Gauge theory on $T^{\ast }C{P}^2$: explicit Sp(2)-instantons, HYM connections, and Spin(7)-instantons

Izar Alonso, Jesse Madnick, Emily Autumn Windes

We construct and classify $SU(3)$-invariant $Sp(2)$-instantons with gauge groups $S=S^1$ and $S=SO(3)$ over the Calabi manifold $X=T^{\ast }C{P}^2$, the unique non-flat, complete, ir…