Physics of F-theory compactifications without section

TL;DR

This work analyzes F-theory compactifications on genus-one fibrations without section by leveraging an M-theory dual, showing that a six-dimensional effective action possesses geometrically massive U(1) vectors coupled to charged hypermultiplets and that nontrivial NS-NS and R-R flux along the compactification circle induce a shift gauging of axions. A fluxed S^1 reduction is shown to be essential to reproduce the five-dimensional theory, where a linear combination of the Kaluza–Klein vector and the massive U(1) remains massless and is identified with the bi-section in the M-theory dual; this identification is confirmed by matching one-loop Chern–Simons terms after integrating out massive states. The paper then builds explicit (X, X̃) pairs related by conifold transitions, demonstrating how a bi-section geometry arises from deformation and how two sections are recovered on the resolved side, with a Higgs mechanism removing the massive U(1) in the five-dimensional theory. Through detailed computations of Chern–Simons terms and anomaly constraints, the authors show consistent spectra across the transitions and provide a general framework to extract matter content from CS data, offering a practical route to studying F-theory models without section and connecting them to familiar sectioned geometries. The results illuminate how conifold transitions and fluxed reductions together yield a tractable description of F-theory without section, with potential applications to more intricate multi-section or fourfold constructions and model-building implications.

Abstract

We study the physics of F-theory compactifications on genus-one fibrations without section by using an M-theory dual description. The five-dimensional action obtained by considering M-theory on a Calabi-Yau threefold is compared with a six-dimensional F-theory effective action reduced on an additional circle. We propose that the six-dimensional effective action of these setups admits geometrically massive U(1) vectors with a charged hypermultiplet spectrum. The absence of a section induces NS-NS and R-R three-form fluxes in F-theory that are non-trivially supported along the circle and induce a shift-gauging of certain axions with respect to the Kaluza-Klein vector. In the five-dimensional effective theory the Kaluza-Klein vector and the massive U(1)s combine into a linear combination that is massless. This U(1) is identified with the massless U(1) corresponding to the multi-section of the Calabi-Yau threefold in M-theory. We confirm this interpretation by computing the one-loop Chern-Simons terms for the massless vectors of the five-dimensional setup by integrating out all massive states. A closed formula is found that accounts for the hypermultiplets charged under the massive U(1)s.

Figures (7)

• Figure 1: Overview of our discussion. The object of interest in the top-right corner, corresponding to the six-dimensional theories coming from F-theory on a space without section $\mathcal{X}$. In the examples we will discuss explicitly these compactifications are closely related (by making some fields massive) to F-theory on spaces with section $\mathbb{X}$, giving the six-dimensional theories in the top-left corner. Compactification of these theories on $S^1$ gives two five-dimensional theories, in the middle row, which can also be obtained by M-theory on the corresponding Calabi-Yau threefolds (shown in the bottom row). The five-dimensional theories are related by Higgsing, or equivalently, by conifold transitions in M-theory.
• Figure 2: Six-dimensional effective theories with a massless and massive $U(1)$ gauge field.
• Figure 3: The different theories related to the resolved manifold $\mathbb{X}$ and their interrelations.
• Figure 4: The different theories related to the deformed manifold $\mathcal{X}$ and their interrelations.
• Figure 5: The two theories obtained by compactifying M-theory on $\mathbb{X}$ and $\mathcal{X}$, respectively, are connected by a conifold transition.