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

1996/04/16 by Ayse Humeyra Bilge
Physics and Astronomy · #hep-th

paper · pdf

published as Int.J.Theor.Phys. 35 (1996) 2507-2516 · 10 pages

arxiv created 1996/04/16 · arxiv updated 2009/11/30

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 P₈ of the skew-symmetric 8× 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 P₈. We propose an eight order action for which the elliptic set is a maximum.

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