2012/05/08 by Albrecht Klemm, Jan Manschot, Thomas Wotschke
Physics and Astronomy · #hep-th
published as Comm. Number Theor. Phys. 6 (2012) 849-917 · 63 pages, 4 figures
arxiv created 2012/05/08 · arxiv updated 2017/12/20
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.