Quantum geometry of elliptic Calabi-Yau manifolds
High Energy Physics - Theory
2017-12-20 v1
Abstract
We study the quantum geometry of the class of Calabi-Yau threefolds, which are elliptic fibrations over a two-dimensional toric base. A holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base. T-duality on the fibre implies that the topological string free energy also captures the BPS-invariants of D4-branes wrapping the elliptic fibre and a class in the base. We verify this proposal by explicit computation of the BPS invariants of 3 D4-branes on the rational elliptic surface.
Keywords
Cite
@article{arxiv.1205.1795,
title = {Quantum geometry of elliptic Calabi-Yau manifolds},
author = {Albrecht Klemm and Jan Manschot and Thomas Wotschke},
journal= {arXiv preprint arXiv:1205.1795},
year = {2017}
}
Comments
63 pages, 4 figures