High Energy Theory Seminar

The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. I will show that this relation can be inverted to reconstruct the bulk stress-energy tensor near the boundary of the bulk spacetime, from the entanglement on the boundary. I will also derive positivity and monotonicity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the CFT, from the positivity of the matter energy density in the bulk.