Novel features of large-N limits: decoherence, entanglement and area operators in AdS/CFT.

Most candidates to quantum gravity theories are "large-N" models. As in more common condensed matter systems and quantum field theories, the study of entanglement and the microscopic structure of quantum states is expected to result in both conceptual and computational developments in these class of models, and potentially in quantum gravity. These questions appear very neatly in the context of AdS/CFT, where entanglement is measured by the area operator, and where the emergence of the geometry and its dynamics are directly related to the large-N limit. In this talk, we will present new general results concerning large-N models. In particular, we will show in different ways that subsystems show perfect decoherence in the limit. Given this decoherence, we will show why in these theories entanglement entropy is given by the expectation value of an observable, and give its expression. From a more technical and general standpoint, the results are encapsulated in a generic expression for the so-called Schmidt decompositions in large-N theories.