Self-dual gauge fields in eight dimensions

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 (Latin small letter esh sign)M(F, F)2 ? ?M P12 on a compact 8-manifold M where p1 is the first Pontrjagin class of the SO(n) Yang-Mills bundle. Self-dual fields realise the lower bound.