### D-branes on elliptic Calabi-Yau manifolds

Manschot, J *(Universität Bonn)*

Monday 28 May 2012, 14:45-15:30

Satellite

#### Abstract

I'll discuss the quantum geometry of elliptically fibered Calabi-Yau threefolds. 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.

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