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

TL;DR

This paper explores how holographic projection of quantum field theory onto the lightfront alters local quantum properties, revealing a universal area law structure and a transverse tensor product foliation that simplifies the theory's analysis.

Contribution

It demonstrates the drastic change in local quantum properties under lightfront holography and introduces a universal entropy related to the horizon, linking to Bekenstein's area law.

Findings

Vacuum polarization is confined to the longitudinal direction.

Operators with transverse separation are free of vacuum correlations.

The lightfront theory exhibits a d-2 dimensional area structure.

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. Key-words: Quantum field theory; Mathematical physics, Quantum gravity