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

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.