Which quantity characterizes the primary fields in CFT?

Scaling dimensions characterize the primary fields in Two-Dimensional Conformal Field Theory (CFT). These dimensions determine how primary fields transform under conformal transformations and govern their behavior in correlation functions. The scaling dimensions of primary fields play a crucial role in classifying operators in CFT and understanding their physical significance. By studying the scaling dimensions of primary fields, researchers can uncover important insights into the symmetries, dynamics, and phase structure of CFT.