Area density of localization-entropy II: double cone-localization and quantum origin of the Bondi-Metzner-Sachs symmetry

The holographic encoding is generalized to subalgebras of QFT localized in double cones. It is shown that as a result of this radically different spacetime encoding the modular group acts geometrically on the holographic image. As a result we obtain a formula for localization entropy which is identical to the previously derived formula for the wedge-localized subalgebra. The symmetry group in the holographic encoding turns out to be the Bondi-Metzner-Sachs group. 1 The aims of this paper In the algebraic setting of QFT the holographic projection changes the natural bulk spacetime indexing of subalgebras contained in a given localized algebra into the spacetime indexing of subregions referring to the causal horizon of the given localization region; in doing that it maintains the original given algebra which by holography is re-interpreted as the algebra on its causal horizon, including the Hilbert space in which it acts as an operator algebra [1]. The only structure which suffers drastic changes is the local substructure. In other words the main difference between the localized bulk algebra and its holographic projection is that the abstract algebraic substrate, not unlike the stem cell material under the action of enzymes, becomes differently organized in space and time. The simplest case is the wedge-localized algebra which is identical to its (say upper) horizon algebra A(W ) = A(Hor(W )); but both spacetime interpretations lead to an entirely different substructure, each one being local in its own setting, but partially non-local relative to the other. In [1] the holographic 1The well-studied conformal holography of AdS→conformal QFT is not a holography in the present sense since its spacetime encoding does not result from projecting AdS onto a null