curves.

Abstract

We identify the Givental formula for the ancestor formal Gromov-Witten potential with a version of the topological recursion procedure for a collection of isolated local germs of the spectral curve. As an application we prove a conjecture of Norbury and Scott on the reconstruction of the stationary sector of the Gromov-Witten potential of $\CP1$ via a particular spectral curve.