A symmetric family of Yang-Mills fields. (English) Zbl 0801.53015
Summary: We examine a family of finite energy SO(3) Yang-Mills connections over \(S^ 4\), indexed by two real parameters. This family included both smooth connections (when both parameters are odd integers), and connections with a holonomy singularity around 1 or 2 copies of \(RP^ 2\). These singular YM connections interpolate between the smooth solutions. Depending on the parameters, the curvature may be self-dual, anti-self-dual, or neither. For the (anti-) self-dual connections, we compute the formal dimension of the moduli space. For the non-self-dual connections we examine the second variation of the Yang-Mills functional, and count the negative and zero eigenvalues. Each component of the non- self-dual moduli space appears to consist only of conformal copies of a single solution.
MSC:
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 58E15 | Variational problems concerning extremal problems in several variables; Yang-Mills functionals |
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