Small n Renyi entropies and entanglement temperatures in QFT

In this talk, I will introduce the notion of entanglement temperatures in QFT, a generalization of the Unruh temperatures valid for states reduced onto arbitrary spatial regions. The entanglement temperatures encode the high energy behavior of the state around a point and are determined by the solutions of an Eikonal problem in Euclidean space. I will show that for theories with a free UV fixed point, the entanglement temperatures determine the state with a large modular temperature. In particular, I will derive a formula that connects the Renyi entropy in the small Renyi parameter limit and the entanglement temperatures. I will briefly comment on some recent progress in the holographic counterpart.