On the Solution and Ellipticity Properties of the Self-duality equations of Corrigan et al in Eight Dimensions

Ayse Humeyra Bilge

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arXiv · hep-th/9604083

On the Solution and Ellipticity Properties of the Self-duality equations of Corrigan et al in Eight Dimensions

Ayse Humeyra Bilge

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Abstract

We show that the two sets of self-dual Yang-Mills equations in 8-dimensions proposed in (E.Corrigan, C.Devchand, D.B.Fairlie and J.Nuyts, {\it Nuclear Physics} {\bf B214}, 452-464, (1983)) form respectively elliptic and overdetermined elliptic systems under the Coulomb gauge condition. In the overdetermined case, the Yang-Mills fields can depend at most on $N$ arbitrary constants, where $N$ is the dimension of the gauge group. We describe a subvariety ${\cal P}_8 $ of the skew-symmetric $8\times 8$ matrices by an eigenvalue criterion and we show that the solutions of the elliptic equations of Corrigan et al. are among the maximal linear submanifolds of ${\cal P}_8$. We propose an eight order action for which the elliptic set is a maximum.

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Ayse Humeyra Bilge. 1996-04-16. On the Solution and Ellipticity Properties of the Self-duality equations of Corrigan et al in Eight Dimensions. https://arxiv.org/abs/hep-th/9604083

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