Instantons on the six-sphere and twistors

Abstract

We consider the six-sphere S6 = G2/SU(3) and its twistor space \documentclass[12pt]{minimal}\begin{document}${\cal Z}= G_2/$\end{document}Z=G2/U(2) associated with the SU(3)-structure on S6. It is shown that a Hermitian Yang-Mills connection (instanton) on a smooth vector bundle over S6 is equivalent to a flat partial connection on a vector bundle over the twistor space \documentclass[12pt]{minimal}\begin{document}${\cal Z}$\end{document}Z. The relation with Tian's tangent instantons on \documentclass[12pt]{minimal}\begin{document}${\mathbb {R}}^7$\end{document}R7 and their twistor description are briefly discussed.