Holographic entanglement obeys strong subadditivity

Aron Wall

Aron Wall is a member of the School of Natural Sciences at the Institute for Advanced Study. In his spare time he blogs at Undivided Looking. He was the 2013 recipient of the Bergmann-Wheeler thesis prize, which is sponsored by Classical and Quantum Gravity.

Gauge-gravity duality allows us to calculate properties of certain quantum field theories (QFT) from classical general relativity. One famous piece of this conjecture, due to Ryu and Takayanagi, relates the entanglement entropy in a QFT region to the area of a surface in the gravitational theory. In addition to being a clue about quantum gravity, this proposal is one of the few tools which allow us to calculate entanglement entropy analytically. Since the entanglement entropy is of increasing interest for field theory and condensed matter applications, it is important to check if the conjecture is true.

One important property of the entropy is strong subadditivity (SSA). This quantum inequality says that the sum of the entropies in two regions is always greater than the sum of the entropies of their union and intersection. My article uses proof Continue reading