Towards the minimal renormalizable supersymmetric E6E_6 model

We find an explicit renormalizable supersymmetric $E_6$ model with all the ingredients for being realistic. It consists of the Higgs sector $351'+\overline{351'}+27+\overline{27}$, which breaks $E_6$ directly to the Standard Model gauge group. Three copies of $27$ dimensional representations then describe the matter sector, while an extra $27+\overline{27}$ pair is needed to successfully split the Standard Model Higgs doublet from the heavy Higgs triplet. We perform the analysis of the vacuum structure and the Yukawa sector of this model, as well as compute contributions to proton decay. Also, we show why some other simpler $E_6$ models fail to be realistic at the renormalizable level.Comment: 36 pages, a new section on proton decay added, new reference, results unchanged. To be published in JHE

Yukawa ratio predictions in non-renormalizable SO(10)\mathrm{SO}(10) GUT models

Since $\mathrm{SO}(10)$ GUTs unify all fermions of the Standard Model plus a right-chiral neutrino in a representation $\mathbf{16}$ per family, they have the potential to be maximally predictive regarding the ratios between the masses (or Yukawa couplings) of different fermion types, i.e.~the up-type quarks, down-type quarks, charged leptons and neutrinos. We analyze the predictivity of classes of $\mathrm{SO}(10)$ (SUSY) GUT models for the fermion mass ratios, where the Yukawa couplings for each family are dominated by a single effective GUT operator of the schematic form $\mathbf{16}^2\cdot\mathbf{45}^n\cdot\mathbf{210}^{m}\cdot\mathbf{H}$, for $\mathbf{H}\in\{\mathbf{10},\mathbf{120},\mathbf{\overline{126}}\}$. This extends previous works to general vacuum expectation value directions for GUT-scale VEVs and to larger Higgs representations. In addition, we show that the location of the MSSM Higgses in the space of all doublets is a crucial aspect to consider. We discuss highly predictive cases and illustrate the predictive power in toy models consisting of masses for the 3rd and 2nd fermion family.Comment: 47 pages, 12 figures, 12 table

Trinification from E 6 symmetry breaking

Abstract In the context of E6 Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either SU(3) × SU(3) × SU(3) (trinification) or SU(6) × SU(2). The more common choices of SU(5) and SO(10) GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank 2 tensor) representation 650 of E6 in the scalar sector is the minimal and likely only reasonable possibility to obtain one of the novel intermediate stages. We analyze the renormalizable scalar potential of a single copy of the 650 and find vacuum solutions that support regularly embedded subgroups SU(3) × SU(3) × SU(3), SU(6) × SU(2), and SO(10) × U(1), as well as specially embedded subgroups F4 and SU(3) × G2 that do not contain the SM gauge symmetry. We show that for a suitable choice of parameters, each of the regular cases can be obtained as the lowest among the analyzed minima in the potential