Conformal Field Theory & Operator Product Expansion

This lecture delves into Conformal Field Theory (CFT) and Operator Product Expansion (OPE), exploring the relationship between symmetries in quantum field theory and the existence of topological operators. The instructor discusses the implications of symmetries on the structure of operators, emphasizing the role of conformal transformations. The lecture covers the quantization process in CFT, focusing on the choice of spacetime foliation and the importance of conserved charges. The concept of states in CFT is explained through integrals and the projection of states onto a basis of fields. The OPE is introduced as a method to expand product of operators, leading to a convergent sum with specific coefficients. The lecture concludes with a discussion on the convergence of OPE and the importance of understanding the specific nature of OPE in CFT.