Area density of localization-entropy

Using the holographic lightfront projection, which in the present context is not an independent principle but a consequence of the properties underlying the algebraic formulation of QFT, we derive an area law for the localization-entropy caused by vacuum polarization. Its area density is equal to the localization entropy of an associated auxiliary chiral theory. Its microscopic derivation with the help of angular Euclideanization in the standard setting of statistical mechanics leads to a universal linear divergence multiplied with a strength which only depends on the quantum matter content of the holographic projection. This ultraviolet divergence is conformally equivalent to the missing one-dimensional length factor which together with the area yield a 3-dimensional volume factor. However we do not know whether this close analogy with standard heat bath entropy also holds for the thermodynamic laws, i.e. the validity of a normalizing thermodynamic fundamental law for vacuum polarizationinduced entropy remains open. Whereas the localizationand black holeentropy share the area proportionality, the residual dependence of the former on the holographic quantum matter content poses an interesting (and hopefully enigmatic) contrast to the Bekenstein area law whose resolution may encode aspects of the still elusive quantum gravity.