Physics of F-theory compactifications without section

TL;DR

This paper explores F-theory compactifications without sections using M-theory duals, revealing the emergence of massive and massless U(1) gauge symmetries and their associated spectra through geometric and quantum effects.

Contribution

It introduces a geometric framework for understanding massive U(1)s in F-theory without sections and computes their quantum effects via one-loop Chern-Simons terms.

Findings

Massive U(1)s arise from fluxes in non-section fibrations.

Massless U(1) corresponds to multi-sections in the Calabi-Yau.

One-loop Chern-Simons terms confirm the gauge structure.

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.