Related papers: F-GUTs with Mordell-Weil U(1)'s

We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell--Weil generators. This results…

We analyze general F-theory compactifications with U(1) x U(1) x U(1) Abelian gauge symmetry by constructing the general elliptically fibered Calabi-Yau manifolds with a rank three Mordell-Weil group of rational sections. The general…

We constructed several families of elliptic K3 surfaces with Mordell-Weil groups of ranks from 1 to 4. We studied F-theory compactifications on these elliptic K3 surfaces times a K3 surface. Gluing pairs of identical rational elliptic…

Let $K$ be a field finitely generated over ${\Q}$, and $A$ an Abelian variety defined over $K$. Then by the Mordell-Weil Theorem, the set of rational points $A(K)$ is a finitely-generated Abelian group. In this paper, assuming Tate's…

In this work we prove a bound for the torsion in Mordell-Weil groups of smooth elliptically fibered Calabi-Yau 3- and 4-folds. In particular, we show that the set which can occur on a smooth elliptic Calabi-Yau $n$-fold for ($n\geq 3$) is…

We consider a rational surface with a relatively minimal fibration. Picard number of a such fibred surface is bounded in terms of the genus of a general fibre. When Picard number is the maximum for any given genus, we characterize a such…

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level…

We consider semi-local F-theory GUTs arising from a single E_8 point of local enhancement, leading to simple GUT groups based on E_6, SO(10) and SU(5) with SU(3), SU(4) and SU(5) spectral covers, respectively. Assuming the minimal Z_2…

This article explores possible embeddings of the Standard Model gauge group and its matter representations into F-theory. To this end we construct elliptic fibrations with gauge group SU(3)xSU(2)xU(1)xU(1) as suitable restrictions of a…

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and…

We describe the behaviour of the rank of the Mordell-Weil group of the Picard variety of the generic fibre of a fibration in terms of local contributions given by averaging traces of Frobenius acting on the fibres. The results give a…

We engineer compact SU(5) Grand Unified Theories in F-theory in which GUT-breaking is achieved by a discrete Wilson line. Because the internal gauge field is flat, these models avoid the high scale threshold corrections associated with…

We approach the Minimum Supersymmetric Standard Model (MSSM) from an E_6 GUT by using the spectral cover construction and non-abelian gauge fluxes in F-theory. We start with an E_6 singularity unfolded from an E_8 singularity and obtain E_6…

We study correlations between the massless field spectra of F-theory fibrations supporting an $SU(5)$ gauge symmetry extended by Abelian symmetries and the spectra that arise from the group $E_8$. The adjoint representation of $E_8$ leads…

We prove new cases of the Tate conjecture for abelian varieties over finite fields, extending previous results of Dupuy--Kedlaya--Zureick-Brown, Lenstra--Zarhin, Tankeev, and Zarhin. Notably, our methods allow us to prove the Tate…

In F-theory compactifications, the abelian gauge sector is encoded in global structures of the internal geometry. These structures lie at the intersection of algebraic and arithmetic description of elliptic fibrations: While the…

We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\mathbb{Z}_m$ and in particular…

We study the consequences of cancellation of cubic Abelian anomalies in F-theory GUT models that utilise hypercharge flux in the presence of additional U(1) symmetries. We show that a mixed anomaly between the hypercharge and two U(1) gauge…

We show the existence of abelian surfaces $A$ over $\mathbb{Q}_p$ having good reduction with supersingular special fibre whose associated $p$-adic Galois module $V_p(A)$ is not semisimple.

We study the relation between phenomenological requirements and the topology of the surfaces that GUT 7-branes wrap in F-theory compactifications. In addition to the exotic matter free condition in the hypercharge flux scenario of…