arXiv 1206.30132012-06-14hep-th

弯曲时空中（n + 1）维Yang-Mills方程的精确解

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

J. A. Sanchez-Monroy, C. J. Quimbay

备注：: 14 pages
发表信息：: Annals of Physics 327 (2012) 2166-2176
DOI：: 10.1016/j.aop.2012.04.015

摘要：

在矢量规范场可视为经典场的半经典方法的背景下，我们得到了$(n+1)$维弯曲时空中SU（N）Yang-Mills方程的精确静态解.作为对$n=3$情形所得结果的应用，我们考虑反德西特和史瓦西度规的解.我们证明了这些解具有封闭性，可以作为研究弯曲背景下夸克偶素谱修正的第一步。由于我们在这项工作中找到的解决方案也适用于群U（1），$n=2$的情况下是一个描述的$(2+1)$电动力学在存在一个点电荷。在这种情况下，该解具有限制性，可以看作是平面电动力学在弯曲时空中的应用。最后我们发现$n=1$情形的解在宇称变换下是不变的，并且具有线性限制解的形式。

英文摘要：

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.

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