Abstract
We examine a family of finite energySO(3) Yang-Mills connections overS 4, indexed by two real parameters. This family includes both smooth connections (when both parameters are odd integers), and connections with a holonomy singularity around 1 or 2 copies ofRP 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.
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Communicated by S.-T. Yau
This work was partially supported by an NSF Mathematical Sciences Postdoctoral Fellowship
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Sadun, L. A symmetric family of Yang-Mills fields. Commun.Math. Phys. 163, 257–291 (1994). https://doi.org/10.1007/BF02102009
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DOI: https://doi.org/10.1007/BF02102009