Given that QCD and Electromagnetism do not need complex representation, the usual non-go theorem does not apply, does it?
And in D=9 there are at least two ways of building a compactification manifold having an adequate isometry group:
- We can compactify over the sphere $S^5$ whose symmetry group SO(6) is equal to SU(4), and thus it contains SU(3)xU(1), or
- Or we can compactify over the product $CP^2$ x $S^1$, getting separately SU(3) and U(1).
Has it been done, published, or proposed elsewhere? Which is the fermion content of such construction?