Affine Kac-Moody algebras, CHL strings and the classification of tops

Bouchard, Vincent; Skarke, Harald

doi:10.4310/atmp.2003.v7.n2.a1

Cited by 62 publications

(200 citation statements)

References 35 publications

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“…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. Some 4D examples of chiral SU(5) GUTs were constructed in this manner [42,43].…”

Section: Jhep01(2015)142mentioning

confidence: 99%

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

Klevers

Pena²,

Oehlmann³

et al. 2015

J. High Energ. Phys.

137

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: Jhep01(2015)142mentioning

confidence: 99%

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

Klevers

Pena²,

Oehlmann³

et al. 2015

J. High Energ. Phys.

137

570

View full text Add to dashboard Cite

show abstract

“…In this sense our construction differs from the earlier approaches to F-theory Standard Models reported in [75][76][77], which geometrically deform an underlying SU (5) theory to the Standard Model. The structure of singularities in the class of toric SU (3) × SU (2) × U (1) 1 × U (1) 2 models and their resolution is described by the combination of the 3 × 3 possible tops with gauge group SU (3) × SU (2) over polygon 5 in the classification of [78]; of the nine combinations only five are mutually inequivalent. For generic choice of SU (3) and SU (2) divisors on the base, the spectrum of charged matter representations consists, in absence of fluxes, of a state (3, 2), three types of (1, 2)-states and five types of (3, 1)-states plus conjugates, whose U (1) i charges we have computed.…”

Section: Discussionmentioning

confidence: 99%

“…Such types of fibration had previously been considered also in [79]. The ambient space Bl 2 P 2 of the elliptic fibre is a toric space which has the toric diagram represented by polygon 5 in the classification [78] (see also figure 2 in the appendix). Here and in the sequel we will Table 2.1: Classes of the sections appearing in (2.1) for α and β pullback of 'arbitrary' classes of B and K = π −1 K B .…”

Section: F-theory With U (1) × U (1) Gauge Groupmentioning

confidence: 99%

“…The relationship between toric geometry and the geometry of Calabi-Yau hypersurfaces is described in e.g. [78].…”

Section: A Details On the Toric Diagramsmentioning

confidence: 99%

“…For our U (1) 1 × U (1) 2 fibration, there are three tops for SU (2) and SU (3) each [78]. In sections 3 and 4 we compute in turn the structure of matter curves and the geometrically realised Yukawa couplings in models with an extra SU (2) and SU (3) gauge symmetry, respectively.…”

Section: Introductionmentioning

confidence: 99%

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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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Global Tensor‐Matter Transitions in F‐Theory

Dierigl

Oehlmann

Ruehle

2018

Fortschritte der Physik

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We use F-theory to study gauge algebra preserving transitions of 6d supergravity theories that are connected by superconformal points. While the vector multiplets remain unchanged, the hyper-and tensor multiplet sectors are modified. In 6d F-theory models, these transitions are realized by tuning the intersection points of two curves, one of them carrying a non-Abelian gauge algebra, to a (4, 6, 12) singularity, followed by a resolution in the base. The six-dimensional supergravity anomaly constraints are strong enough to completely fix the possible non-Abelian representations and to restrict the Abelian charges in the hypermultiplet sector affected by the transition, as we demonstrate for all Lie algebras and their representations. Furthermore, we present several examples of such transitions in torically resolved fibrations. In these smooth models, superconformal points lead to non-flat fibers which correspond to non-toric Kähler deformations of the torus-fibered Calabi-Yau 3-fold geometry.

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Affine Kac-Moody algebras, CHL strings and the classification of tops

Cited by 62 publications

References 35 publications

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

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

Towards the Standard Model in F-theory

Global Tensor‐Matter Transitions in F‐Theory

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