Topological recursion and mirror curves

TL;DR

This paper demonstrates that topological recursion applied to mirror curves of toric Calabi-Yau threefolds accurately reproduces Gromov-Witten invariants, including constant contributions, extending the remodeling conjecture.

Contribution

It extends the remodeling conjecture to full free energies, including constant terms, and analyzes the role of mirror curve decompositions in topological recursion.

Findings

Recursion reproduces Gromov-Witten invariants with constant contributions

The full free energies relate to the MacMahon function

Recursive construction does not commute with certain mirror curve limits

Abstract

We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi-Yau threefolds. We show that the recursion reproduces precisely the corresponding Gromov-Witten invariants, which can be encoded in powers of the MacMahon function. As a result, we extend the scope of the "remodeling conjecture" to the full free energies, including the constant contributions. In the process we study how the pair of pants decomposition of the mirror curves plays an important role in the topological recursion. We also show that the free energies are not, strictly speaking, symplectic invariants, and that the recursive construction of the free energies does not commute with certain limits of mirror curves.