Higher-dimensional violations of the holographic entropy bound

TL;DR

This paper demonstrates that in high spatial dimensions (around 100 or more), thermal radiation can violate the holographic entropy bound, challenging its universality beyond three dimensions.

Contribution

It provides the first explicit example of holographic bound violation in high-dimensional flat spacetimes, extending the understanding of the bound's limitations.

Findings

Thermal radiation in high dimensions can surpass the holographic entropy limit.

Violations occur for dimensions D ≥ 100.

Challenges the universality of the holographic entropy bound.

Abstract

The holographic bound, $S<=A/4{\ell^2_P}$, asserts that the entropy $S$ of a system is bounded from above by a quarter of the area $A$ of a circumscribing surface measured in Planck areas. This bound is widely regarded as part of the elusive fundamental theory of nature. In fact, the bound is known to be valid for generic weakly gravitating isolated systems in {\it three} spatial dimensions. Nevertheless, the entropy content of a physical system is expected to be an increasing function of the number of spatial dimensions (the more the dimensions, the more ways there are to split up a given amount of energy). Thus, one may expect the challenge to the holographic entropy bound to become more and more serious as the number of spatial dimensions increases. In this paper we explicitly show that thermal radiation in $D$ flat spatial dimensions with $D\gtrsim 10^2$ may indeed violate the holographic entropy bound.