Geometric engineering in toric F-theory and GUTs with U(1) gauge factors

Braun, Volker; Grimm, Thomas W.; Keitel, Jan

doi:10.1007/jhep12(2013)069

Cited by 110 publications

(239 citation statements)

References 47 publications

(108 reference statements)

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“…The Calabi-Yau manifold X F 13 has Mordell-Weil group Z 2 , X F 15 has Mordell-Weil group Z ⊕ Z 2 and the fibration X F 16 has Mordell-Weil group Z 3 [41,46]. We confirm these findings by explicitly working out the WSF of these toric hypersurface fibrations, which are shown to precisely take the standard form of WSF's with these MW-torsion groups, cf.…”

Section: Fibrations With Gauge Groups Of Rank 5 and 6 And Mw-torsionsupporting

confidence: 70%

“…Elliptic fibers with an increasing number of rational points and their corresponding elliptically fibered Calabi-Yau manifolds X with a Mordell-Weil group (MW-group) of rational sections of increasing rank have been systematically constructed and studied [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. 7 The free part of the MW-group leads to U(1)-gauge fields in F-theory 8 [2] and the torsion part yields non-simply connected gauge groups [53].…”

Section: Jhep01(2015)142mentioning

confidence: 99%

“…We note that the 16 toric hypersurface fibrations X F i were considered in [41], where a thorough classification of their toric MW-groups was carried out. Further specializations of the X F i corresponding to toric tops [64,65] (see [66] for a systematic approach based on Tate's algorithm for elliptic fibers in Bl 1 P 2 (1, 1, 2)) permitted the engineering of toric Ftheory models with certain gauge groups, in particular with an SU(5) GUT-group.…”

Section: Jhep01(2015)142mentioning

confidence: 99%

“…The Stanley-Reisner ideal of P F 7 is given by In total there are six rational sections of the elliptic fibration of X F 7 with four of them being linearly independent [41]. Their coordinates arê Using Nagell's algorithm we compute the Weierstrass form (2.1) of (3.95).…”

Section: Polyhedronmentioning

confidence: 99%

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F-theory on all toric hypersurface fibrations and its Higgs branches

Klevers

Pena²,

Oehlmann³

et al. 2015

J. High Energ. Phys.

140

570

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We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in P 2 , P 1 × P 1 and the recently studied P 2 (1, 1, 2), yield F-theory realizations of SUGRA theories with discrete gauge groups Z 3 , Z 2 and Z 4 . This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I 2 -fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. We also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP 1 has a U(1)-gauge field JHEP01 (2015)142 induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.

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Section: Fibrations With Gauge Groups Of Rank 5 and 6 And Mw-torsionsupporting

confidence: 70%

Section: Jhep01(2015)142mentioning

confidence: 99%

Section: Jhep01(2015)142mentioning

confidence: 99%

Section: Polyhedronmentioning

confidence: 99%

See 2 more Smart Citations

F-theory on all toric hypersurface fibrations and its Higgs branches

Klevers

Pena²,

Oehlmann³

et al. 2015

J. High Energ. Phys.

140

570

View full text Add to dashboard Cite

show abstract

“…1 This is to be contrasted with most constructions of Calabi-Yau manifolds with MW rank-one in the literature, a small sample of which is collected in the bibliography [7][8][9][10][11][12][13][14][15][16], where the Weierstrass model of the manifold takes the form (1.2).…”

Section: Jhep10(2016)033mentioning

confidence: 99%

Tall sections from non-minimal transformations

Morrison

Park

2016

J. High Energ. Phys.

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In previous work, we have shown that elliptic fibrations with two sections, or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass model of a certain form, namely, the Jacobian of a P 112 model. Most constructions of elliptically fibered Calabi-Yau manifolds with two sections have been carried out assuming that the image of this birational map was a "minimal" Weierstrass model. In this paper, we show that for some elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the Jacobian of the P 112 model is not minimal. Said another way, starting from a Calabi-Yau Weierstrass model, the total space must be blown up (thereby destroying the "Calabi-Yau" property) in order to embed the model into P 112 . In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.

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Towards the Standard Model in F-theory

2015

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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) × SU (2) × U (1) × U (1) as suitable restrictions of a Bl 2 P 2 -fibration with rank-two MordellWeil group. We analyse the five inequivalent toric enhancements to gauge group SU (3) × SU (2) along two independent divisors W 3 and W 2 in the base. For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental (3, 2), three types of (1, 2) representations and five types of (3, 1) representations (plus conjugates), in addition to charged singlet states. The precise spectrum of zero-modes in these representations depends on the 3-form background. We analyse the geometrically realised Yukawa couplings among all these states and find complete agreement with field theoretic expectations based on their U (1) charges. We classify possible identifications of the found representations with the Standard Model field content extended by right-handed neutrinos and extra singlets. The linear combination of the two abelian gauge group factors orthogonal to hypercharge acts as a selection rule which, depending on the specific model, can forbid dangerous dimension-four and -five proton decay operators.

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Geometric engineering in toric F-theory and GUTs with U(1) gauge factors

Cited by 110 publications

References 47 publications

F-theory on all toric hypersurface fibrations and its Higgs branches

F-theory on all toric hypersurface fibrations and its Higgs branches

Tall sections from non-minimal transformations

Towards the Standard Model in F-theory

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