Four‐dimensional N=1 vacua of F‐theory are determined by three discrete choices. A topological type of elliptically fibered Calabi‐Yau fourfolds, a choice of flux and a minimum of the corresponding scalar potential. While there are several constructions that together provide an abundance of elliptic Calabi‐Yaus, the choice of properly quantized flux is in general more involved. The talk will start with a brief review of F‐theory and the geometry of Calabi‐Yau fourfolds. I will then explain how topological string theory and homological mirror symmetry can be used to determine properly quantized choices for a particular class of fluxes. Additional comments will be about certain Fourier‐Mukai transformations that act on the underlying basis of topological branes and lead to modular properties of the Gromov‐Witten potentials on non‐singular
Calabi‐Yau fourfolds.
Thorsten Schimannek (Germany): Fourfolds, integral Fluxes and Modularity
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