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

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)SU(N) Yang–Mills equations in an (n+1)(n+1)-dimensional curved space–time, for the cases n=1,2,3n=1,2,3. As an application of the results obtained for the case n=3n=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)U(1), the case n=2n=2 is a description of the (2+1)(2+1) electrodynamics in the 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=1n=1 is invariant under a parity transformation and has the form of a linear confining solution.

► We study exact static confining solutions of the SU(N)SU(N) Yang–Mills equations in an (n+1)(n+1)-dimensional curved space–time.
► The solutions found are a first step in the study of the corrections on the spectra of quarkonia in a curved background.
► A expression for the confinement potential in low dimensionality is found.