Quantum Field Theory: Classification and Constraints

This lecture delves into the fundamentals of Quantum Field Theory (QFT), focusing on the classification of Conformal Field Theories (CFTs) in different dimensions and the constraints imposed by the S-matrix Bootstrap approach. The instructor explores the space of QFTs, from the classification of CFTs in 1+1 dimensions to the implications of Gravity as a path to QFT. Key topics include the Conformal Bootstrap, the holographic principle, and the AdS/CFT correspondence. Through scattering thought experiments and analytical tools, the lecture demonstrates how general principles like Lorentz invariance, causality, and unitarity shape the understanding of QFTs.