论文标题
在四个维度上,紧密耦合的紫外线固定点具有8kähler-dirac费米子
Emergent strongly coupled ultraviolet fixed point in four dimensions with 8 Kähler-Dirac fermions
论文作者
论文摘要
长期以来,在四维晶格模型中存在强烈耦合的紫外线固定点。具有8个基本费米子的SU(3)仪表系统是研究这种现象的好候选者,因为预计它将非常接近共形窗口的打开。我使用手性限制的交错晶格费米子研究系统。我的数值模拟采用了改进的晶格动作,包括重型Pauli-Villars(PV)型玻色子。这种修饰不会影响红外动力学,但会大大降低紫外线的波动,从而可以研究比以前可能更强大的重新归一化耦合。我认为两种不同的PV动作,发现两者在8味系统中都显示出明显的连续相变。 我使用重新归一化的梯度流量耦合的有限尺寸缩放研究了临界行为。有限尺寸缩放曲线折叠分析预测,在没有PV玻色子的系统中,系统中的不连续性指数$ν= 1/4 $一致。使用PV玻色子作用的缩放分析与一阶相变不一致。数值数据通过“步行缩放”对应于对应于重新归一化的$β$函数的“步行缩放”,该函数恰好触摸零,$β(g^2)\ sim(g^2 -g^2 -g^2_ \ star)^2 $,尽管不能排除二阶缩放。步行缩放可能意味着8型风味系统是共形窗口的打开,令人兴奋的可能性可能与该系统的T'Hooft异常有关。
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.