Entropy Bound with Generalized Uncertainty Principle in General Dimensions

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.

8 pages, topos corrected and references added