Entropy bound and local quantum field theory

TL;DR

This paper critiques a previous result linking entropy bounds in quantum field theory to holography, identifies a subtle mistake, and derives a more restrictive, non-holographic entropy bound.

Contribution

It clarifies the validity of entropy bounds in local quantum field theory by correcting a previous derivation and proposing a more restrictive bound.

Findings

Yurtsever's holographic entropy bound contains a subtle mistake.

A more restrictive, non-holographic entropy bound is derived.

The corrected bound challenges the holographic interpretation in this context.

Abstract

I comment on Ulvi Yurtsever's result, which states that the entropy of a truncated bosonic Fock space is given by a holographic bound when the energy of the Fock states is constrained gravitationally. The derivation given in Yurtsever's paper contains an subtle mistake, which invalidates the result. A more restrictive, non-holographic entropy bound is derived.