Open Gromov-Witten invariants and mirror maps for semi-Fano toric manifolds

TL;DR

This paper establishes a precise relationship between Lagrangian Floer superpotentials and toric mirror maps for semi-Fano toric manifolds, enabling computation of open Gromov-Witten invariants via mirror symmetry.

Contribution

It proves the equality of two superpotentials for semi-Fano toric manifolds, providing a new method to compute open Gromov-Witten invariants using mirror symmetry.

Findings

Lagrangian Floer superpotential equals toric mirror superpotential under certain conditions.

Provides a practical approach to compute open Gromov-Witten invariants.

Establishes a link between Floer theory and mirror symmetry for semi-Fano toric manifolds.

Abstract

We prove that for a compact toric manifold whose anti-canonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya-Oh-Ohto-Ono is equal to the superpotential written down by using the toric mirror map under a convergence assumption. This gives a method to compute open Gromov-Witten invariants using mirror symmetry.