Interpretation of Yang–Mills instantons in terms of locally conformal geometry

Abstract

BPST instanton and multi-instanton solutions to Yang–Mills equations are studied in the spin–charge separation formalism and in the related conformal gravity formalism. In the former instantons give non-trivial solutions to a gauged Grassmannian model, in the latter the instanton solution describes a locally conformally flat doubly wrapped cigar manifold or a more complicated manifold for multi-instanton solutions.