an:06195757
Zbl 1270.81180
Klemm, Albrecht; Manschot, Jan; Wotschke, Thomas
Quantum geometry of elliptic Calabi-Yau manifolds
EN
Commun. Number Theory Phys. 6, No. 4, 849-917 (2012).
00321855
2012
j
81T30 81T50 14D21 53D45 14N35 14M25 14J30 14J32
Summary: 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 \(D\)4-branes wrapping the elliptic fibre and a class in the base. We verify this proposal by explicit computation of the BPS invariants of 3 \(D\)4-branes on the rational elliptic surface.