arXiv 1012.40572010-12hep-thhep-phmath-phmath.MP

希格斯相中的非阿贝尔单极

Non-Abelian Monopoles in the Higgs Phase

Muneto Nitta, Walter Vinci

备注：: 37 pages, no figures; v2: refs. added
发表信息：: Nucl.Phys.B848:121-154,2011
DOI：: 10.1016/j.nuclphysb.2011.02.014

摘要：

利用模矩阵方法研究了在N = 2超对称U（N）规范理论的Higgs相中，当物质超多重态的质量为非零时，涡旋支持的1/4 BPS扭结的模空间.我们集中在退化质量的情况下。在这些特殊情况下，旋涡获得新的方向自由度，并成为“非阿贝尔”。扭结也获得了新的自由度，我们称之为“非阿贝尔”。正如在阿贝尔情形中已经注意到的那样，非阿贝尔扭结必须对应于SU（N）杨-米尔斯的完整相位的非阿贝尔单极子。在某些特殊情况下，我们证明了两个对象的模空间是一一对应的。我们认为，在最一般的情况下，对应成立。我们的结果的后果是双重的。首先，它给出了另一种方法来构造非阿贝尔单极子，除了其他众所周知的技术（Nahm变换，谱曲线，有理映射）。第二，通过考虑更简单的非阿贝尔扭结，它为研究非阿贝尔单极子的量子物理开辟了道路。

英文摘要：

We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N = 2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become "non-Abelian". Kinks acquire new degrees of freedom too, and we will refer to them as "non-Abelian". As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU(N) Yang-Mills. We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the corre- spondence holds in the most general case. The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other well- known techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the study of the quantum physics of non- Abelian monopoles, by considering the simpler non-Abelian kinks.

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