HET seminar: Sebastian Fischetti

Speaker: Sebastian Fischetti

Title: An Energy Bound on Renormalized Entanglement Entropy

Abstract: Despite its important role in fields ranging from condensed matter to QFT to quantum gravity, entanglement entropy remains difficult to understand explicitly.  Useful formal statements can be made by defining a modular Hamiltonian, but this state-dependent operator is also typically intractable to study explicitly.  I will show that in the context of AdS_4/CFT_3, it is possible to obtain a bound on the renormalized entanglement entropy of regions in general states of the CFT using a geometric flow called the inverse mean curvature flow.  The bound constrains the entanglement entropy in terms of a state-dependent weighted energy density over the entangling region; in the case of spherical entangling regions in the vacuum state, this bound becomes the modular Hamiltonian, and we recover the first law of entanglement.  I will comment on its validity away from the classical regime, possible connections to the complexity/volume duality, and extensions to higher dimensions.