论文标题
共形膨胀的保形窗口
Conformal window from conformal expansion
论文作者
论文摘要
我们研究包含$ n_f $ fermion物质的渐近自由量表理论的保形窗口，这些窗口转换为矢量和$ so（n），〜su（n）$（n）$和$ sp（2n）$ g量表的两个指数表示。对于$ so（n）$，我们还考虑旋转表示。我们通过使用在红外固定点的fermion birinear的异常尺寸上使用构想的临界条件，确定对应于保形窗口的下端的临界数量$ n_f^{\ rm cr} $，对应于保形窗口的下端。 $γ_ {\ bar单ψ}（2-γ_ {\ bar单ψ}）= 1 $。要计算异常维度，我们采用了银行 - Zaks的一致扩展至$δ_{n_f} = n_f^{\ rm af} -n_f $ at $Δ_{n_f} = n_f^{\ rm af} {\ n_f^{\ n_f^{\ rm af} $，表明我们的情况就可以很好地表明，我们在其中表明了这一范围的效果。 为了量化我们的分析中的不确定性，这些分析可能源于非扰动效应，我们通过分别假设保形膨胀的大阶行为（即趋同或发散渐近线）提出了两种不同的方法。在前一种情况下，我们将padé近似值的差异与临界条件的两个定义相差，而在后一种情况下，请考虑与鲍勒平面中的奇异性相关的截断误差。我们的结果与其他分析方法以及文献中可用的晶格结果进行了比较。特别是，我们发现$ su（2）$带有六个和$ su（3）$带有十种基本口味的$（3）$，可能位于保形窗口的下边缘，这与最近的晶格结果一致。我们还预测，具有基本和反对称费米的$ sp（4）$理论分别具有大约十和五种的临界数量。
We study the conformal window of asymptotically free gauge theories containing $N_f$ flavors of fermion matter transforming to the vector and two-index representations of $SO(N),~SU(N)$ and $Sp(2N)$ gauge groups. For $SO(N)$ we also consider the spinorial representation. We determine the critical number of flavors $N_f^{\rm cr}$, corresponding to the lower end of the conformal window, by using the conjectured critical condition on the anomalous dimension of the fermion bilinear at an infrared fixed point, $γ_{\barψψ}=1$ or equivalently $γ_{\barψψ}(2-γ_{\barψψ})=1$. To compute the anomalous dimension we employ the Banks-Zaks conformal expansion up to the $4$th order in $Δ_{N_f}=N_f^{\rm AF}-N_f$ with $N_f^{\rm AF}$ denoting the onset of the loss of asymptotic freedom, where we show that the latter critical condition provides a better performance along with this conformal expansion. To quantify the uncertainties in our analysis, which potentially originate from nonperturbative effects, we propose two distinct approaches by assuming the large order behavior of the conformal expansion separately, either convergent or divergent asymptotic. In the former case, we take the difference in the Padé approximants to the two definitions of the critical condition, whereas in the latter case the truncation error associated with the singularity in the Borel plane is taken into account. Our results are further compared to other analytical methods as well as lattice results available in the literature. In particular, we find that $SU(2)$ with six and $SU(3)$ with ten fundamental flavors are likely on the lower edge of the conformal window, which are consistent with the recent lattice results. We also predict that $Sp(4)$ theories with fundamental and antisymmetric fermions have the critical numbers of flavors, approximately ten and five, respectively.
