Tate’s algorithm for F-theory GUTs with two U(1)s

Lawrie, Craig; Sacco, Damiano

doi:10.1007/jhep03(2015)055

Cited by 18 publications

(33 citation statements)

References 78 publications

(181 reference statements)

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“…The general solution to (3.1) with relatively prime s 8 and s 9 is then given by (cf. [32]) The constraint (3.1) can also be solved simply by setting…”

Section: Unhiggsing U(1) → Su(2) In Geometrymentioning

confidence: 99%

Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models

Klevers

Taylor

2016

J. High Energ. Phys.

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Abstract:We give an explicit construction of a class of F-theory models with matter in the three-index symmetric (4) representation of SU(2). This matter is realized at codimension two loci in the F-theory base where the divisor carrying the gauge group is singular; the associated Weierstrass model does not have the form associated with a generic SU(2) Tate model. For 6D theories, the matter is localized at a triple point singularity of arithmetic genus g = 3 in the curve supporting the SU(2) group. This is the first explicit realization of matter in F-theory in a representation corresponding to a genus contribution greater than one. The construction is realized by "unHiggsing" a model with a U(1) gauge factor under which there is matter with charge q = 3. The resulting SU(2) models can be further unHiggsed to realize non-Abelian G 2 × SU(2) models with more conventional matter content or SU(2) 3 models with trifundamental matter. The U(1) models used as the basis for this construction do not seem to have a Weierstrass realization in the general form found by Morrison-Park, suggesting that a generalization of that form may be needed to incorporate models with arbitrary matter representations and gauge groups localized on singular divisors.

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“…The general solution to (3.1) with relatively prime s 8 and s 9 is then given by (cf. [32]) The constraint (3.1) can also be solved simply by setting…”

Section: Unhiggsing U(1) → Su(2) In Geometrymentioning

confidence: 99%

Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models

Klevers

Taylor

2016

J. High Energ. Phys.

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“…The remaining three models all give rise to the µ-term with two singlet insertions. Interesting flavor textures for these models, which have only a single 10, cannot be generated through the U (1) symmetries, however these models have the advantage of having a concrete geometric realization: none of the geometries in the literature [7][8][9][10]15] generate this particular combination of charges, however we will determine elliptic fibrations for these models in section 7.…”

Section: Two U (1) Models With Hypersurface Realizationmentioning

confidence: 99%

“…Here, we label our models as in [15], where the vanishing orders, n c i , are given in the order (n s 1 , n s 2 , n s 3 , n s 5 , n s 6 , n s 8 , n a 1 , n b 1 , n a 2 , n b 2 , n a 3 , n b 3 ) . (7.5) Furthermore it will be necessary to consider so-called non-canonical models, where the enhancement of the discriminant to O(z 5 ), occurs not by simply specifying the vanishing order of the coefficients, but by subtle cancellations between the coefficients, which are non-trivially related see e.g.…”

Section: Sectionmentioning

confidence: 99%

Froggatt-Nielsen meets Mordell-Weil: a phenomenological survey of global F-theory GUTs with U(1)s

Krippendorf

Schäfer‐Nameki

Wong

2015

J. High Energ. Phys.

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In F-theory, U(1) gauge symmetries are encoded in rational sections, which generate the Mordell-Weil group of the elliptic fibration of the compactification space. Recently the possible U(1) charges for global SU(5) F-theory GUTs with smooth rational sections were classified [1]. In this paper we utilize this classification to probe global Ftheory models for their phenomenological viability. After imposing an exotic-free MSSM spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the presence of U(1) gauge symmetries), absence of dimension four and five proton decay operators and other R-parity violating couplings, and the presence of at least the third generation top Yukawa coupling, we generate the remaining quark and lepton Yukawa textures by a Froggatt-Nielsen mechanism. In this process we require that the dangerous couplings are forbidden at leading order, and when re-generated by singlet vevs, lie within the experimental bounds. We scan over all possible configurations, and show that only a small class of U(1) charge assignments and matter distributions satisfy all the requirements. The solutions give rise to the exact MSSM spectrum with realistic quark and lepton Yukawa textures, which are consistent with the CKM and PMNS mixing matrices. We also discuss the geometric realization of these models, and provide pointers to the class of elliptic fibrations with good phenomenological properties.

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“…It was not surprising that F-theory benefited immensely from their efforts. Indeed, the introduction of the so-called Shioda-map to the F-theory community in [18,19] sparked the explicit construction of many abelian F-theory models [17,[20][21][22][23][24][25][26][27][28][29][30][31][32]. The more formal approach to U (1)s via the Mordell-Weil group not only led to new insights about physical phenomena such as gauge symmetry breaking/enhancement or the global structure of the gauge group.…”

Section: Introductionmentioning

confidence: 99%

TASI Lectures on Abelian and Discrete Symmetries in F-theory

Cvetič¹,

Lin²

2018

Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)

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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 Mordell-Weil lattice is related to the continuous abelian sector, the Tate-Shafarevich group is conjectured to encode discrete abelian symmetries in F-theory. In these notes we review both subjects with a focus on recent findings such as the global gauge group and gauge enhancements. We then highlight the application to F-theory model building.

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Tate’s algorithm for F-theory GUTs with two U(1)s

Cited by 18 publications

References 78 publications

Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models

Three-index symmetric matter representations of SU(2) in F-theory from non-Tate form Weierstrass models

Froggatt-Nielsen meets Mordell-Weil: a phenomenological survey of global F-theory GUTs with U(1)s

TASI Lectures on Abelian and Discrete Symmetries in F-theory

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