Proof of the universal density of charged states in QFT
Javier M. Magan
TL;DR
The paper proves a conjecture by Harlow and Ooguri: in QFTs with a finite-group global symmetry, the high-energy density of states is universal across representations, with $\rho_r(E)=\frac{d_r^2}{|G|}\,\rho(E)$. It argues this via an entropic-order/entropic-disorder (certainty) relation in the Thermofield Double state, together with DHR-inspired charge reconstruction and Cuntz algebras to control the representation content. The result also clarifies entropy equipartition, showing that the universal density arises from the regular representation dominating the large-representation fusion, and connects these high-energy facts to vacuum-sector structures and the physics of entanglement. The framework generalizes to non-compact manifolds and offers a coherent, algebraic underpinning for universal charged-state statistics in QFT.
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.