= Anti-self-dual connection
{title2=$F_A^+=0$}
= ASD connection
{c}
{synonym}
A <unitary connection> $A$ on an oriented Riemannian four-manifold is anti-self-dual when $F_A^+=(F_A+*F_A)/2=0$. Its curvature is covariantly closed by the <Bianchi identity> and solves the <Yang-Mills equations>. With anti-Hermitian matrices and the fundamental trace, $k=c_2(E)[X]=(8\pi^2)^{-1}\int_X\operatorname{Tr}(F_A\wedge F_A)=\|F_A\|_2^2/(8\pi^2)$ for an $SU(2)$ bundle. Thus its charge is nonnegative.
// Destination: geometry-and-topology.bigb
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