# Area Law Saturation of Entropy Bound from Perturbative Unitarity in Renormalizable Theories

## TL;DR

This paper demonstrates that in certain renormalizable quantum field theories, solitons like monopoles and baryons exhibit an area-law entropy saturation similar to black holes, linked to perturbative unitarity and weak coupling.

## Contribution

It reveals that the area-law entropy saturation extends beyond gravity to non-gravitational theories, connecting confinement and entropy bounds in QCD.

## Key findings

- Magnetic monopoles saturate the Bekenstein bound at unitarity limit.
- Solitons exhibit an area-law entropy similar to black holes.
- QCD baryons show the same entropy behavior at large N.

## Abstract

We study the quantum information storage capacity of solitons and baryons in renormalizable quantum field theories that do not include gravity. We observe that a 't Hooft-Polyakov magnetic monopole saturates the Bekenstein bound on information when the theory saturates the bound on perturbative unitarity. In this very limit the monopole entropy assumes the form of an area-law, strikingly similar to a black hole entropy in gravity. The phenomenon appears universal and takes place for other solitons and non-perturbative objects. We observe the same behaviour of entropy of a baryon in QCD with large number of colors. These observations indicate that the area-law form of the entropy bound extends beyond gravity and is deeply rooted in concepts of weak coupling and perturbative unitarity. One provoked idea is that confinement in QCD may be understood as a prevention mechanism against violation of Bekenstein entropy bound by colored states.