论文标题
4D n = 1个超对称阳米的域壁
Domain Walls in 4d N=1 Supersymmetric Yang-Mills
论文作者
论文摘要
$ 4D $ $ {\ MATHCAL N} = 1 $ SUPER YANG-MILLS（SYM），简单连接的量规组$ G $具有$ h $ gapped vatua是由自发损坏的离散$ r $ -smymmetry产生的，其中$ h $是$ h $的$ h $ $ g $ $ g $。因此，该理论接受了任何两个真空之间插值的稳定域壁，但是确定域壁上的低能理论是一个非扰动问题。我们为所有域墙提出了一个明确的答案，以$ g = su（n），sp（n），spin（n）$和$ g_2 $，以及与任意$ g $连接相邻真空的最小域墙。我们建议域壁理论支持特定的非平凡拓扑量子场理论（TQFTS），其中包括Acharya-vafa对$ su（n）$提出的Chern-Simons理论。我们通过与我们提出的红外TQFTS中计算的sym对称性扭曲的符合重新归一化的分区函数来为我们的建议提供非平凡的证据。这种匹配中的一个关键元素是构建了自旋TQFT的希尔伯特空间，即取决于时空的自旋结构和录取费米金状态的理论 - 我们详细介绍了这一主题。
$4d$ ${\mathcal N}=1$ 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.
