Entropy Bound with Generalized Uncertainty Principle in General Dimensions

TL;DR

This paper investigates how the generalized uncertainty principle (GUP), which predicts a minimal length, affects the entropy bounds of quantum fields in higher dimensions, revealing a universal correction scaling.

Contribution

It extends the analysis of entropy bounds under GUP to arbitrary dimensions and compares bosonic and fermionic fields, highlighting a universal correction form.

Findings

GUP induces a universal entropy correction scaling in higher dimensions.

Both bosonic and fermionic fields exhibit similar correction scaling despite coefficient differences.

GUP effects become significant at short distance scales.

Abstract

In this letter, the entropy bound for local quantum field theories (LQFT) is studies in a class of models of the generalized uncertainty principle(GUP) which predicts a minimal length as a reflection of the quantum gravity effects. Both bosonic and fermionic fields confined in arbitrary spatial dimension $d\geq4$ ball ${\cal B}^{d}$ are investigated. It is found that the GUP leads to the same scaling $A_{d-2}^{(d-3)/(d-2)}$ correction to the entropy bound for bosons and fermions, although the coefficients of this correction are different for each case. Based on our calculation, we conclude that the GUP effects can become manifest at the short distance scale. Some further implications and speculations of our results are also discussed.