General relativistic analog solutions for Yang-Mills theory

TL;DR

This paper explores solutions to Yang-Mills theory derived from analogies with general relativity, highlighting potential links to confinement phenomena and analyzing particle motion in these backgrounds.

Contribution

It introduces a method to find Yang-Mills solutions using known general relativity solutions and discusses their possible physical implications.

Findings

Yang-Mills solutions analogous to Schwarzschild solutions

Potential connection between these solutions and confinement

Analysis of test particle motion in the analog solutions

Abstract

Finding solutions to non-linear field theories, such as Yang-Mills theories or general relativity, is usually difficult. The field equations of Yang-Mills theories and general relativity are known to share some mathematical similarities, and this connection can be used to find solutions to one theory using known solutions of the other theory. For example, the Schwarzschild solutions of general relativity can be shown to have a mathematically similar counterpart in Yang-Mills theory. In this article we will discuss several solutions to the Yang-Mills equations which can be found using this connection between general relativity and Yang-Mills theory. Some comments about the possible physical meaning of these solutions will be discussed. In particular it will be argued that some of these analog solutions of Yang-Mills theory may have some connection with the confinement phenomenon. To this end we will briefly look at the motion of test particles moving in the background potential of the Schwarzschild analog solution.