Open Topological String Amplitudes on Calabi-Yau Threefolds by Extended Holomorphic Anomaly Equation

TL;DR

This paper develops a recursive method to compute open topological string amplitudes on Calabi-Yau threefolds using an extended holomorphic anomaly equation, and extracts BPS invariants via mirror symmetry.

Contribution

It introduces an extended holomorphic anomaly equation approach for calculating high-genus open string amplitudes on Calabi-Yau threefolds.

Findings

Recursive solutions for amplitudes with high genus and boundaries.

Extraction of BPS invariants from computed amplitudes.

Validation of the method through mirror symmetry techniques.

Abstract

In this paper, we study the open topological string amplitudes on Calabi-Yau threefolds by the extended holomorphic anomaly equation. The disk two-point function determined by the domainwall tension, together with the Yukawa couplings, solves the amplitudes with high genus and boundaries recursively. The BPS invariants encoded in the amplitudes are extracted by mirror symmetry.