Representations Of E6 Research Articles

Dark matter in E6 Grand unification

We discuss fermionic dark matter in non-supersymmetric E6 Grand Unification. The fundamental representation of E6 contains, in addition to the standard model fermions, exotic fermions and we argue that one of them is a viable, interesting dark matter candidate. Its stability is guaranteed by a discrete remnant symmetry, which is an unbroken subgroup of the E6 gauge symmetry. We compute the symmetry breaking scales and the effect of possible threshold corrections by solving the renormalization group equations numerically after imposing gauge coupling unification. Since the Yukawa couplings of the exotic and the standard model fermions have a common origin, the mass of the dark matter particles is constrained. We find a mass range of 3 · 109 GeV ≲ mDM ≲ 1 · 1013 GeV for our E6 dark matter candidate, which is within the reach of next-generation direct detection experiments.

Vectorlike particles, Z′ and Yukawa unification in F-theory inspired E6

We explore the low energy implications of an F-theory inspired E6 model whose breaking yields, in addition to the MSSM gauge symmetry, a Z′ gauge boson associated with a U(1) symmetry broken at the TeV scale. The zero mode spectrum of the effective low energy theory is derived from the decomposition of the 27 and 27‾ representations of E6 and we parametrise their multiplicities in terms of a minimum number of flux parameters. We perform a two-loop renormalisation group analysis of the gauge and Yukawa couplings of the effective theory model and estimate lower bounds on the new vectorlike particles predicted in the model. We compute the third generation Yukawa couplings in an F-theory context assuming an E8 point of enhancement and express our results in terms of the local flux densities associated with the gauge symmetry breaking. We find that their values are compatible with the ones computed by the renormalisation group equations, and we identify points in the parameter space of the flux densities where the t−b−τ Yukawa couplings unify.

Localized modes in type II and heterotic singular Calabi-Yau conformal field theories

We consider type II and heterotic string compactifications on an isolated singularity in the noncompact Gepner model approach. The conifold-type ADE noncompact Calabi-Yau threefolds, as well as the ALE twofolds, are modeled by a tensor product of the SL(2,R)/U(1) Kazama-Suzuki model and an N=2 minimal model. Based on the string partition functions on these internal Calabi-Yaus previously obtained by Eguchi and Sugawara, we construct new modular invariant, space-time supersymmetric partition functions for both type II and heterotic string theories, where the GSO projection is performed before the continuous and discrete state contributions are separated. We investigate in detail the massless spectra of the localized modes. In particular, we propose an interesting three generation model, in which each flavor is in the 27+1 representation of E6 and localized on a four-dimensional space-time residing at the tip of the cigar.

LOCALIZED MODES IN SINGULAR CALABI-YAU CONFORMAL FIELD THEORIES

We construct spacetime supersymmetric, modular invariant partition functions for type II and heterotic strings on the conifold-type singularities such that they include contributions coming from the discrete-series representations of SL(2, R). In particular for the E8 × E8 heterotic case, they are in the 27 representation of E6 and localized on a four-dimensional "brane" at the tip of the cigar geometry.

A singular representation of 𝐸₆

Algebraic properties of a singular representation of E 6 {{\mathbf {E}}_6} are studied. This representation has the Joseph ideal as its annihilator and it remains irreducible when restricted to F 4 {{\mathbf {F}}_4} .

On the intersections of A1subgroups in the exceptional simple Lie groups E6, E7and E8

The authors determine reductions of irreducible representations of E6, E7 and E8 according to the chain of subgroups EkA1Tk, k=6, 7, 8, for all A1 subgroups of Ek. Here A1 is either SU(2) or O(3) and T6, T7, T8 are respectively the tetrahedral, octahedral and icosahedral groups. The result is the list of coinciding branching rules for EkTk proceeding via different subgroups A1.

Yet more versions of d=11 supergravity

Extending previous results, the authors construct two further versions of d=11 supergravity. The transformation laws are given in a form where the SO(1,10) local Lorentz group is replaced by SO(1,4)*USp(8) and SO(1,5)*(SO(5)*SO(5)), respectively. The spinless fields are assigned to the corresponding representations of E6(+6) and E5(+5).

PRODUCTION AND DECAYS OF EXTRA GAUGE BOSONS IN A LEFT-RIGHT E6 SUPERSTRING MODEL

We examine the production and decays of extra gauge bosons Z2 and WR in a recently proposed left-right E6 superstring model with alternative assignments of the fermions in the 27 representation of E6. We find that either [Formula: see text] or [Formula: see text] decay modes may have a branching fraction as high as 6% and 13%, respectively. The bosonic decays of the Z2 are similar to those found in the minimal rank 5 E6 superstring model, except for a possible new [Formula: see text] mode. Allowed regions of Z2 mass versus the Z, Z′ mixing are determined from neutral current data.

Supergrand exceptional unification and quark-lepton constituents

Supersymmetric gauge multiplets (1,2), whether based on simple (_~ = 1) or extended (N > 1) sypersymmetries, associate fermions in the adjoint representation of the gauge group as supersymmetric partners to the vector gauge fields. Supporting the possibility that matter and gauge fields may be supersymmetrically unified at very high energies, we would like to examine whether the presently known quark-lepton SU 5 or S01o multiplets (3) can be accommodated among these gauge fermions. The S U 5 scheme of unification describes the chiral fields of each generation of quarks and leptons in a reducible representation 15 ~ 10 ~-7, while the S01o scheme includes these in the irreducible spinor representation 16 which decomposes like 16 = 10 § 5 ~ 1 with respect to SUs; the extra singlet being the right-chiral neutrino component. Now it is clear that the adjoint representation of SU~>5 cannot accommodate the antisymmetrie second-rank SU5 tensor 10. The adjoint representation of S0~>1o cannot contain spinor representations in its decomposition with respect to subgroups. Hence it cannot contain the 16 of SOlo or the 10 of SUs. The adjoint representat ion fo SP2~v~SU, v• U1 decomposes with respect to SU~ as (,4-~ 1-}{2} ~{2}*), where ,4 is the adjoint representation of SUN and {2} (and {2}*) is a symmetric secondrank SU~ tensor (and complex conjugate). Hence it cannot accommodate 10 of SU 5. Thus we are left with the five exceptional groups (~). Certainly G~ and F 4 cannot contain SU 5 or S01o. Now we shall present the decompositions of the adjoint representations of E6, E 7 and E s.