Classifications of elliptic fibrations of a singular K3 surface

Bertin, Marie José; Garbagnati, Alice; Hortsch, Ruthi; Lecacheux, Odile; Mase, Makiko; Salgado, Cecília; Whitcher, Ursula

doi:10.48550/arxiv.1501.07484

Cited by 2 publications

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“…This confirms that the elliptic fibration (24) has a type II * fiber at Thus, the corresponding singularity type is E 8 E 7 A 2 A 1 , and according to [128] an attractive K3 surface with this singularity type is unique, being S [6 0 2] . We conclude from this that the 14 The types of elliptic fibrations of the attractive K3 surface S [6 0 2] were studied in [129].…”

Section: Unbroken E 8 E 7 Gauge Algebramentioning

confidence: 99%

Nongeometric heterotic strings and dual F-theory with enhanced gauge groups

Kimura

2019

J. High Energ. Phys.

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Eight-dimensional nongeometric heterotic strings were constructed as duals of Ftheory on Λ 1,1 ⊕ E 8 ⊕ E 7 lattice polarized K3 surfaces by Malmendier and Morrison. We study the structure of the moduli space of this construction. There are special points in this space at which the ranks of the non-Abelian gauge groups on the 7-branes in F-theory are enhanced to 18. We demonstrate that the enhanced rank-18 non-Abelian gauge groups arise as a consequence of the coincident 7-branes, which deform stable degenerations on the F-theory side. This observation suggests that the non-geometric heterotic strings include nonperturbative effects of the coincident 7-branes on the Ftheory side. The gauge groups that arise at these special points in the moduli space do not allow for perturbative descriptions on the heterotic side.We also construct a family of elliptically fibered Calabi-Yau 3-folds by fibering K3 surfaces with enhanced singularities over P 1 . Highly enhanced gauge groups arise in F-theory compactifications on the resulting Calabi-Yau 3-folds. 5 Connections of lattice polarized K3 surfaces, O + (Λ 2,2 )-modular forms, and non-geometric heterotic strings were discussed in [31]. K3 surfaces with Λ 1,1 ⊕ E 7 ⊕ E 7 lattice polarization and the construction of nongeometric heterotic strings were studied in [32].6 See [42] for the construction of the Jacobians of elliptic curves.

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Section: Unbroken E 8 E 7 Gauge Algebramentioning

confidence: 99%

Nongeometric heterotic strings and dual F-theory with enhanced gauge groups

Kimura

2019

J. High Energ. Phys.

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“…12 Elliptic fibrations with a global section, and their Weierstrass forms, of an attractive K3 surface whose transcendental lattice has the intersection matrix 4 0 0 2 are classified in [58]. Elliptic fibrations with a global section of an attractive K3 surface whose transcendental lattice has the intersection matrix 6 0 0 2 are studied in [59].…”

Section: Enhancement To Models With U (1)mentioning

confidence: 99%

Enhancements in F-theory models on moduli spaces of K3 surfaces with ADE rank 17

Kimura

Mizoguchi

2018

Progress of Theoretical and Experimental Physics

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We study the moduli of elliptic K3 surfaces with a section with the ADE rank 17. While the Picard number of a generic K3 surface in such moduli space is 19, the Picard number is enhanced to 20 at special points in the moduli. K3 surfaces become attractive K3 surfaces at these points. Either of the following two situations occurs at such special points: i) the Mordell-Weil rank of an elliptic K3 surface is enhanced, or ii) the gauge symmetry is enhanced. The first case i) is related to the appearance of a U (1) gauge symmetry. In this note, we construct the moduli of K3 surfaces with ADE types E 7 D 10 and A 17 . We determine some of the special points at which K3 surfaces become attractive in the moduli of K3 surfaces with ADE types E 7 D 10 and A 17 . We investigate the gauge symmetries in F-theory compactifications on attractive K3 surfaces which correspond to such special points in the moduli times a K3 surface. U (1) gauge symmetry arises in some F-theory compactifications. arXiv:1712.08539v3 [hep-th]

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Classifications of elliptic fibrations of a singular K3 surface

Cited by 2 publications

References 0 publications

Nongeometric heterotic strings and dual F-theory with enhanced gauge groups

Nongeometric heterotic strings and dual F-theory with enhanced gauge groups

Enhancements in F-theory models on moduli spaces of K3 surfaces with ADE rank 17

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