Generalized Uncertainty Principle, Extra-dimensions and Holography

TL;DR

This paper explores generalized uncertainty principles incorporating gravity and extra dimensions, analyzing their holographic properties and identifying conditions under which holographic counting is consistent.

Contribution

It introduces explicit forms of generalized uncertainty principles in higher dimensions and examines their holographic implications, highlighting the unique case matching holographic counting without extra dimensions.

Findings

Holographic counting matches only in 4D case

Explicit GUP expressions in higher dimensions derived

Extra dimensions alter holographic degrees of freedom

Abstract

We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4+n dimensions are given and their holographic properties investigated. In particular, we show that the predicted number of degrees of freedom enclosed in a given spatial volume matches the holographic counting only for one of the available generalizations and without extra dimensions.