Quantum Chaos in Conformal Field Theories

Understanding quantum chaos in conformal field theories is extremely important. Chaotic dynamics can explain why so many systems can be studied with statistical mechanics, and why systems reach ``typical’’ states so quickly. Outside of the simplest, highly symmetric systems, all systems are expected to be described by chaotic dynamics; whether and how these dynamics can appear in theories with conformal symmetry is thus essential to further our understanding of most CFTs. Moreover, the AdS/CFT correspondence suggests that chaotic CFTs are important for understanding black holes, which themselves are chaotic systems.

However, the highly symmetric structure of these systems can tend to hide the underlying chaotic behaviour; this unique structure requires us to find the right language and diagnostics for discussing chaotic phenomenon. In this thesis we make significant progress to this end: we demonstrate the part of the energy spectrum that is unconstrained by symmetry and displays chaotic behaviour; we study the link between quantum chaos and the strange properties of ``arithmetic chaos''; we create an effective field theory for analyzing chaotic behaviour and its link to standard CFT technology; and we analyze CFTs with a boundary and their AdS/CFT dual, which have been used to model chaotic black holes.