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Register a new userF-GUTs with Mordell-Weil U(1)s
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In this note we study the constraints on F-theory GUTs with extra $U(1)$s in the context of elliptic fibrations with rational sections. We consider the simplest case of one abelian factor (Mordell-Weil rank one) and investigate the conditions that are induced on the coefficients of its Tate form. Converting the equation representing the generic hypersurface $P_{112}$ to this Tates form we find that the presence of a U(1), already in this local description, is consistent with the exceptional ${cal E}_6$ and ${cal E}_7$ non-abelian singularities. We briefly comment on a viable ${cal E}_6times U(1)$ effective F-theory model.
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In this paper we study the interplay between the recently proposed F-theory GUTs and cosmology. Despite the fact that the parameter range for F-theory GUT models is very narrow, we find that F-theory GUTs beautifully satisfy most cosmological constraints without any further restrictions. The viability of the scenario hinges on the interplay between various components of the axion supermultiplet, which in F-theory GUTs is also responsible for breaking supersymmetry. In these models, the gravitino is the LSP and develops a mass by eating the axino mode. The radial component of the axion supermultiplet known as the saxion typically begins to oscillate in the early Universe, eventually coming to dominate the energy density. Its decay reheats the Universe to a temperature of ~ 1 GeV, igniting BBN and diluting all thermal relics such as the gravitino by a factor of ~ 10^(-4) - 10^(-5) such that gravitinos contribute a sizable component of the dark matter. In certain cases, non-thermally produced relics such as the axion, or gravitinos generated from the decay of the saxion can also contribute to the abundance of dark matter. Remarkably enough, this cosmological scenario turns out to be independent of the initial reheating temperature of the Universe. This is due to the fact that the initial oscillation temperature of the saxion coincides with the freeze out temperature for gravitinos in F-theory GUTs. We also find that saxion dilution is compatible with generating the desired baryon asymmetry from standard leptogenesis. Finally, the gravitino mass range in F-theory GUTs is 10-100 MeV, which interestingly coincides with the window of values required for the decay of the NLSP to solve the problem of Li(7) over-production.
We compute characteristic numbers of elliptically fibered fourfolds with multisections or non-trivial Mordell-Weil groups. We first consider the models of type E$_{9-d}$ with $d=1,2,3,4$ whose generic fibers are normal elliptic curves of degree $d$. We then analyze the characteristic numbers of the $Q_7$-model, which provides a smooth model for elliptic fibrations of rank one and generalizes the E$_5$, E$_6$, and E$_7$-models. Finally, we examine the characteristic numbers of $G$-models with $G=text{SO}(n)$ with $n=3,4,5,6$ and $G=text{PSU}(3)$ whose Mordell-Weil groups are respectively $mathbb{Z}/2mathbb{Z}$ and $mathbb{Z}/3 mathbb{Z}$. In each case, we compute the Chern and Pontryagin numbers, the Euler characteristic, the holomorphic genera, the Todd-genus, the L-genus, the A-genus, and the eight-form curvature invariant from M-theory.
In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the mu term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare mu and B mu terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value mu ~ 10^2 - 10^3 GeV when the hidden sector scale of supersymmetry breaking is F^(1/2) ~ 10^(8.5) GeV. Further, the B mu problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant f_a ~ M_(GUT) * mu / L, where L ~ 10^5 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio mu / L ~ M_(GUT)/M_(pl) ~ 10^(-3). We find f_a ~ 10^12 GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about 10^1 - 10^2 MeV, and a bino-like neutralino is (typically) the NLSP with mass of about 10^2 - 10^3 GeV. Compatibility with electroweak symmetry breaking also determines the value of tan(beta) ~ 30 +/- 7.
Motivated by potential phenomenological applications, we develop the necessary tools for building GUT models in F-theory. This approach is quite flexible because the local geometrical properties of singularities in F-theory compactifications encode the physical content of the theory. In particular, we show how geometry determines the gauge group, matter content and Yukawa couplings of a given model. It turns out that these features are beautifully captured by a four-dimensional topologically twisted N=4 theory which has been coupled to a surface defect theory on which chiral matter can propagate. From the vantagepoint of the four-dimensional topological theory, these defects are surface operators. Specific intersection points of these defects lead to Yukawa couplings. We also find that the unfolding of the singularity in the F-theory geometry precisely matches to properties of the topological theory with a defect.
We present a novel string-derived $U(1)$ combination that satisfies necessary properties to survive to low scales. We discuss previous attempts at acquiring such an abelian gauge symmetry from two different string embeddings and the pitfalls associated with them. Finally, we give an example of how a satisfactory model may be constructed within our framework.
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