Complex structure on the six dimensional sphere from a spontaneous symmetry breaking

Existence of a complex structure on the 6 dimensional sphere is proved in this paper. The proof is based on re-interpreting a hypothetical complex structure as a classical ground state of a Yang–Mills–Higgs-like theory on S6. This classical vacuum solution is then constructed by Fourier expansion (dimensional reduction) from the obvious one of a similar theory on the 14 dimensional exceptional compact Lie group G2.