Self-Dual Yang-Mills Fields in Eight Dimensions

Abstract

Strongly self-dual Yang-Mills fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fields $F_{\mu \nu }$. We derive a topological bound on ${\mathbf{R}}^8$, ${\int }_M(F,F{)}^2\ge k{\int }_M{p}_1^2$ where $p_1$ is the first Pontrjagin class of the SO(n) Yang-Mills bundle and $k$ is a constant. Strongly self-dual Yang-Mills fields realise the lower bound.

10 pages, Latex, no figures, to appear in Lett. Math. Phys

Cited by in corpus (4)

• Self-Duality in D <= 8-dimensional Euclidean Gravity
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• A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models
• An Explicit Construction of Self-dual 2-forms in Eight Dimensions