Quantum geometry of elliptic Calabi-Yau manifolds
arXiv:1205.1795
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.
63 pages, 4 figures
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- Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
- Thermodynamic limit of the Nekrasov-type formula for E-string theory
- Exact solutions to quantum spectral curves by topological string theory
- Mirror Symmetry and Modularity
- Topological String on elliptic CY 3-folds and the ring of Jacobi forms