Light-ray Operators: Generalization and Applications

This lecture discusses the concept of light-ray operators within the framework of conformal field theory (CFT). It begins with an outline of the general properties of the Null Energy Condition (NEC) operator and its significance in operator product expansions (OPE). The instructor introduces the light transform of an operator, which serves as a foundation for defining light-ray operators. The lecture emphasizes the connection between light-ray operators and the Lorentz inversion formula, which is crucial for extracting conformal data. The discussion includes the Lycan limit, where two operators approach each other, and how this limit leads to the definition of the Non-Negative Energy Condition (NNEC). The instructor also explores the generalization of these concepts to more complex local operators, highlighting the role of auxiliary variables and the implications for spinning operators. The lecture concludes with a discussion on the properties of light-ray operators and their relevance in the broader context of CFT, including their relationship with three-point functions and operator densities.