AdS/CFT as classical to quantum correspondence in a virtual extra dimension

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. The recurrence in time and space of ordinary particles enters in fact into the equations of motions in formal duality with the cyclic extra dimension of a Kaluza-Klein theory. The kinematics of the particle in a generic interaction scheme can be described as modulations of the spacetime recurrence and encoded in corresponding geometrodynamics. The quantization is obtained semiclassically by means of periodic boundary conditions, so that the interference of the classical paths with different windings numbers associated to the resulting recurrence turns out to be described by the ordinary Feynman Path Integral. This semiclassical description applied to Quark-Gluon-Plasma yields basic aspects of AdS/QCD phenomenology.