Holography, Dimensional Reduction and the Bekenstein Bound

TL;DR

This paper explores how dimensional reduction affects the covariant entropy bound and Bekenstein bound in holography, revealing refined bounds and conditions for saturation involving warping factors and gauge fields.

Contribution

It introduces a new local Bekenstein bound in D dimensions derived from D+1 dimensions, accounting for warping factors and gauge fields, and discusses implications for holographic saturation.

Findings

Refined local Bekenstein bound in D dimensions

Possibility of saturating holography with nonzero expansion

Stronger bounds with electromagnetic contributions subtracted

Abstract

We consider dimensional reduction of the lightlike holography of the covariant entropy bound from D+1 dimensional geometry of M X S to the D dimensional geometry M. With a warping factor, the local Bekenstein bound in D+1 dimensions leads to a more refined form of the bound from the D dimensional view point. With this new local Bekenstein bound, it is quite possible to saturate the lightlike holography even with nonvanishing expansion rate. With a Kaluza-Klein gauge field, the dimensional reduction implies a stronger bound where the energy momentum tensor contribution is replaced by the energy momentum tensor with the electromagnetic contribution subtracted.