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Instantons on the six-sphere and twistors. (English) Zbl 1278.81129
Summary: We consider the six-sphere \(S^6 = G_2/{\text SU}(3)\) and its twistor space \({\mathcal Z}= G_2/{\text U}(2)\) 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 \({\mathcal Z}\). The relation with Tian’s tangent instantons on \({\mathbb{R}}^7\) and their twistor description are briefly discussed.
©2012 American Institute of Physics

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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