Anomalous spatial dimensions and the F-theory model

We consider a class of F-theory models with extra dimensions. We study the anomalous dimensions of the models with extra dimensions and find that the extra dimensions are connected by a transverse fiber on the sphere and a transverse fiber on the horizon. We show that the extra dimensions correspond to the geodesic and geodesic-horizon directions. We also show that there are two classes of F-theory models with extra dimensions, the first class correspond to the geodesic direction and the second to geodesic direction-horizon connection.