Comments on the Holomorphic Anomaly in Open Topological String Theory

TL;DR

This paper demonstrates that solutions to open topological string holomorphic anomaly equations can be derived from closed string solutions by shifting moduli, revealing a deep connection between open and closed string theories.

Contribution

It establishes a method to obtain open string solutions from closed string solutions through specific moduli shifts, clarifying the relationship between open and closed topological strings.

Findings

Open string solutions are derived from closed string solutions via moduli shifts.

The approach connects open and closed topological string theories.

The method simplifies solving open string anomaly equations.

Abstract

We show that a general solution to the extended holomorphic anomaly equations for the open topological string on D-branes in a Calabi-Yau manifold, recently written down by Walcher in arXiv:0705.4098, is obtained from the general solution to the holomorphic anomaly equations for the closed topological string on the same manifold, by shifting the closed string moduli by amounts proportional to the 't Hooft coupling.