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

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.

39 pages, 12 figures

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• Learning non-Higgsable gauge groups in 4D F-theory
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion
• An infinite swampland of U(1) charge spectra in 6D supergravity theories
• Automatic Enhancement in 6D Supergravity and F-theory Models
• On the Elliptic Calabi-Yau Fourfold with Maximal $h^{1,1}$
• Natural F-theory constructions of Standard Model structure from $E_7$ flux breaking
• Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory
• Orders of Vanishing and U(1) Charges in F-theory