Solutions to Yang—Mills equations that are not self-dual

AUTOR(ES)
RESUMO

The Yang—Mills functional for connections on principle SU(2) bundles over S4 is studied. Critical points of the functional satisfy a system of second-order partial differential equations, the Yang—Mills equations. If, in particular, the critical point is a minimum, it satisfies a first-order system, the self-dual or anti-self-dual equations. Here, we exhibit an infinite number of finite-action nonminimal unstable critical points. They are obtained by constructing a topologically nontrivial loop of connections to which min—max theory is applied. The construction exploits the fundamental relationship between certain invariant instantons on S4 and magnetic monopoles on H3. This result settles a question in gauge field theory that has been open for many years.

Documentos Relacionados