论文标题
CFT I中的分布
Distributions in CFT I. Cross-Ratio Space
论文作者
论文摘要
我们表明，共形场理论中的四点函数被定义为在保形块扩展区域的边界上的分布。共形块膨胀在此边界上的分布意义上收敛，即可以根据适当的测试功能按学期整合。这可以解释为提供新的功能，该功能在应用于交叉方程时满足交换属性，我们会评论我们的构建与其他类型功能的关系。我们的语言在涉及融合区域边界的所有考虑因素中都是有用的，例如用于得出分散关系。我们通过基本方法建立结果，仅依靠交叉对称性和保形块扩展的标准收敛性。这是保形场理论中相关函数的分布特性的一系列论文中的第一篇。
We show that the four-point functions in conformal field theory are defined as distributions on the boundary of the region of convergence of the conformal block expansion. The conformal block expansion converges in the sense of distributions on this boundary, i.e. it can be integrated term by term against appropriate test functions. This can be interpreted as a giving a new class of functionals that satisfy the swapping property when applied to the crossing equation, and we comment on the relation of our construction to other types of functionals. Our language is useful in all considerations involving the boundary of the region of convergence, e.g. for deriving the dispersion relations. We establish our results by elementary methods, relying only on crossing symmetry and the standard convergence properties of the conformal block expansion. This is the first in a series of papers on distributional properties of correlation functions in conformal field theory.
