String Theory seminar - Sebastian Fischetti Seminar

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.