Orbifold Grand Unified Theories Research Articles

Searching for realistic 4d string models with a Pati–Salam symmetry. Orbifold grand unified theories from heterotic string compactification on a [formula omitted] orbifold

Motivated by orbifold grand unified theories, we construct a class of three-family Pati–Salam models in a Z 6 Abelian symmetric orbifold with two discrete Wilson lines. These models have marked differences from previously-constructed three-family models in prime-order orbifolds. In the limit where one of the six compactified dimensions (which lies in a Z 2 sub-orbifold) is large compared to the string length scale, our models reproduce the supersymmetry and gauge symmetry breaking pattern of 5d orbifold grand unified theories on an S 1 / Z 2 orbicircle. We find a horizontal 2 + 1 splitting in the chiral matter spectra—2 families of matter are localized on the Z 2 orbifold fixed points, and 1 family propagates in the 5d bulk—and identify them as the first-two and third families. Remarkably, the first two families enjoy a non-Abelian dihedral D 4 family symmetry, due to the geometric setup of the compactified space. In all our models there are always some color triplets, i.e., ( 6 , 1 , 1 ) representations of the Pati–Salam group, survive orbifold projections. They could be utilized to spontaneously break the Pati–Salam symmetry to that of the Standard Model. One model, with a 5d E 6 symmetry, may give rise to interesting low energy phenomenology. We study gauge coupling unification, allowed Yukawa couplings and some of their phenomenological consequences. The E 6 model has a renormalizable Yukawa coupling only for the third family. It predicts a gauge-Yukawa unification relation at the 5d compactification scale, and is capable of generating reasonable quark/lepton masses and mixings. Potential problems are also addressed, they may point to the direction for refining our models.

Softening the supersymmetric flavor problem in orbifold grand unified theories

The infra-red attractive force of the bulk gauge interactions is applied to soften the supersymmetric flavor problem in the orbifold SU(5) GUT of Kawamura. Then this force aligns in the infra-red regime the soft supersymmetry breaking terms out of their anarchical disorder at a fundamental scale, in such a way that flavor-changing neutral currents as well as dangerous CP-violating phases are suppressed at low energies. It is found that this dynamical alignment is sufficiently good compared with the current experimental bounds, as long as the diagonalization matrices of the Yukawa couplings are CKM-like.

Constructing 5d orbifold grand unified theories from heterotic strings

A three-generation Pati–Salam model is constructed by compactifying the heterotic string on a particular T6/Z6 Abelian symmetric orbifold with two discrete Wilson lines. The compactified space is taken to be the Lie algebra lattice G2⊕SU(3)⊕SO(4). When one dimension of the SO(4) lattice is large compared to the string scale, this model reproduces many features of a 5d SO(10) grand unified theory compactified on an S1/Z2 orbifold. (Of course, with two large extra dimensions we can obtain a 6d SO(10) grand unified theory.) We identify the orbifold parities and other ingredients of the orbifold grand unified theories in the string model. Our construction provides a UV completion of orbifold grand unified theories, and gives new insights into both field theoretical and string theoretical constructions.

Constructing 5d orbifold grand unified theories from heterotic strings

Constructing 5d orbifold grand unified theories from heterotic strings

The flavour hierarchy and see-saw neutrinos from bulk masses in 5d orbifold GUTs

In supersymmetric grand unified theories (GUTs) based on S 1/( Z 2× Z′ 2) orbifold constructions in 5 dimensions, Standard Model (SM) matter and Higgs fields can be realized in terms of 5d hypermultiplets. These hypermultiplets can naturally have large bulk masses, leading to a localization of the zero modes at one of the two branes or to an exponential suppression of the mass of the lowest-lying non-zero mode. We demonstrate that these dynamical features allow for the construction of an elegant 3-generation SU(5) model in 5 dimensions that explains all the hierarchies between fermion masses and CKM matrix elements in geometrical terms. Moreover, if U(1) χ (where SU(5)×U(1) χ ⊂SO(10)) is gauged in the bulk, but broken by the orbifold action at the SM brane, the right-handed neutrino mass scale is naturally suppressed relative to M GUT. Together with our construction in the charged fermion sector this leads, via the usual see-saw mechanism, to a realistic light neutrino mass scale and large neutrino mixing angles.

A minimal S1/( Z2× Z2′) orbifold GUT

We investigate supersymmetric SU(5) grand unified theories (GUTs) realized in 5 space time dimensions and broken down to the MSSM by SU(5)-violating boundary conditions on a S 1/( Z 2× Z 2′) orbifold with two 3-branes. The doublet-triplet splitting problem is entirely avoided by locating the MSSM Higgs doublets on the brane on which SU(5) is not a good symmetry. An extremely simple model is then described in which the MSSM matter is also located on this SU(5)-violating brane. Although this model does not unify the MSSM matter within SU(5) multiplets, it explains gauge coupling unification. A second model with MSSM matter in the SU(5)-symmetric bulk preserves both the SU(5) explanation of fermion quantum numbers as well as gauge-coupling unification. Both models naturally avoid problematic SU(5) predictions for the Yukawa couplings of the first two generations and are consistent with proton decay constraints. We analyse the running of gauge couplings above the compactification scale in terms of a 5d effective action and derive the implications for the values of compactification scale, unification scale and of the scale at which the bulk gauge theory becomes strongly coupled.