By A. Garrett Lisi
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Additional info for An Exceptionally Simple Theory of Everything
The fermions fit together perfectly in chiral representations under graviweak so(7, 1), and the frame-Higgs has all the correct interactions. This frame-Higgs naturally gets a φ4 potential and produces a positive cosmological constant. Finally, and most impressively, the fit of all fields of the standard model and gravity to E8 is very tight. The structure of E8 determines exactly the spinor multiplet structure of the known fermions. There are also aspects of this theory that are poorly understood.
Quantum gravity and the standard model,” hep-th/0603022. G. Kac, Infinite dimensional Lie algebras, Cambridge University Press (1990).
There are also aspects of this theory that are poorly understood. The relationship between fermion generations and triality is suggested by the structure of E8 but is not perfectly clear — a better description may follow from an improved understanding of the new w + xΦ fields and their relation to ω + eφ. This relationship may also shed light on how and why nature has chosen a non-compact form, E IX, of E8. Currently, the symmetry breaking and action for the theory are chosen by hand to match the standard model — this needs a mathematical justification.
An Exceptionally Simple Theory of Everything by A. Garrett Lisi