Addendum to ‘Area density of localization entropy: I. The case of wedge localization’

Abstract

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.

Bondi-Metzner-Sachs Symmetry, Holography on Null-surfaces and Area Proportionality of “Light-slice” Entropy

“…Whereas the first and third subsection are extensions of already published results [2][3][4], the derivation of the BMS symmetry from null-space holography is new.…”

“…The most prominent case is the lightfront (LF) holography which is essentially the old lightfront quantization but now with a more careful formulation of what in the old days has been always neglected, namely the relation with the original bulk description. 7 From the point of symmetries, the restriction of the global bulk to the LF leaves a 7-parametric subgroup of the 10-parametric Poincaré group of 4-dimensional Minkowski spacetime: 5 parameters account for a lightlike translation, a lightlike dilation (the wedgepreserving boost transformation projected onto the LF) and the 3-parametric transverse Euclidean group, whereas the remaining two parameters are less obvious since they are the 2 "translations" of the Wigner little group (3 dimensional Euclidean subgroup of the 6 parametric Lorentzgroup) which leaves the lightray invariant [2][3][4].…”

“…On the other hand it reminds us that there are important aspects in standard QFT which, as a result of our Lagrangian prejudices, we have not been aware of paragraph. The fact that only the event horizons in black hole physics are objective placed horizons, whereas the causal horizons of quantum matter in Minkowski spacetime are somewhat subjective (observer-dependent) Gedanken-horizons, is no counter-argument since Gedankenexperiments as that of Unruh often lead to corrections in our way of thinking; in addition the constants which appear in the leading entropy behavior for the sheet size R → 0 are interesting characteristics of the entire model, similar to Virasoro's constant in chiral theories 4 and not just of individual observables within the model.…”

“…Although Tomita discovered it, the theory would not have arrived at how we know it without essential contributions by Takesaki [10]. 4 The divergence of the localization entropy for R → 0 is the only divergence with an intrinsic significance i.e. which cannot be subsumed under operator-valued distributions (as fields and their correlations) and renormalization.…”

“…Likewise the holography used in the present work is a rigorous property within the general setting of QFT 6 and there are two different ways of implementing it; one which starts with pointlike bulk fields and produces pointlike generators of the holographic projected quantum matter through intermediate semi-local steps, and the other starting from wedge-localized algebras with the local substructure on its causal horizon being constructed by algebraic intersections [4]. Both methods coalesce on observables which are local in the sense of the lightfront and only arise from integer dimensional bulk variables.…”