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

Gabor Etesi
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Abstract

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 $S^6$. 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 ${\rm G}_2$.

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Gabor Etesi. 2015-09-08. Complex structure on the six dimensional sphere from a spontaneous symmetry breaking. https://doi.org/10.1063/1.4918540%2C%2010.1063%2F1.4930560

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