论文标题
在保形场理论中的机器学习效果
Machine Learning Etudes in Conformal Field Theories
论文作者
论文摘要
我们证明，共形场理论的各个方面都可以适合机器学习。相对适中的进发神经网络能够区分三分函数的尺度和形式不变性，并确定交叉对称的四点函数至近百分之一百的精度。此外，神经网络还能够识别出在假定的CFT四点函数中出现的共形块，并预测相应的OPE系数的值。神经网络还通过检查OPE数据在CFT中的离散对称性下，通过离散对称性成功地将主要运算符分类。我们还证明了神经网络能够在3D ISING模型中学习针对标量相关函数的可用OPE数据，并通过回归预测出现在标量OPE通道中的高速旋转算子的曲折。
We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and identify a crossing-symmetric four-point function to nearly a hundred percent accuracy. Furthermore, neural networks are also able to identify conformal blocks appearing in a putative CFT four-point function and predict the values of the corresponding OPE coefficients. Neural networks also successfully classify primary operators by their quantum numbers under discrete symmetries in the CFT from examining OPE data. We also demonstrate that neural networks are able to learn the available OPE data for scalar correlation function in the 3d Ising model and predict the twists of higher-spin operators that appear in scalar OPE channels by regression.
