Dark Matter from 𝐸8⊃𝐸6×SU(3)𝐹 Unification: A Higgs Portal Mechanism with Gravitational Compatibility

We present a quantitative dark matter model within the 𝐸8⊃𝐸6×SU(3)𝐹 unification framework, which incorporates gravity via the noncompact real form 𝐸8(−24). The Standard Model singlet 𝜒=(1,1)0 from the 𝐸627 representation is absolutely stable due to a 𝑍2 remnant symmetry from the 𝐸6→𝑆𝑂(10)×𝑈(1)→SM breaking. In the gravitational embedding, the previously assumed light 𝑍′ boson becomes heavy and decouples; we instead propose a Higgs portal interaction between 𝜒 and the Standard Model Higgs doublet 𝐻 (which also resides in the 27). We derive the mass of 𝜒 from a higher-dimensional operator 1𝑀Pl𝜒2Φ2, which naturally yields 𝑚𝜒≈10 TeV when ⟨Φ⟩∼𝑀GUT. The thermal relic density is computed including Sommerfeld enhancement, giving a prediction for the coupling 𝜆ℎ𝜒=2.0±0.5 for 𝑚𝜒=10 TeV. Direct detection cross sections are predicted to be 𝜎SI≈(4±2)×10−46 cm2, within reach of next-generation experiments (DARWIN, XLZD). This work provides a quantitatively predictive dark matter candidate within the 𝐸8 unification program.