Gauge fluxes in F-theory and type IIB orientifolds

Krause, Sven; Mayrhofer, Christoph; Weigand, Timo

doi:10.1007/jhep08(2012)119

Cited by 75 publications

(251 citation statements)

References 70 publications

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“…Around here, the fiber equation (65) locally has the binomial structure of a deformed Kodaira I 2 equation x y = z 1 z 2 , which describes nothing but this SU (2) R gauge symmetry [26,27,33,34]. Therefore the small resolution gives the P 1 fiber (66) over the locus P e c = 0, which we now call S .…”

Section: Matter Curves For (31)mentioning

confidence: 99%

“…Again, one hint can be embedding all the groups in a unified group, which would provide a two-form for the Abelian group in a similar fashion to the non-Abelian group. The socalled U (1)-restricted model was the first successful model to describe such a global U (1) cycle for SU (5) × U (1) by embedding the U (1) group into SU (2) [26][27][28][29][30]. However, this process heavily depends on a clever choice of ansatz unique to SU (5), and extending this technique to the general gauge group is not straightforward.…”

Section: Introductionmentioning

confidence: 99%

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On the standard model group in F-theory

Choi

2014

Eur. Phys. J. C

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We analyze the standard model gauge group SU (3) × SU (2) × U (1) constructed in F-theory. The nonAbelian part SU (3) × SU (2) is described by a surface singularity of Kodaira type. Blow-up analysis shows that the nonAbelian part is distinguished from the naïve product of SU (3) and SU (2), but that it should be a rank three group along the chain of E n groups, because it has non-generic gauge symmetry enhancement structure responsible for desirable matter curves. The Abelian part U (1) is constructed from a globally valid two-form with the desired gauge quantum numbers, using a similar method to the decomposition (factorization) method of the spectral cover. This technique makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU (5) is achieved, without requiring a threshold correction from the flux along the hypercharge direction.

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Section: Matter Curves For (31)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the standard model group in F-theory

Choi

2014

Eur. Phys. J. C

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“…In presence of such fluxes, the chiral index of matter in representation R localised on matter curve C R ⊂ B is given by the topological intersection number [49,50,52,[136][137][138][139][140] …”

Section: Fluxes and Chiral Spectrummentioning

confidence: 99%

“…This problem is beautifully solved in F-theory models, where such a coupling arises at a non-perturbative point of E 6 enhancement [5][6][7][8]. Such enhancement points signal that the brane configuration is not smoothly connected in moduli space to a well-defined Type IIB limit [43,44] and one should think of the matter states as arising from multi-pronged [p, q]-strings, which are perturbatively absent. Equivalently, the underlying reason for existence of a 10 10 5 coupling in F-theory is that the structure of U (1) gauge symmetries in F-theory can be much more general than in the subclass of perturbative Type IIB models.…”

Section: Introductionmentioning

confidence: 99%

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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“…Such a singularity is a serious problem, especially for GUT model building, as it makes the theory at weak coupling ill-defined for any kind of computation. These conifold singularites can be avoided at the cost of working with elliptic fibrations for which the conifold points a 1 = σ = a 2,1 = 0 do not actually occur due to the intersection theory of the base [45]. Such geometries can be algorithmically constructed starting from type IIB, as explained in [36].…”

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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Gauge fluxes in F-theory and type IIB orientifolds

Cited by 75 publications

References 70 publications

On the standard model group in F-theory

On the standard model group in F-theory

Towards the Standard Model in F-theory

Tate form and weak coupling limits in F-theory

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