AdS/CFT as classical to quantum correspondence in a Virtual Extra Dimension

TL;DR

This paper explores how the AdS/CFT correspondence can be understood as a classical-to-quantum transition through a virtual extra dimension, linking geometric recurrences with quantum behavior and applying it to QGP phenomenology.

Contribution

It provides a semiclassical interpretation of AdS/CFT using geometrodynamics and recurrence relations, connecting extra dimensional geometry with quantum mechanics.

Findings

Quantum recurrences relate to extra dimensional dynamics.

Semiclassical quantization via boundary conditions reproduces Feynman Path Integrals.

Application to QGP freeze-out offers insights into AdS/QCD phenomenology.

Abstract

The correspondence between classical extra dimensional geometry and quantum behavior, typical of the AdS/CFT, has a heuristic semiclassical interpretation in terms of undulatory mechanics and relativistic geometrodynamics. We note, in fact, that the quantum recurrence of ordinary particles enters into the equations of motions in formal duality with the extra dimensional dynamics of a Kaluza-Klein theory. The kinematics of the particle in a generic interaction scheme can be described as modulations of the spacetime recurrences and encoded in corresponding geometrodynamics. The quantization can be obtained semiclassically by means of boundary conditions, so that the interference of the classical paths with different windings numbers associated to the resulting recurrences turns out to be described by the ordinary Feynman Path Integral. This description applied to the Quark-Gluon-Plasma freeze-out yields basic aspects of AdS/QCD phenomenology.