Entanglement Entropy and Non-relativistic Systems in the AdS/CFT correspondence

Résumé

Entanglement Entropy In this chapter we will introduce the concept of entanglement entropy and its uses in the context of quantum field theory (QFT) as well as a prescription to compute it in holographic duals of QFTs. We will mainly review results available in the literature. In the first section we will give a general overview of entanglement entropy. Then we will focus of how to compute it and what is known about it in QFT. These results apply to (conformal) theories in 1+1 dimensions and free theories in higher dimensions. Then we will present a prescription to calculate the entanglement entropy from holographic duals, expanding much more what can be learnt in interacting theories. We will present the evidence in favor of this holographic ansatz as well as the results one obtains for (strongly interacting) conformal field theories in arbitrary dimension.