High Energy Theory Seminar

The construction of Abelian gauge symmetries in global F-theory compactifications has been more elusive than the well studied non-Abelian case. In this talk, I present a systematic approach to engineer Abelian gauge factors in F-theory, which are related to the Mordell-Weil group of rational points on elliptic curves. I will construct explicitly the general elliptic curves with rank two and three Mordell-Weil groups, leading to a U(1)xU(1) and U(1)xU(1)xU(1) Abelian sector, and their Calabi-Yau elliptic fibrations. These can be fully classified and have new heterotic duals. The matter spectrum of F-theory on these Calabi-Yau manifolds is worked out, both in six and four dimensions and also in the presence of additional SU(5) GUTs. Closed expressions for the four-dimensional chiral indices of matter for entire families of F-theory compactifications are presented. In terms of 3D Chern-Simons terms in the dual M-theory compactifications new conditions on chirality-inducing G4-flux are formulated, which guarantee a consistent lift to F-theory. These G4-flux conditions are more general than earlier ones derived from arguments based on 4D Lorentz symmetry.