Charting the AdS/CFT Landscape

What are the bounds of the AdS/CFT correspondence? Which quantities in conformal field theory have simple descriptions in terms of classical anti-de Sitter spacetime geometry? These foundational questions in holography may be meaningfully addressed via the study of CFT correlation functions, which map to amplitudes in AdS. I will show that a basic building block in any CFT -- the conformal block -- is equivalent to an elegant geometric object in AdS, which moreover greatly streamlines and clarifies calculations of AdS amplitudes. By studying correlators with certain Lorentzian kinematics, one can constrain the space of consistent theories of AdS quantum gravity itself. In particular, by harnessing a recent bound on the rate of onset of chaos in thermal states, I will rule out the existence of certain classes of putative 2D CFTs and their 3D gravity duals, and argue that others exhibit signatures of Regge trajectories of string theory. This may be viewed as a novel, Lorentzian counterpart of the conformal bootstrap, relating dynamical constraints on the development of quantum chaos to the determination of the AdS/CFT landscape.