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Chirality in an $E_8$ model of elementary particles
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abstract
We show how chirality emerges naturally from an embedding of the standard model of particle physics into $E_{8(-24)}$. The well-known argument that there is no chiral theory of fundamental physics in $E_8$ is avoided by implementing chirality not as a property of the complexified Lorentz group, but as a property of the complex representations of the real Lorentz group, combined with a real scalar. This avoids the problems of complexification, and ensures that the model is completely contained in the real Lie group.
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Embeddings of the Standard Model in $E_8$
A modified E8 model puts the Standard Model inside the so(7,3) subalgebra with compact SU(3), and uses particle coordinates in four dimensions to compute several mixing angles and mass relations.
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