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arXiv · 2110.05439

$SU(2)^2$-invariant gauge theory on asymptotically conical Calabi-Yau 3-folds

Jakob Stein
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Abstract

We give a complete description of the behaviour of Calabi-Yau instantons and monopoles with an $SU(2)^2$-symmetry, on Calabi-Yau 3-folds with asymptotically conical geometry and $SU(2)^2$ acting with co-homogeneity one. We consider gauge theory on the smoothing and the small resolution of the conifold, and on the canonical bundle of $\mathbb{CP}^1 \times \mathbb{CP}^1$, with their known asymptotically conical co-homogeneity one Calabi-Yau metrics, and find new one-parameter families of invariant instantons. We also entirely classify the relevant moduli-spaces of instantons and monopoles satisfying a natural curvature decay condition, and show that the expected bubbling phenomena occur in these families of instantons.

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Jakob Stein. 2023-03-14. $SU(2)^2$-invariant gauge theory on asymptotically conical Calabi-Yau 3-folds. https://doi.org/10.1007/s12220-022-01168-8

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