From local to global in F-theory model building

Andreas, Bjorn; Curio, Gottfried

doi:10.1016/j.geomphys.2010.03.008

Cited by 58 publications

(115 citation statements)

References 15 publications

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“…In the context of SU (5) unification, these extra-singularities are a blessing in disguise since they open the door to a sequence of enhancements of the singular fiber that can provide the matter fields and Yukawa couplings required for a realistic physical model. The structure of the discriminant locus of a SU(5) model has been carefully analyzed by Andreas and Curio [22]. They gave several indications supporting the existence of the successive enhancements demanded by SU(5) phenomenology (Ã 5 andD 5 in codimension-one,D 6 andẼ 6 in codimensionthree).…”

Section: The Conjectured Fiber Geometry Of Su(5) Modelsmentioning

confidence: 99%

“…It is conjectured that the I 5 fiber enhances to a I 6 fiber over Σ 5 and to a I * 1 fiber over Σ 10 (see for example [22,29]):…”

Section: Conjectured Fiber Geometrymentioning

confidence: 99%

“…The curve Σ 5 contains additional points Π 7 : w = P = R = 0 over which the singular fiber I 6 is conjectured to enhance further to a fiber of type I 7 [22,29]:…”

Section: Conjectured Fiber Geometrymentioning

confidence: 99%

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Small resolutions of SU(5)-models in F-theory

Esole

Yau

2013

Advances in Theoretical and Mathematical Physics

125

311

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We provide an explicit desingularization and study the resulting fiber geometry of elliptically fibered four-folds defined by Weierstrass models admitting a splitÃ 4 singularity over a divisor of the discriminant locus. Such varieties are used to geometrically engineer SU(5) grand unified theories in F-theory. The desingularization is given by a small resolution of singularities. TheÃ 4 fiber naturally appears after resolving the singularities in codimension-one in the base. The remaining higher codimension singularities are then beautifully described by a four-dimensional affine binomial variety which leads to six different small resolutions of the elliptically fibered four-fold. These six small resolutions define distinct four-folds connected to each other by a network of flop transitions forming a dihedral group. The location of these exotic fibers in the base is mapped to conifold points of the three-folds that defines the type IIB orientifold limit of the F-theory. The full resolution has interesting properties, specially for fibers in codimension-three: the rank of the singular e-print archive: http://lanl.arXiv.org/abs/1107.0733v2 MBOYO ESOLE AND SHING-TUNG YAUfiber does not necessary increase and the fibers are not necessary in the list of Kodaira and some are not even (extended) Dynkin diagrams.

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Section: The Conjectured Fiber Geometry Of Su(5) Modelsmentioning

confidence: 99%

“…It is conjectured that the I 5 fiber enhances to a I 6 fiber over Σ 5 and to a I * 1 fiber over Σ 10 (see for example [22,29]):…”

Section: Conjectured Fiber Geometrymentioning

confidence: 99%

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Small resolutions of SU(5)-models in F-theory

Esole

Yau

2013

Advances in Theoretical and Mathematical Physics

125

311

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“…As we have θ 31 ≈ 1.5 × 10 16 GeV and M GUT ≈ 2 × 10 16 GeV , the ratio of the GUT scale to the U(1) ⊥ breaking scale is only a factor of 1.5 and we do not regard anomalies in such a small energy interval as being problematic, especially bearing in mind the error in our energy scale estimates.…”

Section: Anomaly Cancellationmentioning

confidence: 72%

Gauge coupling unification in E 6 F-theory GUTs with matter and bulk exotics from flux breaking

Callaghan

King

Leontaris

2013

J. High Energ. Phys.

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We consider gauge coupling unification in E 6 F-Theory Grand Unified Theories (GUTs) where E 6 is broken to the Standard Model (SM) gauge group using fluxes. In such models there are two types of exotics that can affect gauge coupling unification, namely matter exotics from the matter curves in the 27 dimensional representation of E 6 and the bulk exotics from the adjoint 78 dimensional representation of E 6 . We explore the conditions required for either the complete or partial removal of bulk exotics from the low energy spectrum. In the latter case we shall show that (miraculously) gauge coupling unification may be possible even if there are bulk exotics at the TeV scale. Indeed in some cases it is necessary for bulk exotics to survive to the TeV scale in order to cancel the effects coming from other TeV scale matter exotics which would by themselves spoil gauge coupling unification. The combination of matter and bulk exotics in these cases can lead to precise gauge coupling unification which would not be possible with either type of exotics considered by themselves. The combination of matter and bulk exotics at the TeV scale represents a unique and striking signature of E 6 F-theory GUTs that can be tested at the LHC.

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“…Global completions of GUT models have also been intensively studied [35][36][37][38][39][40][41][42][43], with special focus on SU(5) configurations. See [44] for a review on the subject and a more complete list of references.…”

Section: Absractmentioning

confidence: 99%

Tate form and weak coupling limits in F-theory

Esole

Savelli

2013

J. High Energ. Phys.

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AbsractWe consider the weak coupling limit of F-theory in the presence of non-Abelian gauge groups implemented using the traditional ansatz coming from Tate's algorithm. We classify the types of singularities that could appear in the weak coupling limit and explain their resolution. In particular, the weak coupling limit of SU(n) gauge groups leads to an orientifold theory which suffers from conifold singulaties that do not admit a crepant resolution compatible with the orientifold involution. We present a simple resolution to this problem by introducing a new weak coupling regime that admits singularities compatible with both a crepant resolution and an orientifold symmetry. We also comment on possible applications of the new limit to model building. We finally discuss other unexpected phenomena as for example the existence of several non-equivalent directions to flow from strong to weak coupling leading to different gauge groups.

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From local to global in F-theory model building

Cited by 58 publications

References 15 publications

Small resolutions of SU(5)-models in F-theory

Small resolutions of SU(5)-models in F-theory

Gauge coupling unification in E 6 F-theory GUTs with matter and bulk exotics from flux breaking

Tate form and weak coupling limits in F-theory

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