Quantum mechanics and general relativity are fundamental building blocks in our understanding of physics. Despite decades of effort, merging them into a unified theory of quantum gravity remains one of the great challenges for modern physics. The holographic principle has been radically changing our approach, suggesting that spacetime and gravity are statistical phenomena emerging from the collective quantum behavior of a large number of underlying degrees of freedom. Today, the best available framework to study this idea is the AdS/CFT correspondence, which indicates that a complete theory of quantum gravity in anti de Sitter (AdS) should be fully captured by a class of conformal field theories (CFT), referred to as holographic CFTs. Understanding the emergence of gravity in AdS thus goes back to revisiting conformal field theories under a new perspective, uncovering when and how their degrees of freedom rearrange to act according to the laws of gravity. The goal of this proposal is to advance our comprehension of the structure of holographic CFTs and of the emergence of spacetime by: investigating the role of different states in relation to the existence of multiple gravitational saddles; identifying within conformal theories characteristic manifestations of AdS gravity, their technical origin and whether some of them are shared by simpler theories with fewer degrees of freedom. The objectives will be attained mainly via the study of conformal correlators in the framework provided by the AdS3/CFT2 correspondence, paying particular attention to the way general requirements like single-valuedness, crossing and modular invariance are retained in the map between CFT and gravity. Investigating how holographic CFTs encode gravity will both help to unfold the mysteries of quantum gravity and also refine our comprehension of problems from a variety of fields that can be described by conformal methods, as illustrated by several examples in the recent past.

 Federico Galli - INFN Firenze