arXiv 2004.113952020-04hep-th

4d N=1超对称Yang-Mills的畴壁

Domain Walls in 4d N=1 Supersymmetric Yang-Mills

Diego Delmastro, Jaume Gomis

备注：: 57 pages

摘要：

具有单连通规范群$G$的$4d$ ${\mathcal N}=1$ super Yang-Mills（SYM）具有由自发破缺的离散$R$ -对称性产生的$h$带隙真空，其中$h$是$G$的对偶Coxeter数.因此，该理论允许在任意两个真空之间插入稳定的畴壁，但确定畴壁上的低能理论是一个非微扰问题。对于$G=SU(N),Sp(N), Spin(N)$和$G_2$的所有畴壁，以及对于任意$G$连接相邻真空的最小畴壁，我们提出了一个明确的答案.我们提出畴壁理论支持特定的非平凡拓扑量子场论，其中包括很久以前由Acharya-Vafa为$SU(N)$提出的Chern-Simons理论。我们提供了非平凡的证据，我们的建议完全匹配的重整化群不变的配分函数扭曲的全局对称性的SYM计算在紫外线与我们提出的红外TQFT计算。这种匹配的一个关键要素是构建自旋TQFT的希尔伯特空间，也就是说，依赖于时空的自旋结构并承认费米子态的理论-我们详细研究的主题。

英文摘要：

$4d$ ${\mathcal N}=1$ super Yang-Mills (SYM) with simply connected gauge group $G$ has $h$ gapped vacua arising from the spontaneously broken discrete $R$-symmetry, where $h$ is the dual Coxeter number of $G$. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We put forward an explicit answer to this question for all the domain walls for $G=SU(N),Sp(N), Spin(N)$ and $G_2$, and for the minimal domain wall connecting neighboring vacua for arbitrary $G$. We propose that the domain wall theories support specific nontrivial topological quantum field theories (TQFTs), which include the Chern-Simons theory proposed long ago by Acharya-Vafa for $SU(N)$. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions twisted by global symmetries of SYM computed in the ultraviolet with those computed in our proposed infrared TQFTs. A crucial element in this matching is constructing the Hilbert space of spin TQFTs, that is, theories that depend on the spin structure of spacetime and admit fermionic states -- a subject we delve into in some detail.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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