Bulk locality breakdown Burning black holes & precarious precursors

Broadly speaking, this work focuses on how fundamental subjects in theoretical physics such as general relativity, thermodynamics and quantum information are connected. Various connections exist, manifested notably in black holes, holography, and the AdS/CFT correspondence in particular. All three of these related subjects will be touched upon in this work, with locality playing an interconnecting role. Chapter 1 gives a pedagogical introduction to these subjects, while chapters 2, 3, 4 and 5 give a more technical exposition of the main results. Chapter 2 discusses the black hole firewall paradox, and geometrically shows that ingredients necessary to construct the paradox generically do not fit within an infalling causal patch. Chapter 3 studies a puzzling aspect of the AdS/CFT correspondence, which is that a single bulk operator can be mapped to multiple different boundary operators, or precursors. The use of a holographic toy model allows explaining this puzzle both in terms of boundary gauge invariance, and entanglement in the CFT. Thereafter chapter 4 proposes the language of BRST symmetry as a natural framework for the aforementioned precursor ambiguities. Chapter 5 addresses the question which CFTs have local bulk duals, by studying the same toy model introduced in chapter 3 which turns out to have some surprising properties concerning bulk locality. This leads to a conjecture for which CFT2’s are dual to a gravitational theory with sub-AdS scale locality. Finally, chapter 6 summarizes and concludes the main results, while commenting on some remaining open questions and giving some interesting future directions of research.