Energy trapping from Hagedorn densities of states

TL;DR

This paper introduces simple stochastic models to study how energy distributions evolve in holographic gauge theories, revealing energy trapping phenomena associated with Hagedorn densities that may explain long-lived gravitational states.

Contribution

It constructs toy models incorporating energy conservation and thermodynamics to explore the effects of different density of states, especially Hagedorn regimes, on energy dynamics in gauge theories.

Findings

Hagedorn densities cause long-term energy trapping in the models.

Typical field theory densities lead to diffusive energy spread.

Energy trapping may explain long-lived black hole states in gravity.

Abstract

In this note, we construct simple stochastic toy models for holographic gauge theories in which distributions of energy on a collection of sites evolve by a master equation with some specified transition rates. We build in only energy conservation, locality, and the standard thermodynamic requirement that all states with a given energy are equally likely in equilibrium. In these models, we investigate the qualitative behavior of the dynamics of the energy distributions for different choices of the density of states for the individual sites. For typical field theory densities of states (\log(\rho(E)) ~ E^{\alpha<1}), the model gives diffusive behavior in which initially localized distributions of energy spread out relatively quickly. For large N gauge theories with gravitational duals, the density of states for a finite volume of field theory degrees of freedom typically includes a Hagedorn regime (\log(\rho(E)) ~ E). We find that this gives rise to a trapping of energy in subsets of degrees of freedom for parametrically long time scales before the energy leaks away. We speculate that this Hagedorn trapping may be part of a holographic explanation for long-lived gravitational bound states (black holes) in gravitational theories.