The exceptional eightfold way to a possible Higgs field

The exceptional Lie symmetry groups are intimately connected to octions and build various forms of hierarchies. We show that these hierarchies have invariant total dimensions equal to a few well known key numbers of high energy elementary particle-like states. More specifically, the total dimension of E8, E7, E6, E5 and E4 is equal to N = 528 of Witten’s p = 5 Brane theory. Adding the standard model, then one can infer the possibility of a missing eight dimensional field akin to the Higgs field. The present short paper considers the various ramifications of the interplay between the exceptional Lie symmetry groups hierarchy and particle physics of the standard model.