Fixing D7-brane positions by F-theory fluxes

To do realistic model building in type IIB supergravity, it is important to understand how to fix D7-brane positions by the choice of fluxes. More generally, F-theory model building requires the understanding of how fluxes determine the singularity structure (and hence gauge group and matter content) of the compactification. We analyse this problem in the simple setting of M-theory on K3×K3K3×K3. Given a certain flux which is consistent with the F-theory limit, we can explicitly derive the positions at which D7 branes or stacks of D7 branes are stabilised. The analysis is based on a parameterization of the moduli space of type IIB string theory on T2/Z2T2/Z2 (including D7-brane positions) in terms of the periods of integral cycles of M-theory on K3. This allows us, in particular, to select a specific desired gauge group by the choice of flux numbers.