Tuned and Non-Higgsable U(1)s in F-theory

TL;DR

This paper develops a formula for tuning U(1) gauge fields in F-theory, revealing universal features of non-Higgsable U(1)s, and provides the first example of a threefold base with such U(1)s.

Contribution

It introduces a formula for minimal tuning of U(1)s in F-theory and identifies universal properties of bases with non-Higgsable U(1)s, including a novel threefold example.

Findings

Universal features of non-Higgsable U(1)s identified

A formula for tuning U(1) gauge fields derived

First example of a threefold base with non-Higgsable U(1)s constructed

Abstract

We study the tuning of U(1) gauge fields in F-theory models on a base of general dimension. We construct a formula that computes the change in Weierstrass moduli when such a U(1) is tuned, based on the Morrison-Park form of a Weierstrass model with an additional rational section. Using this formula, we propose the form of "minimal tuning" on any base, which corresponds to the case where the decrease in the number of Weierstrass moduli is minimal. Applying this result, we discover some universal features of bases with non-Higgsable U(1)s. Mathematically, a generic elliptic fibration over such a base has additional rational sections. Physically, this condition implies the existence of U(1) gauge group in the low-energy supergravity theory after compactification that cannot be Higgsed away. In particular, we show that the elliptic Calabi-Yau manifold over such a base has a small number of complex structure moduli. We also suggest that non-Higgsable U(1)s can never appear on any toric bases. Finally, we construct the first example of a threefold base with non-Higgsable U(1)s.