论文标题
在Skyrme模型的背景下的自以为是
Self-Duality in the Context of the Skyrme Model
论文作者
论文摘要
我们研究了Skyrme模型最近提出的修改，该模型具有精确的自偶联扇形，导致具有任意拓扑（Baryon）电荷的精确的Skyrmion溶液。除了通常的三个SU（2）Skyrme字段之外，引入还可以通过引言来实现自我双重扇区，该扇区的六个标量字段组装在对称且可逆的三维矩阵H中。该动作在Skyrme领域的衍生物中呈现了二次和四分之一的术语，但与SU（2）杀戮形式签约的小组指数在二次术语中与H-Matrix签约，并且在四分之一的术语中与H-Matrix签约。由于这些额外的字段，该模型的静态版本及其自偶性方程在三维空间r^3上是完美的。我们表明，这种理论的静态和自偶联领域是等效的，因此唯一的非自我偶对方案必须取决于时间。我们还表明，对于Skyrme SU（2）字段的任何配置，H-Fields都会调整自己以满足自偶性方程，因此该理论具有大量的非平凡拓扑解决方案。我们使用全体形态有理Ansatz以及基于共形对称性的环形ANSATZ提出了明确的溶液。我们指出了破坏保形对称性和自动划分领域的模型的可能扩展，这可能会导致有趣的物理应用。
We study a recently proposed modification of the Skyrme model that possesses an exact self-dual sector leading to an infinity of exact Skyrmion solutions with arbitrary topological (baryon) charge. The self-dual sector is made possible by the introduction, in addition to the usual three SU(2) Skyrme fields, of six scalar fields assembled in a symmetric and invertible three dimensional matrix h. The action presents quadratic and quartic terms in derivatives of the Skyrme fields, but instead of the group indices being contracted by the SU(2) Killing form, they are contracted with the h-matrix in the quadratic term, and by its inverse on the quartic term. Due to these extra fields the static version of the model, as well as its self-duality equations, are conformally invariant on the three dimensional space R^3. We show that the static and self-dual sectors of such a theory are equivalent, and so the only non-self-dual solution must be time dependent. We also show that for any configuration of the Skyrme SU(2) fields, the h-fields adjust themselves to satisfy the self-duality equations, and so the theory has plenty of non-trivial topological solutions. We present explicit exact solutions using a holomorphic rational ansatz, as well as a toroidal ansatz based on the conformal symmetry. We point to possible extensions of the model that break the conformal symmetry as well as the self-dual sector, and that can perhaps lead to interesting physical applications.
