Toric Geometry and Enhanced Gauge Symmetry of F-Theory/Heterotic Vacua

We study F-theory compactified on elliptic Calabi-Yau threefolds that are realised as hypersurfaces in toric varieties. The enhanced gauge group as well as the number of massless tensor multiplets has a very simple description in terms of toric geometry. We find a large number of examples where the gauge group is not a subgroup of E8xE8, but rather, is much bigger (with rank as high as 296). The largest of these groups is the group recently found by Aspinwall and Gross. Our algorithm can also be applied to elliptic fourfolds, for which the groups can become extremely large indeed (with rank as high as 121328). We present the gauge content for two of the fourfolds recently studied by Klemm et al.