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arXiv 2004.08295hep-thmath-phmath.MPnlin.SI
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Skyrme模型中的自我二重性

Self-Duality in the Context of the Skyrme Model

L. A. Ferreira, L. R. Livramento

备注：
25 pages, no figures, version published in JHEP 09 (2020) 031
发表信息：
JHEP 09 (2020) 031
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摘要：

我们研究了最近提出的修改的Skyrme模型，拥有一个精确的自对偶部门导致无限的精确Skyrmion解决方案与任意拓扑（重子）收费。除了通常的三个SU（2）Skyrme场外，还引入了六个组装在对称可逆三维矩阵h中的标量场，从而使自对偶扇区成为可能。作用量在Skyrme场的导数中呈现二次项和四次项，但群指数不是由SU（2）Killing形式收缩，而是在二次项中与h矩阵收缩，并在四次项中与其逆矩阵收缩。由于这些额外的场，模型的静态形式以及它的自对偶方程在三维空间R上是保形不变的^[3]。我们表明，这样的理论的静态和自对偶部门是等价的，所以唯一的非自对偶的解决方案必须是时间依赖的。我们还证明了对于Skyrme SU（2）场的任何组态，h场都能自适应地满足自对偶方程，因此该理论有大量的非平凡拓扑解。我们提出了明确的精确解，使用全纯理性的ananomaly，以及一个环形anomaly的基础上的共形对称。我们指出可能的扩展模型，打破共形对称性以及自对偶部门，这也许可以导致有趣的物理应用。

英文摘要：

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.

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