F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections

Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan

doi:10.1007/jhep06(2013)067

Cited by 114 publications

(346 citation statements)

References 77 publications

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“…All these results are base-independent in the sense that they follow directly from the geometry of the fiber C F i . The only dependence on the base B enters through the choice of two divisors on B that label the possible Calabi-Yau fibrations of C F i [39]. We highlight the following interesting geometrical findings of our analysis of F-theory on the Calabi-Yau manifolds X F i :…”

Section: Summary Of Resultsmentioning

confidence: 88%

“…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%

“…cently, starting with [37,39,43]. This permits the introduction of discrete degrees of freedom in the construction of the fibration of the elliptic curve over the base B yielding a finite number of strata in the moduli space of X.…”

Section: Jhep01(2015)142mentioning

confidence: 99%

“…The divisor classes that support Abelian gauge fields in F-theory [34,39,77], see also [22,31,78] Here π(·) denotes the projection of a codimension two variety in X to a divisor in the base B and [K B ] is the canonical bundle of B. The last term encodes contributions from 14 The fibers that do not have an associated group GI are the unconventional fibers in table 2 of [61].…”

Section: Divisors On Genus-one Fibrations and Their Intersectionsmentioning

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.

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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: Summary Of Resultsmentioning

confidence: 88%

Section: Jhep01(2015)142mentioning

confidence: 99%

Section: Jhep01(2015)142mentioning

confidence: 99%

Section: Divisors On Genus-one Fibrations and Their Intersectionsmentioning

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.

Self Cite

140

570

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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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F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections

Cited by 114 publications

References 77 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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