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arXiv 1503.02060hep-thhep-ph
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非阿贝尔约瑟夫森结中的约瑟夫森瞬子和约瑟夫森单极子

Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction

Muneto Nitta

备注：
30 pages, 6 figures, v3: published version
发表信息：
Phys. Rev. D 92, 045010 (2015)
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摘要：

非阿贝尔约瑟夫森结是一种非阿贝尔色超导体包围绝缘体的结，其低能动力学可用具有常规π介子质量的$U(N)$主手征模型描述。非阿贝尔约瑟夫森涡旋是位于结内的非阿贝尔涡旋（彩色磁通量管），称为非阿贝尔正弦戈登孤子。本文提出了Josephson瞬子和Josephson单极子，即非阿贝尔约瑟夫森结中的Yang-Mills瞬子和单极子，并证明了它们在无和有扭曲质量项的$U(N)$主手征模型中分别被描述为$SU(N)$ Skyrmions和$U(1)^{N-1}$涡旋.具有扭曲边界条件的瞬子被简化（或T-对偶）为单极子，这意味着${\mathbb C}P^{N-1}$团块是涡旋内${\mathbb C}P^{N-1}$扭结的T-对偶。这里我们发现$SU(N)$ Skyrmions是壁内$U(1)^{N-1}$涡旋的T-对偶。我们的组态表明，从不同的宿主孤子看，在${\mathbb C}P^{N-1}$团块和$SU(N)$ Skyrmions之间以及在${\mathbb C}P^{N-1}$扭结和$U(1)^{N-1}$涡旋之间存在另一种对偶性。他们还建议之间的分数瞬子和bions的${\mathbb C}P^{N-1}$模型和那些在$SU(N)$主手征模型的对偶性。

英文摘要：

Non-Abelian Josephson junction is a junction of non-Abelian color superconductors sandwiching an insulator, or non-Abelian domain wall if flexible, whose low-energy dynamics is described by a $U(N)$ principal chiral model with the conventional pion mass. A non-Abelian Josephson vortex is a non-Abelian vortex (color magnetic flux tube) residing inside the junction, that is described as a non-Abelian sine-Gordon soliton. In this paper, we propose Josephson instantons and Josephson monopoles, that is, Yang-Mills instantons and monopoles inside a non-Abelian Josephson junction, respectively, and show that they are described as $SU(N)$ Skyrmions and $U(1)^{N-1}$ vortices in the $U(N)$ principal chiral model without and with a twisted mass term, respectively. Instantons with a twisted boundary condition are reduced (or T-dual) to monopoles, implying that ${\mathbb C}P^{N-1}$ lumps are T-dual to ${\mathbb C}P^{N-1}$ kinks inside a vortex. Here we find $SU(N)$ Skyrmions are T-dual to $U(1)^{N-1}$ vortices inside a wall. Our configurations suggest a yet another duality between ${\mathbb C}P^{N-1}$ lumps and $SU(N)$ Skyrmions as well as that between ${\mathbb C}P^{N-1}$ kinks and $U(1)^{N-1}$ vortices, viewed from different host solitons. They also suggest a duality between fractional instantons and bions in the ${\mathbb C}P^{N-1}$ model and those in the $SU(N)$ principal chiral model.

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