On the Maldacena Type Conjecture in Relation with Scale Relativity Theory

Abstract

A Maldacena type conjecture in relation with Scale Relativity Theory using Schrödinger representations of fractal type dynamics of any physical system is proposed. The operational procedure developed by the authors is based on the phase coherences of the dynamics, involving, through dual “holographic implementations”, one in the usual space and the other in scales space, apolar transport of the temporal cubics of fractal type. In the Riemannian spaces associated with the cubics, their apolar transport becomes equivalent to the parallel transport of the hyperbolic planes. In this way, it is shown that any dynamics which reflects SL (2R) “processes” has intrinsic hyperbolic geometries, harmonic mappings, from usual and scales spaces to the hyperbolic one, implying correlations between the General Relativity, in Ernst sense, and Skyrme Theory.

Keywords

• maldacena type conjecture
• scale relativity theory
• schrödinger representation
• fractal type dynamics
• holographic implementation
• riemannian space