标题： 自对偶性与广义BPSTSkyrme模型中的全纯假设 显示英文标题

标题： Self-duality and the Holomorphic Ansatz in Generalized BPS Skyrme Model

摘要： 我们提出了一种针对简单紧致李群 $G$的BPS Skyrme模型的推广，这导致了厄米对称空间。 在这样的理论中，Skyrme场的取值为 $G$，而其他场对应于一个对称、正定且可逆的 $\dim G \times \dim G$维矩阵 $h$。 我们还使用了 $S^2 \rightarrow G/H \times U(1)$之间的全纯映射假设来研究该理论的自对偶部分，这推广了 $S^2 \rightarrow CP^N$之间的全纯假设。 该假设是利用了对于紧致厄米对称空间的两个 $S^2$球面的稳定调和映射是全纯或反全纯这一事实构建的。 除了某些特殊情况外，自对偶方程并不能完全根据Skyrme场确定矩阵$h$，Skyrme场是完全自由的，正如原始自对偶Skyrme模型中的情况一样，对于$G=SU(2)$。 一般来说，$h$场的自由度随着$G$的维度增大而增加。 全纯假设使我们能够为每个整数拓扑电荷值以及在$N \geq 1$的每个值情况下，对于$CP^N$情况，以及在$SU(p+q)/SU(p)\otimes SU(q)\otimes U(1)$情况下每个$p,\,q\geq 1$值的情况下，构建无限多个精确的自对偶Skyrmions。 显示英文摘要

摘要： We propose a generalization of the BPS Skyrme model for simple compact Lie groups $G$ that leads to Hermitian symmetric spaces. In such a theory, the Skyrme field takes its values in $G$, while the remaining fields correspond to the entries of a symmetric, positive, and invertible $\dim G \times \dim G$-dimensional matrix $h$. We also use the holomorphic map ansatz between $S^2 \rightarrow G/H \times U(1)$ to study the self-dual sector of the theory, which generalizes the holomorphic ansatz between $S^2 \rightarrow CP^N$. This ansatz is constructed using the fact that stable harmonic maps of the two $S^2$ spheres for compact Hermitian symmetric spaces are holomorphic or anti-holomorphic. Apart from some special cases, the self-duality equations do not fix the matrix $h$ entirely in terms of the Skyrme field, which is completely free, as it happens in the original self-dual Skyrme model for $G=SU(2)$. In general, the freedom of the $h$ fields tend to grow with the dimension of $G$. The holomorphic ansatz enable us to construct an infinite number of exact self-dual Skyrmions for each integer value of the topological charge and for each value of $N \geq 1$, in case of the $CP^N$, and for each values of $p,\,q\geq 1$ in case of $SU(p+q)/SU(p)\otimes SU(q)\otimes U(1)$.