Polynomial Structure of the (Open) Topological String Partition Function

TL;DR

This paper demonstrates that the polynomial structure of topological string partition functions applies broadly to Calabi-Yau manifolds and extends to open strings, generalizing previous specific results.

Contribution

It generalizes the polynomial structure of topological string partition functions from the quintic to arbitrary Calabi-Yau manifolds and extends these results to open topological strings.

Findings

Polynomial structure holds for any Calabi-Yau manifold with multiple moduli.

Results are extended to open topological string partition functions.

Reproduces Walcher's results for the real quintic.

Abstract

In this paper we show that the polynomial structure of the topological string partition function found by Yamaguchi and Yau for the quintic holds for an arbitrary Calabi-Yau manifold with any number of moduli. Furthermore, we generalize these results to the open topological string partition function as discussed recently by Walcher and reproduce his results for the real quintic.