Area density of localization entropy: I. The case of wedge localization

Using an appropriately 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 lightlike 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 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.