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R_3 \times S_1上的类QCD理论：从小到大r（S_1）的双迹形变光滑过程

QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations

Mikhail Shifman, Mithat Unsal

备注：
49 pages, 2 figures
发表信息：
Phys.Rev.D78:065004,2008
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摘要：

我们考虑在规范群SU $(N)$的各种表示中具有一个无质量费米子的类QCD理论。这些理论是在$R_3\times S_1$上制定的。在大$r(S_1)$的解压缩极限下，所有这些理论的特征在于禁闭、质量间隙和（离散）手征对称性的自发破缺（$χ$ SB）。在小的$r(S_1)$，为了使这些理论的真空稳定在中心对称点，我们建议进行双迹变形。有了这些变形，手头的理论是在弱耦合在小$r(S_1)$，但表现出的基本功能的大$r(S_1)$限制：限制和$χ$ SB。我们计算弦张力，质量间隙，双费米子凝聚和$θ$依赖。双迹变形在大$r(S_1)$处变得与动力学无关。尽管事实上，在小$r(S_1)$禁闭是阿贝尔，而预计将是非阿贝尔在大$r(S_1)$，我们认为，小和大- $r(S_1)$物理是连续连接。如果是这样的话，人们可以使用小型的$r(S_1)$实验室在$R_4$上提取关于QCD和类QCD理论的课程。

英文摘要：

We consider QCD-like theories with one massless fermion in various representations of the gauge group SU$(N)$. The theories are formulated on $R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ($χ$SB). At small $r(S_1)$, in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small $r(S_1)$ and yet exhibit basic features of the large-$r(S_1)$ limit: confinement and $χ$SB. We calculate the string tension, mass gap, bifermion condensates and $θ$ dependence. The double-trace deformation becomes dynamically irrelevant at large $r(S_1)$. Despite the fact that at small $r(S_1)$ confinement is Abelian, while it is expected to be non-Abelian at large $r(S_1)$, we argue that small and large-$r(S_1)$ physics are continuously connected. If so, one can use small-$r(S_1)$ laboratory to extract lessons about QCD and QCD-like theories on $R_4$.

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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