Continuous $eta$ function for the SU(3) gauge systems with two and twelve fundamental flavors
Continuous $eta$ function for the SU(3) gauge systems with two and twelve fundamental flavors
复制标题
具有两种和十二种基本风格的 SU(3) 量规系统的连续 $eta$ 函数
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
O. Witzel
中科院分区：
文献类型：
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作者：
A. Hasenfratz;O. Witzel
如果将粗粒度步骤合并为计算期望值的一部分，则梯度流变换可以解释为连续实空间重整化群变换。该方法可以预测强耦合系统的关键特性，包括重正化群 $eta$ 函数和非微扰不动点处的异常尺寸。在这篇文章中，我们讨论了基于该方法的 SU(3) 规范理论中 $N_f=2$ 和 $N_f=12$ 基本风格的连续重正化群 $eta$ 函数的新分析。我们遵循 arXiv:1910.06408 中为 $N_f=2$ 系统开发和测试的方法。在这里，我们提供有关分析的更多信息，强调连续 $eta$ 函数计算的鲁棒性和直观特征。我们还讨论了连续 $eta$ 函数计算在共形系统中的适用性，扩展了可能的相图以包括 4-费米子相互作用。 $N_f=12$ 的数值分析使用与 arXiv:1909.05842 中的步长缩放函数生成和分析的同一组集合。新分析使用 $L ge 20$ 的体积，并确定 $c=0$ 梯度流重正化方案中的 $eta$ 函数。连续$eta$函数预测共角不动点的存在，并且在不同算子之间是一致的。尽管步长缩放和连续 $eta$ 函数的确定使用不同的重正化方案，但它们都预测 $g^2sim 6$ 周围存在共形不动点。
The gradient flow transformation can be interpreted as continuous real-space renormalization group transformation if a coarse-graining step is incorporated as part of calculating expectation values. The method allows to predict critical properties of strongly coupled systems including the renormalization group $eta$ function and anomalous dimensions at nonperturbative fixed points. In this contribution we discuss a new analysis of the continuous renormalization group $eta$ function for $N_f=2$ and $N_f=12$ fundamental flavors in SU(3) gauge theories based on this method. We follow the approach developed and tested for the $N_f=2$ system in arXiv:1910.06408. Here we present further information on the analysis, emphasizing the robustness and intuitive features of the continuous $eta$ function calculation. We also discuss the applicability of the continuous $eta$ function calculation in conformal systems, extending the possible phase diagram to include a 4-fermion interaction. The numerical analysis for $N_f=12$ uses the same set of ensembles that was generated and analyzed for the step scaling function in arXiv:1909.05842. The new analysis uses volumes with $L ge 20$ and determines the $eta$ function in the $c=0$ gradient flow renormalization scheme. The continuous $eta$ function predicts the existence of a conformal fixed point and is consistent between different operators. Although determinations of the step scaling and continuous $eta$ function use different renormalization schemes, they both predict the existence of a conformal fixed point around $g^2sim 6$.