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 R(8), integral(M)(F, F)(2) greater than or equal to k integral(M) p(1)(2), where p(1) is the first Pontryagin class of the SO(n) Yang-Mills bundle, and k is a constant. Strongly self-dual Yang-Mills fields realise the lower bound.