Instantons on the six-sphere and twistors

TL;DR

This paper explores the relationship between Hermitian Yang-Mills instantons on the six-sphere and flat partial connections on its twistor space, linking these to Tian's tangent instantons and their twistor descriptions.

Contribution

It establishes an equivalence between instantons on S^6 and flat partial connections on its twistor space, providing new insights into their geometric structure.

Findings

Hermitian Yang-Mills instantons correspond to flat partial connections on twistor space.

The relation between S^6$ instantons and Tian's tangent instantons is clarified.

Twistor description offers a new perspective on instanton solutions.

Abstract

We consider the six-sphere S^6=G_2/SU(3) and its twistor space Z=G_2/U(2) associated with the SU(3)-structure on S^6. It is shown that a Hermitian Yang-Mills connection (instanton) on a smooth vector bundle over S^6 is equivalent to a flat partial connection on a vector bundle over the twistor space Z. The relation with Tian's tangent instantons on R^7 and their twistor description are briefly discussed.