论文标题
3D无质量CS-QCD的红外阶段和大$ N_F $
Infrared phases of 3d massless CS-QCD and large $N_f$
论文作者
论文摘要
我们计算四分位运算符的异常维度，这些维度是$ \ mathrm {u}（n_f）$ yang-mills Theories的全局对称性下的单元，其中包括Chern-Simons级别$ K $在三个维度上，耦合到$ n_f $ dirac fermions。为了获得分析性控制，我们考虑了$ n_f \ gg n_c \ gg 1 $，其中该问题减少到了风味 - 选择性的研究和风味 - 柔软的双线性，它们的正方形为Quartic five of Import five而言。我们提供的证据表明，这些操作员遇到了边缘性，信号不稳定性，对于$ \ frac {2k} {n_f} <1 $，这表明全局对称性的自发断裂，而没有对称性破坏。对于$ k = n_f/2-1 $（对应于$θ=π$ 4D QCD的域墙的值，临界值$ n_f^*$非常接近QCD $ _4 $的保串窗口的下端，并在其4D理论和4D理论中的全球对称性之间存在连接和全球对称性之间的破坏。我们还研究了$ k = 0 $，其他四分之一的操作员在$ \ mathrm {u} \ left（\ frac {n_f} {2} {2} {2} \ right）\ times \ times \ times \ mathrm {u} \ left（\ frac {n_f} {n_f} {2} $ pinderation时，堂兄。使用相同的技术，我们研究了玻色粒CS-QCD $ _3 $，在适用我们的分析的情况下没有发现对称破坏的暗示。
We compute anomalous dimensions of quartic operators which are singlets under the $\mathrm{U}(N_f)$ global symmetry in Yang-Mills theories with Chern-Simons level $k$ in three dimensions coupled to $N_f$ Dirac fermions. In order to have analytic control, we consider the regime $N_f\gg N_c\gg 1$, where the problem is reduced to the study of a flavor-adjoint and a flavor-singlet bilinears whose square give the quartic operators of interest. We provide evidence that these operators hit marginality, signaling instabilities which, for $\frac{2k}{N_f}<1$ suggest the spontaneous breaking of the global symmetry, and no symmetry breaking otherwise. For $k=N_f/2-1$ (the value corresponding to the domain walls of 4d QCD at $θ=π$), the critical value $N_f^*$ is tantalizingly close to the lower end of the conformal window of QCD$_4$, suggesting a connection between conformal and global symmetry breaking in the 4d theory and in its domain walls. We also study, at $k=0$, other quartic operators containing a singlet when branched under $\mathrm{U}\left(\frac{N_f}{2}\right)\times \mathrm{U}\left(\frac{N_f}{2}\right)$, finding that they hit marginality precisely at the same point as their flavor-neutral cousins. Using the same technology we study bosonic CS-QCD$_3$, finding no hint of symmetry breaking where our analysis is applicable.
