Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces

Understand

We construct a general class of Calabi--Yau threefolds from fiber products of rational elliptic surfaces with section, generalizing a construction of Schoen to include all Kodaira fiber types.

• The resulting threefolds each have two elliptic fibrations with section over rational elliptic surfaces and blowups thereof.
• These elliptic fibrations generally have nonzero Mordell--Weil rank.
• Each of the elliptic fibrations has a physical interpretation in terms of a six-dimensional F-theory model with one or more non-Higgsable abelian gauge fields.