Exact solutions of (n + 1)-dimensional Yang-Mills equations in curved space-time

TL;DR

This paper derives exact static solutions to SU(N) Yang-Mills equations in various curved space-times, revealing confining behaviors relevant for quarkonia spectra and planar electrodynamics.

Contribution

It provides new exact solutions for Yang-Mills fields in (n+1)-dimensional curved backgrounds, including anti-de Sitter and Schwarzschild metrics, with implications for confinement and quantum spectra.

Findings

Solutions exhibit confining behavior in curved backgrounds.

Solutions applicable to both SU(N) and U(1) gauge groups.

Solutions for different dimensions show distinct symmetry properties.

Abstract

In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in a $(n+1)$ dimensional curved space-time, for the cases $n = 1, 2, 3$. As an application of the results obtained for the case $n=3$, we consider the solutions for the anti-de Sitter and Schwarzschild metrics. We show that these solutions have a confining behavior and can be considered as a first step in the study of the corrections of the spectra of quarkonia in a curved background. Since the solutions that we find in this work are valid also for the group U(1), the case $n=2$ is a description of the $(2+1)$ electrodynamics in presence of a point charge. For this case, the solution has a confining behavior and can be considered as an application of the planar electrodynamics in a curved space-time. Finally we find that the solution for the case $n=1$ is invariant under a parity transformation and has the form of a linear confining solution.