Abstract
We constructed several families of elliptic K3 surfaces with Mordell-Weil groups of ranks from 1 to 4. We studied F-theory compactifications on these elliptic K3 surfaces times a K3 surface.Gluing pairs of identical rational elliptic surfaces with nonzero Mordell-Weil ranks yields elliptic K3 surfaces, the Mordell-Weil groups of which have nonzero ranks. The sum of the ranks of the singularity type and the Mordell-Weil group of any rational elliptic surface with a global section is 8. By utilizing this property, families of rational elliptic surfaces with various nonzero Mordell-Weil ranks can be obtained by choosing appropriate singularity types. Gluing pairs of these rational elliptic surfaces yields families of elliptic K3 surfaces with various nonzero Mordell-Weil ranks.We also determined the global structures of the gauge groups that arise in F-theory compactifications on the resulting K3 surfaces times a K3 surface. U(1) gauge fields arise in these compactifications.
Highlights
F-theory [1,2,3] provides a useful framework for model building in particle physics
To show that the technique of the quadratic base change of rational elliptic surfaces to yield elliptic K3 surfaces can be useful in studying the structures of U(1) gauge symmetries in F-theory compactifications, in this note, we considered the rational elliptic surfaces with the singularity types (2.3)–(2.6)
The Mordell-Weil group of a generic elliptic K3 surface (4.12) is isomorphic to Z2. We deduce from these results that the global structure of the gauge group that arises in F-theory compactifications on generic elliptic K3 surfaces (4.12) times a K3 surface is
Summary
F-theory [1,2,3] provides a useful framework for model building in particle physics. SU(5) grand unified theories with matter fields in SO(10) spinor representations are naturally realized in F-theory. A U(1)-gauge field arises in F-theory compactifications on the families of K3 surfaces with nonzero Mordell-Weil ranks that we constructed in this study. The MordellWeil rank of the resulting K3 surface S and that of rational elliptic surface X are equal for a generic quadratic base change; the Mordell-Weil rank of K3 surface S becomes strictly larger than the Mordell-Weil rank of the original rational elliptic surface X when the parameters of the quadratic base change assume special values.. The MordellWeil rank of the resulting K3 surface S and that of rational elliptic surface X are equal for a generic quadratic base change; the Mordell-Weil rank of K3 surface S becomes strictly larger than the Mordell-Weil rank of the original rational elliptic surface X when the parameters of the quadratic base change assume special values.4 3[31] classified the types of singular fibers of the extremal rational elliptic surfaces. 4[21] discusses some situations in which the Mordell-Weil ranks of K3 surfaces, obtained as the quadratic base changes of an extremal rational elliptic surface, are enhanced for specific quadratic base changes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
