Title Area density of localization-entropy I: the case of wedge-localization

TL;DR

This paper derives an area law for localization-entropy on a wedge horizon using holographic lightfront projection, revealing a relation between entropy density and heat bath entropy, with implications for black hole entropy understanding.

Contribution

It introduces a holographic approach to derive an area law for localization-entropy, linking it to lightfront algebra and conformal invariance, and discusses its relevance to black hole entropy.

Findings

Derived an area law for localization-entropy on a wedge horizon.

Established a relation between entropy density and heat bath entropy.

Linked short-distance divergence to lightlike length contributions.

Abstract

Using an appropriatly formulated holographic lightfront projection, we derive an area law for the localization-entropy caused by vacuum polarization on the horizon of a wedge region. Its area density has a simple kinematic relation to the volume extensive heat bath entropy of the lightfront algebra. Apart from a change of parametrization the infinite lighlike length contribution to the lightfront volume factor corresponds to the short-distance divergence of the area density of the localization entropy. This correspondence is a consequence of the conformal invariance of the lightfront holography combined with the well-known fact that in conformality relates short to long distances. In the explicit calculation of the strength factor we use the temperature duality relation of rational chiral theories whose derivation will be briefly reviewed. We comment on the potential relevance for the understanding of Black hole entropy.