Breaking GUT Groups in F-Theory

Donagi, Ron; Wijnholt, Martijn

doi:10.48550/arxiv.0808.2223

Cited by 158 publications

(520 citation statements)

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“…9 Here, we do not pay attention to a possible factor 2 associated with orientifold projection. 10 A beautiful study of GUT scale threshold corrections is found in [36]. See also [39,35], [40] and [41].…”

Section: Estimation Of the Majorana Mass Scalementioning

confidence: 96%

“…6 Therefore, the Majorana masses of complex structure moduli (and hence of right-handed neutrinos) are in the energy scale just below Kaluza-Klein scale 1/R 6 , as we consider in a regime where R 6 is larger than the string length l s . The SU(5) GUT symmetry can be broken by introducing U(1) Y flux on the locus of A 4 ≃ SU(5) singularity [10,35,36], 7 in which case, the GUT scale is identified with the Kaluza-Klein scale. Thus, the Majorana masses of the right-handed neutrinos are typically somewhat below the GUT scale.…”

Section: Estimation Of the Majorana Mass Scalementioning

confidence: 99%

“…Although we have so far only talked about the vacuum configuration ϕ P (a 0 ) = ϕ P in (32,36), the same process defines a set of corresponding ϕ P (a) for any deformed complex structure moduli a = δa + a 0 (where δa need not be infinitesimal). Because of the procedure above, the resulting ϕ P (a)'s determines a field configuration ϕ(a)-a (2,0)-form on S-taking its value in the Cartan part of the structure group G ′ .…”

Section: Moduli (Massless) Fluctuationsmentioning

confidence: 99%

“…Since all the ϕ eigenvalues (e.g. in (32,36)) in g ′ are different generically, all the 2-cycles for the roots in G ′ -adj. are blown up, and the corresponding fields become massive.…”

Section: Moduli (Massless) Fluctuationsmentioning

confidence: 99%

“…No conditions are imposed on other sections such as A r 's in (62) [1,36]. Under this choice of complex structure of X, the defining equation of the c( 5) matter curve of SU( 5) GUT models vanish identically on S:…”

Section: Su(6) Scenariomentioning

confidence: 99%

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Right-handed neutrinos in F-theory compactifications

2009

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F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-handed neutrinos are in F-theory compactifications and how their Majorana mass terms are generated together with developing a theoretical framework where effective Yukawa couplings involving both SU(5)-neutral and charged fields can be calculated. We find that the complex structure moduli chiral multiplets of F-theory compactifications are good candidates to be right-handed neutrinos, and that their Majorana masses are automatically generated in flux compactifications. The mass scale is predicted to be somewhat below the GUT scale, which is in nice agreement with the ∆m 2 of the atmospheric neutrino oscillation through the see-saw mechanism. We also discuss various scenarios of solving the dimension-4 proton decay problem in supersymmetric F-theory compactifications, along with considering the consequences of those scenarios in the nature of right-handed neutrinos.

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Section: Estimation Of the Majorana Mass Scalementioning

confidence: 96%

Section: Estimation Of the Majorana Mass Scalementioning

confidence: 99%

Section: Moduli (Massless) Fluctuationsmentioning

confidence: 99%

“…Since all the ϕ eigenvalues (e.g. in (32,36)) in g ′ are different generically, all the 2-cycles for the roots in G ′ -adj. are blown up, and the corresponding fields become massive.…”

Section: Moduli (Massless) Fluctuationsmentioning

confidence: 99%

Section: Su(6) Scenariomentioning

confidence: 99%

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Right-handed neutrinos in F-theory compactifications

2009

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On the computation of non‐perturbative effective potentials in the string theory landscape – IIB/F‐theory perspective –

Cvetič

García-Etxebarria

Halverson

2011

Fortschritte der Physik

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Abstract:We discuss a number of issues arising when computing non-perturbative effects systematically across the string theory landscape. In particular, we cast the study of fairly generic physical properties into the language of computability/number theory and show that this amounts to solving systems of diophantine equations. In analogy to the negative solution to Hilbert's 10th problem, we argue that in such systematic studies there may be no algorithm by which one can determine all physical effects. We take large volume type IIB compactifications as an example, with the physical property of interest being the low-energy non-perturbative F-terms of a generic compactification. A similar analysis is expected to hold for other kinds of string vacua, and we discuss in particular the extension of our ideas to F-theory. While these results imply that it may not be possible to systematically answer certain physical questions about generic type IIB compactifications, we identify particular Calabi-Yau manifolds in which the diophantine equations become linear, and thus can be systematically solved.As part of the study of the required systematics of F-terms, we develop technology for computing Z 2 equivariant line bundle cohomology on toric varieties, which determines the presence of particular instanton zero modes via the Koszul complex. This is of general interest for realistic IIB model building on complete intersections in toric ambient spaces.

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Yukawa couplings in F‐theory SU(5)

Leontaris

2011

Fortschritte der Physik

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The fermion mass textures are discussed in the context of F-theory SU (5) GUT. The tree-level up, down and charged lepton Yukawa couplings are computed in terms of the integrals of overlapping wavefunctions at the intersection points of three matter curves. All remaining entries in the fermion mass matrices can also be reliably estimated from higher order non-renormalizable Yukawa couplings mediated by heavy string modes and/or Kaluza-Klein states. Wavefunction overlapping IntegralsIn F-theory GUTs the trilinear Yukawa couplings are realised at the intersections of three matter curves where the zero-modes of two fermion fields and a Higgs boson reside. The structure of the zero-mode wavefunctions is found by solving the corresponding differential equations emerging from the twisted eight-dimensional Yang-Mills action [1]. The third generation up, down and charged lepton mass matrices are then computed in terms of the integrals of overlapping wavefunctions at the intersection point of three matter curves [2]. Furthermore, assuming that higher order non-renormalizable Yukawa couplings are generated through mediation of heavy string modes and/or Kaluza-Klein states, the calculation of all entries in the fermion mass matrices can be reduced to a similar computation. In fact, in this approach a rigorous and consistent application of the described method can be developed [3], by computing the relevant integrals for the NR-terms involving zero-mode and massive KK-mode overlapping wavefuctions. The complete calculation of all 3 × 3 Yukawa entries for the entire charged fermion mass spectrum shows that all the Yukawa coefficients are found within a reasonable range of values (≤ O(1)) while the predicted fermion mass eigenvalues and Cabibbo Kobayashi Maskawa (CKM)-mixing in accordance to the experimental expectations. The tree-level Yukawa couplings are computed by the wavefunction overlap integralswhere S is the compact 4-d manifold wrapped by 7-brane surface associated to the gauge symmetry (here SU (5)). To compute the integral we use our knowledge of the wavefunctions' profile close to the intersection point. For localized solutions the zero-mode equations lead to a Gaussian profile of the general formwhere m is a mass parameter related to a background Higgs vacuum expectation value (vev) Φ , z 1,2 complex coordinates on S and q i are U (1) charges (q = q 2 1 + q 2 2 ). To make a reliable computation of

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Breaking GUT Groups in F-Theory

Cited by 158 publications

References 0 publications

Right-handed neutrinos in F-theory compactifications

Right-handed neutrinos in F-theory compactifications

On the computation of non‐perturbative effective potentials in the string theory landscape – IIB/F‐theory perspective –

Yukawa couplings in F‐theory SU(5)

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