论文标题
非亚伯仪理论领域的自由能
Free Energy on the Sphere for Non-Abelian Gauge Theories
论文作者
论文摘要
我们使用$ε$ - $ expansion在$ d = 4 $的情况下计算了连续$ d $的固定点的$ s^d $分区功能。我们详细说明了计算的技术方面，包括固定程序产生的所有因素，以及处理幽灵零模型的方法。我们获得了最高NLO的结果，即包括两循环真空图。根据单循环β函数的符号，有一个固定点，其中$ d> 4 $或$ d <4 $中的真实量规耦合。在第一种情况下，我们通过SUSY损坏的$ e_1 $ scft的变形，将$ 5D $ $ su（2）$ su-mills的UV固定点构造的最近提议的uv固定点进行测试。我们发现$ f $定理允许拟议的RG流。在第二种情况下，我们将$ d = 3 $推出，以测试QCD $ _3 $带有量规组$ su（n_c）$和$ n_f $基本问题字段流向CFT还是在对称阶段。我们发现，在实际量规联耦合近$ d = 4 $的政权中，CFT阶段始终受到青睐。对于$ n_f $的较低值，我们将两个复杂固定点之间的$ f $的平均值与在对称阶段的值之间的平均值进行比较，以使临界值的上限$ n_f^*$低于对称性阶段的接管。
We compute the $S^d$ partition function of the fixed point of non-abelian gauge theories in continuous $d$, using the $ε$-expansion around $d=4$. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in $d>4$ or $d<4$. In the first case we extrapolate to $d=5$ to test a recently proposed construction of the UV fixed point of $5d$ $SU(2)$ Yang-Mills via a susy-breaking deformation of the $E_1$ SCFT. We find that the $F$ theorem allows the proposed RG flow. In the second case we extrapolate to $d=3$ to test whether QCD$_3$ with gauge group $SU(n_c)$ and $n_f$ fundamental matter fields flows to a CFT or to a symmetry-breaking phase. We find that within the regime with a real gauge coupling near $d=4$ the CFT phase is always favored. For lower values of $n_f$ we compare the average of $F$ between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value $n_f^*$ below which the symmetry-breaking phase takes over.
