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F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces

Research paper by Yusuke Kimura

Indexed on: 14 Feb '18Published on: 14 Feb '18Published in: arXiv - High Energy Physics - Theory



Abstract

We construct several families of elliptic K3 surfaces with the Mordell-Weil groups of ranks from 1 to 4. We study F-theory compactifications on these elliptic K3 surfaces times a K3 surface. Gluing pairs of identical rational elliptic surfaces with non-zero Mordell-Weil ranks yields elliptic K3 surfaces, the Mordell-Weil groups of which have non-zero 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. Utilizing this property, families of rational elliptic surfaces with various non-zero 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 non-zero Mordell-Weil ranks. We also determine 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.