具有8个Kähler-Dirac费米子的四维强耦合紫外不动点的涌现
Emergent strongly coupled ultraviolet fixed point in four dimensions with 8 Kähler-Dirac fermions
摘要：
在四维晶格模型中，当它们进入共形窗口时，存在强耦合的紫外不动点一直是假设。具有8个基本费米子的SU（3）规范系统是研究这种现象的一个很好的候选者，因为预计它非常接近共形窗口的打开。我研究的系统中使用交错晶格费米子的手征限制。我的数值模拟采用改进的晶格作用，包括重保利-维拉尔（PV）型玻色子。这种修改不影响红外动力学，但大大减少了紫外波动，从而使研究更强的重整化耦合比以前可能的。我考虑了两种不同的PV作用，发现在8味体系中，两者都表现出明显的连续相变。我调查的临界行为，使用有限尺寸标度的重整化梯度流耦合。有限尺寸标度曲线坍缩分析预测了在无PV玻色子的系统中与不连续指数$ν=1/4$一致的一级相变。与PV玻色子作用的标度分析是不一致的一阶相变。数值数据很好地描述了“步行标度”对应于重整化群$β$函数，它刚好接近零，$β(g^2) \sim (g^2 - g^2_\star)^2$，尽管不能排除二阶标度。步行缩放可能意味着8味系统是共形窗口的开放，一个令人兴奋的可能性，可能与特胡夫特异常取消系统。
英文摘要：
The existence of a strongly coupled ultraviolet fixed point in 4-dimensional lattice models as they cross into the conformal window has long been hypothesized. The SU(3) gauge system with 8 fundamental fermions is a good candidate to study this phenomenon as it is expected to be very close to the opening of the conformal window. I study the system using staggered lattice fermions in the chiral limit. My numerical simulations employ improved lattice actions that include heavy Pauli-Villars (PV) type bosons. This modification does not affect the infrared dynamics but greatly reduces the ultraviolet fluctuations, thus allowing the study of stronger renormalized couplings than previously possible. I consider two different PV actions and find that both show an apparent continuous phase transition in the 8-flavor system. I investigate the critical behavior using finite size scaling of the renormalized gradient flow coupling. The finite size scaling curve-collapse analysis predicts a first order phase transition consistent with discontinuity exponent $ν=1/4$ in the system without PV bosons. The scaling analysis with the PV boson actions is not consistent with a first order phase transition. The numerical data are well described by "walking scaling" corresponding to a renormalization group $β$ function that just touches zero, $β(g^2) \sim (g^2 - g^2_\star)^2$, though second order scaling cannot be excluded. Walking scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that could be related to t'Hooft anomaly cancellation of the system.
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