Conformal Field Theories in AdS: Energy Spectra and Unitarity

This lecture delves into the energy spectra of free scalar fields in Anti-de Sitter space (AdS), revealing a correspondence with conformal field theories (CFTs). The instructor discusses the primary and descendant states, emphasizing the unitarity constraints on the energy levels. By exploring the solutions to the Klein-Gordon equation and the role of isometries in AdS, the lecture uncovers the quantization of energies and the significance of the BF bound. The presentation concludes with a detailed analysis of the hypergeometric functions and the construction of the full representations of the conformal group. The ultimate goal is to establish a comprehensive dictionary between AdS and CFTs, shedding light on the intricate relationship between gravitational theories and quantum field theories.