Facundo Camano, University of Waterloo
Dimensional Reduction of S^1-Invariant Instantons on the Multi-Taub-NUT
In this talk I will discuss the dimensional reduction of S^1-invariant instantons on the multi-Taub-NUT space to singular monopolos on R^3. I will first introduce the multi-Taub-NUT space, followed up by a discussion on S^1-equivariant principal bundles. Next, I will go over the natural decomposition of S^1-invariant connections into horizontal and vertical pieces, and then show how the self-duality equation reduces to the Bogomolny equation under said decomposition. I will then show how the smoothness of the instanton over the NUT points determines the asymptotic conditions for the singular monopole. Finally, I will go over the reverse construction: starting with a singular monopole on R^3 and building up to an S^1-invariant instanton on the multi-Taub-NUT space.
MC 5403