Spin(7) Instantons and Hermitian Yang-Mills Connections for the Stenzel Metric

We use the highly symmetric Stenzel Calabi-Yau structure on T-star S-4 as a testing ground for the relationship between the Spin(7) instanton and Hermitian-Yang-Mills (HYM) equations. We reduce both problems to tractable ODEs and look for invariant solutions. In the abelian case, we establish local equivalence and prove a global nonexistence result. We analyze the nonabelian equations with structure group SO(3) and construct the moduli space of invariant Spin(7) instantons in this setting. This is comprised of two 1-parameter families-one of them explicit-of irreducible Spin(7) instantons. Each carries a unique HYM connection. We thus negatively resolve the question regarding the equivalence of the two gauge theoretic PDEs. The HYM connections play a role in the compactification of this moduli space, exhibiting a removable singularity phenomenon that we aim to further examine in future work.