论文标题
梯度流下的位错及其对重新归化耦合的影响
Dislocations under gradient flow and their effect on the renormalized coupling
论文作者
论文摘要
在量规效力系统的手性限制中禁止非零拓扑电荷，因为任何intsanton都会创建零dirac操作员的零模式。但是，在晶格上，几何$ q_ \ text {geom} = \ langle f {\ tilde f} \ rangle /32π^2 $拓扑费的定义不一定消失，即使梯度流平滑，梯度流平滑。费米子看不见的小真空波动（位错）可以通过梯度流将其促进到类似激体状的物体。我们证明，流量的这些伪像导致梯度流量重新归一化的量规耦合以增加和运行速度。在步进研究中，这种伪像的术语随着体积的增加而造成了术语。通常的$ a/l \至0 $连续限制限制外推会导致结果不正确。在本文中，我们调查了带有域壁费物皮的SU（3）10型风味系统中的这些拓扑晶格伪像，以及带有交错费用的8风效系统。两种系统在强耦合时均表现出非零拓扑电荷，尤其是在使用Symanzik梯度流动时。我们演示了这种伪影如何影响重新归一化的量规耦合的确定和阶梯缩放$β$函数。
Non-zero topological charge is prohibited in the chiral limit of gauge-fermion systems because any instanton would create a zero mode of the Dirac operator. On the lattice, however, the geometric $Q_\text{geom}=\langle F{\tilde F}\rangle /32π^2$ definition of the topological charge does not necessarily vanish even when the gauge fields are smoothed for example with gradient flow. Small vacuum fluctuations (dislocations) not seen by the fermions may be promoted to instanton-like objects by the gradient flow. We demonstrate that these artifacts of the flow cause the gradient flow renormalized gauge coupling to increase and run faster. In step-scaling studies such artifacts contribute a term which increases with volume. The usual $a/L\to 0$ continuum limit extrapolations can hence lead to incorrect results. In this paper we investigate these topological lattice artifacts in the SU(3) 10-flavor system with domain wall fermions and the 8-flavor system with staggered fermions. Both systems exhibit nonzero topological charge at the strong coupling, especially when using Symanzik gradient flow. We demonstrate how this artifact impacts the determination of the renormalized gauge coupling and the step-scaling $β$ function.
