Monopoles on Sasakian Three-folds

TL;DR

This paper studies monopoles with Dirac singularities on quasiregular Sasakian three-folds, establishing a correspondence with holomorphic twisted bundle triples on the base surface and proposing a spectral curve classification.

Contribution

It introduces a novel correspondence between monopoles with singularities on Sasakian three-folds and holomorphic twisted bundle triples, along with a spectral curve classification method.

Findings

Monopoles correspond to holomorphic twisted bundle triples.

Spectral curve construction classifies these monopoles.

Conjectural classification of monopoles via spectral data.

Abstract

We consider monopoles with singularities of Dirac type on quasiregular Sasakian three-folds fibering over a compact Riemann surface $\Sigma$, for example the Hopf fibration $S^3\longrightarrow S^2$. We show that these correspond to holomorphic objects on $\Sigma$, which we call twisted bundle triples. These are somewhat similar to Murray's bundle gerbes. A spectral curve construction allows us to classify these structures, and, conjecturally, monopoles.