N=8 Supergravity coupled to E8xE8 N=4 Super Yang-Mills unified in 19 Dimensions?

N=8 Supergravity coupled to E8xE8 N=4 Super Yang-Mills unified in 19 Dimensions?


Pure N=8 supergravity can be derived from a compactification of an 11 dimensional action. The massless(?) sector of Heterotic String Theory contains 256 + 248x2x16 = 213 particles. This suggests that it could be the compactification of a higher dimension action in 19 dimensions. It should be related to a 16 dimensional lattice. Only up to 11D has group structure.

fermion = (D-3)x2(D-3)/2
graviton = (D-2)(D-1)/2-1
antisymmetric n-tensor (D-2)(D-3)(D-4)..(D-n-1)/n!


11D: graviton (44) + antisymmetric-3-tensor(84) + fermion (128)  = 28 components.

(Root vectors of E8 240 roots, 16 less)

19D: graviton (152) + 232 x vector(17)+ fermion (4096) = 213 components. (136, 680, 2380, 6188)

(Root vectors of 16D lattice...? E8xE8? D16? (too small) Coexter? ~ 8160 roots? 32 less? 4320 densest in 16 dimensions?)

27D: 196608 components.

(Root vectors of Leech lattice 196560 components, 48 less)

232 = O(22) x U(1) = 231 + 1
or SU(15) x SU(3) = 224+8
or E7 x SU(10) =133+99 (11D Supergravity has E7 symmetry).

Interestingly a 27D Supergravity action should have 48 more components than there are root vectors in the Leech Lattice. Is this just a coincidence?
We know that wrapping 26D string theory on the 24D Leech Lattice gives has symmetries relating to the Monster Group.
It's all connected, but the connections are not always obvious.

It implies that there is some intermediate string theory in 18 dimensions with some interesting properties.






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