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

TL;DR

This paper constructs a broad class of Calabi-Yau threefolds from fiber products of rational elliptic surfaces, revealing non-Higgsable abelian gauge symmetries in six-dimensional F-theory models and exploring their physical and geometric properties.

Contribution

It generalizes previous constructions to include all Kodaira fiber types and analyzes the physical implications of non-Higgsable abelian gauge fields in F-theory.

Findings

Many models have mild singularities without Calabi-Yau resolution.

Some abelian gauge fields cannot be unHiggsed without unphysical singularities.

The models demonstrate T-duality in certain little string theories.

Abstract

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. Many of the models in this class have mild singularities that do not admit a Calabi--Yau resolution; this does not seem to compromise the physical integrity of the theory and can be associated in some cases with massless hypermultiplets localized at the singular loci. In some of these constructions, however, we find examples of abelian gauge fields that cannot be "unHiggsed" to a nonabelian gauge field without producing unphysical singularities that cannot be resolved. The models studied here can also be used to exhibit T-duality for a class of little string theories.