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.
Highlights
Background flux and theM-theory to F-theory limit for multi-sectionsIn this subsection we argue that a simple circle reduction is not sufficient when considering F-theory on the Calabi-Yau threefold X with a multi-section
We study the physics of F-theory compactifications on genus-one fibrations without section by using an M-theory dual description
In this paper we studied the effective physics of F-theory compactifications on elliptically fibered Calabi-Yau threefolds that do not have sections, but instead admit a bi-section
Summary
We introduce the six-dimensional effective theories that we claim to arise in F-theory compactifications on a genus-one fibered Calabi-Yau threefold X with a multisection. T + 1 arise from the T tensor multiplets and the gravity multiplet, and the symmetric constant matrix Ωαβ and the constant vectors (aα, bα) are crucial to determine the couplings of the six-dimensional supergravity theory Recall that both (aα, bα) and Ωαβ are naturally determined by the topology of the compactification manifold X as aα = −Ωαβ Dβ · [π∗c1(B2)] , B2 bα = −Ωαβ DU2 (1) · Dβ. We propose that in this case one finds a massive U(1) vector multiplet that can be described by a massless U(1) vector multiplet coupled to a hypermultiplet by a Stuckelberg mechanism In addition to this non-linearly charged hypermultiplet, HU(1) − 1 matter hypermultiplets will be part of the six-dimensional effective theory. While this theory is a valid effective theory at the massless level, we will see in the section 3 that it cannot be used in order to perform the F-theory to M-theory duality
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