关于Faddeev-Hopf模型的强耦合极限
On the Strong Coupling Limit of the Faddeev-Hopf Model
摘要：
研究了一般Riemannian域上Faddeev-Hopf模型和一般Kaehler目标空间在强耦合极限下的变分计算。在这个极限下，该模型与纯杨-米尔斯理论有关键的相似之处，即4维的共形不变性和无限维的对称群。计算了第一和二阶变分公式，并得到了几个稳定解的例子。特别是，它被证明，所有沉浸式解决方案是稳定的。拓扑较低的能量边界被发现在2和4维。给出了Hopf映射S^3 -> S^2的谱行为的显式描述，并证明了Ward关于该映射在完全Faddeev-Hopf模型中稳定性的猜想。
英文摘要：
The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. The first and second variation formulae are calculated and several examples of stable solutions are obtained. In particular, it is proved that all immersive solutions are stable. Topological lower energy bounds are found in dimensions 2 and 4. An explicit description of the spectral behaviour of the Hopf map S^3 -> S^2 is given, and a conjecture of Ward concerning the stability of this map in the full Faddeev-Hopf model is proved.
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