论文标题

手性对称打破和限制:分开量表

Chiral symmetry breaking and confinement: separating the scales

论文作者

Evans, Nick, Rigatos, Konstantinos S.

论文摘要

我们回顾了当夸克双线性冷凝水的尺寸通过一个($γ= 1 $)时触发手性对称性破裂的论点。这是差距方程和最近全息模型支持的。然后,限制可能是纯阳米尔斯理论的单独属性,低于动态产生的夸克质量的规模,该夸克质量发生在深度IR运行中的极规模上。在这里,我们使用驱动性结果来运行量规耦合和$γ$ in渐近的su($ n_c $)量规理论,其中具有更高维度表示的,以寻求最佳的候选理论,在这些理论中,可以最大程度地分开限制和手感对称性。例如,在$ S_3 $(尺寸4)表示中具有单个Weyl Quark的SU(2)量规理论可能具有20倍的比例。可以在晶格上模拟这种理论以测试分离。我们还建议研究多代表理论,其中较高的维表示形成一个尺度的冷凝物,可以与第二表示问题的凝结量表完全分开。限制量表大概将低于第二量表。例如,具有Weyl伴随费用和十个基本夸克的SU(3)仪表理论也可能具有20倍的分离。

We review arguments that chiral symmetry breaking is triggered when the quark bilinear condensate's dimension passes through one ($γ=1$). This is supported by gap equations and more recently holographic models. Confinement may then be a separate property of the pure Yang-Mills theory below the scale of the dynamically generated quark mass, occurring at the scale of the pole in the deep IR running. Here, we use perturbative results for the running of the gauge coupling and $γ$ in asymptotically free SU($N_c$) gauge theories with matter in higher dimension representations to seek the best candidate theories where confinement and chiral symmetry breaking can be maximally separated. For example, SU(2) gauge theory with a single Weyl quark in the $S_3$ (dimension 4) representation may have a factor of 20 separation in scale. Such a theory could be simulated on the lattice to test the separation. We also propose studying multi-representation theories where the higher dimension representation forms a condensate at one scale that can be quite separate from the condensation scale of the second representation matter. The confinement scale would presumably be below the second scale. For example, SU(3) gauge theory with a Weyl adjoint fermion and ten fundamental quarks may have a separation of a factor of 20 also.

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