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

TL;DR

This paper classifies and describes the behavior of $SU(2)^2$-invariant gauge instantons and monopoles on asymptotically conical Calabi-Yau 3-folds with cohomogeneity-one symmetry, revealing new families and bubbling phenomena.

Contribution

It provides a complete classification of invariant instantons and monopoles on specific Calabi-Yau 3-folds with cohomogeneity-one symmetry, including new one-parameter families.

Findings

Found new one-parameter families of invariant instantons.

Classified moduli spaces of instantons and monopoles.

Demonstrated bubbling phenomena in these families.

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.