Polynomial Structure of Topological String Partition Functions

TL;DR

This paper reviews how topological string partition functions exhibit a polynomial structure derived from holomorphic anomaly equations and explores their connection to modular forms in special Kähler geometry.

Contribution

It elucidates the polynomial structure of topological string partition functions and links the ring of propagators to almost-holomorphic modular forms.

Findings

Partition functions satisfy holomorphic anomaly equations.

Connection established between propagator rings and modular forms.

Provides a unified view of polynomial structures in topological strings.

Abstract

We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special K\"ahler geometry and the ring of almost-holomorphic modular forms defined on modular curves.