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arXiv 0803.3320hep-th
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SU（N）纯阳Mills理论中的显式非阿贝尔单极子和瞬子

Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory

Alexander D. Popov

备注：
16 pages; v2: subsection on topological charges added, title expanded, some coefficients corrected, version to appear in PRD
发表信息：
Phys.Rev.D77:125026,2008
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摘要：

众所周知，Minkowski空间R^{3，1}上的纯Yang-Mills理论不存在静态非Abel解。我们证明了在SU（N）规范理论中，在Minkowski签名为（-+）的空间R^2 \times S^2和R^1 \times S^1 \times S^2上存在这样的解。在时间规范中，它们是T^1 \times S^2上纯杨-米尔斯理论的解，其中T^1是R^1或S^1。也就是说，通过施加SO（3）-不变性和某些现实条件，我们一致地将上述空间上的杨-米尔斯模型简化为一个非阿贝尔的类似于N_4扭结模型的模型，其静态解通过上述对应给出了空间R^{1，1} \times S ^2上的SU（N）N（-反对称）组态。这些解也可以看作是2+1维Yang-Mills理论的瞬子组态。R^1 \times S^1上的扭结模型也存在周期性的sphaleron型解，该解描述了n个围绕圆S^1分布的扭结-反扭结对的链，其中任意n>0。它们对应于空间R^1 \times S^1 \times S^2上的n个静态自旋-反自旋对的链，在有限温度（热时间圆）下，这也可以解释为2+1维纯杨-米尔斯理论中的瞬子组态。我们还描述了在S^1 \times S^3上的欧几里得SU（N）规范理论中的类似解，将其解释为n个瞬子-反瞬子对的链。

英文摘要：

It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T^1\times S^2, where T^1 is R^1 or S^1. Namely, imposing SO(3)-invariance and some reality conditions, we consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the ϕ^4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R^{1,1}\times S^2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R^1\times S^1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R^1\times S^1\times S^2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). We also describe similar solutions in Euclidean SU(N) gauge theory on S^1\times S^3 interpreted as chains of n instanton-antiinstanton pairs.

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