High Energy Theory Seminar

The classical concepts of space and time, including the very notion of a point in space, are likely to break down below the Planck ale. I use the holographic duality (AdS/CFT) -- an equivalence between quantum gravity in anti-de Sitter space and a lower-dimensional field theory without gravity -- to illustrate how pacetime emerges from the underlying fundamental theory. A useful tool for this goal is the Ryu-Takayanagi proposal -- an equality between a classical object in gravity (area of a minimal surface) and an essentially quantum quantity in field theory (entanglement entropy).

Working in the settings of AdS3/CFT2, I explain how to use this proposal to give a non-perturbative definition of a point in space in the language of the dual field theory. The answer involves an information theoretic characterization of the field theory state, which is neatly captured by "the kinematic space" -- an auxiliary Lorentzian geometry whose points correspond to intervals in the boundary field theory. The metric of the kinematic space is given
directly in terms of the strong subadditivity of boundary entanglement entropy, which makes manifest the connection between the gravitational
spacetime and the entanglement among the field theory degrees of freedom. One corollary is that lengths of bulk curves quantify how far various collections of boundary intervals are from saturating the strong subadditivity of entanglement entropy.