论文标题
$ \ Mathbb {r}^3 \ Times \ Mathbb {s}^1 $和双弦崩溃的限制
Confinement on $\mathbb{R}^3 \times \mathbb{S}^1$ and Double-String Collapse
论文作者
论文摘要
我们研究$ {\ cal {n}} = 1 $ supersymmetric $ su（n_c）$ yang-mills理论的限制字符串在$ \ mathbb {r}^{1,2} \ times \ times \ times \ mathbb {s}^1 $上。预计静态夸克将被由两个域墙组成的双字符串限制 - 它们是$ \ mathbb {r}^2 $的行，而不是单个磁通管。每个域壁都带有夸克染色体通量的一部分。我们从数字上研究了这种机制，并发现所有$ n $ alimit的字符串都具有双弦限制，除了基本夸克之间的串联。我们表明，对于$ n_c \ ge 5 $，两个域墙限制了$ n $ n $ quarks吸引并形成非BPS绑定状态，从而崩溃到单个磁通线。我们以$ 2 \ le n_c \ le 10 $确定字符串张力的$ n $ - 性依赖性。与已知的缩放定律相比，我们发现一个较弱的，几乎扁平的$ n $ - 性依赖性，这是由BPS域壁的性质定性解释的。我们还通过包括虚拟“ $ w $ -bosons”的效果来增加$ \ mathbb {s}^1 $大小而定量研究限制字符串的行为，并表明双重弦乐限制的定性特征持续存在。
We study confining strings in ${\cal{N}}=1$ supersymmetric $SU(N_c)$ Yang-Mills theory in the semiclassical regime on $\mathbb{R}^{1,2} \times \mathbb{S}^1$. Static quarks are expected to be confined by double strings composed of two domain walls - which are lines in $\mathbb{R}^2$ - rather than by a single flux tube. Each domain wall carries part of the quarks' chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all $N$-alities, except for those between fundamental quarks. We show that, for $N_c \ge 5$, the two domain walls confining unit $N$-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the $N$-ality dependence of the string tensions for $2 \le N_c \le 10$. Compared to known scaling laws, we find a weaker, almost flat $N$-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the $\mathbb{S}^1$ size by including the effect of virtual "$W$-bosons" and show that the qualitative features of double-string confinement persist.
