Proof of the universal density of charged states in QFT

TL;DR

This paper proves a universal formula for the density of charged states in quantum field theory, linking entropic order parameters and the certainty principle, and extends the understanding of entropy distribution in such systems.

Contribution

It establishes a universal high-energy charged state density formula in QFT for finite group symmetries, connecting entropic order parameters with the density of states.

Findings

Proves the universal density formula for charged states in QFT.

Shows the connection between entropic order parameters and the density of states.

Generalizes the results to QFTs on non-compact manifolds.

Abstract

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. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT's on non-compact manifolds.