Exact Schwarzschild-Like Solution for Yang-Mills Theories

TL;DR

This paper derives an exact Schwarzschild-like solution for SU(2) Yang-Mills fields coupled with a scalar, suggesting a potential mechanism for confinement analogous to black hole horizons.

Contribution

It presents the first exact classical solution for SU(2) Yang-Mills fields with scalar coupling, extending the analogy with black hole solutions.

Findings

Exact Schwarzschild-like solution for Yang-Mills fields

Potential link between confinement and horizon analogy

Analysis of special cases of the solution

Abstract

Drawing on the parallel between general relativity and Yang-Mills theory we obtain an exact Schwarzschild-like solution for SU(2) gauge fields coupled to a massless scalar field. Pushing the analogy further we speculate that this classical solution to the Yang-Mills equations shows confinement in the same way that particles become confined once they pass the event horizon of the Schwarzschild solution. Two special cases of the solution are considered.