Flipped SU(5) X U(1)_X Models from F-Theory

We discuss F-theory SU(5) GUTs in which some or all of the quark and lepton families are assigned to different curves and family symmetry enforces a leading order rank one structure of the Yukawa matrices. We consider two possibilities for the suppression of baryon and lepton number violation. The first is based on Flipped SU(5) with gauge group SU(5)\times U(1)_\chi \times SU(4)_{\perp} in which U(1)_{\chi} plays the role of a generalised matter parity. We present an example which, after imposing a Z_2 monodromy, has a U(1)_{\perp}^2 family symmetry. Even in the absence of flux, spontaneous breaking of the family symmetry leads to viable quark, charged lepton and neutrino masses and mixing. The second possibility has an R-parity associated with the symmetry of the underlying compactification manifold and the flux. We construct an example of a model with viable masses and mixing angles based on the gauge group SU(5)\times SU(5)_{\perp} with a U(1)_{\perp}^3 family symmetry after imposing a Z_2 monodromy.Comment: Typos corrected. 1 reference added. Version to appear in Nucl. Phys.

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“…The adjoint representation of E 8 then has the SO(10) × SU (4), SU (5) × U (1) χ × SU (4) decomposition given by 248 → (45, 1) + (16, 4) + (16,4)…”

Section: Flipped Su(5) In F-theorymentioning

confidence: 99%

Family symmetries in F-theory GUTs

King¹,

Leontaris²,

Ross³

2010

Nuclear Physics B

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“…As in the case of gauge fields one can absorb the parts proportional to k a by redefinition of the initial gauge coupling. Further, it is anticipated that on appropriate bundle structures such corrections will diminish or be negligible compared to other (from light degrees of freedom or supersymmetry) threshold effects [29]- [32].…”

Section: The Inclusion Of Chiral Mattermentioning

confidence: 99%

Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs

Leontaris

Tracas²,

Tsamis³

2011

Eur. Phys. J. C

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Recent progress in F-theory model building [1][2][3][4][5][6][7][8] 1 has shown that old successful GUTs, including the Georgi-Glashow minimal SU(5), the SO(10) model etc, are naturally realised on the world-volume of non-perturbative seven branes wrapping appropriate compact surfaces. The rather interesting fact in F-theory constructions is that they are defined on a compact elliptically fibered Calabi-Yau complex four dimensional manifold thus the exceptional groups E 6 , E 7 , E 8 , can be naturally incorporated into the theory too [1][2][3]6]. Although exceptional gauge symmetries suffer from several drawbacks when realized in the context of four-dimensional grand unified theories, in the case of F-theory models they are more promising as new possibilities arise for the symmetry breaking mechanisms and the derivation of the desired massless spectrum.Present studies on F-theory model building have been concentrated on three generation -mainly SU (5)-GUT models which fall into the following two distinct categories: those where all three families with the same Standard Model representation content are assigned to a single matter curve [11][12][13][14], and variants [15][16][17][18][19][20][21] where some or all of the quark and lepton families are assigned to different curves. Several of these constructions built up to these days have attempted to give solutions to fundamental GUT problems as is the case of doublet-triplet splitting, the rapid proton decay, the Higgs mixing term, the neutrino sector and other related issues [3,6,10,16,[21][22][23]. To analyse the phenomenological properties one should extract the relevant information from the superpotential which can be readily constructed once a particular assignment of the fermion families and Higgs on the matter curves has been chosen. Of course, dominant rôle on the estimation of such effects is played by the Yukawa couplings, thus the theory's predictive power depends on the calculability of the latter.In F-theory GUTs the trilinear Yukawa couplings are realised at the intersections of three matter curves Σ i , i = 1, 2, 3 where the zero-modes of two fermion fields and a Higgs boson reside. Along these curves the G S symmetry is enhanced G Σ i ⊃ G S ×U (1) i while the corresponding zero modes are charged under the U (1) i . To determine the most general structure of the zero-mode wavefunctions one has to solve their corresponding differential equations of motion emerging from the twisted eight-dimensional Yang-Mills action [2], (see also [14,[24][25][26]). In general, the solutions are found to exhibit the expected gaussian [24,25] profile which falls off exponentially away from the curve while their exact form is specified by a mass scale characterizing the size of the compact space and the particular U (1) i -charge of the relevant zero-mode. The Yukawa couplings of the {33}-entries of the up, down and charged lepton mass matrices are then computed in terms of the integrals of overlapping wavefunctions of the aforementioned form at the intersection point ...

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“…Larger GUT groups than SU (5) have also been considered, such as the F-theory E 6 model of ref [49] where non-Abelian fluxes are introduced to break the symmetry. Flipped SU (5) [13,22,28,50,52] has also been considered, including an attempt using an SU (4) spectral cover [51]. Some examples of SO (10) F-theory models were also considered in [13,32,33].…”

Section: Introductionmentioning

confidence: 99%

Towards a realistic F-theory GUT

Callaghan

King

Leontaris

et al. 2012

J. High Energ. Phys.

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We consider semi-local F-theory GUTs arising from a single E 8 point of local enhancement, leading to simple GUT groups based on E 6 , SO(10) and SU (5) with SU (3), SU (4) and SU (5) spectral covers, respectively. Assuming the minimal Z 2 monodromy, we determine the homology classes and the associated spectra after flux breaking for each case. Our analysis includes the GUT singlets which have hitherto been ignored but which play a crucial role in phenomenology. Using these results we construct an E 6 based model that demonstrates, for the first time, that it is possible to construct a phenomenologically viable model which leads to the MSSM at low energies. The exotics that result from flux breaking all get a large mass when singlet fields acquire vacuum expectation values driven by D-and F-flatness. Due to the underlying GUT symmetry and the U (1)s descending from E 8 , bare baryon-and lepton-number violating terms are forbidden up to and including dimension 5. As a result nucleon decay is naturally suppressed below present bounds. The µ-term is forbidden by the U (1) but is generated at the SUSY breaking scale when a further singlet field acquires a TeV scale vacuum expectation value, driven by the spontaneous breaking of the electroweak symmetry. After including the effect of flux and instanton corrections acceptable quark and charged lepton masses and mixing angles can be obtained. Neutrinos get a mass from the see-saw mechanism through their coupling to singlet neutrinos that acquire large Majorana mass as a result of the monodromy. 1

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Flipped SU(5) X U(1)_X Models from F-Theory

Cited by 24 publications

References 48 publications

Family symmetries in F-theory GUTs

Family symmetries in F-theory GUTs

Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs

Towards a realistic F-theory GUT

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