论文标题
CFT的分析和数值引导带有$ O（M）
Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
论文作者
论文摘要
通过对关键现象的应用和开放理论问题的启发，我们以$ o（m）\ times o（times o（n）$ $ d = 3 $ d = 3 $ spacetime dimensions中的$ o（m）\ times o（times o（n）$全局对称性）研究保形田地理论。我们使用分析和数值引导技术。使用分析性引导程序，我们将异常的维度和OPE系数计算为功率系列，$ \ varepsilon = 4-d $，以$ 1/n $为单位，并以一种概括为任意全球对称性的方法。只要可以比较，我们的结果就与文献中使用图解方法获得的早期结果一致。使用数值引导程序，我们获得了各种各样的操作员尺寸边界，并且在参数空间中找到了几个岛屿（隔离允许区域），$ o（2）\ times o（times o（n）$（n）$的理论的各种值为$ n $。这些岛中的一些可以归因于诸如$ \ varepsilon $和大型$ n $扩展等扰动方法预测的固定点，而其他岛屿的固定点似乎是由于固定点而出现的，这些固定点被认为存在于扰动beta beta函数中。
Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with $O(m)\times O(n)$ global symmetry in $d=3$ spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in $\varepsilon=4-d$ and in $1/n$, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for $O(2)\times O(n)$ theories for various values of $n$. Some of these islands can be attributed to fixed points predicted by perturbative methods like the $\varepsilon$ and large-$n$ expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.
