Geometric singularities and enhanced gauge symmetries

Abstract Using “Tate's algorithm,” we identify loci in the moduli of F-theory compactifications corresponding to enhanced gauge symmetry. We apply this to test the proposed F-theory/heterotic dualities in six dimensions. We recover the perturbative gauge symmetry enhancements of the heterotic side and the physics of small SO (32) instantons, and discover new mixed perturbative/nonperturbative gauge symmetry enhancements. Upon further toroidal compactification to four dimensions, we derive the chain of Calabi-Yau threefolds dual to various Coulomb branches of heterotic strings.