Yang-Mills Solutions on Euclidean Schwarzschild Space

TL;DR

This paper demonstrates that certain Yang-Mills solutions in Euclidean Schwarzschild space are actually static monopoles and dyons, challenging previous assumptions about their time dependence and tunneling behavior.

Contribution

It shows that known Yang-Mills instantons in this space are time-independent and identifies them as monopoles and dyons, proposing no time-dependent solutions exist.

Findings

Solutions are time-independent monopoles and dyons.

No tunneling occurs due to constant potential along time.

Conjecture that no time-dependent solutions exist in this background.

Abstract

We show that the apparently periodic Charap-Duff Yang-Mills `instantons' in time-compactified Euclidean Schwarzschild space are actually time independent. For these solutions, the Yang-Mills potential is constant along the time direction (no barrier) and therefore, there is no tunneling. We also demonstrate that the solutions found to date are three dimensional monopoles and dyons. We conjecture that there are no time-dependent solutions in the Euclidean Schwarzschild background.