Abstract
We will show that the Hopf map\(S^{15} \xrightarrow{{S^7 }}S^8\) admits a sourceless, topologically non-trivial gauge field. This result will be cast in the form of a solution to eight dimensional Euclidean Yang-Mills field equations with topological chargeQ=1. This solution is Spin (9) symmetric and leads to a new generalized duality conditionF∧F=±(F∧F)*.
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Communicated by A. Jaffe
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Grossman, B., Kephart, T.W. & Stasheff, J.D. Solutions to Yang-Mills field equations in eight dimensions and the last Hopf map. Commun.Math. Phys. 96, 431–437 (1984). https://doi.org/10.1007/BF01212529
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DOI: https://doi.org/10.1007/BF01212529