标题： 凯勒空间中具有一个全纯等距的杨-米尔斯瞬子 显示英文标题

标题： Yang-Mills instantons in Kaehler spaces with one holomorphic isometry

摘要： 我们研究了4维Kähler空间中的自对偶Yang-Mills瞬子，这些空间具有一条全纯等距，并证明它们满足Bogomol'nyi方程的一个推广形式，该形式适用于某些三维度量上的磁单极子。 接着，我们在度规的等距群（即规范群）与度规的等距群相同的情况下（分别为SO(3)，SO(1,2)和ISO(2)），在由二维球面、双曲面或平面组成的三维度量中寻找此方程的解。 利用广义刺猬假设，Bogomol'nyi方程约化为径向变量的简单微分方程，该方程允许存在通用解以及在某些情况下的特定解，最终从中恢复出原始Kähler空间中的瞬子解。 我们完全处理了一些有趣的Kähler空间的具体例子。 显示英文摘要

摘要： We consider self-dual Yang-Mills instantons in 4-dimensional Kaehler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We then search for solutions of this equation in 3-dimensional metrics foliated by 2-dimensional spheres, hyperboloids or planes in the case in which the gauge group coincides with the isometry group of the metric (SO(3), SO(1,2) and ISO(2), respectively). Using a generalized hedgehog ansatz the Bogomol'nyi quations reduce to a simple differential equation in the radial variable which admits a universal solution and, in some cases, a particular one, from which one finally recovers instanton solutions in the original Kaehler space. We work out completely a few explicit examples for some Kaehler spaces of interest.