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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.17119 |
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Table of Contents:
- We construct and classify $SU(3)$-invariant primitive Hermitian Yang-Mills connections and $Sp(2)$-instantons with gauge groups $S = S^1$ and $S = SO(3)$ over the Calabi manifold $X = T^*CP^2$, the unique non-flat, complete, cohomogeneity-one hyperkahler 8-manifold. Moreover, in the case of $S = S^1$, we also classify the $SU(3)$-invariant $Spin(7)$-instantons over $X$ in the following sense. Letting $Φ_I$, $Φ_J$, $Φ_K$ denote the $Spin(7)$-structures on $X$ induced from the complex structures $I$, $J$, $K$ in the hyperkahler triple, we prove that on each invariant $S^1$-bundle $\widetilde{E}_k \to X$, $k \in \mathbb{Z}$, the space of invariant $Spin(7)$-instantons with respect to $Φ_L$ forms a one-parameter family modulo gauge. Moreover, every pair of one-parameter families of $Φ_I$-, $Φ_J$-, and $Φ_K$-$Spin(7)$-instantons intersects only at the unique invariant $Sp(2)$-instanton on $\widetilde{E}_k$, which is non-flat when $k \neq 0$.