Abstract
Self-dual gauge fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of F. We derive a new topological bound \int_{M} ( F,F )^2 \geq \int_{M} p_1^2 on a compact 8-manifold M where p_1 is the first Pontrjagin class of the SO(n) Yang-Mills bundle. Self-dual fields realise the lower bound.
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