The paradigm of the area law and the structure of transversal and longitudinal lightfront degrees of freedom

Abstract

It is shown that an algebraically defined holographic projection of a QFT onto the lightfront changes the local quantum properties in a very drastic way. The expected ubiquitous vacuum polarization characteristic of QFT is confined to the lightray (longitudinal) direction, whereas operators whose localization is transversely separated are completely free of vacuum correlations. This unexpected "transverse return to QM" combined with the rather universal nature of the strongly longitudinal correlated vacuum correlations (which turn out to be described by rather kinematical chiral theories) leads to a d-2 dimensional area structure of the d-1 dimensional lightfront theory. An additive transcription in terms of an appropriately defined entropy related to the vacuum restricted to the horizon is proposed and its model independent universality aspects which permit its interpretation as a quantum candidate for Bekenstein's area law are discussed. The transverse tensor product foliation structure of lightfront degrees of freedom is essential for the simplifying aspects of the algebraic lightcone holography.

How Far does the Analogy Between Causal Horizon-Induced Thermalization with the Standard Heat Bath Situation go?

“…This is quite different from [17]; the box of those authors should be causally completed to a double cone, but even then a treatment paralleling the present would be much more difficult as a result of the nongeometric nature of the associated modular group [5] [6].…”

“…In these lecture notes we will show that there is an important aspect of a properly defined algebraic holographic projection onto the horizon which sets the stage for an area density, namely the total absence of vacuum polarization on the horizon in directions transverse to the light ray direction [5] [6]. We explicitly illustrate this phenomenon 1 in the case of the Rindler-Unruh [4] wedge situation (for which the linear extension of the horizon is the lightfront) and argue that it any potential entropy-like measure for the impurity which results from restricting the vacuum to the horizon must necessarily follow an area law where the area is that of the edge of the wedge or its horizon.…”

“…The second line formulates lightfront restriction on the dense set of wedge supported test functions which factorize into a longitudinal and a transverse part [5] [6]. The third line is the statement that holographically projected Weyl generators (and therefore also the algebras they generate) have no transverse fluctuations; the holographic projection compresses all vacuum fluctuations into the lightlike direction.…”

“…This is also true in the general non-free situation. We will skip the generalization of the proof to interacting theories since an explanation of the methods (involving modular inclusions and intersections [5][6]) goes beyond the scope of this talk.…”

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

“…Although a detailed derivation of the localization structure on the horizon of the wedge requires a substantial use of theorems about modular inclusions and intersections (for which we refer to [21][22][23]), the tensor factorization of the horizon algebra relies only on the following structural theorem in operator algebras:…”