Entanglement entropy and RG irreversibility

I will start reviewing the set up in which vacuum entanglement entropy can be used to prove the c and F theorem of 2 and 3 dimensions. In the case of four dimension new ideas are needed to prove the (entropic) a theorem. The new key ingredient for this (besides Strong Subadditivity, Lorenz invariance, Causality and Unitarity) is what we have called the Markov property of the vacuum. I will comment on some of its meanings and its role in the a theorem.

The talk is based on this papers arXiv:1704.01870, arXiv:1703.10656, arXiv:1611.00016.