High Energy Theory Informal Seminar

I will describe several issues related to the combined constraints imposed by strong subadditivity and Lorentz covariance on the entanglement entropy in QFT. In particular I will show the emergence of the two dimensional c-theorem from properties of the entanglement entropy and its generalization to three dimensions. This last one coincides with the conjectured monotonous running of the free energy on a three sphere under renormalization group transformations (F-theorem). I will also discuss possible generalizations to higher dimensions and some intriguing relations between strong subadditivity and reflection positivity.