Proof of the universal density of charged states in QFT

Understand

We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups.

• An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author.
• Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states.
• The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof.