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Gauge theory on $T^*CP^2$: explicit Sp(2)-instantons, HYM connections, and Spin(7)-instantons
We construct and classify $SU(3)$-invariant $Sp(2)$-instantons with gauge groups $S = S^1$ and $S = SO(3)$ over the Calabi manifold $X = T^*CP^2$, the unique non-flat, complete, irreducible hyperkahler $8$-manifold admitting a cohomogeneity-one action by a compact simple Lie group. Moreover, in the
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